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    What Is The Geometry Of Spacetime? — Introduction
    By David Halliday | April 28th 2012 10:07 AM | 185 comments | Print | E-mail | Track Comments

    Many people struggle with, and even rail against, Einstein's Special Theory of Relativity.  The way it is usually taught or presented often seems to make it appear to be ever so complex, far too abstract and opaque, and even downright "hokey".*  My experience certainly allows me full empathy for such struggles.

    However, through my journey through these struggles, I did find the kernel, the "missing piece", even the "gem", so to speak, behind the theory.  I suspect that this kernel may be what is missing in the understanding of those that struggle with, or, maybe, even rail against, Einstein's Special Theory of Relativity.  I know I could have easily fallen into this category.

    Through this (hopefully rather short) series I shall endeavor to illuminate this kernel, and, hopefully, develop a better approach to introducing Einstein's Special Theory of Relativity.

    First, though, I wish to share with you my journey with this theory, since I suspect many who struggle, and maybe even many who rail against, this theory may be able to identify with, at least, how my journey began.

    My Journey:  A Confession

    First Exposure, and Impressions

    I first learned about Einstein's Special Theory of Relativity from a book I read on Einstein and his theories in Junior High School (about 7th or 8th grade, what is sometimes termed "Middle School").  The explanation involved such things as "time dilation", "space contraction", "Lorentz transformations", and a strange way to "add" velocities—all stuff that is, I'm sure, quite familiar to any that have learned of the subject.

    My immediate feeling was "What?!?  This can't possibly be the way the universe really works!"  While I didn't doubt that all this "stuff" actually matched the experimental observations, I was sure there had to be a better explanation:  There had to be something happening "under the hood", so to speak, that was the real reason behind these appearances.

    Revolutionary by xkcd

    Now, unlike most of the "crackpots" and "cranks" out there (no offense intended to any), I knew that if I was going to "get to the bottom of this" I was going to have to learn all I could about all aspects of Physics, and about as much of the experimental evidence, and the nature of the experiments as I possibly could.  That's when I decided to get a Ph.D. in Theoretical Physics.  (Back in the fifth or sixth grade I had already decided that since I was good at both mathematics and science I was going to be a physicist.  I'm sure that my dad being a Nuclear Physicist had some influence as well.  :)  He never tried to push any of us [my brothers and I] into any particular field, but he did expect excellence.)

    High School and Undergraduate Physics:  No Change

    Later, in High School, taking a Physics class, where we could progress at our own pace, I and one other student went all the way through the lesson packets, all the way to Special Relativity.

    Once again, it was "time dilation", "space contraction", "Lorentz transformations", and a strange way to "add" velocities.  The only substantive difference was that I learned how all this could be derived from the Lorentz Transformations.  However, none of this changed my original assessment of the "hokey" theory.  Oh, sure, everything "worked", some (most?) of it seemingly by "magic" or pure chance, but what was the reality?

    Still later, I'm off in college, learning Physics, Mathematics, etc.  On my way toward a Ph.D. in Theoretical Physics.  I devoured my Physics classes, took more Mathematics and Computer Science classes than required (getting Minors in both Mathematics and Computer Science).  All the while with a "bifurcated mind", as I call it:  While I couldn't take any of the Physics at "face value", since I was questioning it all, I still had to learn it well, since there would be no other way I could see to solve this "mystery"!

    Again, another class on "Modern Physics":  Special Relativity and Quantum Mechanics.  Once again, Special Relativity was taught in essentially the very same way, with all the same "players".  Oh, sure, we spent a lot more time on the subject, and did a lot more exercises, but no further insights.

    I think Minkowski spacetime was introduced, and spacetime invariants, and such, but not one single thing that showed any greater "light" upon the subject.  I was still left with my dilemma, and my "bifurcated mind".

    Graduate School:  No Change, 'till General Relativity

    OK.  Skipping to graduate school, actually taking my courses toward my Ph.D.  I was still of a "bifurcated mind"—that's a long time to have to keep that up, basically having to do "double duty" in all my Physics classes!

    Then, I get into the class on General Relativity:  Everything changed!  The "shackles" fell away, and I was free, at last!

    Now, what made the difference?  True, there are a lot of very new concepts in General Relativity:  Curved spaces, Manifolds, general coordinates and general coordinate transformations, Tangent spaces and their dual spaces, Differential Geometry, etc. etc. etc.  So what changed?  What did it?

    The difference was I finally learned a very general and fundamental concept pertaining to any space where one can "measure" lengths and angles:  The "metric", AKA the inner/dot product.

    Hadn't I learned about the dot and/or inner product before, way back in vector calculous, and abstract algebra classes?  Sure, but they always were "positive definite"!  They were always only applicable to Euclidean Geometry!

    I knew that such things (leading to the Pythagorean Theorem, and such) were fundamental to Euclidean Geometry.  What opened my mind was the introduction of a different kind of "metric", inner/dot product:  One that is not positive definite, but indefinite (a so called "pseudo-metric").

    Everything else proceeded, absolutely naturally, from this extraordinarily simple concept, this most tiny little "change" to what I already knew about (Euclidean) Geometry.  This was what was "happening 'under the hood', so to speak, that was the real reason behind these appearances."  Since all other choices of this fundamental piece of Geometry lead to different "appearances", the only choice left was to accept whatever one matches Nature—the character of the Universe around us:  Science must accept however the Universe shows us it works, regardless of how "odd" we may think it to be—it is what it is.

    The Alternate Teaching Idea, for Einstein's Special Theory of Relativity

    Some time later, while still working on my Ph.D. (though I was all done with course work, and just working on my Dissertation) I attended a Colloquium given by a visiting professor.  He presented an alternative approach to teaching Einstein's Special Theory of Relativity.  A method he found to be the easiest, with the highest success rate—in terms of students actually "getting it".

    The method involved introducing the metric (AKA inner/dot product) in an explicit way, since it is usually rather invisible in much of Euclidean Geometry, because it is the simple identity (when using the usual othonormal coordinate representations).  Once the students were comfortable with the metric, he would show it in its most general form, without imposing the usual positive definiteness restriction of Euclidean Geometry.

    The next step is to enumerate all the possible non-equivalent forms such a metric can take (really a very small set, indeed), and show how each form has distinguishable characteristics.

    All that then remains (before getting into the more usual aspects of Special Relativity) is to determine which of the small number of possible forms match the Universe in which we dwell—since the Universe "is what it is", regardless of our "feelings" on the matter.  After all, the purpose of science is to find out what this Universe is actually like, regardless of any desires, on our part, for what we may think the Universe should be like.

    I recognized this as what I had needed from the beginning (though I had found it on my own, and probably benefited all the more for having gone through my own personal journey).

    The Road Forward

    What I'm Going to Attempt With This Series

    I have tried, in times past, to find teaching materials or web sites that present Einstein's Special Theory of Relativity in this "metric centric" manner.  I wish I knew who this professor was (it may be in my notes, somewhere, in some box, in the shed, being eaten by silverfish).  So, if any readers know of some material on this subject, or anyone that teaches like this, I would be most grateful for any pointers.

    So, lacking any such materials, I have actually attempted to teach someone (a Special Relativity contrarian) using something akin to this "metric centric" approach.  Unfortunately, either due to my own imperfect methods, or something else, I haven't succeeded—at least not with that individual, yet.

    Partly as an attempt to refine my approach, and partly to see if anyone, here, can point me to better methods and/or materials, and, more specifically and immediately, due to the "prodding" and encouragement of friends here on Science 2.0, I'm going to attempt to present a "metric centric" approach to Einstein's Special Theory of Relativity.

    How far we go, and how quickly we proceed will depend upon available time, and reader interest and feedback.

    I will do my best, and I hope I receive a lot of good, constructive feedback, so we can make this the best attempt possible.

    So, next time, we shall take a closer look at vector spaces and the inner/dot product in such spaces (so called inner product spaces).


    *  More recently, I have actually seen a far more opaque, overly formal, and downright "hokey" approach to Einstein's Special Theory of Relativity.  :-{  So I no longer consider the more usual approach to the subject to be the worst.  :-/


    Articles in this series:
    What is the Geometry of Spacetime? — Introduction (this article)
    (next article)
    What Is The Geometry Of Spacetime? — What Kinds Of Inner-Products/Metrics? (third article)

    Comments

    Yeah!

    This sounds like it will be a fun series.
    I think most people find the geometric view much easier once they learn it. I'd be curious if it is a good place to start though. Interesting idea.

    I always had trouble looking back at SR after seeing some GR. When SR is taught we are often given 'vectors' like (ct,x,y,z) and work out the proper time or whatnot between two events. But then in GR we learn that the geometric vectors are really in a tangent space at each point. This is easy for me to visualize for a vector field, but while I can (usually) do the math fine I don't quite get why the stuff we did before with "vectors" made with coordinate labels in SR actually worked. How is anything involving just coordinates of derivatives with respect to coordinates actually a vector? Is the velocity four-vector even a real vector then? If in GR we can always choose our coordinates to have the metric at a point be just diagonal (-1,1,1,1), how and why exactly does this affect the coordinate form of the metric at neighboring points if each tangent space is separate?

    The more I think about it, it seems more "natural" to have the metric be diagonal (-1,1,1,1) for all the tangent spaces, and instead describing geometry with how vectors warp while parallel transporting around. I don't know how to make this mathematical, but I've heard this is essentially how the vierbein (or tetrad or frame field) way of writing GR works. I've always wanted to ask you about this, but was worried Doug might see it as a way to pursue generalizing his way of abusing quaternions to get the spacetime dot product to work in curved spacetime.

    Halliday

    Thanks, CuriousReader.

    I do hope to help this be a fun series.  :)

    As far as "why the stuff we did before with 'vectors' made with coordinate labels in SR actually worked."  The key is that when the manifold (the place where points/locations reside) is (intrinsically) flat, one is able to identify the manifold with its tangent space(s) (thus, at the same time, identifying all the tangent spaces with one-another).

    It's a "mapping" thing.

    To a great extent, it's related to the question of "where do the 'tails' of vectors 'sit' " when one is working with vectors in nearly any area of Physics (other than General Relativity [GR], in general).  All too often we do not distinguish between different "kinds" of vectors, and draw them all within the same "space", with their "tails" scattered about within that "space".  However, it's the identification of the manifold with its tangent space(s) that permits this "sloppiness":  One can translate (parallel transport) any vector over any arbitrary path, with impunity, and without distortion, when the manifold is flat!

    Now, as for the potential for doing GR with the metric being identically "(-1, 1, 1, 1)" everywhere in spacetime:  Yes, it most certainly can be done, but then you have the "difficulties" of dealing with "non-coordinate bases".  Once you understand how non-coordinate bases (for your tangent spaces, and their duals) are handled, one can certainly move to set the metric identical to "(-1, 1, 1, 1)" everywhere (or choose any arrangement in between this and the usual full coordinate basis approach).

    However, now, instead of all the information being encoded within the metric tensor, the information is encoded within a sort of anti-commutation relation between vectors.  (However, be very careful, because this anti-commutation relationship is rather like saying that partial derivatives don't commute [∂2/∂x∂y ≠ ∂2/∂y∂x].)

    Now, "the vierbein (or tetrad or frame field) way of writing GR" is quite another "beast".*  It is related to the Dirac matrices, so sort of a "square root" of the metric.  In addition, these are (usually) "required" to have a certain transformational relationship with Lorentz transformations of the tangent spaces.

    I have yet to see any true utility, let alone "insight" (of any kind), come from this approach.  In fact, within my dissertation, I generalized Dirac's equation in such a way that I get all the "competing" "vierbein (or tetrad or frame field) way[s] of writing GR" that I'm aware of (and much more) in a single system, and find no need for the extra restrictions on the transformations of these entities:  The fact is that these transformations are acting on different, orthogonal spaces.

    To a great extent, I find as little fundamental need for some "vierbein (or tetrad or frame field) way of writing GR" as I do for "gauge fixing".  They both look quite misguided, stemming from some rather fundamental misunderstanding of their respective symmetries.  (Symmetries, by the way, that have extraordinarily similar roots, within Differential Geometry.)

    However, that's not to say that I don't still have open questions in closely related areas.  :}

    David

    *  Of the four different "vierbein (or tetrad or frame field) way[s] of writing GR", that I am aware of, only half of them can be viewed as setting the metric identical to "(-1, 1, 1, 1)" everywhere.

    (-1,1,1,1)? Boo! Hiss! I heard all the cool people were using (1, -1, -1, -1) this year !

    Halliday

    :D

    You are completely correct, 'twistor59':  The overall sign of a metric has no physical significance (at least not so far as we have been able to ascertain).

    This will be used, later, to help decrease the number of different metrics we will need to consider.

    David

    Halliday

    All:

    I updated my post in the hopes of easing readers into my article, and helping them/you know, more up front, what this is all for.

    I hope it helps.  :)

    David

    Bonny Bonobo alias Brat
    Through this (hopefully rather short) series I shall endeavor to illuminate this kernel, and, hopefully, develop a better approach to introducing Einstein's Special Theory of Relativity.
    Well I'm really looking forward to this series David and I am delighted that you have started writing articles here. I searched Youtube looking for 'inner/dot product' and found a couple of incomprehensible teaching videos, the mistake they both made at the start was to assume that laypeople understood all of the basics symbols in their equations, unlike the MinutePhysics videos which assume nothing and are brilliant but much too short. I wish that there was an HourPhysics series and am hoping that this will be it.
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Halliday

    Thanks, Helen, for turning me onto MinutePhysics videos.  Quite nice indeed.  :)

    I think the thing they do that is particularly helpful to the layperson (or anyone, for that matter, not already "well versed" in the subject) is they provide good illustrations, animated as appropriate.

    I have often heard it said that if you want to communicate science effectively you need to master three ways of communicating:  Words, equations, and illustrations/pictures.  Those videos do two very well (not to knock them, in any way):  Perhaps the two that are the most important for communicating to the lay-public—those that will not need anything to due with the equations.

    I will be trying to use all three methods, since the intent is to have people be ready for the "nuts and bolts" of Einstein's Special Theory of Relativity.  I know I'm good at the equations.  I think I'm reasonably good with the words.  The difficulty will be the illustrations/pictures.

    I don't have a lot of good tools for creating such illustrations and pictures.  Besides, a few of the best I can think of would be more like interactive moving "illustrations", so the reader can manipulate the "illustration" directly.  Unfortunately, I'm not sure I'll be able to find or even manufacture what I'm envisioning.  I may just have to settle for GIF "videos".

    Perhaps other readers will be able to supplement what I'm able to find and/or provide, and we will be able to create better materials together.

    David

    Quite interested to see where this goes!

    Halliday
    Thank you.  I'm looking forward to it as well.
    "More recently, I have actually seen a far more opaque, overly formal, and downright "hokey" approach to Einstein's Special Theory of Relativity. :-{ So I no longer consider the more usual approach to the subject to be the worst. :-/"

    The worst I've ever seen, is at least two people advocating starting with the velocity addition formula. They then derive everything from that. There was a professor on physicsforums.com that advocated this, published papers on derivations starting from this, and suggested it would shorten some derivations you'd do for students by teaching this way. To him short was by definition equal to more fundamental or clarifying or something. It was by far the most confusing horrid way to present the subject I've ever seen.

    It was confusing enough, that it was even hard to tell for sure that he wasn't accidentally assuming some of the key things he was trying to derive in the derivations themselves. They did get published in peer reviewed journals though.

    Halliday

    CuriousReader:

    I agree that that's pretty bad.  :(

    However, what I'm thinking is even much worse.  |(  Absolutely worse than I had ever imagined possible.

    I also agree that just because something is "published in peer reviewed journals" doesn't make it good.

    David

    blue-green
    Hello David. Best of luck with this endeavor. Afterward, you can follow up with a series on “Quantum's Lesson and Einstein's Dilemma.” My learning curve began with Mr. Tompkins in Wonderland. Gamow was a very entertaining writer, however, it was not until I came upon the geometric approaches of Wheeler and Misner that I “got it”. Later, while a graduate student in Engineering, I published an article in my college's magazine that quickly derives the essential equations after showing the invariance of the space-time intervals … and then using similar triangles to raise it to the energy and momentum considerations where the real meat lies.

    Below is a link to a scanned version of the 1978 article.

    ((There were some challenges and budget difficulties in getting it typeset (it didn't come out perfectly). It is a bit heavy on the use of algebra, yet not too difficult I hoped for students in engineering. A caption got lost for one of the figures. That was back when one really did Cut and Paste and sometimes a caption would not stick and make it to the printer.))

    >http://www.mountainlake.com/mlp/travel/CErock.pdf

    ~ It's all about fibers ~
    Halliday
    blue-green (or should I call you "Scott"):

    Thanks for sharing the article.  Actually, from what I can see in the article, you started with the constancy/invariance of the speed of light, from Maxwell's equations.  This (and the principle of relativity, as Einstein called it) is what Einstein used in his original paper to derive Special Relativity (SR).

    While you did present the invariant spacetime intervals rather early, it still looks like it falls within the standard mode of presentation of SR.

    Now, ultimately, one must come to a point of "doing the math" of SR.  Additionally, while one can do much with triangles, as you did within that article and as Johannes Koelman has done in some of his articles (like What's Wrong With E=MC^2?, and Sticky Collisions And Atomic Bombs), such still doesn't really get down to the level of what's "happening 'under the hood', so to speak, that [is] the real reason behind these appearances."

    An additional thing that is interesting, at least to me, is that the "metric" (which gives rise to the invariants in the first place) even accounts for why there even is some velocity that is the same for all observers, instead of taking such as a postulate/axiom.  (Of course, it doesn't specify what numeric value such should be.)

    David

    the "metric" (which gives rise to the invariants in the first place) even accounts for why there even is some velocity that is the same for all observers
    Sitting in a traffic jam, thinking about turtles today, it occurred to me that when we draw x-t diagrams we are, strictly speaking, *drawing* space and time, not spacetime. It so happens that we can depict the orthogonality of x and t on Euclidean paper, but in some ways that's confusing. Spacetime is not Euclidean. "In particular", I asked the stop light on the car in front of me, "why does my nice tidy x vs t picture have all those ugly light cones criss-crossing it?" "Ahah!" said a familiar voice behind me. "Oh you daft cat! I suppose you've been asleep in the back all day?" I cried. But she wasn't interested in such mundane matters: "And what exactly do those light cones reprrrrresent?" she purred. "Umm, light rays?" I suggested feebly. "Try again!" "Oh!" I exclaimed, light dawning, "The metric, the metric!" I gibbered incoherently, "s=0! s=0!"  "Prrrrrecisely!" "Minkovskian space doesn't flop straight onto Euclidean paper;" I continued, "the light cones are simply those places on the diagram where s = 0, in a sense a single point." But the cat had lost interest and was investigating an old fish-and-chips wrapper on the floor. Besides which, a frantic commotion informed me that the traffic was on the move again - or would have been if I had not been staring into space, or indeed spacetime, with an ecstatic look on my face oblivious to the fury of the drivers desperate to catch up with the next tail back a few yards ahead. 
    Halliday
    Thanks for sharing that, Derek.  :)

    Absolutely, our pieces of paper, and our computer screens, are Euclidean spaces.  So we are mapping from another space, like Minkowskian spacetime, in a one-to-one and onto mapping to our Euclidean spaces.  The reason we can do that is that any d dimensional real vector space has multiple, reasonably natural mappings (one-to-one and onto mappings) with Rd, the product space of d copies of the real numbers.

    The only problem is that whatever inner/dot product (metric) the space had is lost, and the implicit Euclidean metric is applied (even if the original space had no inner/dot product!).  We have to use our imagination, calculations, or other means to "reapply", or, at least, keep in mind the original metric.

    Another interesting aspect (at least to me) of what you shared is that the "s=0" lines (the so called "light cones") are not truly "a single point".  The "sense" in which they are, or seem to be, is in comparison with Euclidean spaces, where the length between any two points can only go to zero (s=0) if the two points are exactly the same point.  (This stems exactly from the "positive definiteness" of the Euclidean dot/inner product, aka metric.)  So, these non-Euclidean spaces can violate long "cherished" characteristics we have become "trained" to expect from our experiences with Euclidean spaces.

    David

    The only problem is that whatever inner/dot product (metric) the space had is lost, and the implicit Euclidean metric is applied (even if the original space had no inner/dot product!). We have to use our imagination, calculations, or other means to "reapply", or, at least, keep in mind the original metric.
    Perfect! Statements like that convey exactly what I feel about the subject - I don't know whether all your target audience will find it as helpful, you may have to try several angles. But it works for me. Breaking out of the Euclidean mould is a huge thing for all of us and simply running to a set of Transformations doesn't give anyone a feel for what it's about.
     
    I actually find this exciting!

    Mind you, you may have to explain matrix products and their significance. Anyone can Google the definition of inner product but the question is then "So-what?".  Or more importantly, "What's wrong with a quasi-Pythagorian sum?"

    Thanks for clearing up the s=0 business. I'm struggling a bit now to decide what a light cone really means!
    Will be interested to see whatcha got. I sympathize w/being shell shocked by SR when I first took Mod.Physics, Jr.yr.
    My Sr. yr. tho, I took a grad math course targeting physicists interested in GR. Terrified initially, the kindly old prof slowly emboldened our confidence by (would'nt you know it) deriving almost all of SR via the minkowski metric tensor. Time dilation, mass dilation, & length contraction just dropped out in a few lines. No more `light clocks' or other gedanken expts., just simple algebraic invariants & geometric constructions. I still have the notes to this day.
    Hopefully, you'll publish your notes on the arxiv ?

    Halliday
    Jimbo:

    You are absolutely correct that all of Special Relativity (SR) follows directly, and simply from "the Minkowski metric tensor".  However, that alone isn't the reason for the approach I have mentioned, and will be attempting to illuminate.

    While having everything follow from a single entity ("the Minkowski metric tensor") certainly helps focus everything, so it no longer "feels" like a jumble of "disjoint" (seeming) facts, it still falls short of providing any motivation for why one should use "that thing".

    I hope this approach will provide more of a motivation for why one should use "the Minkowski metric tensor", though mostly by simply having it be one of a few possibilities, each having different "appearances", so one can choose based upon experiment.  (One then simply accepts what the universe shows.)

    David

    David,
    Thanx for your feedback ! After I posted my comment, I dropped my jaw: Are You THE `Halliday' of Halliday & Resnick ?
    If so, I am in awe, sir. As a fledgling freshman engineer who eventually switched into physics, I cut my teeth on your very intimidating text.
    You're right about a lack of physical motivation to use guv, after all, my instructor was a mathematician ! Elegance & economy was his only motivation.
    Something very physical however, is the connexion between action & line element in SR. One merely writes,
    {dS = (mc)*ds}^2 . Of course the Mink.metric enters on the right (geometry) & physics on the left (particles, fields), & in that respect, mirrors GR. Allowing the metric to vary in S-T, one can then integrate, set the variation=0, & out pops the geodesic eq., the curved space analog of Newton's 2nd law for a free particle.

    Hank
    Are You THE `Halliday' of Halliday&Resnick ?
    I thought that Halliday died.
    Halliday
    Yes.  That David W. Halliday died, I'm sorry to say.

    While my name is David W. Halliday, I am young enough that I, too, "cut my teeth" on Halliday&Resnick.  (It was rather awkward to actually have fellow students asking whether I wrote the text.  :}  )

    I've bookmarked this blog and will be checking back in. When you said you were looking for a metric centered presentation of SR, I thought of Wheeler and Taylor's Spacetime Physics. That was an excellent book and a prequel to their, equally excellent, Exploring Black Holes introduction to GR. Also, I thought Theodore Frankel's Gravitational Curvature had a section titled The Minkowski Norm was very good and similar to the presentation on page 44 of Einstein's General Theory of Relativity: With Modern Applications in Cosmology By Øyvind Grøn, Sigbjørn Hervik. Which can be viewed on google books.

    http://books.google.com/books?id=COqUEa5M6O0C&lpg=PA44&ots=UFlKvuqgwO&dq=Robb's%20Formula&pg=PR4#v=onepage&q=Robb's%20Formula&f=false

    Halliday
    Thanks.

    As I said in the article, I appreciate any pointers to similar approaches.

    While I have the "tome", Gravitation, by Misner, Thorne, and Wheeler, I have not read Wheeler and Taylor's Spacetime Physics, or many of Wheeler's other (geometric) works on Special Relativity.  I think I should check some out.

    Like I tried to imply in the article, what I would really like to find is the curriculum that visiting professor created, and was using, but, alas...

    David

    The Stand-Up Physicist
    Let me second the recommendation of "Spacetime Physics".  Edwin F. Taylor is much more of a physics teacher than Wheeler who was a front line researcher.  Taylor did give talks about his approach, so he may have been the fellow.  While he was writing the book, he was also teaching from it to see what worked.  When I took the class from Kinkos Copies, part of the assignment was to critique the text, particularly anything that was not clear.  

    The focus is on the distance between events and that pesky minus sign (whether it is one or three).  The book decidedly avoids bringing up Lorentz transformations until page 95 where it is a "special topic".  The first subheading is "L1. Lorentz Transformation: Useful or Not?"  Sounds like your guy :-)

    What I particularly liked was the software that came with the book.  Unfortunately it worked on one of those Mac Plus boxes so I cannot run it any more.  It involved plugging events onto a spacetime diagram and being able to change velocities.

    My preferred starting point is this:
    It is quite quick and easy to show that if we assume that every inertial observer agrees on the speed of light, then they also agree on c^2 t^2 - x^2, where t and x are respectively the time and space separation of any two events. This is the fundamental, and very physical, underpinning of all of special relativity.

    Of course, this is only a small shift in emphasis from what I think you are advocating, but in my humble opinion, starting with the metric itself is putting the cart before the horse!

    Halliday
    Rhys:

    While the approach you advocate starts from (essentially) the initial postulates Einstein used in his original (1905) paper (with the principle of relativity, Einstein's other postulate, being an implied assumption in your approach), it still falls short of a being able to address any form of "why".  For instance, why is there any (finite) speed "that every inertial observer agrees on"?

    Now, I'm not proposing to simply start with any particular metric.  However, I think we can justify why there should even be a metric (inner/dot product) at all.  Then the question basically boils down to "Which metric?"

    So, please feel free to provide constructive criticism, and suggestions for improvement.  I hope you can help refine the approach I am attempting to illuminate.

    David

    "However, I think we can justify why there should even be a metric (inner/dot product) at all."

    That's interesting. The only convincing way I can really think of to do this is the one I just outlined, i.e., starting from the invariance of the speed of light; I'll be curious to see how you go about it.

    Let me mention that I also used Taylor and Wheeler's book as a first year undergraduate, and thought it was very good.

    I explained what has happened at
    http://www.worldnpa.org/site/event/?eventid=524

    Relationship between Newtonian and Einsteinian Physics

    Description
    The mathematical connection between Newtonian and Einsteinian physics will be explained. Essentially it can be viewed as the same bit of maths but subjected to a different language. Special relativity being an interpretation of the equation c'2t'2 = (c2 v2)t2 by setting c' = c with t not equal to t'. While Newtonian physics is interpretation of the same equation as instead: t' = t with c not equal to c'. Newtonian gravitational theory has primary and secondary gravitational effects. When both these effects are considered then Newtonian physics gives same maths as General relativity. It is only that the maths is interpreted by different languages. In the case of Newtonian physics it is interpreted in terms of forces while Einsteinian physics talks of it in terms of space-time curvature. On the experimental side it will be pointed out from a paper by a NASA scientist that Einstein's relativity has never been subjected to a direct experimental test; the tests have only ever been indirect. (Of course certain Einsteinians have deceived themselves to the nature of their experimentation and not realized they have only ever done indirect tests.) Thus it has always been a subjective issue as to whether the maths should be interpreted by Newtonian or Einsteinian language. As to the paradoxes of Einstein's relativity this has been in part caused due to the complicated language used by the Einsteinians obscuring the understanding; while in Newtonian language it is much clearer as to what is happening. Special relativity considers a symmetrical scenario of two observers at relative constant velocity motion, while general relativity breaks that symmetry. Newtonian physics has none of those conceptual problems from its outset. Thus the problems of modern physics can be placed down to the difficulty people have experienced upon learning a new language to describe physical reality.

    Halliday
    I'm sorry, Roger, there are very simple, distinguishable, measurable differences between Newtonian/Galilean space/time, Euclidean space ("spacetime"), and Minkowskian/Einsteinian spacetime.  In fact, we will be relying upon these differences to determine what spacetime geometry most closely matches our Universe/Nature.

    While we will not be addressing the observable differences between Newtonian gravitation and Einstein's Theory of General Relativity in this series, I recommend you learn about the Parameterized Post-Newtonian Formalism, and the tests of General Relativity, and other competing theories.

    You refer to a paper by a NASA scientist.  Is the following quote what you are talking about?

    According to Daniel Y. Gezari of NASA tells us: “In particular, the speed of light (c)
    has never been measured directly with a moving detector to validate the invariance of c to motion of the observer, a necessary condition for the Lorentz invariance of c. The invariance of c can now only be inferred from indirect experimental evidence. It is also not widely recognized that essentially all of the experimental support for special relativity in the photon sector consists of null results.

    Additionally, you have completely misrepresented Thorne's statement, but, since you obvious don't understand the actual theory, it is far from surprising.

    Now, if you wish to stick around, you will hopefully learn a "thing or two".  Perhaps we will see if it makes any difference.

    David

    Dear David

    You say - “distinguishable, measurable differences between Newtonian/Galilean space/time, Euclidean space ("spacetime"), and Minkowskian/Einsteinian spacetime.”

    There isn't. As explained in my lecture it is convention as to whether treat light speed c as variable OR treat it as constant so that have time and space (distance) as varying between observers.

    Before Einstein 1905 there was Poincare and he clearly pointed out it was conventionalism.

    I have spoken to people who believe in Einstein's special relativity and when pressed it turns out they really believe Poincare theory not Einstein's and they are unaware of their deception.

    In the quote by Daniel Y. Gezari of NASA I am referring to the fact that there is no direct measurement of c as constant, it has always been indirect – which means only by convention as per Poincare is c being treated as constant.

    Thorne's statement is clear he refers to general relativity and Newtonian gravity as being the same thing but in different languages.

    So my proposal is that when many people state a belief in special relativity what they should really be referring to is Poincare's theory not Einstein 1905 theory, and then c is only constant by convention supported only by indirect experiments. Until you address these issues you will have the wrong understanding of physics.
    Roger

    Halliday
    Roger:

    You claim that Poincare "clearly pointed out it[the difference in the nature of 'spacetimes'] was[is] conventionalism."  Do you have a reference?

    I know that Poincare and Lorentz had a very different view on the "cause" of the Lorentz transformations (they were trying to still work within Newtonian/Galilean Relativity).  However, it most certainly didn't come down to "conventionalism."

    I would like to see you show how the decay half-life of muons increases as they travel at speeds approaching that of light.  How, even with their increased speed, muons generated by cosmic rays can actually reach the surface of the Earth, even though they take too long to get here for their decay half-life for nearly stationary muons.

    You claim that for your alternate "convention" t = t', which is like unto the temporal transformation of Newtonian/Galilean Relativity, is the one "true" "convention".  Do you actually claim that this "implies" or "means" that your "convention" really is Newtonian/Galilean?

    You do realize that t' = t implies that time advances equally for the muons at rest vs. the high speed muons streaming through our atmosphere?  Doesn't this make an explanation of the observed phenomenon even harder to explain?  Remember, the observed phenomenon is all observable with clocks and measuring "rods" that are all at rest with respect to the Earth, so there is no place for your alternate "convention" to modify the observations, only the explanation.

    Additionally, in order for you to have t' = t, from the equation you started with, are you not aware that you required the speed of light, c, to transform in a manner that is quite inconsistent with Newtonian/Galilean Relativity?

    Besides, what we will be obtaining is completely independent of any "conventionalism."  Of course, that's why we will be obliged to take a look at all the possibilities.

    David

    David
    Sorry this reply starts to get too long if you ask questions. What I want to ask you, given conventionalism – that lightspeed in vacuum can be treated as constant by convention OR treated as not constant by convention. Why when showing the maths to students don't they show both conventions work? BUT I see you have questions about conventionalism, so I will deal with your issues on that before returning to my question:

    Scott picking upon conventionalism : “According to the conventionalist doctrine of space elaborated by the French philosopher-scientist Henri Poincare in the 1890s, the geometry of physical space is a matter of definition, not of fact. Poincare’s Hertz-inspired view of the role of hypothesis in science guided his interpretation of the theory of relativity (1905), which he found to be in violation of the axiom of free mobility of invariable solids. In an effort to save the Euclidean geometry that relied on this axiom, Poincare extended the purview of his doctrine of space to cover both space and time. The centerpiece of this new doctrine is what he called the “principle of physical relativity,” which holds the laws of mechanics to be covariant with respect to a certain group of transformations. For Poincare, the invariance group of classical mechanics defined physical space and time (Galilei spacetime), but he admitted that one could also define physical space and time in virtue of the invariance group of relativistic mechanics (Minkowski spacetime). Either way, physical space and time are the result of a convention.”
    from Hypothesis and Convention in Poincaré’s Defense of Galilei Spacetime, Scott Walter http://www.univ-nancy2.fr/DepPhilo/walter/papers/2009hypothesis.pdf

    So considering scenario of light travelling distance (c-v)t then being reflected back so travels distance (c+v)t multiply these together to give (c^2 -v^2)t^2 then equating this to c'^2t'^2 which is the case of light travelling distance c't' and being reflected and travelling back c't'. I trust you can appreciate the two physical scenarios being equated here. If we set t =t' then have c not equal to c', if we set c=c' then t and t' are not equal. It becomes a matter of convention as to whether treat c =c' or not.

    You say: “I know that Poincare and Lorentz had a very different view on the "cause" of the Lorentz transformations (they were trying to still work within Newtonian/Galilean Relativity).”

    Yes, and it links how Newtonian physics is connected to special relativity.

    Poincare points out experiments and observations are based on the convention being used. So in the case of muon decay lifetimes that when being analysed by the convention of lightspeed c constancy leads to relativistic velocity addition i.e. velocity being treated in different way to Newtonian physics. Thus the convention of lightspeed constancy means the muon decay rate has to be explained by time dilation, but if go by the convention as used in Newtonian physics then that gives answer instead that the muons going at different speeds than claimed by the lightspeed constancy convention.

    You say: “You claim that for your alternate "convention" t = t', which is like unto the temporal transformation of Newtonian/Galilean Relativity, is the one "true" "convention".”

    That's not quite true, there is a deep philosophic issue of what is the nature of time. Time is being treated in a different way by these conventions, and to know what is the “true” convention means you would need to know the “true” nature of time. I hope that answers the question which followed that.

    You say: “You do realize that t' = t implies that time advances equally for the muons at rest vs. the high speed muons streaming through our atmosphere?”

    Yes that would be the convention of how to deal with time in the Newtonian physics setup.

    You say: “Doesn't this make an explanation of the observed phenomenon even harder to explain?”
    Well it would depend upon what observed phenomena you are trying to explain. What we have at present is the problem of unifying Einstein's relativity with quantum physics, and I have disposed of that problem by showing how Einstein's relativity is connected to Newtonian physics, and quantum physics finds it perfectly easy to deal with Newtonian physics.

    You say: “Remember, the observed phenomenon is all observable with clocks and measuring "rods" that are all at rest with respect to the Earth, so there is no place for your alternate "convention" to modify the observations, only the explanation.”

    I don't know what you are really trying to say, but presumably you are talking about the difficulty of setting the measuring instruments up for whatever convention, and yes that is a difficulty but there are methods.

    You say: “Additionally, in order for you to have t' = t, from the equation you started with, are you not aware that you required the speed of light, c, to transform in a manner that is quite inconsistent with Newtonian/Galilean Relativity?”

    Well the setup of light travelling a certain distance then being reflected back to cover another distance and then multiplying these two things together is not the setup that Galilean transformations was created to deal with, those transformations were for only one way speed of light not two way speed of light. And what I pointed out with the equation (c^2-v^2)t^2 = c'^2t'^2 is how Newtonian physics would deal with it namely not have c equal to c' but have instead t = t '.

    You say: “Besides, what we will be obtaining is completely independent of any "conventionalism."”

    It won't be if you are going by how I have seen metrics handled. In the first step they start from implicitly setting c =c'. And as I have pointed out that is a convention. So the issue becomes why are they treating things by the convention of lightspeed constancy when they can treat by the other convention.

    So back to my question to you – By Poincare it is a convention as to whether deal with lightspeed constancy or not. So why show maths dealing with only one convention when the maths using the other convention works perfectly okay as well? Doesn't that mislead the student as to what is really going on with the maths?

    Roger

    Halliday
    Roger:

    Boy.  I "asked for it", didn't I.  :}

    Unfortunately, I must not have expressed myself sufficiently well, since whenever I referred to "the observed phenomenon" I was referring back to the observations of the muons.  I wasn't jumping into other phenomena, or observed phenomena in general.

    Now, as to whether one can describe the same physics, and the same physical "spacetime" using different "conventions", the answer is a big fat Yes.  This is at the very heart of General Relativity (GR), with its ability to accommodate general coordinates, and general coordinate transformations.

    However, GR is outside the scope of this series.  On the other hand, we will be looking at inner product spaces from a very general standpoint, not completely unlike that of GR.

    On the other hand, as I will be showing, as a part of this series, one most definitely cannot use any change in convention to make an Euclidean space look like a Newtonian/Galilean space/time, or a Minkowskian/Einsteinian spacetime, nor even a Newtonian/Galilean space/time look like a Minkowskian/Einsteinian spacetime.

    As I said, they are completely distinguishable, independent of any "conventionalism."

    The fact is, it looks like either you are misinterpreting Scott Walter, or he is confused on even what Poincare was saying in his statement you quoted.*  For, as Poincare did state, and as it is alluded to within your quote:  "For Poincare, the invariance group of classical mechanics defined physical space and time (Galilei spacetime), but he admitted that one could also define physical space and time in virtue of the invariance group of relativistic mechanics (Minkowski spacetime)."

    You see, these two systems involve different "invariance groups"!  One cannot make one into the other!  (These two groups are not isomorphic!)

    Now, you do quote Scott Walter as saying "Either way, physical space and time are the result of a convention."  While this would seem to imply a misunderstanding on the part of Scott Walter, it is also possible that he intends this statement to be interpreted in a manner different than your (apparently) preferred interpretation.  (This could be similar to how you completely misunderstood Thorne, as I pointed out earlier.)

    The only way "Galilei spacetime" (what I refer to as Newtonian/Galilean space/time) and "Minkowski spacetime" (what I refer to as Minkowskian/Einsteinian spacetime) can be considered to be merely "the result of a convention" is when working from an Aristotelian like "pure logic" ("pure" philosophy) with no consideration for experimental tests, or even how these two "spacetimes" will have different appearances.**  Yes, if one simply wishes to "dream up" candidate "spacetimes" (so not just the "physical" one we have to deal with), one can "build" such on many different "conventions" (different "invariance groups").

    However, unlike pure philosophy, science must consider experimental tests!  To do otherwise is not science!

    David

    *  I admit that I haven't read the entire linked paper, which may help illuminate whether Scott Walter actually understood Poincare, or not.  However, I do notice that your entire quote is nothing but his abstract.  That begs the question of whether you actually read anything beyond that.

    **  Even from a "pure logic" ("pure" philosophy) standpoint, it would seem to be wholly incomplete without at least trying to answer the question of the appearances!

    Halliday
    Roger:

    Focusing in on your statement:

    ... What we have at present is the problem of unifying Einstein's relativity with quantum physics, and I have disposed of that problem by showing how Einstein's relativity is connected to Newtonian physics, and quantum physics finds it perfectly easy to deal with Newtonian physics.

    If you think you have solved anything along the lines of the actual "problem of unifying Einstein's relativity with quantum physics" you are deluding yourself.  ;)

    First, Quantum Physics has absolutely no problem whatsoever unifying with Einstein's Special Theory of Relativity (SR).  The fact is all of modern Quantum Physics is always done in a unified way with Einstein's Special Theory of Relativity.  There is no modern Quantum Physics that even considers dealing with Newtonian physics.

    So, secondly, the only "problem of unifying Einstein's relativity with quantum physics" is in unifying Einstein's Theory of General Relativity (GR)—Gravity—with (Relativistic [as in SR]) Quantum Physics.

    Of course, since you misunderstand GR to the point that you claim that "Thorne's statement is clear he refers to general relativity and Newtonian gravity as being the same thing but in different languages" I suppose it's all too natural that you would think that somehow equating SR with Newtonian/Galilean space/time (which is impossible, as will be shown in this series), and GR with Newtonian gravity (which is also impossible, but is outside the scope of this series), that you have, somehow, "solved" the problem of "unification".

    I recommend that you simply wait and see what unfolds in this series.

    David

    Dear David

    You say: “I recommend that you simply wait and see what unfolds in this series.”

    What I want addressed is whether the speed of light in vacuum (c ) in the context of special relativity is being treated as constant as a convention OR not.

    I have talked with many people on this issue, and some think it is convention and some think it is not. So it has clearly not been dealt with properly in the teaching of special relativity that some students can end up with one impression and others with another impression.

    Given two systems, a primed system with x', t' and unprimed one with x,t, what standard texts do is use c in both primed and unprimed systems this glosses over that it is c' in the primed system and that the convention is being taken that c' = c. When that convention of c' = c is not taken then different maths results.

    Are you able to address the question of why one convention is taken instead of the other? i.e. why the maths should be done one way and not the other.

    Often there is an appeal to experiment, but the experiments are also being subjected to convention. i.e. the experiments are interpreted by the maths that is set to the convention of c as constant. So can really interpret them by the other convention.

    As regards Newtonian gravity there are two gravitational effects that of a uniform gravitational field and a non-uniform gravitational field. Acceleration being the result of gravity. Uniform acceleration can be dealt with in the context of special relativity. It is when the acceleration is non-uniform that Einstein went to general relativity. Both types of gravitational effect are part of Newtonian theory as part of the gravitational field, in general relativity that gravitational field is being treated as spacetime curvature by a type of convention if you like, and its still possible to deal with gravity in the existing convention of Newtonian physics.

    You say: “Now, as to whether one can describe the same physics, and the same physical "spacetime" using different "conventions", the answer is a big fat Yes.  This is at the very heart of General Relativity (GR), with its ability to accommodate general coordinates, and general coordinate transformations.”

    Which I see in agreement with what I just said about convention in the context of general relativity whether you fully appreciate the consequences of that convention OR not.

    However you go on to say: “On the other hand, as I will be showing, as a part of this series, one most definitely cannot use any change in convention to make an Euclidean space look like a Newtonian/Galilean space/time, or a Minkowskian/Einsteinian spacetime, nor even a Newtonian/Galilean space/time look like a Minkowskian/Einsteinian spacetime.As I said, they are completely distinguishable, independent of any "conventionalism."”

    So I think you do not appreciate the convention that is being used in special relativity. It is as I explained above that the convention c' =c is being made between primed and unprimed systems and not being explicitly stated as that is what is being done.

    I think you are making claims about Poincare and Scott without properly studying the litearture, because you seemed unaware of what conventionalism was when we first communicated.

    You say: “If you think you have solved anything along the lines of the actual "problem of unifying Einstein's relativity with quantum physics" you are deluding yourself.  ;)”

    Well what I have done is a simple manipulation of the maths and put it in a form that makes sense to me as being the constancy of lightspeed is a convention. I don't see why it should be anything other than manipulate the maths of Einstein's relativity and maths of quantum mechanics so that the maths is of the same type. Its simple and its easy, so why make a big fuss and want something more complicated. If you think it is wrong please address why the maths cannot be manipulated that way.

    I refer you back to the start of your article where you say: “Many people struggle with, and even rail against, Einstein's Special Theory of Relativity.  The way it is usually taught or presented often seems to make it appear to be ever so complex, far too abstract and opaque, and even downright "hokey".*  My experience certainly allows me full empathy for such struggles.”

    Well with us that struggle with being taught the subject of special relativity, we try to make sense of it and when we refer back to Poincare we find it about convention. And for some of us the way we make sense of it is by conventionalism. If its not convention then teaching on this subject must be bad in allowing students to be deceived one way and in another way. So once again I ask you please address the issue of conventionalism or do you no longer have sympathies with those who struggle against relativity?

    Regards
    Roger

    P.S As to other issues that are diversions: Bohr dealt with how quantum mechanics is connected to Newtonian physics by such principles as complementarity. So if Einstein's relativity is put back into terms dealt with by Newtonian physics, then quantum mechanics already deals with how it is connected to that.

    Halliday
    Roger:

    I have already addressed and answered all the aspects of your "conventionalism" that I will address in this comment area.  For the rest, as I said, “I recommend that you simply wait and see what unfolds in this series.”  For I believe the aspects of your "conventionalism" issue that pertain to Einstein's Special Theory of Relativity will be answered.

    I will most certainly not be imposing any "conventionalism".  That, as I have said, is why we will be obliged to take a look at all possibilities (though, as we will quickly see, the number of possibilities for a handful of dimensions is really rather small).

    David

    You read any Newton, David? Look carefully in the Queries at the end of his Optiks and you see he asks whether gravity does not bend the path of light. Newton was not a convinced "Newtonian"!

    Still, wave electromagnetism opened a whole range of new problems, some of which are still toi be solved. My read reference is Melvin Schwartz (of muon neutrino fame), Electrodynamics (Dover, pp. 110-138), where he works from the Lorenz group to observing time-varying fields in moving frames, and shows that magnetism must exist as the second-order field "squaring up" the conserved energy!

    Acceleration of course poses more difficult problems:. Here's inertia viewed as the vacuum "backreaction"! http://arxiv.org/abs/physics/9802031

    Halliday
    Orwin:

    I am reasonably aware of Newton's corpuscular model of light.  If you search on this site, you may find some discussion I have had with others, here, on whether light bends under Newton's theory of gravitation.  (Corpuscular vs. wave-like "light" makes a significant difference in how such react with Newtonian gravity.)

    As far as Newton not being "a convinced 'Newtonian'!"  Newton never seemed comfortable with the "action at a distance" nature of his own theory of universal gravitation.  So, yes, I would tend to agree.

    As far as "wave electromagnetism" and the nature of magnetism.  Are you aware that the magnetic field of a current in a wire is fully explained as the relativistic transformation of the electric field of the moving electrons, even though they are traveling at far less than the speed of light (like 10-5 c)?

    Now, the principle open "problem" that I know of involving electromagnetism is the "self field" interaction with charged particles, especially the electron.  While the "backreaction" of an accelerated charged particle "should" contribute an inertia, it certainly can't be the complete explanation, if for no other reason than the fact that we have three electron-like particles with different masses—the only difference in these three particles is their different masses.

    A highly related issue is whether a charged particle, held stationary in a gravitational field, radiates.

    Now, unfortunately, while all these issues are quite interesting, they are outside the scope of this series.

    David

    Wow, you haven't even got to the teaching material yet, and already the crackpots are coming out of the woodwork.

    Good luck, you are going to need it.

    Halliday
    Thanks for the "Good luck".

    I actually expected to see more "crackpots ... coming out of the woodwork" than I've seen so far.

    Personally, I don't believe someone can be properly "labelled" a "crackpot" or "crank" just from a single message, or even a short exchange (usually).  The reason I say this is that anyone can come up with "crackpot" like ideas about anything they don't fully understand.  So, at least to me, what distinguished a true "crackpot" or "crank" from those that may express "crackpot" like ideas is whether such are willing to change their views based upon additional information.

    Unfortunately, I know that true "crackpots" and "cranks" do exist, because I have had some dealings with such.

    I do hope that this series may help convert some with "crackpot" like ideas, due to a lack of understanding, into people with somewhat greater understanding.

    We shall see...

    David

    mathematical_investigations
    This is a complete stab in the dark, but maybe the teacher was Bernard Schutz. Chapter 3 of his First Course in GR, titled "Tensor Analysis in SR", starts with the metric tensor. He covers it that way because it leads naturally to the  idea of gravity as curvature of spacetime.  That is one of my favorite physics books. 
    Halliday
    Thanks, Barry.

    I'll look into your recommendation.

    Of course, practically all books on General Relativity (GR), besides "popular" books, have to introduce the metric rather early on.  However, what I'm thinking of (what the professor I mentioned said he did) is rather different than how I've ever seen the metric introduced in any book on GR.

    So, perhaps as we move forward you can share how what I will be attempting compares to what you saw in that book.

    David

    mathematical_investigations
    I should have said that Schutz specializes in differential geometry and that is probably why his name came to mind. I'm very curious about the approach you are describing.
    David - I know some readers have started recommending mathematical tomes - and indeed have filled up a great deal of reply space with mathematical jargon. Please don't make this a dull tutorial, we can go anywhere on the Web for stuff like that. I believe you have a genuine desire to get to the heart of the subject. Physics teaching has always gone round the edges, starting with Michelson and Morley and going round and round and round until eventually "abstract" subjects like manifolds and metric spaces are reluctantly tackled... Despite any impression you may have gained to the contrary over the "relativistic mass" argument, I am not a Luddite and I would love to see you plunge straight into the core. This of course is maths, but you don't need to prove theorems, just convey what the idea is. The traditional approach, if anything, reinforces classical thinking, the Lorentz transforms are seen as a wierd "solution" to the "observed" fact of invariance of c. Start with the kinds of space that *could exist* - or back a couple of steps to what we actually mean by space - and then lo and behold, unless I am thoroughly mistaken, all the "physical" relativistic effects turn out to be due to looking at moving objects from a different perspective. See, I'm more than happy to stay with the only real quantities, the invariant ones :) But won't it be an eye-opener to realize that time doesn't really dilate, it's just the way Bob's proper time projects onto Alice's, so that's the way Alice sees it? Ditto space doesn't really contract! I'm sure this can all be done with diagrams and words without obscuring everything with complicated equations that no-one can really" read"  or with hair-splitting jargon. And because you're NOT writing a tutorial, it's not the end of the wprld if people ask for clarification in the comments.
     
    Well that's my two penn 'orth. I don't have any resources for creating animations, but I'm always happy to do diagrams if that helps.
     
    Bonny Bonobo alias Brat
    I agree with Derek (the parts I understand that is) and he does great diagrams!
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Halliday
    Thanks, Derek (and I haven't gotten the impression that you are any kind of "Luddite").

    I wholeheartedly agree with your outlined approach.  It's one of the great things about a more interactive approach, such as a 'blog:  We can provide a more general presentation, and "fill in the gaps" through further discussion, especially since different members of the audience will have significant differences in understanding.  What may be obvious to some will undoubtedly be rather obscure to others.

    It's also one of the reasons I haven't committed to any particular schedule.  (Of course, the other reason is I don't know how much time I will be able to devote in any given week [I do have a demanding full time job, and my family has needs as well], or how quickly I will be able to find or create the needed visuals.)

    I will be trying my best to find and/or produce good diagrams.  I also hope to find and/or produce good animated/interactive diagrams.  I will certainly appreciate your input on diagrams, as you see fit.

    I know I am a visual learner, though I have also become rather adept at creating visuals within my own mind.

    I will also be using some math, though nothing beyond so called Linear Algebra.

    David

    Reading this should be interesting, though it's going to make my mind hurt. My problem with the relativists is that they keep insisting that something hasn't happened until you see it happen - of course, the quantum folks tend to say the same thing...

    Me, I've gotten lost in the Elevator thought experiment, because I can't see the equivalence - two pendulums shows the difference between the elevator under thrust, and the elevator in a gravity field, except at some limit of infinity where the gravity field is "flat".

    And, of course, there's the problem of simultaneously observing the clocks on Earth and Alpha Centauri while in flight between at relativistic speeds, and seeing time slowed down on Earth, while it's sped up on Alpha Centauri - but ... I thought that's not what I'm supposed to see, since I'm travelling at a constant relativistic speed - I though *EVERYTHING* was supposed to be slowed down - just shifted in frequency.

    And somewhere in there, the Mach Principle and how that bucket of water knows its spinning keeps needling me... The Cosmic Microwave Background?

    Halliday
    Tara:

    I hope that if "it's going to make [your] mind hurt", that it only hurts "good", as in the "pain" that brings "gain".

    Now, unfortunately, many of the things you bring up, here, are beyond the scope of what this series will cover, since they go into General Relativity (GR).

    However, we may be able get into GR subjects in subsequent articles, especially "thought experiments".

    David

    vongehr
    David: No No No, please not. The metric is maths that fits, that describes the physics. However much it may have helped you, such cannot be "the real reason", the machine under the hood. Think about emergent relativity, think about SO(2,1) inside graphene for example, and do not tell people that something like a piece of mathematical description can be the reason (rather than the model, the language) for anything. Especially the crackpots will only take this as further proof of that relativity theory is wrong.

    There are two, and only these two reasons, for relativity:
    1) Either it is emergent, then it is plainly due to a pseudo particle with a finite propagation speed being our most fundamental excitation and thus measure.
    2) If relativity is fundamental all the way (phenomenal space-time is the fundamental space-time and not just some string membrane), then it is the relational emergence of space via the time that entangled systems shift relative to each other.

    In both cases, special relativity can be completely understood by tracing light. Do not even start with an x-axis! Just start with a world line of the observer and then let her measure with light beams and mirrors - they do not even need to go straight or at 45 degrees! Straightness is relative to the light! Everything falls out from the light reflections serving as a clock alone! The metric serves nothing but utter confusion. One can explain the whole of SRT to kids without using a single equation!
    Halliday
    Sascha:

    Unfortunately, you have a hidden assumption within your prescription:

    In both cases, special relativity can be completely understood by tracing light. Do not even start with an x-axis! Just start with a world line of the observer and then let her measure with light beams and mirrors - they do not even need to go straight or at 45 degrees! Straightness is relative to the light! Everything falls out from the light reflections serving as a clock alone! The metric serves nothing but utter confusion. One can explain the whole of SRT to kids without using a single equation!

    Do you even recognize your hidden assumption?

    David

    vongehr
    There are many assumptions, starting with the topology of the emerging space-time being singly connected. Please tell me what assumption you have in mind and why they would demand the primacy of a metric.
    Halliday
    Sascha:

    You were the one that made the claim I quoted.  You were the one that claimed that "Everything falls out from the light reflections serving as a clock alone!"  What I asked was whether "you even recognize your hidden assumption[s]?"

    You are correct that there are "many assumptions".  However, there are some quite important assumptions you have skipped over that lead to Special Relativity, vs. other forms of relativity.  Such are the assumptions I was focusing on with my question I posed to you.

    David

    vongehr
    No time for cryptic games - not worth on a small web portal full of right leaning crackpots and worse. You go ahead and add another drop to the enormous pile of drivel excreted every year about Einstein and relativity, "physics for dogs" and all, I won't hold you back. At least with you, there won't be any complete f-ups like there are consistently with sweet dough's quaternion nonsense, so in this sense, I encourage you.
    Just one thing: You know well that there are many levels of understanding with relativity. Sure you know how it feels like if the engineering type claims to "understand" it after having learned all the formulas and thus "knowing" that things become more massive due to accumulating kinetic energy or some such nonsense, while rejecting SO(d-1,1) as "philosophy". So, don't be surprised about somebody telling you that there is another level, even after you now maybe for the third time or more have the feeling of "now I finally get it". (BTW: I am a little bit more confident now because I see the relation to quantum mechanics - i.e. relativity is already a modal realism of all possible observer's past light cones, quantum mechanics is merely the entanglement between them.)
    BTW: I am a little bit more confident now because I see the relation to quantum mechanics - i.e. relativity is already a modal realism of all possible observer's past light cones, quantum mechanics is merely the entanglement between them.
    Practically in the bag then.
    [Bright red flashing with sirens.]
     
    Halliday
    :D
    vongehr
    You may not appreciate "a little bit more" enough, but apart from that: Yes, actually, once you look at it in hindsight, it was pretty much in the bag all along! Later generations will be puzzled about our generations' refusing to understand quantum mechanics in a natural and obvious way.
    Halliday
    Sascha:

    Yes, "there are many levels of understanding" of many things, including many forms of relativity (not just Special Relativity through to General Relativity).  There are also many levels of speculative thoughts that attempt to be "understanding".*  However, I am trying to avoid clouding the issue too much.  After all, I don't want "Especially the crackpots" to take any such as some form of "further proof of that relativity theory is wrong", or some such folly.

    I won't say some of the things I could say of your comments, here, due to my desire not to "feed" the "crackpots" or "cranks".  (No.  That is not meant to suggest that I think you are a "crackpot" or a "crank", but I cannot say much more without "feeding" any true such.)  I'm sorry.  :(

    David

    *  Whether such become true understanding, or failures at such, will only become apparent with time, and the advancement of experimental observations:  The usual proviso of science, vs. "pure" philosophy, pure mathematics, etc.

    vongehr
    You do not want to tell me precisely what assumption you have in mind because trolls get fed? Delete the trolls; focus on the serious people. (Serious people can discuss issues to do with my articles under my articles directly where there has never been a good argument deleted. Life is too short to care about trolls.)
    Halliday
    Sascha:

    First, "trolls" are not the same thing as actual, potential, or apparent "crackpots" or "cranks".  It's the later set that I am concerned with, most especially the potential or apparent "crackpots" or "cranks", since they are the ones that can be potentially informed and turned from appearing to be "crackpots" or "cranks", or they could be "pushed" further into becoming actual "crackpots" or "cranks":  They are the "impressionable" ones.

    I know you are one of "the serious people".  I also know that you are not in "danger" of becoming an actual "crackpot" or "crank" in the way some others of the audience may be.

    Now, as to your "hidden assumption"...  I was hoping you already recognized it, so you were not unaware of it.  (Either that, or that you would "stick your foot in it" by claiming you were making no assumption!  That would have been fun.  ;)  )

    I'm sure you will recognize your "hidden assumption" if you simply modify your prescription by replacing "light beams" with ping-pong balls, say.

    I'm reasonably certain I know what your response will be, but I'll wait for it.  :)  (Of course, my having written that has just shifted the likelihood in another direction.  ;)  )

    David

    vongehr

    or they could be "pushed" further into becoming actual "crackpots" or "cranks":  They are the "impressionable" ones.

    Sounds like me about two years ago. I understand what you mean - good luck, don't be too disappointed. ;-)

    or that you would "stick your foot in it" by claiming you were making no assumption!

    You do not know me well enough yet. About knowing what hidden assumptions there are and what hidden assumption you might hold most important: again, I have no fun guessing. The physics is one thing, people's personal hangups are very diverse and often surprising. ["Bulk processing" anybody ;-)]

    I'm sure you will recognize your "hidden assumption" if you simply modify your prescription by replacing "light beams" with ping-pong balls

    Well, you claim to know my answer to that, so why stay cryptic? (To readers who may still follow our argument: David may mean pseudo-particle excitations inside a medium by "ping-pong" balls, in which case, if there were a world that indeed fully emerged from these, frictionless balls bouncing around, the type of relativity in the thereby emerging space-time (the phenomenal space-time observed by the systems made from the ping-pong ball's patterns) may depend on the ping-pong balls' collision kinetics' details, SO(d-1,1) however being like the first term of a Taylor expansion, i.e. at low energies to be expected.)

    Halliday
    HarHarHardyHarHar...

    Sascha, do you remember when I said

    I'm reasonably certain I know what your response will be, but I'll wait for it.  :)  (Of course, my having written that has just shifted the likelihood in another direction.  ;)  )

    Well, your response, quoted below, is quite consistent with where I was "seeing" the likelihood shifting, once I wrote what I did!  You said:

    ... (To readers who may still follow our argument: David may mean pseudo-particle excitations inside a medium by "ping-pong" balls, in which case, if there were a world that indeed fully emerged from these, frictionless balls bouncing around, the type of relativity in the thereby emerging space-time (the phenomenal space-time observed by the systems made from the ping-pong ball's patterns) may depend on the ping-pong balls' collision kinetics' details, SO(d-1,1) however being like the first term of a Taylor expansion, i.e. at low energies to be expected.)

    I won't go into the problems with all "pseudo-particle" and "emergent" "SO(d-1,1)" symmetries we have observed (completely independent of the "the first term of a Taylor expansion, i.e. at low energies" aspects).

    I'm reasonably certain you know both what I was getting at, and to what I am referring to.  Your a bright boy.

    We can discus "emergent" "SO(d-1,1)" symmetries and issues elsewhere, when I have the time.  However, in the context of this series, it doesn't depend upon whether the inner product space is fundamental, or "emergent", in some sense.  (Hey, I'm all in favor of some Wheelerian* "pre-geometry" [some non-geometry that "gives rise to" geometry, or from which geometry is "emergent"].  I just have yet to see it.)

    David

    *  Was it John A. Wheeler's idea, or one of the other two authors of the Gravitation tome?  I'm not certain, and I'm away from my copy, right now.

    David Halliday wrote (05/09/12 | 13:16 PM):
    > Hey, I'm all in favor of some [...] non-geometry that "gives rise to" geometry, or from which geometry is "emergent".
    > I just have yet to see it.

    Then this looks like a good place to concentrate our efforts, right now; doesn't it.
    (You are still capable of judging order or coincidence of your observations, and of granting as much to everyone else, at least in principle, aren't you?)

    > Wheelerian* "pre-geometry"

    Wheeler may have coined the fashionable term.
    Priority for idea itself (that statements about geometric relations ought to be results of evaluating given observations), however, can certainly be claimed for Einstein, and perhaps even for Robb, and other precursors.

    Halliday
    Frank (you.name.them):

    By the way, why have you renamed yourself from Frank Wappler to "Frank W ~@) R"?

    No, observations do not a geometry make, in and of themselves.  However, they can help determine what geometry is there, provided the observation form a consistent set.

    So, no, "Then this [most certainly does not] look like a good place to concentrate our efforts, right now".  However, as far as that other thread that you allude to:

    Frank:

    You ask:

    Are you suggesting that Einstein (Marconi?, Hertz?, ...) were not by default considering indications with plain first observations, but indications after those, or (even) indications before?

    I am most certainly saying that they "were not by default considering indications with plain first observations"—most especially not Einstein (he knew better than the others you list that such is invalid, in general!)!

    Now, in saying this, I most certainly am not saying that they (especially Einstein) were "considering" "indications after those [plain first observations], or (even) indications before".  No, the question of whether the one special class of "signal" (namely light!) they were considering would be before or after any other "indications with plain first observations" was completely irrelevant!

    If you think otherwise, then you have a great deal of relearning to do.  (Or maybe a great deal of unlearning.)

    Yes, this looks like a good place to concentrate our efforts, right now.  :)

    David

    We can continue that discussion, there, if you are finally ready.

    David

    David Halliday wrote (05/09/12 | 18:50 PM):
    > No, observations do not a geometry make, in and of themselves.

    Right, obviously. Therefore the great concern for thought-experiments, especially in RT:
    for presenting operational methods how to derive geometric valuations from pre-geometric observational data given to each participant individually, to express relations between several participants in mutual agreement.

    > However, they can help determine what geometry is there, provided the observation form a consistent set.

    So you've seen/recognized some "pregeometric" notions after all? ...

    > that other thread that you allude to [...] We can continue that discussion, there, if you are finally ready.

    You implying the importance of "unlearning" seemed a fitting closing remark there. I was just trying to let you know that I remain curious about how much "unlearning" might be featured in your upcoming installment(s).

    Meanwhile I'm about to write up, too: some "Relativistic pregeometry", i.e. just short of forgetting what to make of "unlearning". Finishing might still take perhaps one or two weeks; depending on how much I'd be able to (un)learn from your much appreciated trailblazing.

    p.s.
    > By the way, why have you renamed yourself from Frank Wappler to "Frank W ~@) R"?

    Well -- I've registered as a user with my plain name; so now I cannot sign my comments with this name anymore. (You know, unless I'd go through all that unusual hassle of logging in or somesuch.) Therefore I use my logographic signature which, by the way, I've been using already way back when ... I first appreciated the importance of some unlearning.

    Halliday
    Frank (being.physicists.we.approach.this.without.any.preconceptions.whatsoever.except.for.approaching.it.as.physicists--paul.henckels):

    Why do you think it's "all that unusual hassle of logging in or somesuch"?  I'm logged in almost all the time, since I don't tend to close my browsers much at all, or log off my computers (except at work).  Even if you do log off computer systems and/or close browsers periodically, logging in is a one-time thing for each session, unlike the capcha system that is required on each post.

    Additionally, you gain the benefits of a more powerful message editor, as well as your name providing a link to your profile, so people can come to know you better, and even find whatever you choose to "write up" in your 'blog.


    Now as for " 'pregeometric' notions", your concept of "how to derive geometric valuations from pre-geometric observational data", can have nothing to do with Wheelerian pre-geometry.  For, with Wheelerian pre-geometry there is no geometry "there" for "observational data" to determine.

    You are, therefore, using the term in a completely different manner.  The same goes for your earlier claim that:

    Priority for idea itself (that statements about geometric relations ought to be results of evaluating given observations), however, can certainly be claimed for Einstein, and perhaps even for Robb, and other precursors.

    The reason I can make this claim is because Wheelerian pre-geometry has nothing to do with "statements about geometric relations ought to be results of evaluating given observations".  It is an idea that goes much deeper than that.  An idea, as I said, that I have yet to see anyone realize (as in making a real/actual system that expresses or is based upon Wheelerian pre-geometry).

    David

    Halliday
    By the way, Frank, if by "which, by the way, I've been using already way back when" you mean that you have been using your "logographic signature" (i.e. "Frank W ~@) R") for some little while on this site, then, yes, I had already noticed that.  I just hadn't asked you about it, until you showed up here.

    David

    Sascha,
    I've read some of your articles. In one you claimed that SR, causality, and faster than light travel were all compatible.

    For people that need a reminder, here's a quote of Sascha's amazing "logic skills":
    http://www.science20.com/alpha_meme/faster_light_neutrinos_do_not_time_t...
    "Superluminal velocities do generally not violate relativity, or help you to time-travel, or violate causality as long as there is only a single reference frame relative to which the propagation happens instantaneously."

    But wait, doesn't requiring that the physics is such that we can only send superluminal signals in a single reference frame violate the requirement that physics has Lorentz symmetry? No worries. Sascha even starts to realize his error, so he solves it by ... invoking a preferred frame!!
    "If Bob can do the same, causality is violated. However, assume for example that Alice can only do so because she happens to be almost at rest relative to the cosmic microwave background (CMB), which is a rather special reference system left over from the big bang."

    So Sascha, you should NOT be giving advice on how to teach SR.

    (David, feel free to apply your definition of "crackpot" to Sascha here. I'm pretty sure no amount of logic can make him realize his mistake, since people have already tried.)

    vongehr
    doesn't requiring that the physics is such that we can only send superluminal signals in a single reference frame violate the requirement that physics has Lorentz symmetry?
    No, it does not. Bye bye.
    I think AnnoyedReader's logic is pretty straightforward. If the laws of physics had the same form in all inertial frames, then if one inertial observer can send a superluminal signal, then another inertial observer could as well.

    While I'd agree that special relativity doesn't rule out superluminal propagation by itself, SR + faster than light signals + causality are not compatible.

    vongehr
    I think CuriousReader and AnnoyedReader and SurprisedReader all need to learn one thing before becoming AnnoyingCommenter: To read!
    (Did the comment by SurprisedReader get deleted?)

    Sascha,
    Maybe there is just some miscommunication.

    Just to be entirely clear --
    Let's say the vacuum ground state did somehow give a preferred inertial frame at rest with respect to the CMB.

    I think most physicists would say that means the vacuum doesn't have Lorentz symmetry and therefore SR doesn't hold in such a universe.

    Sascha are you saying that such a vacuum ground state is compatible with SR?

    vongehr
    Maybe there is just some miscommunication.
    Tide goes in, tide goes out - never any miscommunication.
    Jeremy: Why would we take David's comment section hostage? I hope he deletes this stuff - I would.
    Stop being evasive. A reply with some logical reasoning would be very helpful, but even a simple yes or no would be fine as well.

    Sascha are you saying that such a vacuum ground state is compatible with SR?

    Jeremy, as already explained, Sascha is a crackpot. It's highly unlikely he'll ever give a straight answer, and even then you won't be satisfied as it will still conflict with some of his other comments. In my mind, he's the worse kind of crackpot, the one that could actually seriously mislead students. For that reason as well, I don't think David will delete these warnings on Sascha's illogic.

    From what I've seen, David represents everything that is good about scientists taking their time to teach on the internet; Sascha represents some of the worst.
    I really wish Hank would encourage more "David's" and strongly discourage the "Sascha's" on here.

    Let's say the vacuum ground state did somehow give a preferred inertial frame at rest with respect to the CMB. I think most physicists would say that means the vacuum doesn't have Lorentz symmetry and therefore SR doesn't hold in such a universe.
    It needn't be anything to do with the ground state of the vacuum. Those wannabe-superluminal neutrinos could have been pushing against the core of the earth for all we knew.
    Sascha invoked a preferred frame from the big bang, so he wasn't talking about some arrrangement of material in the earth.

    Regardless, if some arrangement of material allowed one to send instantaneous signals according to one inertial frame, AND the physics has Lorentz symmetry, then in principle that experiment could be reproduced in any inertial frame. Sascha's "logic" can be paraphrased as: superluminal propagation of information doesn't violate SR+causality if we allow the physics that describes this propagation to violate SR. It is nonsense.

    Can we at least agree that if the vaccuum ground state violated lorentz symmetry, that violates SR?

    The only other way I can think of interpretting his statment is to have a field / medium in which the signal propagation is instantaneous (and this medium is at rest with respect to the CMB). Then one could claim that the physics has Lorentz symmetry, but just not the experimental setup. But then just as before, it would be possible in principle to setup this medium (say in two different tubes or conduits) to allow instantaneous communication according to two different inertial coordinate systems. But Sascha is requiring that this is not possible. The only way to make it impossible _even_in_principle_ to manipulate or reproduce this field to run equivalent propagation experiments in other inertial frames, is if the physics describing this field violates Lorentz symmetry.

    Sascha invoked a preferred frame from the big bang, so he wasn't talking about some arrrangement of material in the earth.
    Depends what you mean by "preferred".  Preferred in relativity, no he did not; preferred in the universe as happens to be, yes. Furthermore I queried the appropriateness of using the CMB arguing that it was just a stand-in for the centre of momentum of the universe.  However, for your thought-experiment to invalidate this "preferred frame that is compatible with SR" you would need Bob to be able to drag around another universe complete with its own CMB at relativistic speeds and for the two centres of momentum to remain separate and distinct so that whatever needs to couple to them can do so.
     
    Yes I agree that Sascha was not talking about local matter. I was. I was answering your claim that a physical process which refers to the CMB would break lorentz symmetry. I'm telling you that *any* physical process that refers to something that has its own frame will do the job, even something as mundane as local bulk matter. Or come to that, the CoM of the beam at CERN.
    Can we at least agree that if the vacuum ground state violated lorentz symmetry, that violates SR?
    Absolutely not.  As far as I know, SR does not say anything about particle physics; it is entirely about the geometry of spacetime. It may well be that this is its shortcoming. Even so if, say, the Higgs field provided absolute position and a preferred frame, it would still be distinct from SR.



     
    Halliday
    Jeremy:

    I don't know if I have seen a post by "SurprisedReader" here or not.  As best I can determine, there have only been two deletions on this 'blog:  Hank deleted an obvious SPAM (I was just about to delete it myself) none of you would have ever seen (since it was marked as SPAM by the system, and was awaiting moderation), and Barry Barrett deleted one (probably one of his own).

    David

    WOW!
    People can't even agree if special relativity requires The Principle of Relativity!
    David, this "geometry first" way of teaching SR may be harder than I originally thought.

    Derek wrote:
    "As far as I know, SR does not say anything about particle physics; it is entirely about the geometry of spacetime."

    I hadn't thought about it in these terms. David, if you teach SR by starting with the metric, how can you then connect back to Einstein's postulate that the laws of physics were the same in all inertial frames? It seems "clear" to me, but it obviously isn't since I can't articulate it well. There must be assumptions I'm making that I'm having trouble making explicit.

    Or, with a more specific "geometry <--> physics" example, how can you say the path length of a clock is the time it measures without just stating this by fiat?

    And to Derek (I'm sure David can explain this better as I still have a ton to learn about QFT myself), SR says a lot of very useful things about particles physics. The symmetry requirements from SR are very powerful and are a key ingredient in the spin-statistics theorem, particles are often defined by choice of representation in the Lorentz group (and other symmetries internal to the theory), the symmetry requirements allows restricting the possible terms in a Lagrangian (to the point where people often just write out every possible allowed interaction that is renormalizable), it also allows deriving the invariance of CPT in quantum field theory, etc.

    David, I think this approach is looking more difficult that I first expected. It seems to already be leading to a lot of confusion. I'm really looking forward to see how you decide to present all these ideas.

    Halliday
    CuriousReader:

    It's one of the aspects of this approach that is very different from that of Einstein, or the way his Special Theory of Relativity is usually taught or presented.  Einstein's two postulates fill very different places in this approach.

    1. Einstein's second postulate—the "constancy" or invariance of the speed of light—is only used as an experimentally backed reason for deciding which "spacetime", of all possible "spacetimes" (we will look at all possibilities, for a given number of dimensions), matches the characteristics our Universe.
    2. Einstein's first postulate—The Principle of Relativity (especially in its most general form, as opposed to the form he used in his "On the Electrodynamic of Moving Objects" paper [that being "the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good"])—becomes split into two aspects:
      1. The first doesn't have so much to say about whether "the laws of physics [are] the same in all inertial frames", but is actually derivable from this "geometry first" approach:  One can find a set of transformations that preserve the form of the metric (if you wish to do so), and that such form a group (an invariance group)—a symmetry.
      2. The second becomes a statement more about the "permissible" forms of "the laws of physics", given the first.  It become more akin to Einstein's concept of "general covariance/invariance" as he used within the context of General Relativity.
    I believe that once we proceed (I will be writing this weekend) it should become much more clear.  Please feel free to let me know if I seem to just make things more "muddy".

    David

    And to Derek (I'm sure David can explain this better as I still have a ton to learn about QFT myself), SR says a lot of very useful things about particles physics.
    Has it ever occurred to you that if someone says something that is quite obviously incorrect and which doesn't fit with the rest of what they are saying that it may just be that they did not express themselves properly? Yes, this actually happens. Such a mistake does not require a detailed rebuttal: generally the intended meaning can be inferred; if not, you can always ask. 
      
    I'm sorry I misunderstood. Either way it pointed out some stuff about the 'metric first' approach that I'm not quite understanding, so it was thought provoking.

    "if not, you can always ask."

    To be honest, I reread and I'm still getting the same thing out of it. Your entire answer to the vacuum question seems to be saying you don't think SR requires the laws of physics to have Lorentz symmetry. Can you please clarify what you meant?

    If I understand it correctly, "the Einstein Postulate" is not so much that the laws of physics have Lorentz symmetry but that they can all be cast in Lorentz-covariant form. SR guarantees this, it is not an assumption you have to make in order to derive the Lorentz transformations.

    Anyway David has just said what I was going to suggest. That's good.
     
    So to cut straight to your question, if it turns out there is "fixed" frame of reference, (all those Higgs particles have got to "be somewhere"!) you are perfectly free to apply SR to it. It does not enter into the derivation of the Lorentz transforms, so SR remains free of "preferred frames".
    The universe already has at least one special frame (special - not "preferred" by SR). The CMB is not particularly fundamental but it is well-coupled to the centre of momentum; which is. Even my "core of the earth" is coupled to it (because the universe is cool enough for most massive particles to be non-relativistic).
     
    Now if you want to call such a phenomenon a "law of physics", you are free to do so. And, to be sure, it will NOT have Lorentz symmetry, it wouldn't even have Newtonian symmetry in Euclidean space! But then, neither would a "law of physics" which says "Derek is in Cardiff". These are particular facts, not fundamental laws, but the Einstein postulate applies to both: there is a Lorentz covariant way to describe the phenomena. I expect David to show that this is practically tautological in a geometry-based derivation of SR, unlike the tradition equations-based approach which makes it sound like a crazy idea Einstein had which happens to be true.
    Of course if (huge "if") superluminal neutrinos kicked off from such a universal frame, the physics behind it would be best described in Lorentz covariant terms - the "stiff vacuum" would simply be a player in the system.
     
    Anyway, my head is spinning, I was not well yesterday and to judge from David's remarks, above, all this is going to be made very clear very soon, so let's leave it to him now.

    blue-green

    Start with the appearance of the nightsky and the distinct separations between us and the myriad points of light. Relativists know that s = 0 or better s^2 = 0 for the spacetime separation s between the emission and reception of each speckle of light. Locally, in each tangent space, the dot product of the displacement vector ds for each light ray with itself is zero. Our Prometheus, David Halliday, has scaled the wild and craggy heights, had his liver pecked out and is ready to bring down from the gods a gift of fire (whether we can be trusted with it or not). So why the 0 in s^2 = 0 = <ds|ds>.

    If it were not exactly and universally balanced at zero, then electromagnetism would be a very different animal than the one we know. Zero is the best of numbers. Having a zero simplifies, balances and equalizes everything in the sense that different observers moving uniformly relative to each other will see the same kind of physics.

    Even with the addition of matter, s^2=0. Otherwise Einstein's Equations would be vastly more complicated. The equivalence principle would not hold. Nor would there be a simple Least Action principle as employed by David Hilbert in 1915 to derive General Relativity. Nor would conservation of energy and momentum be independent of one's frame of reference. The zero in s^2=0 is as fundamental as the general rule of algebraic topology that "the boundary of a boundary is zero" … or is it?

    Whether you are DH for David Hilbert or David Halliday, the task remains to bring the fire down from the empyrean ...

    Why the 2 in s^2 = 0? It is there because we are dealing with two objects and contracting or projecting one vector onto another. More generally, we can consider the raising and lowering of the subscripts and superscripts of tensors of rank greater than 1. Each such operation involves the use of an underlying metric. How many distinguishable classes of metric are physically reasonable? How constraining is the Principle of Relativity?

    Why the minus sign in the Lorentz signature? Back in Einstein's day, one used the multiplier ic to put time on the same footing as space so that one could calculate with just apples instead of apples and oranges. The square of the imaginary i gives one two 90 degree turns or an about face to 180 degrees to give the ii=i^2 = -1 in the Lorentz metric. Are we closer now to seeing what makes the engine run under the bonnet? Or is DH a coyote . ... a trickster in new clothes? 

    For each displacement 4-vector ds = (dt, dr) for matter moving along its world line, there is a rescaled energy-momentum 4-vector (mc/ds)(dt, dr) with time-like and space-like components proportional to mc(dt)/(ds) = E/c^2 and mc(dr)/ds = p respectively. The underlying metric that makes ds-dot-ds = 0 for light rays, also makes in each local tangent space, (E/c^2)^2 – p^2 = m^2 for more general trajectories. Metrics that are of a different flavor than the Lorentz metric will violate this equation and not ensure that photons have zero rest-mass.

    ~ sorry for rambling ~

    Halliday
    I won't and don't claim to be a Prometheus, and I'm certainly trying not to be "a coyote . ... a trickster in new clothes".

    Thanks for the contribution.  While there may have seemed to be some "rambling" to the way you chose to express yourself, there are good insights in what you have expressed.  (Well, with a few small "units" issues, but who's paying attention to such trivialities.  ;)  )

    David

    Why the minus sign in the Lorentz signature? Back in Einstein's day, one used the multiplier ic to put time on the same footing as space so that one could calculate with just apples instead of apples and oranges. The square of the imaginary i gives one two 90 degree turns or an about face to 180 degrees to give the ii=i^2 = -1 in the Lorentz metric. Are we closer now to seeing what makes the engine run under the bonnet? Or is DH a coyote . ... a trickster in new clothes?
    David has already said what he is going to do.  The metric approach leads to only a very small set of possibilities and we must go to nature to find out which one applies to our universe. (Actually he said "nearest to" or some such cautious phrase.)
    The square of the imaginary i gives one two 90 degree turns or an about face to 180 degrees to give the ii=i^2 = -1 in the Lorentz metric.
    Does it? Which space would this 90 degree turn be in and what is it that turns?

    I use complex numbers in electronics and the  representation all the time, but when I say there's a phase shift of 90 degrees I don't mean anything turns around through a right angle!

    I originally posted a long overview of why we get to talk in terms of angles at all but then I decided we've had enough rambling.


    blue-green
    Yes, there is a misplaced c in there ... I would want to get the units right so that with each equation every term is dimensionless or just meters or just kilograms .... Using c =1 would hide the magic.
    Dear David

    I have some more questions. But first there is an interesting paper by Galina Weinstein at: http://arxiv.org/abs/1205.0922

    Weinstein says: “In 1905 Einstein presented the Clock Paradox and in 1911 Paul Langevin expanded Einstein's result to human observers, the "Twin Paradox." I will explain the crucial difference between Einstein and Langevin. Einstein did not present the so-called "Twin Paradox." Later Einstein continued to speak about the clock paradox. Einstein might not have been interested in the question: what happens to the observers themselves. The reason for this could be the following; Einstein dealt with measurement procedures, clocks and measuring rods. Einstein's observers were measuring time with these clocks and measuring rods. Einstein might not have been interested in so-called biology of the observers, whether these observers were getting older, younger, or whether they have gone any other changes; these changes appeared to be out of the scope of his "Principle of relativity" or kinematics. The processes and changes occurring within observers seemed to be good for philosophical discussions. Later writers criticized Einstein's clock paradox. Einstein quickly replied with witty, smart and clever retorts.”

    So my questions are – does special relativity only apply as measurement procedures for clocks and measuring rods OR does it have a biological effect on observers as well? Also how are you going to prove it either way? And if you can't prove it either way then does this mean yours and others understanding of special relativity is incomplete? My position of course is that its conventionalism and mere math manipulation to convert from having observers set clocks to go at same rate to a proceduree where instead lightspeed (c ) is set constant.

    Halliday
    Roger:

    Einstein's Special Theory of Relativity applies to all methods of "measuring"/"observing" the "passage" of "time", or changes that occur over "time".  We see this in the way that all clocks behave consistently, even the decays of fundamental particles, like muons (which is why I brought them up, earlier).

    Biological processes are, at a fundamental level, chemical clocks.  Chemical processes are governed by electromagnetic interactions, between atoms and molecules.  So it is absolutely expected that they, like any other "clock" (just like Einstein's "light clocks") will exhibit the same behaviors.

    Now, can we "prove" it?  No.  Science cannot "prove" anything.  "Proving" things is not within the purview of science.  Science has a two pronged methodology:  1) Try to explain as much of the physical world/universe as we can; and 2) test and observe as much of the physical world/universe as we can, in order to find evidence either for or against all applicable explanations.  While it would be "nice" to be able to "prove" or "disprove" any (or even all) applicable explanations (theories), it simply isn't possible by the scientific method.

    So don't try to make science something it is not.

    On the other hand, mathematics can prove and disprove propositions, within the context of a given mathematical system under consideration.  Science does take advantage of this, from time to time, to show what explanations are or are not consistent with other observable/experimental information.

    For instance, we are able to measure length and relative directions of vector-like quantities, at least to the limits of our instrumentation.  So, if we can properly model our "system" as a vector space, then we know that our vector space must have a dot or inner product (what physicists refer to as a "metric" [in essence, that which is used to measure]), so our vector space is an inner product space.  Even if we don't have the inner or dot product "handed" to us, we are able to make measurements that allow us to construct it, within some finite precision.

    However, due to the nature of all possible inner/dot products on a finite dimensional space (again, as can be proven from mathematics) we can distinguish between the various, incompatible possibilities long before we are able to determine such to a high degree of precision:  The distinguishability only requires moderate precision!  It's much like being able to determine whether a surface slopes up or down, long before being able to determine what angle the slope is.

    This is why the difference is not simply about "conventionalism".

    David

    P.S.  I was writing my next installment this past weekend, but still didn't quite get it finished by the end of the weekend.  So I have been "stealing" what time I can since then, in order to get it ready for y'all.

    I think it's just about ready.  I have a friend previewing it today.  So I hope to have it ready this evening (if he can finish going through it before he goes home this evening).

    Bonny Bonobo alias Brat
    P.S.  I was writing my next installment this past weekend, but still didn't quite get it finished by the end of the weekend.  So I have been "stealing" what time I can since then, in order to get it ready for y'all.
    I think it's just about ready.  I have a friend previewing it today.  So I hope to have it ready this evening (if he can finish going through it before he goes home this evening).

    No need to rush David, please take your time! This comment alone is a quite brilliant explanation of the passage of time, spacetime and the limitations surrounding the scientific ways we have of measuring it.

    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Halliday
    Thank you, Helen.

    I was on the verge of thinking that my exchange with Roger was nothing but a waste of time, and seriously considering doing some deep "pruning".  However, you have shown me that it hasn't all been for naught.

    Thanks.  :)

    David

    Dear David
    You say in regard to biological and chemical processes: “ So it is absolutely expected that they, like any other "clock" (just like Einstein's "light clocks") will exhibit the same behaviors.” - But that is an assumption is it not; an arbitrarily added extra assumption because you refer to no test that confirms it. Thus someone else might add some different arbitrary contrary assumption. That indicates understanding of the theory is incomplete does it not?

    You say: “Einstein's Special Theory of Relativity applies to all methods of "measuring"/"observing" the "passage" of "time", or changes that occur over "time".” But how are you going to prove or test or show that. Surely it should be pointed out to students being taught this subject that there are many untested claims being added to what they are taught, so that different teachers of the subject might make contradictory claims? It would be unfair to the students not to do this.

    You say “Science has a two pronged methodology …........ 2) test and observe as much of the physical world/universe as we can.... “ But you do make untested claims such as about biology as we just noted, and surely that then makes such claims unscientific?

    You say: “Science cannot "prove" anything.” To prove something in science which is an empirical subject is to show the test. To say its not been proven or tested - that is an admission then that many pseudo-religious untested beliefs are being taught instead of tested claims is it not?

    You say: “On the other hand, mathematics can prove and disprove propositions, within the context of a given mathematical system under consideration.....” And in the context of maths all that is done in getting special relativity is just a bit of maths manipulation is it not? So how can you show that your interpretation of that maths is correct?
    You say: “This is why the difference is not simply about "conventionalism".”
    Well I disagree, if we go by Stanford Encyclopedia of Philosophy http://plato.stanford.edu/entries/einstein-philscience/ it says: “Albert Einstein (1879–1955) is well known as the most prominent physicist of the twentieth century. Less well known, though of comparable importance, are his contributions to twentieth-century philosophy of science. Einstein's own philosophy of science is an original synthesis of elements drawn from sources as diverse as neo-Kantianism, conventionalism, and logical empiricism, its distinctive feature being its novel blending of realism with a holist, underdeterminationist form of conventionalism. Of special note is the manner in which Einstein's philosophical thinking was driven by and contributed to the solution of problems first encountered in his work in physics. Equally significant are Einstein's relations with and influence on other prominent twentieth-century philosophers of science, especially Moritz Schlick and Hans Reichenbach.”
    So how are you to prove or test that your application of Einstein's philosophy (especially in regard to conventionalism) are correct? Or are you asking for the privilege of making untested and unproven claims pretending it to be science?

    Sorry to bring all this up but you do say - “Many people struggle with, and even rail against, Einstein's Special Theory of Relativity.  The way it is usually taught or presented often seems to make it appear to be ever so complex, far too abstract and opaque, and even downright "hokey".*  My experience certainly allows me full empathy for such struggles.”

    So you did have empathy for that position at one time, and the problem is that the subject does raise numerous questions which the teacher tries to avoid or dodge, and when teacher replies then engages in making numerous untested and unproven claims.

    So in conclusion you are just making untested and unproven claims are you not? Should that not be pointed out to the student that the vast bulk of the subject they are about to be taught fails to conform to the ideals of science?

    Good luck with your next posting, I am preparing myself to complain about some unjustified manipulation of the maths. I think you have not had a student like myself who is prepared to point out the fallacies that are presented in special relativity lectures. If there were more like myself then it might be that eventually the teachers would realise they were talking unscientific nonsense and making stuff up.

    Roger

    Halliday
    Roger:

    First, I would greatly appreciate it if you would observe the common courtesy, of threaded discussion forums such as this, of using the "Reply to This >>" link, so as to preserve the proper flow of any thread of discussion here.

    Second, your concept of "conventionalism" is a far cry from that of Einstein (the use of that term within the quoted encyclopedia article may or may not actually reflect Einstein's own views).  I have already noticed that you make people "an offender for a word" simply by assuming or pretending their use of any given word is your chosen use.

    Third, you obviously don't understand or appreciate the interconnectedness of science.  One need not test every combination, modification, iteration, etc. of a proposition to have a sufficient expectation of any given outcome.

    On the other hand, we, as scientists, are keenly aware of the potential for the "unforeseen".  Regardless of how "obvious" any given possibility may be, given other knowledge and tests, our intellectual honesty compels us to always admit that there is some "possibility"—regardless of how remote—that some other system may behave differently.  (Lawyers and politicians "hate" scientists, and science, for this reason.  They want clear cut, black and white, yes or no, unequivocal answers, but that's not what science is about.)

    For instance, to the extent that biological systems are chemical systems—that are governed by the laws of electromagnetism*—then there is absolutely no way such a system will deviate from the behavior of any other electromagnetically governed system.  On the other hand, there is the bare possibility that biological systems may have "something extra", and that "something extra" may have unforeseen characteristics that may violate such expectations.

    However, I already accounted for this possibility in my previous answer when I used the term "expected", rather than trying to assert that such is "known", or any other "absolutism".

    I'm certainly willing to entertain an experiment involving biological organisms as "clocks".  Unfortunately, the inherent uncertainties in such "clocks", as well as the uncertainties in what external influences have on such, make their use quite problematic.  So, until we have the ability to attain far higher velocities than present, for sufficient lengths of time, the results of such will remain a firm expectation, but not directly testable.**

    So?

    This simply shows the wisdom of Einstein in not using the changes in biological organism in his thought experiments (Gedankenexperiments).

    Besides, as I've already pointed out to CuriousReader, above, the approach I'm trying to illuminate turns many of the arguments about the foundations of Einstein's Special Theory of Relativity, and especially the place of his Principle of Relativity, around (not quite "on their head", but something not too dissimilar), from a quite different perspective.

    For instance, you will notice that my next installment never mentions the speed of light, let alone any "assumption", or otherwise, about its "constancy" or "invariance".  It doesn't even deal with coordinates, or any choice thereof.

    I think you'll find very little traction for your arguments, there.  (Even the installment after that, that will actually look at choices of "bases" will not advocate any particular "basis", but will show the mathematical basis behind a certain "nice choice", for any given class of inner product space.  However, even then we will not be imposing a particular choice, and certainly not "requiring" some "constancy" or "invariance" of some particular "speed" of some particular "thing".)

    Yea.  Like I've said before, "I recommend that you simply wait and see what unfolds in this series."

    David

    *  Einstein's actual Principle of Relativity, in the form he used in his "On the Electrodynamic of Moving Objects" paper, is translated to be "the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good".  So he already stated that systems governed by the laws of electrodynamics and mechanics are subject to his theory.

    **  Maybe you could get funding for a bacteria accelerator?

    Gerhard Adam
    I think you have not had a student like myself who is prepared to point out the fallacies that are presented in special relativity lectures. If there were more like myself then it might be that eventually the teachers would realise they were talking unscientific nonsense and making stuff up.
    Consider yourself lucky that David is as patient and kind as he is.  I'd have booted your silly ass a long time ago.  I expect it won't be too long before we see your agenda.
    Mundus vult decipi
    you are being offensive

    Gerhard Adam
    You see, Roger, that's the difference between David and myself.  I don't give a damn.

    However, I won't hijack David's post, so I won't be saying any more.
    Mundus vult decipi
    does that make you feel good?

    Why does David allow you to be offensive, is it hypocrisy?

    Halliday
    Did I not give you plenty of leeway for your offenses?
    No you have not, because I have not been. Please apologise for your slur.

    Roger

    Dear David,

    >>your concept of "conventionalism" is a far cry from that of Einstein

    How are you going to prove or give test evidence of such a claim; it maybe that your understanding of it is incorrect? How, for instance do you apply conventionalism to special relativity?

    >> I have already noticed that you make people "an offender for a word"

    What are you now talking about, is that supposed to be Einstein's relativity. I am merely asking questions and you are trying to avoid giving straight answers, is that not the case?

    >>Third, you obviously don't understand or appreciate the interconnectedness of science.

    How are you going to prove or show or whatever that your understanding of the interconnectedness is correct? Is this still Einstein's relativity?

    >> One need not test every combination, modification, iteration, etc. of a proposition

    How are you going to do that?

    >>Lawyers and politicians "hate" scientists, and science, for this reason. They want clear cut, black and white, yes or no, unequivocal answers, but that's not what science is about.

    How are you going to show that science is clear black and white without any grey?

    >>For instance, to the extent that biological systems are chemical systems—that are governed by the laws of electromagnetism*—then there is absolutely no way such a system will deviate from the behavior of any other electromagnetically governed system.

    My immediate response would be to ask how are you going to show that; but I will let that pass because you reverse your decision next--

    >> On the other hand, there is the bare possibility that biological systems may have "something extra", and that "something extra" may have unforeseen characteristics that may violate such expectations.

    So you admit to maybe being wrong, so when you make the previous claim, you are just stating a guess or making up another unproven and untested claim is that not true? What use are you claims if suppose your claim X and admit that you might be wrong, there is no value to your claims is that not true?

    >>I'm certainly willing to entertain an experiment involving biological organisms as "clocks".  Unfortunately, the inherent uncertainties in such "clocks", as well as the uncertainties in what external influences have on such, make their use quite problematic.  So, until we have the ability to attain far higher velocities than present, for sufficient lengths of time, the results of such will remain a firm expectation, but not directly testable.

    Yes so why do you make claims of things that you don't know? You make a claim X and then admit it might be wrong, that is the same as saying you don't know is that not true?

    >>This simply shows the wisdom of Einstein in not using the changes in biological organism in his thought experiments (Gedankenexperiments).

    Related to-

    >>Einstein's actual Principle of Relativity, in the form he used in his "On the Electrodynamic of Moving Objects" paper, is translated to be "the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good".  So he already stated that systems governed by the laws of electrodynamics and mechanics are subject to his theory.

    It says nothing about whether taking biology into account. Would we need a unified theory dealing with all the forces of nature if we were considering biology, how would you prove or test or show what was the case?

    >>For instance, you will notice that my next installment never mentions the speed of light, let alone any "assumption", or otherwise, about its "constancy" or "invariance". It doesn't even deal with coordinates, or any choice thereof.

    Is such a theory Einstein's theory or are you making a different theory?

    In summary you just make numerous unproven and untested claims, and when pressed about these claims you admit that you might be wrong, so that is equivalent to stating you don't know, is that not the case? Let us look at your claim that science is clear black and white, are you stating your personal belief or are you still dealing with special relativity? In the context of special relativity how do you know its a case of clear black and white? What additional assumptions are you bringing to special relativity that is not in the two assumptions we are given, and which are maybe only peculiar to yourself?

    So restating conclusion – you are making unproven and untested claims and don't know if those claims are true or not, and when pressed on these claims you respond merely by making more unproven and untested claims, is that not the case?

    Roger

    Halliday
    Roger:

    Consider this your second and final warning.  You used to properly use the "Reply to This >>" link.  Why are you now flaunting you disregard for "the common courtesy, of threaded discussion forums such as this, of using the 'Reply to This >>' link, so as to preserve the proper flow of any thread of discussion here"?

    If you do this again, I will create a properly placed version of your message (which, unfortunately, will then look as if it is from me) before I reply to it.

    This is your final warning.  You will not get another, because your next violation will be your third strike.

    David

    David

    Sorry. But you are being draconian. There is no rulebook as to behaviour as far as I am aware. So your attitude of making up arbirary rules out of thin air which you apply to special relativity is just something you apply to everything is that not so?

    So I protest and want my human rights.

    Roger

    Halliday
    Roger:

    Thank you for having the decency to use proper reply etiquette .

    The rules are far from arbitrary.  Even you used to use the proper etiquette.  I don't know what happened, did you simply start violating proper etiquette in "protest"?

    Now, as to your off topic post, and your abuse, I will not count this as an additional violation, since my warning was posted after you posted this message.

    There are no human rights, or other rights, violated by insisting upon proper etiquette.

    In fact, even if I do end up editing or deleting any of your messages, there is still no violations of any of your rights.  Your expected protestations to the contrary.  (Sascha Vongehr has a reasonably good article on "So Called Censorship and Real Censorship".  While I will not be as "draconian" as he has been, I stand by my right to moderate this forum.)

    David

    David

    >>>Thank you for having the decency to use proper reply etiquette .

    Ok. But its more by accident than by any design.

    >>>The rules are far from arbitrary.  Even you used to use the proper etiquette.  I don't know what happened, did you simply start violating proper etiquette in "protest"?

    Computer post replies wherever they like do they not? I have only just seen this posting of yours after seeing the later ones.

    >>Now, as to your off topic post, and your abuse, I will not count this as an additional violation, since my warning was posted after you posted this message.

    What abuse? I am only questioning your numerous claims. And as to postings they appear out of order.

    >>There are no human rights, or other rights, violated by insisting upon proper etiquette.
    How are you going to prove or whatever such a claim?

    >>>In fact, even if I do end up editing or deleting any of your messages, there is still no violations of any of your rights.  Your expected protestations to the contrary.  (Sascha Vongehr has a reasonably good article on "So Called Censorship and Real Censorship".

    Where?

    Roger

    Halliday
    Roger:

    You posted:

    >>>In fact, even if I do end up editing or deleting any of your messages, there is still no violations of any of your rights.  Your expected protestations to the contrary.  (Sascha Vongehr has a reasonably good article on "So Called Censorship and Real Censorship".

    Where?

    Use the search box (the one with the "Go" button to its right) near the top right of the pages on this site.

    As for whether "Computer post replies wherever they like do they not?"  No, they do not, because computers have no feelings, nor do they "think", they simply follow instructions called programs.

    As for you comment that "as to postings they appear out of order."  If you expect the postings/messages to be a linear list ordered by date, then, yes, they are "out of order".  This is called a threaded discussion list:  Subsequent messages, when proper reply etiquette is followed (meaning one actually uses the "Reply to This >>" link when replying to another message, here), are placed directly under the message they are replying to.  If there are multiple replies to a single message, then all such replies are listed in chronological order, at the same nesting level, under the message they are replying to.  This helps us all keep track of multiple conversation threads, rather than having everything "mashed together" as a single (though chronologically ordered) list.

    Have you never seen a threaded discussion forum before?  It's really nothing new, it's been around since before the World Wide Web was invented, even many e-mail clients support the ability.  However, I must admit that there are way too many 'bogs, out there, that simply mash everything together.  (That works OK when the intent is to only have one-off comments on an article, but is horrid for discussions.)

    David

    David

    >>As for you comment that "as to postings they appear out of order."  If you expect the postings/messages to be a linear list ordered by date, then, yes, they are "out of order".

    Ok so this system is a mess then as it makes everything appear out of order and too difficult
    for me to follow.

    >>That works OK when the intent is to only have one-off comments on an article, but is horrid for discussions.

    This system is particularly horrid for discussion.

    Roger

    Halliday
    Roger:

    Now you're simply being a contrarian pain, maybe even just a crank.

    A threaded discussion approach, such as is being used here, is the only simple way of keeping track of multiple, simultaneous threads of discussion.

    I'm sorry it seems to be too difficult for you.  Perhaps if you work with it, and give it a chance, and recognize how it is structured as threads of messages and replies, you will learn, and it will work for you.

    How would you propose to keep track of multiple discussion treads?

    David

    Halliday
    Roger:

    As for your message...  I will only respond to a few points, primarily those that illustrate your errors in logic.

    For instance, you provide a partial quote of what I said (the more full quote, with your partial quote in bold):

    ... we, as scientists, are keenly aware of the potential for the "unforeseen".  Regardless of how "obvious" any given possibility may be, given other knowledge and tests, our intellectual honesty compels us to always admit that there is some "possibility"—regardless of how remote—that some other system may behave differently.  (Lawyers and politicians "hate" scientists, and science, for this reason.  They want clear cut, black and white, yes or no, unequivocal answers, but that's not what science is about.)

    Then you follow it with the non sequitur:

    How are you going to show that science is clear black and white without any grey?

    Did you truly misunderstand what I wrote to this extent?  Didn't I just say that "science is [not] clear black and white without any grey"?  So is it is not a complete non sequitur to then ask how I am going to show that it is something that it is not?

    In fact, you fall for the same problem that plagues lawyers and politicians, when it comes to science.  You exclaim:

    ... What use are you claims if suppose your claim X and admit that you might be wrong, there is no value to your claims is that not true?

    Hey, I'm simply being an intellecually honest scientist.  ;)

    Rail against it if you must, but it will be to no good avail.

    Later, you make a similar exclamation:

    Yes so why do you make claims of things that you don't know? You make a claim X and then admit it might be wrong, that is the same as saying you don't know is that not true?

    If you define "know" as in to know an absolute truth, then no, I cannot claim that use of the term "know" with regard to scientific knowledge.  However, note the use of "know" in that term "scientific knowledge".  No, scientific knowledge does not lay claim to be "knowledge of absolute truth", it only lays claim to be knowledge that has been gained by scientific means—scientific knowledge.

    Again, it's as I expressed in the paragraph you only partially quoted, and as I illustrated in the following paragraph.

    After all, as I said, before:

    However, I already accounted for this possibility in my previous answer when I used the term "expected", rather than trying to assert that such is "known", or any other "absolutism".

    However, instead of reading what I wrote for understanding, you appear to have read it to make me "an offender for a word".

    Again, with your misunderstanding, you say:

    ... Would we need a unified theory dealing with all the forces of nature if we were considering biology, how would you prove or test or show what was the case?

    Had I not, earlier said:

    For instance, to the extent that biological systems are chemical systems—that are governed by the laws of electromagnetism*—then there is absolutely no way such a system will deviate from the behavior of any other electromagnetically governed system.  On the other hand, there is the bare possibility that biological systems may have "something extra", and that "something extra" may have unforeseen characteristics that may violate such expectations.

    In fact, the quote you used, from me, before your "rant" about "need[ing] a unified theory dealing with all the forces of nature" was precisely the footnote referenced by the asterisk after "electromagnetism" in my quote, above.  It was placed there to help your understanding.

    You see, "to the extent that biological systems are chemical systems—that are governed by the laws of electromagnetism", we already have the applicable "unified theory dealing with all the forces of nature" necessary for understanding how such will be modified by Einstein's Special Theory of Relativity.

    So, are you actually going to learn something—even asking good, pointed questions about what I present—or are you simply here in search of more "words" you may use to accuse me of being "an offender"?

    You may ask all the pointed questions you wish, on the subject I am actually presenting.  Be as critical—in the critical thinking sense, that is—as you wish.  I will not shy away from hard questions, provided they are on topic.

    However, if you are simply going to continue trying to make me "an offender for a word"—being abusive and misconstruing my words—and/or otherwise "hijacking" the discussion here, I reserve the right to edit or delete your messages.  (Unfortunately, if I edit your messages, they will appear to be from me.  There's nothing I can do about that.)

    Consider this your first warning on this "hijacking" issue.  You have already broken past three strikes, but I will give you another chance.

    David

    Halliday
    OK, Roger, you asked for it:

    [Edited version of Roger's post]
    Roger J. AndertonDavid ...
    [The gist of Roger's post is that if we, as scientists, or me in particular, don't know the absolute truth about something, then we/I must admit that we/I know nothing.]
    ... Roger
    Halliday
    Roger:

    Fallacious thinking, I'm sorry.

    By the way, when you are ready to get back on topic, I'm ready.

    David

    how are you going to prove or show by test anything that supports such a claim?

    blue-green
    The state of science is …. not | clear black and white without any grey > … in other words not | absolute>

    Of course David's wording was better. Roger, put your whole expression “clear black and white without any grey” in parentheses and transform it with not.

    Get used to subjunctive meanings and contingent data. Riddles like “What is Truth?” are put in the mouth of Pilates for mass consumption of the Gospels. That's convention for you!
    >>Riddles like “What is Truth?” are put in the mouth of Pilates for mass consumption of the Gospels. That's convention for you!

    we have similar problem with special relativity as to what is truth.

    I ask questions and get bluffed off with numerous unproven and untested claims.

    Halliday
    Roger:

    You haven't even seen my claims, yet.*

    I haven't addressed my "claims" here, since I will be making them through the course of this series.

    I have told you that many times.

    Otherwise, I did address some of your misstatements, and false claims about what people like Einstein and Kip Thorne have said.

    I have also tried to be gracious and address some related issues that I could without going into what I already have planned for this series, or (I had hoped) without going to far afield.  Unfortunately, you took advantage of my hospitality, and turned our conversation into something altogether different and uncalled for.

    Now, if you are willing to see what my true claims are, and, perhaps actually learn something, then you are welcome to stick around.

    David

    *  Unfortunately, my friend that was going to review my next installment was not able to get to it, today.  He says he will read it tomorrow morning.

    David

    As usual you make mistaken claims, even going so far as to mistakenly claim that you have not made claims. Then on the Einstein issue etc you have made claims and done nothing to back up those claims. But I suppose oh well we have to wait for your next article.

    Roger

    David
    >>Then you follow it with the non sequitur: How are you going to show that science is clear black and white without any grey?

    What I meant by it is how are you going to prove or whatever that science is clear black and white OR prove or whatever that science is black and white and grey?

    So you have answered nothing. And just making unproven and untested claims.

    Roger

    Halliday
    Roger:

    Again with the non sequiturs.  You again require:

    What I meant by it is how are you going to prove or whatever that science is clear black and white OR prove or whatever that science is black and white and grey?

    The opposite of "clear black and white" is not "black and white and grey".

    I simply claimed the very well known fact that science is neither black nor white.  What I said, more precisely, is that people like lawyers, politicians, and, apparently yourself, "want clear cut, black and white, yes or no, unequivocal answers, but that's not what science is about."

    If something does not claim to be "clear black and white", then it is "grey", so to speak, and there is nothing to "prove or whatever" about such a lack of claim.

    David

    David

    >>I simply claimed the very well known fact that science is neither black nor white. What I said, more precisely, is that people like lawyers, politicians, and, apparently yourself, "want clear cut, black and white, yes or no, unequivocal answers, but that's not what science is about."

    you have not shown why it should be as you want. If you are to make a claim and admit you aren't sure, then the claim has not much worth.

    scientist makes claim.
    lawyer: are you sure?
    scientist: no, I am not sure, science does not work that way.
    lawyer: so your claim is worthless because it could be wrong

    Presumably what you have are claims that you are sure about and others which you are unsure. That being the case then students should be made aware.

    Roger

    Halliday
    Roger:

    Since science does not claim to be "clear cut, black and white, yes or no, unequivocal", there is nothing to prove.

    Furthermore, it is a logical fallacy to claim, as your hypothetical "lawyer" does, that because something is not "clear cut, black and white, yes or no, unequivocal" that it "is worthless because it could be wrong".

    As for making "students" "aware" of the nature of science, scientists do.  (As to whether non-scientist "teachers" do, I cannot speak for or against that.)  In fact, I find that "students" become more interested in and excited about science when they learn that science is not simply about (dry) facts, and the "holder" of "absolute truth".

    So, can you appreciate science for what it is, or are you going to persist in insisting that science must be (or become) something it is not?

    David

    David

    >>>So, can you appreciate science for what it is, or are you going to persist in insisting that science must be (or become) something it is not?

    Well I am questioning your beliefs as to what science is, and you avoid giving evidence for your point-of-view.

    Roger

    Halliday
    Roger:

    May I recommend that you immerse yourself in the following web site:  Understanding Science:  How science really works.  It is reasonably extensive, so take your time.  Educate yourself.

    David

    Bonny Bonobo alias Brat
    Wow. great website David, thanks for sharing this!
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Halliday
    Helen:

    I ran into that web site a number of years ago.  I can't remember exactly how I ran into it, perhaps someone posted a link, just as I have.

    I have actually used that site, or many portions of it, when talking to many different people about what is and what is not science.  (They do point out, on their "philosophy of science" portion of the site, that a fine/exact line between science and non-science has never been successfully drawn, but that does not mean that far enough from the "fuzzy line" one cannot determine an unequivocal distinction.)

    It is one of the best sites on the subjects of "what is science" and "understanding science" (including "what is the scientific method") I have seen, so far.

    I'm very glad you like it.

    David

    ''How are you going to show that science is clear black and white without any grey?''

    I believe 'black and white' refers to the fact that science can be accurate in a way that the Law and Politics cannot.
    Maybe this is what was meant.

    Halliday
    Ken:

    Actually, while science "can be accurate in a way the Law and Politics" is often not, the Law (and contracts, similarly) are often far more "black and white" than science can usually ever be.  (Politics is its own "animal" with its very own fuzzy shades of grey.  :(  )

    Roger has been trying to make science into something it is not, while, almost simultaneously, railing against science for not doing what he thinks it "should" do if it were what he is trying to make it out to be (which it is not).  (If that sounds confusing, then welcome to his world, I suppose.)

    Much of such arguments, from Roger, appear to be attempts to set up a "straw-man" version of science that he can then "knock down".  His trouble, of course, is that anyone that knows what science is actually like cannot fall for such arguments.

    David

    Gerhard Adam
    Good luck David.  Unfortunately, I expect Roger will prove to be a disappointment.
    Mundus vult decipi
    Halliday
    Eh.  He will either learn something, or he will prove himself to be a "crank" and/or "crackpot".  As the saying goes, "better to be thought ..."
    Gerhard Adam
    True enough.  In any case, I do wish you good luck with this series, since it promises to provide a lot of information that will be useful.
    Mundus vult decipi
    Halliday
    Thank you, Gerhard.  :)
    Gerhard Adam
    BTW, David.  Despite some of my comments here, feel free to delete any of mine that you deem necessary.  I certainly won't be offended and I wanted to be clear that I simply do not wish to detract from your post [any more than I have already done].
    Mundus vult decipi
    isn't that being offensive?

    mathematical_investigations
    Are you the same Roger Anderton that created einsteinconspiracy.co.uk ?

    I'm checking in for the next blog post. I hope these digressions haven't impeded its progress. 

    Considering the experimental success of relativity, the issue of conventionalism belongs more to the philosophy of space and time than the science of space and time. You have mentioned Poincare, but have you read Reichenbach? He said that relativity requires us to impose Coordinative Definitions. Scientists have assumptions like "two rods of equal length remain of equal length when separated" (Actually, that isn't assumed in GR. It was assumed for SR).   These are Coordinative Definitions, not empirical facts. These assumptions aren't a problem unless the equations fail to work. When the equations fail, THEN these Coordinative Definitions should be questioned. These assumptions are there, but why would you question reasonable assumptions prior to any evidence against them? 
      
    "Coordinative definition has two major features. The first has to do with coordinating units of length with certain physical objects. This is motivated by the fact that we can never directly apprehend length. Instead we must choose some physical object, say the Standard Metre at the Bureau International des Poids et Mesures (International Bureau of Weights and Measures), or the wavelength of cadmium to stand in as our unit of length. The second feature deals with separated objects. Although we can, presumably, directly test the equality of length of two measuring rods when they are next to one another, we can not find out as much for two rods distant from one another. Even supposing that two rods, whenever brought near to one another are seen to be equal in length, we are not justified in stating that they are always equal in length. This impossibility undermines our ability to decide the equality of length of two distant objects. Sameness of length, to the contrary, must be set by definition.

    Such a use of coordinative definition is in effect, on Reichenbach's conventionalism, in the General Theory of Relativity where light is assumed, i.e. not discovered, to mark out equal distances in equal times. After this setting of coordinative definition, however, the geometry of spacetime is set."

    -Wikipedia. Philosophy of Space and Time

    Halliday
    Barry:

    I appreciate your "checking in for the next blog post."

    I felt like I had it just about ready a few days ago, and gave a copy to a friend for review.  Unfortunately, with work and all, it has taken him longer than either of us expected to be able to read through it.

    I just want to make sure I wasn't too long winded, or didn't explain something well enough, or didn't motivate something sufficiently.  He's an environmental engineer, and hasn't studied Special Relativity or much mathematics beyond engineering math, so I think his take of what I have presented is a good alternate perspective for this forum.

    By the way, this aspect of "Coordinative Definitions", especially as regards General Relativity (where, incidentally, we don't even have to set light "to mark out equal distances in equal times"*) is an additional reason for the focus I have taken in my next installment:  We will not have to deal with "two rods" being "separated", or such.  ;)  Essentially, we do it all by way of a very highly localized approach.**

    David

    *  Case in point is the way people, even physicists, talk glibly about the speed of light "slowing down" in a gravitational "field".  This is neither strictly true, nor strictly false or "incorrect".  It is, in fact, a feature of the ability of General Relativity (GR) to use general coordinates, and general coordinate transformations between such:  One may choose a system of coordinates where light "mark[s] out equal distances in equal times", or not; it's all the same to GR.

    **  Of course, in the process of determining a "match" for empirically observed phenomena, one will have to deal with not quite so local phenomena.

    David

    >>Case in point is the way people, even physicists, talk glibly about the speed of light "slowing down" in a gravitational "field". This is neither strictly true, nor strictly false or "incorrect".

    a case of grey maybe in a world of black, white and grey; or maybe of convention

    >> It is, in fact, a feature of the ability of General Relativity (GR) to use general coordinates, and general coordinate transformations between such: One may choose a system of coordinates where light "mark[s] out equal distances in equal times", or not; it's all the same to GR.

    sounds like a convention of what coordinate system to use.

    same then as only being a convention if do by Newtonian physics or by general relativity.

    Roger

    Halliday
    Roger:

    I hate to say this, but your ignorance is showing.  You may want to do something about that.

    The point is that General Relativity (GR) is completely independent of any and all "convention[s] of what coordinate system to use."

    However, there is absolutely no choice of "convention of what coordinate system to use" that will turn GR into Newtonian physics, or Newtonian physics into GR.

    This is why I could state with such confidence that you had completely misconstrued Thorne's statement.  (Actually, you don't quote Thorne, not even a quote from one of his books for non-scientists [Black Holes and Time Warps: Einstein's Outrageous Legacy], but some "paraphrase" of Thorne.)  One can see where the Newtonian "tidal gravity" is given as an approximation to parts of the space-time curvature (Tensor) of GR, but it does not, nor can it give the full thing.  It is but an approximation.

    So, the question I put to you is:  Do you want to learn true aspects of Einstein's theories of Relativity, or do you wish to wallow in your ignorance?

    David

    David

    >>However, there is absolutely no choice of "convention of what coordinate system to use" that will turn GR into Newtonian physics, or Newtonian physics into GR.

    Give evidence for that.

    >>One can see where the Newtonian "tidal gravity" is given as an approximation to parts of the space-time curvature (Tensor) of GR, but it does not, nor can it give the full thing.  It is but an approximation.

    Give evidence for that.

    Far as I am concerned a bit of maths manipulation and different maths can be shown related. So give maths and I will show a way of connecting them.

    Roger

    Halliday
    Roger:

    The nature and the limitations of the relationship between General Relativity and Newtonian mechanics and gravity is quite outside the scope of this series, as I have said many times before.  Maybe, just maybe, if you are a good boy, and/or if there is sufficient interest among others, I may delve into this issue at a later time.

    In the meantime, two thoughts:

    1. If Newtonian/Galilean space/time cannot be transformed into Minkowskian/Einsteinian spacetime, or vice versa—as I will show in this series—then there is no "maths manipulation" that will convert from General Relativity to Newtonian mechanics and gravity, or vice versa.  The spaces are simply incompatible.
    2. Are you not aware that the mathematical language of General Relativity—namely, Differential Geometry—was actually used with Newtonian mechanics and gravity long before Einstein even heard of it?  Riemann's geometry was invented back in the nineteenth century, after all.  So, there is no true "different language" issue.  However, once they are expressed within the same language their differences become even more stark and obvious!

    So, once again, something to educate yourself about.

    David

    David

    OK don't deal with general relativity then; that is after all a dumping ground for those dealing with special relativity and not explaining properly the transition from Newton to Einstein. A bit of maths manipulation can actually go a long way. Before Einstein 1905 there were others working on the maths of Lorentz transformations. I know about Riemann, he created that maths because he wanted to apply it to gravity, so its another bit of maths manipulation before Einstein. As to language differences – general relativity talks of space-time curvature while Newtonian physics talks of forces.

    Roger

    Halliday
    Roger:

    You claim:

    ... I know about Riemann, he created that maths because he wanted to apply it to gravity, ...

    Do tell, where did you get this notion?

    David

    Halliday
    [Since Roger Anderton seems to have difficulty understanding, or, at least, using a threaded forum, such as we have here, I'm placing the portion of his comment, below, that pertains to my message, above, in this proper location.]

    Roger J. AndertonDavid

    >>>me: You claim: .. I know about Riemann, he created that maths because he wanted to apply it to gravity, …
    >>David: Do tell, where did you get this notion?

    Ans: Gravitation, Misner et al p 220-221

    ...

    Roger

    [Roger Anderton (not verified) | 05/15/12 | 17:14 PM]
    Halliday
    Roger:

    I actually noticed that box (Box 8.5  Georg Friedrich Bernhard Riemann) earlier today, when I was looking for something else.

    Unfortunately (for you) you have your chronology backward:  He "created that maths" before 1853; only years later (like twelve, dying of tuberculosis) was he "occupied with an attempt at a unified explanation of gravity and electromagnetism".  Of course, his approach was more focused upon "chang[ing] the connectivity character of the piece" of "surface".  (Of course, he had "created that maths" to deal with curved surfaces of arbitrary topology.  So it's only natural that he would try to use it in the way he did.)

    You simply need to get you facts straight.  ;)

    Now, within your earlier statement, you said "so its[Riemann's use of his geometry in his attempt to unify the explanations of gravity and electromagnetism] another bit of maths manipulation before Einstein."  Yes.  In fact the above mentioned Box even has a nice quote from Einstein acknowledging how far ahead Riemann was in considering space to be potentially dynamic.

    (Another piece of science history trivia is that Einstein not only didn't "re-invent" Riemannian geometry, he didn't even know about Riemann's geometry until a mathematician friend of his suggested that it just might be what Einstein was looking for.)

    So?

    David

    Dear David

    So the book does not deal with the full history, it was only a short piece on it. Riemann was inspired to look at that maths because of Gauss, Gauss wanting to know the geometry of space etc.

    You say >>Now, within your earlier statement, you said "so its[Riemann's use of his geometry in his attempt to unify the explanations of gravity and electromagnetism] another bit of maths manipulation before Einstein."  Yes.  In fact the above mentioned Box even has a nice quote from Einstein acknowledging how far ahead Riemann was in considering space to be potentially dynamic.

    Which leads to the issue of when was the “theory” really created (or started) – it seems very arbitrary to give a date as say 1915.

    >>>(Another piece of science history trivia is that Einstein not only didn't "re-invent" Riemannian geometry, he didn't even know about Riemann's geometry until a mathematician friend of his suggested that it just might be what Einstein was looking for.) So?

    Yes, so what? Did Einstein then latch onto working on an already existing “theory” and work further on it, or did he then invent a new “theory” (GR)? If we go by it was an earlier “theory” then in that context it was still just a bit of maths manipulation but in the context of Newtonian physics. If we go by some people who interpret Einstein in a way I disagree with then its an abandonment of lots of Newtonian stuff. So what are you teaching?? And do you and your other teachers make it clear to your students what you are teaching? How are you connecting the bits together in other words, and how do you support such a claim? If we look to Einstein, all he seems to be doing is playing around a bit with maths manipulation and giving no references for what he's working from. I can do that easy – just a bit of maths manipulation and I can connect it all back to Newtonian physics. So I ask you am I allowed to do that? And if not why not? Please try to stop avoiding my questions. And I remind you that “don't know” is a perfectly valid answer along with all the other possibles.

    Roger

    Halliday
    Roger:

    You respond with:

    So the book does not deal with the full history, it was only a short piece on it. ...

    Yes, it was but a short piece, but enough to show that your chronology was incorrect.  So, now you switch to the claim:

    ... Riemann was inspired to look at that maths because of Gauss, Gauss wanting to know the geometry of space etc.

    Where did you get this claim?  Wikipedia's article on Riemann?  Or some other source?

    David

    David

    You are setting this all up as a diversion. I asked questions and you try to dodge answering them. Read the stories of these great mathematicians they were inspired to create their maths to solve practical problems. Newton created calculus to handle his theory. The Encyclopedia of Science tells us:

    “But Gauss didn't confine his thinking to a curved two-dimensional surface floating in a flat three-dimensional universe. In a letter to Ferdinand Schweikart in 1824, he dared to conceive that space itself is curved: "Indeed I have therefore from time to time in jest expressed the desire that Euclidean geometry would not be correct." This brilliant inspiration was to take root in the mind of Gauss' most talented apprentice.”

    The apprentice was Riemann of which says:

    “German mathematician who was the first person to provide a thorough treatment of non-Euclidean geometry and to see how it might be applied in physics; he thus helped pave the way for Einstein's general theory of relativity.“

    http://www.daviddarling.info/encyclopedia/R/Riemann.html

    Roger

    Halliday
    Roger:

    Thanks for the link to that article.  It's very good.

    Yes, Riemann most certainly laid the foundation upon which Einstein later built.  However, as it states at the bottom of the article you referred to (and quoted from):

    One major obstacle had blocked Riemann's further progress. He thought only of space and its topography. Einstein's great epiphany was that, in building a new theory of gravity, he also had to deal with time – with spacetime and spacetime curvature.

    This is one of the reasons we physicists refer to the mathematical underpinnings of Einstein's General Theory of Relativity as Riemannian Geometry, even though mathematicians insist upon making a distinction between the form of Geometry considered by Riemann (Riemannian Geometry) and that used by Einstein (pseudo-Riemannian Geometry).

    You see, not only was Riemann thinking "only of space and its topology", but he was thinking in terms of Galilean/Newtonian space/time, and not the Einsteinian/Minkowskian spacetime of Lorentzian geometry.

    It is the distinction between Euclidean like geometries vs. Lorentzian and other non-Euclidean like geometries that is why mathematicians refer to the form used by Einstein as pseudo-Riemannian Geometry.

    While we physicist consider the difference in the metric to be a "small thing" (though certainly significant), mathematicians consider it to be not at all like what Riemann created.  (Riemannian Geometry, to the mathematicians, only pertains to a positive definite metric, the only "true" inner product.  Anything else is a pseudo-inner product, or pseudo-metric.)

    Of course, the differences in the metric/inner-product are precisely what I'm talking about in this series.

    David

    Halliday
    Roger:

    On another issue, you claim:

    ... As to language differences – general relativity talks of space-time curvature while Newtonian physics talks of forces.

    That's the "General Relativity" "popular press" version.

    However, more generally and properly, both talk of forces being what causes deviations from inertial motion.  Additionally, when I talked of the ability to use the language of Differential Geometry (which certainly predates Einstein) to put General Relativity and Newtonian mechanics with gravity into the same language, that can go well beyond simply using Differential Geometry to "express the math", but one can ask the question of what "space/time" geometry corresponds with Newtonian mechanics with gravity.  (See, for example, a rather extensive treatment in Chapter 12 [Newtonian Gravity in the Language of Curved Spacetime], of the book [tome] Gravitation by Misner, Thorne, and Wheeler.)*

    David

    *  Yes, I dare you.  I double dare you.  ;)

    David

    >>>me: You claim: .. I know about Riemann, he created that maths because he wanted to apply it to gravity, …
    >>David: Do tell, where did you get this notion?

    Ans: Gravitation, Misner et al p 220-221

    >>me: On another issue, you claim: ... As to language differences – general relativity talks of space-time curvature while Newtonian physics talks of forces.
    >>David: That's the "General Relativity" "popular press" version.

    So you confirmed my claim that different languages are used. Now as to your claim – that relativists talk different language for “popular press” – (1) why do that? (2) where is your authoritative source telling you that you can do that? (3) is this a deviation from Einstein?

    >>David: However, more generally and properly, both talk of forces being what causes deviations from inertial motion.  Additionally, when I talked of the ability to use the language of Differential Geometry (which certainly predates Einstein) to put General Relativity and Newtonian mechanics with gravity into the same language, that can go well beyond simply using Differential Geometry to "express the math", but one can ask the question of what "space/time" geometry corresponds with Newtonian mechanics with gravity.  (See, for example, a rather extensive treatment in Chapter 12 [Newtonian Gravity in the Language of Curved Spacetime], of the book [tome] Gravitation by Misner, Thorne, and Wheeler.)*

    I am aware of it, it says I quote: “To return to the world of Newton, forget everything discovered in the last century about special relativity, light cones, the limiting speed of light, and proper time. Return to the 'universal time' t of earlier centuries.” Are you able to do that and address my question. People I am in contact with think that taking speed of light in vacuum (c ) is a convention, so if don't take that convention then it is a return to Newtonian physics. Do you agree, if not why not?

    At last we may be on the same page of the same book?

    Roger

    Halliday
    Roger:

    You have:

    >>me: On another issue, you claim: ... As to language differences – general relativity talks of space-time curvature while Newtonian physics talks of forces.
    >>David: That's the "General Relativity" "popular press" version.

    So you confirmed my claim that different languages are used. Now as to your claim – that relativists talk different language for “popular press” – (1) why do that? (2) where is your authoritative source telling you that you can do that? (3) is this a deviation from Einstein?

    Now, you might recall that your comment, to which I was responding, was your response to my point:

    Are you not aware that the mathematical language of General Relativity—namely, Differential Geometry—was actually used with Newtonian mechanics and gravity long before Einstein even heard of it?  Riemann's geometry was invented back in the nineteenth century, after all.  So, there is no true "different language" issue.  However, once they are expressed within the same language their differences become even more stark and obvious!

    Which, in turn, was directed toward your repeated claims that if one were to but put General Relativity into the same mathematical language as Newtonian mechanics with gravity ("maths manipulation"), then one would find that they are the same, that there is no difference.  This is further related to your claim that you had accomplished just such a "maths manipulation", and, thus (supposedly) shown this very equivalence.

    On the other hand, while I have never claimed that General Relativity was expressed, in general, in the same language as Newtonian mechanics with gravity; I was, of course, pointing out that they can be placed in the same (mathematical) language.  (That was what I was pointing out in the quote you were responding to, first [the one I have listed last].)

    So, you then change your claim of mathematical equivalence to one of "space-time curvature" vs. "force".

    What I was quickly disposing of was the fact that this rather simplistic characterization of (one of) the distinctions between General Relativity and Newtonian mechanics with gravity is principally within the "popular press" characterizations of General Relativity.  (I went into much further detail in the subsequent paragraph, which was intended to be taken with the statement you quoted.)

    For those that know the more full details of General Relativity, and who may care about any deeper details of the differences between that theory and Newton's mechanics and gravity, they have, typically, already gone through the details of those differences—far beyond the distinctions in mathematical language, and far beyond the distinctions of "space-time curvature" vs. "force".

    As to "why" the "popular press' " version of General Relativity is presented in such starkly simplistic terms?  It's the "popular press", after all.  Need I say more?  Don't they always express things in simplistic terms?

    As to your second question ("(2) where is your authoritative source telling you that you can do that?"):  I wasn't "do[ing] that", nor do I "do that".  So, once again, you have a non sequitur.

    As for your third question ("(3) is this a deviation from Einstein?"):  Is what "a deviation from Einstein?"  Is the "popular press" deviating from Einstein's view of how his theory (General Relativity) differs from Newtonian mechanics and gravity?  I'm not sure I would characterize it that way so much as I would say, once again, that the "popular press" tends to express things in simplistic terms.  Einstein was much more highly nuanced.

    Need I say more?

    David

    David

    >>As to "why" the "popular press' " version of General Relativity is presented in such starkly simplistic terms?  It's the "popular press", after all.  Need I say more?  Don't they always express things in simplistic terms?

    That's not answering the question, that's just raising more questions.

    >>On the other hand, while I have never claimed that General Relativity was expressed, in general, in the same language as Newtonian mechanics with gravity; I was, of course, pointing out that they can be placed in the same (mathematical) language.  (That was what I was pointing out in the quote you were responding to, first [the one I have listed last].)

    Ok.

    >>So, you then change your claim of mathematical equivalence to one of "space-time curvature" vs. "force".

    No change in claim, is as I stated different languages and that is example.

    >>>As to your second question ("(2) where is your authoritative source telling you that you can do that?"):  I wasn't "do[ing] that", nor do I "do that".  So, once again, you have a non sequitur.

    I was referring to your claim of popular press version of general relativity, which you end up dismissing from consideration.

    >>As for your third question ("(3) is this a deviation from Einstein?"):  Is what "a deviation from Einstein?"  Is the "popular press" deviating from Einstein's view of how his theory (General Relativity) differs from Newtonian mechanics and gravity?  I'm not sure I would characterize it that way so much as I would say, once again, that the "popular press" tends to express things in simplistic terms.  Einstein was much more highly nuanced.

    Picking up on “I am not sure I would characterize it that way” so its an option you are not sure of . Then its again with you dismissing anything being said contrary to you as “popular press” way of doing things. When there is option they are right and you are wrong, and all you are doing is merely dismissing that possibility.

    >>Need I say more?

    No

    Roger

    Halliday
    Roger:

    Have you not noticed, for yourself, the penchant of the "popular press" to overly simplify?

    David
    Halliday
    Roger:

    You end with:

    >>David: However, more generally and properly, both talk of forces being what causes deviations from inertial motion.  Additionally, when I talked of the ability to use the language of Differential Geometry (which certainly predates Einstein) to put General Relativity and Newtonian mechanics with gravity into the same language, that can go well beyond simply using Differential Geometry to "express the math", but one can ask the question of what "space/time" geometry corresponds with Newtonian mechanics with gravity.  (See, for example, a rather extensive treatment in Chapter 12 [Newtonian Gravity in the Language of Curved Spacetime], of the book [tome] Gravitation by Misner, Thorne, and Wheeler.)*

    I am aware of it, it says I quote: “To return to the world of Newton, forget everything discovered in the last century about special relativity, light cones, the limiting speed of light, and proper time. Return to the 'universal time' t of earlier centuries.” Are you able to do that and address my question. People I am in contact with think that taking speed of light in vacuum (c ) is a convention, so if don't take that convention then it is a return to Newtonian physics. Do you agree, if not why not?

    At last we may be on the same page of the same book?

    While you do give a proper quote from that chapter, you skipped the two sentence before that (emphasis added):  "The equivalence principle is not unique to Einstein's description of the facts of gravity.  What is unique to Einstein is the combination of the equivalence principle and local Lorentz geometry."

    You see, what I will be showing in this series is the difference in the local geometry of Einsteinian/Minkowskian spacetime vs. Galilean/Newtonian space/time.  That is what makes all the difference.  Additionally, I will be further showing that there is no "speed of light in vacuum (c ) ... convention" or not that will transform one into the other.  They are distinct and eminently distinguishable.

    David

    David
    The quote I gave : “To return to the world of Newton, forget everything discovered in the last century about special relativity, light cones, the limiting speed of light, and proper time. Return to the 'universal time' t of earlier centuries.” should have been clear enough as to what was being done as regards the Lorentz transformations.

    >>You see, what I will be showing in this series is the difference in the local geometry of Einsteinian/Minkowskian spacetime vs. Galilean/Newtonian space/time.  That is what makes all the difference.  Additionally, I will be further showing that there is no "speed of light in vacuum (c ) ... convention" or not that will transform one into the other.  They are distinct and eminently distinguishable.

    I think not. Given two bits of maths there is way of connecting them by introducing a bit more maths. Einstein assumes lightspeed in vacuum as constant so sets two observations of it as c = c' in frame O and O' so relativity texts usually start from setting c in O and O' then get t and t' as different. Where set t and t' as same then get c and c' different. Poincare dealt with relativity before Einstein, so how are you going to show that the treatment of Lorentz transformations should not be done Poincare's way? And besides there are a great many articles saying it is convention. So either they are wrong or you are wrong. How are you going to show it one way or the other.

    Roger

    Halliday
    Roger:

    You begin with:

    The quote I gave : “To return to the world of Newton, forget everything discovered in the last century about special relativity, light cones, the limiting speed of light, and proper time. Return to the 'universal time' t of earlier centuries.” should have been clear enough as to what was being done as regards the Lorentz transformations.

    I see you don't wish to even consider the full context of the quote you gave.

    Furthermore, I'm not talking about the Lorentz transformations, I'm talking about local Lorentz geometry (or, more correctly, as I already stated, "the local geometry of Einsteinian/Minkowskian spacetime vs. Galilean/Newtonian space/time" [as well as local Euclidean geometry, of course]).  That's one of the reasons I placed your quote within its broader context.

    You continue with your tired "saw":

    >>You see, what I will be showing in this series is the difference in the local geometry of Einsteinian/Minkowskian spacetime vs. Galilean/Newtonian space/time.  That is what makes all the difference.  Additionally, I will be further showing that there is no "speed of light in vacuum (c ) ... convention" or not that will transform one into the other.  They are distinct and eminently distinguishable.

    I think not. Given two bits of maths there is way of connecting them by introducing a bit more maths. ...

    Are you completely unaware that there are whole branches of Mathematics dedicated to the question of what things (like "two bits of maths") can vs. cannot be transformed into one-another "by introducing a bit more maths"?

    If what you claim were true, then all of Mathematics could be made the same "by introducing a bit more maths".

    I told you I would show the "distinct and eminently distinguishable" character of "the local geometry of Einsteinian/Minkowskian spacetime vs. Galilean/Newtonian space/time."

    You'll see...

    Since I will not be "assum[ing] lightspeed in vacuum as constant so set[ing] two observations of it as c = c' in frame O and O' [such as the way] relativity texts usually start from setting c in O and O' then get t and t' as different", your criticism simply doesn't apply.  This is actually an unexpected benefit of my approach.  ;)

    You go on with:

    ... And besides there are a great many articles saying it is convention. ...

    I suppose it depends upon what you mean by saying "it is convention".

    If by "it" you mean simply whether one takes the speed of light (in a vacuum) as some fixed numerical quantity, I have already pointed out that such a convention has no effect upon the differences in the geometry.  It's one of the reasons for focusing upon the geometry.

    If by "it" you mean that the "lightspeed in vacuum as constant" "convention" is the sole distinction between"the local geometry of Einsteinian/Minkowskian spacetime vs. Galilean/Newtonian space/time", then you (and they) have a great deal to learn about the true distinctions.

    David

    Halliday
    Roger:

    Before this gets too lost...

    I am quite glad you have a copy of Gravitation, by Misner, Thorne, and Wheeler.  I am also glad you have Chapter 12 (Newtonian Gravity in the Language of Curved Spacetime).

    Now, the crucial question is:  Do you understand Chapter 12?

    David

    David

    >>>I'm not talking about the Lorentz transformations, I'm talking about local Lorentz geometry
    Its related

    >>Are you completely unaware that there are whole branches of Mathematics dedicated to the question of what things (like "two bits of maths") can vs. cannot be transformed into one-another "by introducing a bit more maths"?

    And are you dealing with that?

    >>If what you claim were true, then all of Mathematics could be made the same "by introducing a bit more maths".

    Interconnectedness

    >>I told you I would show the "distinct and eminently distinguishable" character of "the local geometry of Einsteinian/Minkowskian spacetime vs. Galilean/Newtonian space/time." You'll see...

    ok

    >>Since I will not be "assum[ing] lightspeed in vacuum as constant so set[ing] two observations of it as c = c' in frame O and O' [such as the way] relativity texts usually start from setting c in O and O' then get t and t' as different", your criticism simply doesn't apply.  This is actually an unexpected benefit of my approach.  ;)

    So can you show that it is dealing with special relativity and not some other theory?

    >>You go on with:... And besides there are a great many articles saying it is convention. … I suppose it depends upon what you mean by saying "it is convention".

    yes

    >>If by "it" you mean simply whether one takes the speed of light (in a vacuum) as some fixed numerical quantity, I have already pointed out that such a convention has no effect upon the differences in the geometry.  It's one of the reasons for focusing upon the geometry.

    So you are not dealing with what the geometry means?

    >>If by "it" you mean that the "lightspeed in vacuum as constant" "convention" is the sole distinction between"the local geometry of Einsteinian/Minkowskian spacetime vs. Galilean/Newtonian space/time", then you (and they) have a great deal to learn about the true distinctions.

    Well a few more things can be added. But it is I think a vital point.

    Roger

    Halliday
    Roger:

    "Interconnectedness" is not at all the same as claiming that "a little maths manipulation" shows that Einstein's relativity (whether Special or General) is just Newtonian mechanics with gravity in some new guise.

    So, are you simply claiming "Interconnectedness", in some nebulous sense (for instance, if instead of using a metric/inner-product with Minkowskian character, we use a completely different metric, one that cannot be transformed into or be transformed from one of Minkowskian character)?

    Or, are you claiming, as you did in your "Relationship between Newtonian and Einsteinian Physics" that Einstein's Special Relativity and General Relativity are simply Newtonian mechanics (with gravity, in the case of General Relativity) expressed in some different mathematical language ("the same bit of maths but subjected to a different language", "Newtonian gravitational theory has primary and secondary gravitational effects. When both these effects are considered then Newtonian physics gives same maths as General relativity. It is only that the maths is interpreted by different languages.")?

    So, to get down to "brass tacks", are you claiming that one can transform Einstein's Special Relativity into Newtonian mechanics, and vice versa?

    Are you claiming that one can transform Einstein's General Relativity into Newtonian mechanics with gravity (Newton's theory of Universal Gravitation, of course), and vice versa?

    I've been laboring under the impression that the answer to both these last two questions are to be answered affirmatively.  If, instead, you merely claim some nebulous "Interconnectedness", such as claiming that if one replaces some fundamental part or aspect of one then you can obtain the other, then I don't see that we have much to argue about.

    David

    David

    I was referring to interconnectedness that can be achieved in the maths by a little manipulation. I am sorry if you have difficulty with that. Anyway, this conversation is getting too long on your first article, when you have posted your second.

    >>So, to get down to "brass tacks", are you claiming that one can transform Einstein's Special Relativity into Newtonian mechanics, and vice versa?

    A bit of math manipulation and they are more closely related than many people realise.

    >>If, instead, you merely claim some nebulous "Interconnectedness", such as claiming that if one replaces some fundamental part or aspect of one then you can obtain the other, then I don't see that we have much to argue about.

    OK. As per the way that Einstein and Eddington were originally portraying general relativity it was update to Newtonian gravity theory. Newton physics deemed to give half the bending of light and needed to add extra bit to get the full bending as observed in 1919. So as part of mathematical modelling process start with basic maths model (in this case Newton) add more to the model to extend it when necessary, so was continuation of Newtonian physics. It was not too clear from the workings of Einstein because he did not give references in his papers. But to a certain extent we can treat Einstein as working on Riemann's theory of physics when he dealt with general relativity, and so by links such as these we can see a longer tradition stretching back to Newtonian physics etc.

    Anyway, on to your second article: Sorry I think its not very illuminating to someone new to special relativity, its introducing maths that's not normally presented to students until past 15, and special relativity is supposedly presentable in simple basic maths. So you are going on to more complicated maths and in the traditional simple maths presentation there is a lot of argument anyway. Good luck though,
    Roger

    Halliday
    Roger:

    So, are you refusing to commit one way or the other?

    So, if I show that there is a thing called N, that characterizes Newtonian mechanics (Galilean/Newtonian space/time), and a thing called E, that characterizes Einstein's Special and General Relativity (Einsteinian/Minkowskian spacetime); and, further that there is no invertible transformation that can transform N into E or vice versa—so there is no function, f, that has an inverse, f-1, such that N = f(E) and E = f-1(N)—would this still allow you to claim that "A bit of math manipulation and they are more closely related than many people realise"?  Or would such evidence preclude what you have been claiming?

    Now, you never answered my question:  "Now, the crucial question is:  Do you understand Chapter 12?"  (You know, the chapter entitled "Newtonian Gravity in the Language of Curved Spacetime".)

    Unfortunately, your complaint about the linear algebra—algebra that is far easier than solving quadratic equations—in my next article in this series suggests that you may have a very difficult time understanding that chapter.  Is that so?

    If so, that's unfortunate, since you will probably have just as much trouble understanding the calculations of the deflection of light around the Sun, whether for General Relativity or Newtonian mechanics with gravity (taking into account all the aspects of gravity around a ball, like the Sun—it is most certainly not just a constant gravitational field portion of Newton's theory, but the full thing!).

    However, it is very important to recognize that the prediction preceded any observations!  Einstein and Eddington made the prediction, based upon General Relativity, prior to anyone even trying to make such measurements.  However, they both knew that a solar eclipse was soon to be available for making just such a measurement, so they feverishly worked on making the prediction early enough that scientists could prepare to make the needed measurements.

    It was the success of the prediction of General Relativity, vs. the failure of Newtonian mechanics with gravity, that caused scientists to actually take notice of General Relativity.

    By the way, do you know that Einstein published many papers along the way as he was struggling with what gravity must "mean" in light of his Special Theory of Relativity?  He most certainly didn't start from Riemann's work (that came much later).  Instead, his papers show his thought experiments, as he was trying to understand what gravity "must be like".

    You may find his journey rather interesting, maybe even enlightening.

    I highly recommend that you read what he wrote along the way to General Relativity.

    David

    David

    >>So, if I show that there is a thing called N, that characterizes Newtonian mechanics (Galilean/Newtonian space/time), and a thing called E, that characterizes Einstein's Special and General Relativity (Einsteinian/Minkowskian spacetime); and, further that there is no invertible transformation that can transform N into E or vice versa—so there is no function, f, that has an inverse, f-1, such that N = f(E) and E = f-1(N)—would this still allow you to claim that "A bit of math manipulation and they are more closely related than many people realise"?  Or would such evidence preclude what you have been claiming?

    Well do that then show your N and your E, because you have not done anything like that so far. Further on I will point out that you seem to have defined N incorrectly ----**

    >>Now, you never answered my question:  "Now, the crucial question is:  Do you understand Chapter 12?"  (You know, the chapter entitled "Newtonian Gravity in the Language of Curved Spacetime".)

    Of course I understand it in my way, such a type of question is not really meant to be answered, its just some mocking attempt, is it not.

    >>Unfortunately, your complaint about the linear algebra—algebra that is far easier than solving quadratic equations—in my next article in this series suggests that you may have a very difficult time understanding that chapter.  Is that so?

    No I am perfectly happy with it. My point was that as an introduction to special relativity for a novice what is required is it to be the simplest possible and it fails that.

    >>If so, that's unfortunate, since you will probably have just as much trouble understanding the calculations of the deflection of light around the Sun, whether for General Relativity or Newtonian mechanics with gravity (taking into account all the aspects of gravity around a ball, like the Sun—it is most certainly not just a constant gravitational field portion of Newton's theory, but the full thing!).

    Newton's theory can also deal with non-constant gravitational field are you taking that into account? ** It sounds like you have defined N incorrectly. N can deal with non-constant gravitational field.

    >>However, it is very important to recognize that the prediction preceded any observations!  Einstein and Eddington made the prediction, based upon General Relativity, prior to anyone even trying to make such measurements.  However, they both knew that a solar eclipse was soon to be available for making just such a measurement, so they feverishly worked on making the prediction early enough that scientists could prepare to make the needed measurements.

    Others such as Soldner I think did predictions before them Einstein.Gauss and Riemann were wondering about the non-Euclidean nature of the universe and had their theory, so should have been a test of their theory. But it was a test of their theory if we can treat Einstein as working on it.

    >>It was the success of the prediction of General Relativity, vs. the failure of Newtonian mechanics with gravity, that caused scientists to actually take notice of General Relativity.

    But it failed to be debated at the time as to whether Einstein had genuinely replaced Newton. I think it was Silberstein at the time who pointed out Newtonian physics gave same as general relativity.

    >>By the way, do you know that Einstein published many papers along the way as he was struggling with what gravity must "mean" in light of his Special Theory of Relativity?  He most certainly didn't start from Riemann's work (that came much later).  Instead, his papers show his thought experiments, as he was trying to understand what gravity "must be like".

    It is important as to what maths he used and he used Riemann's and thus was tapping into Riemann's theory of physics.

    Roger

    Halliday
    Roger:

    When you say "Newton's theory can also deal with non-constant gravitational field", are you referring to "non-constant" in space—what physicists refer to as non-uniform, such as the gravitational field around a ball, like the Sun—or are you saying "non-constant" in time?

    I have indeed stated that the non-uniformity of the gravitational field around a ball, such as the Sun, was taken into account.  I was addressing the claim I already saw within your "Relationship between Newtonian and Einsteinian Physics" presentation.

    If you are claiming that the Sun's gravitational field varies with time, what is your evidence?

    David

    David

    Gravitational field can change in Newtonian physics. F = Gm1m2/r^2. F = force. G = gravitational constant, m1 = mass of point-mass and m2 = mass of other point-mass, r = distance between them. Strength of field changes by changes in r. If you are going to change in time then one possibility is to have the masses change with time. Say for the earth, the mass of the earth is increasing a small amount with time because of meteors falling on to earth and adding more mass. The basic set-up of Newtonian physics can be expanded upon with ever increasing sophisticated mathematical models taking into account more factors. In the case of the Sun, its radiating particles so losing mass, so some change in its mass there, resulting in change of gravitational field. Also objects falling into sun I think, so a gain of mass from that.

    Roger

    Halliday
    [My reply is below.]
    ''Considering the experimental success of relativity, ..............''

    Relative success, I'd say, considering there is no real definition of what constitutes a 'frame of reference''.
    Relativity theory as it is now taught and understood [poorly and incompletely] is as substantial as the Emperor's new clothes. There is a new paradigm on the way, which is good news, but resistance to it amongst PhysMaths will impede its introduction.

    Halliday
    Ken:

    Here, you seem to be confused about what "relativity theory" is.

    Einstein's Special Theory of Relativity is quite explicit about "what constitutes a 'frame of reference'."

    Now, I suppose that your understanding of Einstein's Special Theory of Relativity may well be described as "[poorly and incompletely] is as substantial as the Emperor's new clothes."  However, that most certainly doesn't pertain to all people.

    I don't know what "new paradigm" you seem to think is "on the way".

    If its some "pet theory" of your own or of someone you are a "fan" of, then I suppose you are in "good" company with so many crackpots and cranks who all think that the only reason their "pet theory" is not being accepted is due to "resistance to it amongst PhysMaths".  Of course, the real problem is a significant misunderstanding of what science actually is and how it really works.

    David

    David :)
    Considering your ignorance [of my qualifications and the reasons I have for making such assertions] I am a little disappointed that what you HAVE learned seems to be impeding your ability to take on new ideas. I guess age has its drawbacks as well as its advantages.
    I would apologise for any offense you might take to my posting personal comments but that consideration did not stop you from doing precisely that.
    You don't know what 'new paradigm' is on the way? Is yours not another crank/crackpot theory until it becomes mainstream science?
    The key elements of a good theory are accuracy, beauty and simplicity.

    Halliday
    Ken:

    I asked you about the so called "new paradigm" you alluded to, but this is your response?

    Do you have any intention to actually share?

    David

    Gerhard Adam
    Well, that didn't take long.
    Mundus vult decipi
    Halliday
    [This is in response to Roger's comment above.]
    Roger:

    Everything you have said is true, so long as you maintain the fundamental structure of Newton's Theory of Universal Gravitation:  F12 = -G (m1 m2)r12/r123, for point particles m1 and m2 with straight line spacial separation given by the vector r12.  However, the change in mass of the Earth is irrelevant for the question of the bending of light around the Sun, and the rate at which the Sun's mass changes is absolutely negligible over the short period of time that the Sun's gravitational field will act upon light passing by it.

    As you have already pointed out, above, "Others such as Soldner I think did predictions [of the bending of light around an object such as the Sun] before them Einstein."  So, take a look at such predictions, and compare them to the observations!  (Of course, I stated that no-one had tried to actually measure such, until after Einstein and Eddington made their bold prediction that contradicted with any prediction based upon Newtonian mechanics with gravity.  I made absolutely no claim that no-one had ever made any such prediction.)

    Incidentally, back in that previous message of yours, you also claim:

    But it failed to be debated at the time as to whether Einstein had genuinely replaced Newton. ...

    Boy!  Do you ever have a warped sense of the history!

    "Failed to be debated"?  Even Einstein's far simpler theory of Special Relativity was far too controversial for the Nobel prize to be awarded, so they chose to award Einstein with the Nobel prize for his explanation of the photoelectric effect.

    Yeah, right.  "Failed to be debated"...

    However, you then go on with:

    ... I think it was Silberstein at the time who pointed out Newtonian physics gave same as general relativity.

    Do you have any references?

    By the way, post-dictions are notorious for straining credibility in their attempts to fit, after the fact, the results of some measurement that contradicts the theory upon which they are based.*  That's why the predictions before the fact are usually given greater weight in any "debate".  That's why I especially recommend that you take a good hard look at any predictions of the bending of light around an object, such as the Sun, based upon Newtonian mechanics and gravitation, made prior to the measurements.  They are the least biased!

    David

    This is especially true when the error is something like a factor of two (2), since it is "easy" to try and "double count" the effects in an attempt to make the "correction".  (We saw something similar with at least one "explanation" of the seemingly super-luminal neutrinos.)

    Dear David

    I am aware of Einstein's relativity was too controversial for Einstein to get a Nobel prize. There has been no debate as far as I know that has come to a definitive conclusion that Einstein did replace Newtonian physics, else it should be cited as to where the evidence is that Einstein did do that. Silberstein was the main one saying that it did not replace Newtonian physics. Rather than address the controversy that happened in 1919 onwards, it has just been forgotten and ignored, resulting in theories being taught that have not been agreed by debate..

    Silberstein, “The True Relation of Einstein's to Newton's Equations of Motion.” Nature Dec 1923 p 788 -789 tells us: “Now, as has recently occurred to me, the true relation of Einstein's equations to those of Newton is of a much more intimate nature, and remains valid, no matter how strong the field and how much space deviates from Euclidean behaviour.”

    http://www.nature.com/nature/journal/v112/n2822/abs/112788b0.html
    or
    http://gsjournal.net/Science-Journals/Historical%20Papers-Relativity%20T...

    As far as I am concerned it is the mathematical process whereby a mathematical model can be updated, thus taking a mathematical model in the context of Newtonian physics it can be updated if experimental evidence requires it, in this way Newtonian physics cannot be replaced. (Only extra concepts might be added.) Your talk of a theory being replaced by predictions not being confirmed is as far as I am concerned philosophically wrong and for which there is no evidence, proof or anything to substantiate it and fails totally to take into account how maths is performed. Given a theory that is as consistent as Newtonian physics is, it cannot be replaced, all that can happen is a mathematical model based upon Newtonian physics might need updating, but the theory itself of Newtonian physics cannot be replaced. In 1919 the newspapers hailed that there had been a revolution in physics that Newtonian physics had been overturned, this was a gross distortion of the facts, there had been no such thing. All it was – was a total disregard of how science should be performed for the sake of making up a story to sell newspapers. As Einstein and Eddington were initially pointing out – it was merely an update to Newtonian physics. The misreporting by the news media has done a great disservice to science leading people to have philosophical beliefs that are not proper science, and a failure to recognise that at its foundational level modern physics is still based on Newtonian physics. I apologise if I sound like I am coming on too strong.

    Roger

    Halliday
    Roger:

    Once again, you portray a false sense of what science is truly like, "how science really works."  Go back to my earlier post where "I recommend[ed] that you immerse yourself in the [aforementioned] web site".

    Of course, if you refuse to learn, then there's little I can do, but to "get rid" of your falsehoods, from this forum.

    First off, any theory that worked well, in the past, will still, and always, work just as well within the domain of its applicability.  The only thing that changes, in this process, for such an old theory, is that its domain of applicability shrinks in comparison to new, more universally applicable theories, and greater experimental precision (and/or any need for greater precision for any desired application, such as the Global Positioning System).

    Secondly, you are correct that just because an old theory has been found to incorrectly predict a certain experimental result dose not cause such an old theory to simply be "thrown out", or summarily "replaced" by an "usurper" theory.  There are multiple paths that can be taken in the process of science:

    1. The old theory can be "adapted", "corrected", "added to", etc., in order to match the new experimental results.  (See, for example, "epicycles".)
    2. If there is a new "up and coming" theory that does a better job of explaining the results—or even if it cannot, at face-value, do as well as the old theory:
      1. there may be other compelling reasons to adopt (and extend/adjust) the new theory while practically forgetting the old theory (at least, eventually).  (See, for example, the Geocentric vs. Heliocentric models of planetary motion.)
      2. the new theory may simply win out for those cases where it is superior, while the old theory may continue to be used when it is simpler, and sufficiently accurate.  (See my "First off" paragraph.  This is the case for Newtonian physics vs. Einsteinian Relativistic physics.)

    You see, your perception simply doesn't match reality.  You claimed:

    ... There has been no debate as far as I know that has come to a definitive conclusion that Einstein did replace Newtonian physics, else it should be cited as to where the evidence is that Einstein did do that. ...

    You see, while there most certainly was ample "debate", your concept that there would, necessarily, be some "definitive conclusion that Einstein did replace Newtonian physics", and, even worse, that such would be characterized by some "citable" "evidence" "that Einstein did do that", is simply antithetical to "how science really works."

    So, no wonder you think something is amiss, since on the one hand you think that science works differently than it really does, while, on the other hand, you (correctly) recognize that there is an ability, using mathematics, to, often (not necessarily always), "update" a theory (when it makes sense to do so).  (Of course, as I pointed out, while one may well be able to add "correction" upon "correction" to a mathematical model, such as Newton's Theory of Universal Gravitation, science most certainly doesn't always take that approach either.  After all, sometimes the old concepts, like "epicycles", simply don't remain viable in light of new concepts, like Elliptical orbits or Newton's theories.)

    So, like I have already said, "I recommend that you immerse yourself in the [aforementioned] web site".

    David

    P.S.  Thanks for the references to Silberstein.  I've read it (it is quite short, since, after all, it is only a "letter to the editor").

    I haven't gone through it in detail.  However, since he is taking the "reference frame" to be co-moving (in a certain instantaneous sense) with a point particle ("its own rest-system") the conditions for the Newtonian approximation (to the equations of motion) are well satisfied in almost all cases.  (He claims that it is well satisfied in all cases.  However, I'm reasonably certain that there are pathological cases that can, likely, cause some troubles.  But I'm willing to set that aside, for now.)

    Unfortunately for you, while Silberstein's prescription provides an equation of motion such that "in the rest-system of the free particle, the general relativistic equations (I) become identical with the Newtonian equations of motion, rigorously", they have lost all semblance of a force derived from "Newton's Theory of Universal Gravitation:  F12 = -G (m1 m2)r12/r123, for point particles m1 and m2 with straight line spacial separation given by the vector r12."  Instead, Silberstein's prescription requires that one start from the metric derived from Einstein's Theory of General Relativity!  In other words, the "gravitational potential" (Ω, in Silberstein's "letter to the editor") is not obtained from Newton's Theory of Universal Gravitation, but from the metric obtained from General Relativity.

    Halliday
    [Once again, since Roger Anderton seems to have difficulty understanding, or, at least, using a threaded forum, such as we have here, I'm placing the portion of his comment, below, that pertains to my message, above, in this proper location.]
    Roger J. AndertonDavid
    How authorative is that source http://undsci.berkeley.edu/ supposed to be, as far as I am concerned it is just offering an opinion; and an opinion that might be wrong. Going by Galileo who is usually treated as the founder of modern physics then physics is mathematical, and going by it as maths then it is mathematical modelling. If you disagree with Galileo approach to physics how are you going to show otherwise; please tell.

    You say: “First off, any theory that worked well, in the past, will still, and always, work just as well within the domain of its applicability.” I agree, but what you have to take into account is different mathematical models can be constructed within the context of a theory.

    You say: “Secondly, you are correct that just because an old theory has been found to incorrectly predict a certain experimental result dose not cause such an old theory to simply be "thrown out", or summarily "replaced" by an "usurper" theory.” I agree. But when you talk of an “old theory” being adapted etc., for example by epicycles, are you really taking into account that different mathematical models can be constructed within the context of a theory, so adding a bit more maths is not really changing the theory? [For instance the theory of geocentricism- adding the maths of epicycles does not change the theory that of geocentricism. Another example – adding Riemann geometry to Newtonian physics (keeping its other things of universal time and so forth) does not change the theory of Newtonian physics.] You see as far as I am concerned you seem to be getting mathematical model and theory confused, you talk of change in theory from old to new, but it looks to me just change of mathematical model.
    You say: “You see, while there most certainly was ample "debate", your concept that there would, necessarily, be some "definitive conclusion that Einstein did replace Newtonian physics", and, even worse, that such would be characterized by some "citable" "evidence" "that Einstein did do that", is simply antithetical to "how science really works."” Well I disagree and the issue is how are you going to establish that the source you cite is authoritative and how are you going to establish your point-of view?

    As to my position - If we go by an authoritative historian of Einstein - Professor J D Norton says: “In November 1915, Einstein completed his general theory of relativity. Almost eight decades later, we universally acclaim his discovery as one of the most sublime acts of human speculative thought.” He then goes on to point out “we” don't know what Einstein discovered: “ However, the question of precisely what Einstein discovered remains unanswered, for we have no consensus over the exact nature of the theory's foundations.” ref: Rep. bog. Phys. 56 (1993) 791458. Printed in the UK General covariance and the foundations of general relativity: eight decades of dispute John D Norton.

    So surely that should be pointed out in the teaching of Einstein's relativity – that there is long running dispute-- and it is not agreed what the theory IS.

    You say: “After all, sometimes the old concepts, like "epicycles", simply don't remain viable in light of new concepts, like Elliptical orbits or Newton's theories.” - I would have thought that working from circular orbits with epicycles to a mathematical model with elliptical orbits was just another mathematical update, do you disagree?

    You say: “Unfortunately for you, while Silberstein's prescription provides an equation of motion such that "in the rest-system of the free particle, the general relativistic equations (I) become identical with the Newtonian equations of motion, rigorously", they have lost all semblance of a force derived from "Newton's Theory of Universal Gravitation:  F12 = -G (m1 m2)r12/r123, for point particles m1 and m2 with straight line spacial separation given by the vector r12."  Instead, Silberstein's prescription requires that one start from the metric derived from Einstein's Theory of General Relativity!  In other words, the "gravitational potential" (Ω, in Silberstein's "letter to the editor") is not obtained from Newton's Theory of Universal Gravitation, but from the metric obtained from General Relativity.” That does not worry me because of the equivalence between different languages for tidal gravity that I have mentioned to you earlier, so it all stays within the realm of mathematical modelling updates.

    ...

    Roger



    Roger Anderton (not verified) | 05/30/12 | 06:00 AM
    Halliday
    Roger:

    I find the following comment, of yours, quite interesting, especially in light of you criticizing me for my disparaging comments about the "popular press" (emphasis added):

    ... In 1919 the newspapers hailed that there had been a revolution in physics that Newtonian physics had been overturned, this was a gross distortion of the facts, there had been no such thing. All it was – was a total disregard of how science should be performed for the sake of making up a story to sell newspapers. As Einstein and Eddington were initially pointing out – it was merely an update to Newtonian physics. The misreporting by the news media has done a great disservice to science leading people to have philosophical beliefs that are not proper science, and a failure to recognise that at its foundational level modern physics is still based on Newtonian physics. ...

    So, your answer to my question ("Have you not noticed, for yourself, the penchant of the 'popular press' to overly simplify?"), above, must be a resounding YES.

    David

    Halliday
    [Since Roger Anderton seems to have difficulty understanding, or, at least, using a threaded forum, such as we have here, I've edited his message to retain only the portion of his comment that pertains to my message, above.]
    Roger J. AndertonDavid
    ...

    You say: “So, your answer to my question ("Have you not noticed, for yourself, the penchant of the 'popular press' to overly simplify?"), above, must be a resounding YES.” OK it is a yes, but I place most of the blame on the scientists involved, they are not accurate in what they tell reporters. The main point is that they have not been accurate in reporting on Einstein's relativity to the press, and instead have presented myths. There was no change from Newtonian physics, it was merely updates and presenting the myth utters confuses physics students. It should be taught in logical fashion – starting from Newtonian physics and then explained the steps that led to Einstein's physics, not presented as a myth of some radical change.

    Roger

    Roger Anderton (not verified) | 05/30/12 | 06:00 AM
    David - if you are going to move people's posts around or edit them, as of course you know, the system insists on replacing their avatar with yours. I don't think you can do anything about that but I would suggest you insert theirs as a simple picture near the top - it gives the lazy brain a visual cue :)
                                                                                                                                                                                                                                                                                                                                 
    Halliday
    Derek:

    Yes, I truly wish there were some way to move or edit someone's post without making it "mine".

    Of course, your avatar suggestion would be good, except that "Roger Anderton (not verified)" doesn't have any avatar.  Even using the "no avatar" avatar would be different than what non-users, such as Roger, show up as.

    Of course, I suppose I could use his actual "mug" found at http://www.worldnpa.org/site/member/?memberid=950.  Namely:

    Roger J.Anderton

    David

    P.S.  Unfortunately, having tried that, above, it sure makes Roger and I look "chummy".  :(

    P.P.S.  I've been able to make us look not quite so "chummy".

    Halliday
    Roger:

    While scientists are human, so we do, on occasion, see them engage in overt self promotion, that doesn't seem to be what you are "blam[ing]" them for.

    So, "the scientists involved" are to "blame" for "the penchant of the 'popular press' to overly simplify?"

    Or, to go from your comments, above, "the scientists involved" are to "blame" for the newspapers' "total disregard of how science should be performed for the sake of making up a story to sell newspapers"?

    Yeh.  Right.

    Now, as for scientists "reporting on Einstein's relativity to the press", or any other no-trivial scientific topic.  Have you ever tried to explain any non-trivial scientific topic to someone in "the press", or even most any member of the general public?

    If you had (or have) you would have noticed that their eyes tend to "glaze over" very quickly!  They tend not to want such "details".  They seem far more interested in "sound bites".  (Even more so now than in Einstein's day, it would seem.)

    Yeh.  Lay the "blame on the scientists involved".  Right.

    David

    P.S.  I'll use another message to address your assertion that "There was no change from Newtonian physics, it was merely updates", and that "It[Einstein's relativity] should be taught in logical fashion – starting from Newtonian physics and then explained the steps that led to Einstein's physics, not presented as a myth of some radical change."

    Gerhard Adam
    Sorry, David.  I deleted that post since it was just spam that was linking to a site to sell jackets.
    Mundus vult decipi
    Halliday
    Actually, he did it in a more "cleverly concealed" way than most do.  (Probably too concealed to be of much benefit to him, I suspect.)  However, while I was considering simply deleting it, I figured I would give him a chance to respond on topic, first.
    Gerhard Adam
    Unfortunately most of those posts aren't actual individuals, so you'd wait forever to get a response.
    Mundus vult decipi
    Halliday
    I certainly wasn't going to "wait forever", only some reasonable amount of time.
    Gerhard Adam
    When I encounter them, I can leave yours alone.  Normally if they link to a marketing site, they're history.
    Mundus vult decipi
    Halliday
    No problem.
    Here was me thinking this was a scientific discussion, then it turns out to be self-absorbed pseudo-intellectuals posting about avatars and forum etiquette. :( Sad.

    The reason I was interested in this forum was because the opening statements, concerning the way Relativity is currently taught, resounded very strongly for me. I agree that current teaching is, as you stated, David, opaque, confusing and giving the appearance of complete 'hokey'.
    Your response was condescending to say the least and not conducive to any attempt on my part to enlighten you.

    Halliday
    Ken:

    You have yet to provide any actual attempt at "enlightenment".

    If you actually wish to enlighten, then, please do so.

    David