Banner
    Lucky #7 Snarky Puzzle Answers
    By Doug Sweetser | November 29th 2011 12:31 AM | 28 comments | Print | E-mail | Track Comments
    About Doug

    Trying to be a semi-pro amateur physicist (yes I accept special relativity is right!). I _had_ my own effort to unify gravity with other forces in...

    View Doug's Profile
    Oct 25, Gravity is a Mystery (in words, no equations)
    Snarky puzzle
    Is there a handedness to getting older? Is there a handedness to communication? If there is a handedness to either, how would that effect the arrow of spacetime?

    The Back Story:
    Clocks tick on. The universal march of time has no handedness. Put me in an isolation chamber and I will get older at the same rate as having Thanksgiving with the family. [clarification: as noted in the comments, there is no such thing as a complete isolation chamber, it is one of those unreachable ideals.]

    Space is filled with arrows: this over here, that over there. There is a handedness to communication. Reach out to shake hands that are handed.

    Answer:
    There is a handedness to spacetime, all of the handedness coming from space.

    Discussion:
    There are a few scholars such as Julian Barbour  who make their daily bread pondering the "Arrow of time" problem. If they were forced to work on the arrow of spacetime, the problem could be solved already, and people could move on.

    Nov. 1, RETRACTION: Deriving And Fixing The Force Equations (6/5+1)
    Snarky puzzle. 
    Show how to derive the Coulomb force equation if you start from Gauss's law. If you get stuck, read chapter 28-5 of David Halliday and Resnick, "Physics", part 2.

    The Back Story:
    The most important thing about this blog was the RETRACTION. Not many people do that for their own work. The few examples I know about usually involve fraud. It is too bad this is not more commonplace. How many papers on super symmetry will be retracted should no super particles be found at the LHC? Will any papers be withdrawn if the Higgs stays in hiding?  The number of retractions will probably equal the number of these particles found, zero.

    There were two reasons that motivated my retraction. The first is that I got utterly confused about force. The second was I could not see a way to a proposal with local gauge symmetry. Why is that such a big deal for me? If you have a local gauge symmetry, then there is a conserved charge. Mass is conserved, so that conservation requires a local gauge symmetry in the action. I wanted my proposal to join the club of gauge theories like EM, the weak force, the strong force, and general relativity.

    The snarky puzzle comes from why I don't think I have utterly misled the Science20 community. A valid proposal must be consistent every way one looks at it. I didn't pull that off. The thin slice that is only about fields looks like it got the basics right, that like charges attract for the Newtonian field equations, while like charges repel for Gauss's law.

    Answer:
    Assume a point charge at the center of a sphere. This is a situation where the integral form of Gauss's law makes the calculation easier:




    where S is the surface vector of the sphere. Because the source is a point at the center of the sphere, the two vectors E and S are always in line, and the dot product can be dropped, the angle between the two is always the same (zero). The electric field will always be constant over the surface, so it can be pulled outside the integral. The integral ends up being the surface of a sphere, pure geometry:



    I forget what assumptions are needed to set the constant C equal to zero.

    A force law is used to define the electric field E like so:



    Plug the electric field expression from Gauss's law into this definition of an electric field:



    This is Coulomb's law. Like charges will have a positive force, meaning they will push away from each other.

    Discussion:
    There are always details to worry about. One can define the integral form of Gauss's law so that the factor of 4 pi epsilon bows out of the way. Nature has a habit of using integration constants we might toss away. Should we be concerned about how the vectors are handled in the two approaches? And there are those assumptions one doesn't know about, but might hear about in the comments :-)


    Nov. 8, Can't Buy a Gauge Symmetry 
    Snarky puzzle
    The oh-so-familiar conjugate operator is a tool of the quaternion Wall Street elite hiding in a velvet vector dress. The rectangular box world of Z2xZ2 prefers to divide the world in two. Doodle with these:
    Let the Z2 conjugate *i, *j, and *k do flip two signs:

    Form the following products:

    Just for fun, take the sum.

    The Back Story:
    I have limited experience doing calculations that use the Klein 4-group to form a product. Most well-educated people have no such experience. This is a straight forward calculation.

    Answer:












    Discussion:
    Don't read too much into this calculation.


    Nov. 15, Analyzing Actions: Newtonian G (1/3?)
    Snarky puzzle
    Take Newton's gravitational theory and make it consistent with special relativity, nothing more. Oops, that is a totally unfair question. You have to be as good as  Gupta, Thirring, Feynman, Weinberg, or Deser to take that one technical requirement and end up at general relativity.

    The Back Story:
    This issue was discussed in Chapter 7 of "Gravitation" of Misner, Thorne, and Wheeler. Newton's instantaneous gravity theory had to be wrong. Einstein knew that too. I had thought of general relativity as novel, the key new idea being the general equivalence principle, which is actually two principles, the weak and strong equivalence principles. Yet the way it was presented in MTW, it sounded like one could view GR as a repair of broken Newtonian theory. That strikes me as a disturbing idea.

    <more detail>

    Here are the papers cited in Chapter 7:

    Gupta, S. N., 1954, "Gravitation and electromagnetism," Phys. Rev 96, 1683-1685.

    Gupta, S. N., 1957, "Einstein's and other theories of gravitation," Rev. Mod. Phys. 29, 337-350.

    Gupta, S. N., 1962, "Quantum theory of gravitation," in Recent Developments in General Relativity, Pergamon, New York, pp. 251-258.

    Kraichnan, R. H., 1955, "Special-relativistic derivation of generally covariant gravitation theory," Phys. Rv. 55, 1118-1122.

    Thirring, W. E., 1961, "An alternative approach to the theory of gravitation," Ann.Phys. (USA) 16, 96-117.

    Feynman, R. P., 1963, Lectures on Gravitation.

    Weinberg, S., 1965, "Photons and gravitons in perturbation theory: Derivation of Maxwell's and Einstein's equations," Phys. Rev. B 138, 988-1002.

    Deser, S., 1970, "Self-interaction and gauge invariance," Gen. Rel.&Grav. 1, 9-18.

    I see where I got the repair notion. On page 178, in one of those side comments, the three amigos write:

    Best modification (tensor theory in flat space-time) is internally inconsistent: when repaired it becomes general relativity.

    <end detail>

    Answer:


    Discussion:
    <begin ???>
    Any proposal for gravity must have Newton's law as a classical limiting case. The issue is not Right Law (GR) to Useful Limiting Case (Newton), it is this all-star team of physicists appears to do it the other way (I think I looked at two of the papers, but had trouble following the logic). We have plenty of experiments to tell us that gravity changes both time and space. Newton's scalar theory has only one position to store any information about gravity, and it is how gravity changes time. It sounds to me like the first move from Newtonian theory should be to add potentials such that space can be changed by gravity because we know it is.

    This is one of the core reasons I battle on (and it is a battle, I am frustrated at my limited skills, time, and resources). The first move is critical. The standard opening for GR feels wrong in my gut.
    <end ???>

    Nov. 22, Analyzing Actions: EM (2/3?)
    Snarky puzzle
    Construct a spin 2 projection operator. Two factors of 2 will be required.

    The Back Story:
    Why bother with spin? This was a bullet to the head issue.  A spin 1 field indicates like charges repel for a static field theory, while spin 2 will allow like charges to attract. So says Brian Hatfield in his introduction to Feynman's book on gravity. I was forced to embrace that idea when a well-regarded researcher in gravity let me know I should already know that. I don't think anyone is born knowing such details, but now I must respect this bit of physics.

    Answer:
    On page 39 of "Feynman Lectures of Gravitation", he is discusing a rank 2 tensor, which he then says is behaving like this complex product: 



    The projections are +/-2 and a way to represent spin 2.

    Discussion:
    The math is not too bad. I am glad that professor pointed me to this gem from Feynman, or I might never have been able to approach this subject.

    Doug

    Google+ hangout: 11:00-11:45pm Eastern time, Tuesday-Wednesday. http://gplus.to/sweetser

    This could be an efficient way to exchange a few ideas. If you have a question or two, hangout.

    Next Monday/Tuesday: A Local Gauge Symmetry Found

    Comments

    vongehr
    The universal march of time ... Put me in an isolation chamber and I will get older at the same rate
    If you were truly in isolation cut from all quantum entanglement, you would be gone, just gone, period. There is no "universal march of time".

    Hang on. The universe is in an isolation chamber yes? Whilst I TOTALLY agree that there is no universal march of time, and, in fact, there is no march of time at all, why on earth would you disappear?  Do you mean disappear from observability by the rest of the universe? I am happy to learn why two completely unentangled systems cannot both be perfectly real to themselves, but if that is "a given" in your (OK, I know it's not your own invention) version of QM then you are not going to be understood by most of us here without a bit of explanation. No analogies and no maths please, just a simple model that someone who can, as it were, swallow Schrodinger's cat - and even Wigner's friend with a generous pinch of salt.

    If you have already taught everybody else on this, can you please show me where as I missed it, thanks.
     
    Just one question in advance. I was musing in a traffic jam this morning about this stuff and coincidentally I have just stumbled across a mention of the Von Neumann catastrophe in the context of QM. I would assume this is simply the infinite recursion of observers observing observers? If so, what's the problem? The universe, or rather the maths describing it, is an infinite superposition of superpositions of superpositions ad infinitum.  So what? Why is this a catastrophe - other than the difficulty of doing anything with it mathematically. Is there some reason why this object fails to qualify as "real"?
    vongehr
    What I meant to convey is that one simply cannot isolate Doug Sweetser [or anything else that experiences time (aging)] from the rest of the universe.
    I am happy to learn why two completely unentangled systems cannot both be perfectly real to themselves,
    How can you completely unentangle systems? You may not have set up a certain entanglement that you know about, but anything that interacted is entangled.
    Von Neumann catastrophe in the context of QM.
    The catastrophe seems to describe the involved thinking. ;-) I cannot recommend spending time on it. Stick with Wigner's friend - two or three observers observing each other. That is where the next major insight into QM will happen, mark my words.
    The Stand-Up Physicist

    This sounds like such a 60's idea. Good old classical me, made up of about 70 trillion cells, has all kinds of quantum processes going on, some of which can be accurately described by quantum entanglement. I will never be able to separate my classical self because there will always be measurements to be made. My body temperature never gets to absolute zero for example, so there is radiation going out into space at all times. I will be connected to the big Universe no matter what I do. I'll make a note in the blog.

    Ah, the ambiguity of language!  Unentangled - systems that were once entangled and have been unentangled or - systems that are not, and have never been, entangled. No problem.

    Von Neumann - well I'm happy to go for an infinite regress. Makes things all the more mind-boggling. Experimentally though, I'm sure it won't be long before someone sets up a Wigner's friend experiment if it hasn't already been done. Googling "Wigner's friend" comes up with a depressing lot of hits talking about "paradox" so I'm guessing the point isn't terribly well accepted.
    HenryB
    Answer
    There is a handedness to spacetime
    I can understand a handedness for some particles, or some interactions, but a handedness to spacetime itself!?

    Consider a classical universe with EM and gravity which have parity symmetry.  If these were the only interactions, and the matter was only scalar particles, then I wouldn't expect any handedness.  But there still is spacetime, and you are claiming this inherently has a handedness.  How would the "handedness of spacetime" present itself here?
    How many papers on super symmetry will be retracted should no super particles be found at the LHC? Will any papers be withdrawn if the Higgs stays in hiding?  The number of retractions will probably equal the number of these particles found, zero.
    A good theoretical paper presents a theory and derives some properties and experimental consequences.  While experiment may later show that the theory presented doesn't describe nature, that doesn't mean the paper is wrong.  Summing this up as simple logic: the statement "if A then B" is not falsified by finding A is false.  A retraction or errata is only appropriate if the conclusions of the paper itself are flawed.

    Compare that to your situation.  You made all kinds of incorrect statements and conclusions.  I am glad you realized you made some mistakes.  That is indeed commendable, and yes rare on the internet.  There is no "but" or modifier here, it is commendable.

    Snarky puzzle:  Show how to derive the Coulomb force equation if you start from Gauss's law.
    ...
    A force law is used to define the electric field E like so: F = q E
    This assumption you make here is the crux of the problem (and the same mistake you made when making claims about attractive vs repulsive of your theory).  This is one reason your snarky puzzle is not solvable. You have to assume a relationship between the fields and a force, to make the leap to discussing the force.

    Another reason is you have to assume the curl of E is zero (you need the other Maxwell equations).

    I was hoping you learned this after all the discussion and retractions.  I was fully expecting the answer to this snarky puzzle to be: such a derivation is not possible without additional assumptions, now lets examine those assumptions, etc.
    I forget what assumptions are needed to set the constant C equal to zero.
    Try putting C!=0 and see if it still satisfies your starting equations.

    What is going on here: You only get a "constant of integration" when doing an indefinite integral.  Here you have a definite integral over a surface you have chosen (surface of sphere of radius R).  There is no constant of integration here.  Once you made the assumption that E pointed radially, there is no freedom left and the only solution was the definite integral (so C=0).
    There are always details to worry about. One can define the integral form of Gauss's law so that the factor of 4 pi epsilon bows out of the way.
    For clarification, what is happening when people do that is they are changing their units of charge or epsilon.  There are of course many ways to define the units, and it can get confusing sometimes.  In SI, a 4 pi is absorbed into the definition of the vacuum permeability, mu_0 = 4 pi 10^-7 (N/A^2).  
    This is one of the core reasons I battle on (and it is a battle, I am frustrated at my limited skills, time, and resources). The first move is critical. The standard opening for GR feels wrong in my gut.
    This very much worries me, as it often sounds like your "core reasons" are based on misunderstandings.  There is no real way to actually derive GR from Newtonian mechanics.  We can use our intuition and lessons learned to makes some assumptions and intuitive leaps to get to a new theory, but ultimately one must check that theory gives the correct limits, and more generally check that it matches experiment.  I thought this snarky puzzle had some interesting potential, so let me give what I feel is a more appropriate answer.

    First, is the realization that there are multiple ways one can approach trying to get a relativistic version of Newtonian gravity.  Since GR has stood up well to experiment, I'll focus on some previous attempts so that we can learn from history.  The motivations for a theory are necessarily handwavy, but are there to make it clear how it was approached.

    The arguably most straight-forward means to get a relativistic Newtonian gravity is just to change from
    Del^2 phi = rho --->  (Del^2 - partial_t ^2) phi = rho
    but this leaves questions about rho, so more appropriately 
    (Del^2 - partial_t ^2) phi =T
    where T is the trace of the stress energy tensor (which seems appropriate since classically T = m delta(r - R) for a free particle of mass m).
    This doesn't match experiment.

    Some modifications were presented by Nordstrom.  More interesting for this discussion is his second theory of gravity presented in 1913.
    http://en.wikipedia.org/wiki/Nordstr%C3%B6m%27s_theory_of_gravitation

    It has many things we might naively expect from a gravity theory.  Newtonian gravity is regained in an appropriate limit.  We can have gravity waves.  Spacetime is curved.  Naive expectations of redshift of light due to losing "gravitational energy" hold (matches the later Pound-Rebka experiments).  And since light is 'massless' it does not "bend" due to gravity.

    Of course, it turned out that light did "bend" according to experiments, so GR won out.

    Now some could argue "but it makes no sense that massless light 'bends' due to gravity, GR must have a coupling flaw".  However these are arguments over various handwavy motivations or expectations themselves.  Such arguments are often not very useful.  It is more appropriate to look at things like: is the math correct, conclusions consistent, predictions match experiment, etc.

    A case where it IS useful to look into such thoughts is if you can make the question both wide-scope (learn more widely from the example) yet mathematically precise (learn something concrete and not handwavy).  Is there some general feature that makes light act different in the Nordstrom theory? Well it couples only to T, and EM fields have a traceless stress energy tensor.  Any gravity theory coupling only to T, will give the same spacetime curvature regardless of what electromagnetic fields are in the region.
    Why bother with spin? This was a bullet to the head issue.  A spin 1 field indicates like charges repel for a static field theory, while spin 2 will allow like charges to attract. 

    I think this is another example of where you are taking pieces of things out of context and shoving them together.

    Using your logic, simply seeing J_\mu A^\mu means that it is spin 1 and like charges repel.
    Consider EM:

    L = L_free-matter + L_interaction + L_free-field
    where L_interaction is proportional to J_\mu A^\mu

    sure enough, like charges repel in EM.  But now consider:
    L = L_free-matter + L_interaction - L_free-field
    where all the terms are the same as in EM, so the only change is that one relative sign.

    Using your logic, you would call this spin 1 due to a JA coupling, and say that like charges must therefore repel.  But they don't.  This is essentially how you got your previous theory to be an attractive force (although you introduced other oddities by breaking all kinds of symmetry).

    You could consider this a 'relativistic extension' of Newtonian gravity if you want.  It is linear, like charges attract, there is a local gauge symmetry, and there are gravity waves that travel at the speed of light.  It is however ruled out experimentally.

    I really really hope this isn't what you are going to give next week.
    The Stand-Up Physicist

    There needs to be a hand to have handedness. The sea of scalar particles don't have hands, as it were. Should those scalar particles start trading photons, then the photons traveling through space would have handedness. Wherever there is a curl, there is a handedness. I guess that is what I meant by the "communication", the Maxwell equations have a few curls.

    I followed the line of logic in Halliday and Resnick. I thought that might be the issue, the F = q E, and will be interested to hear what David has to say about it.

    I will go get the references to the actual papers and add it to the blog, so anyone interested can do a more detailed study. I don't think these papers are saying the g_00 term can be viewed as the Newtonian potential, which is both true and not too interesting.

    Consider EM:
    L = L_free-matter + L_interaction + L_free-field
    where L_interaction is proportional to J_\mu A^\mu
    But now consider:
    L = L_free-matter + L_interaction - L_free-field
    where all the terms are the same as in EM, so the only change is that one relative sign.

    Are the L_free-fields identical in both? Are they both a contraction of the anti-symmetric field strength tensor Fuv? I will presume the answer is yes.

    EM is a great and robust theory because it is logically consistent: the field equations provide solutions that can be plugged into the force equations that show like charges repel. Both the L_interaction term and the field strength tensor can be shown to represent spin 1 fields, where like charges repel.

    Now we have the -L_free-field trial balloon. The solutions for those equations, plugged into the force equation, will indicate like charges attract. Since nothing has changed with the interaction term nor the field strength tensor, they still are represented by a spin 1 field, which means like charges repel. This proposal is logically inconsistent, so is ruled out before any experiments need to be done. This is not what I will do next week, which only concerns local gauge symmetry.





    HenryB
    Since nothing has changed with the interaction term nor the field strength tensor, they still are represented by a spin 1 field, which means like charges repel.
    NO!
    The entire point of that was to make you understand that your "reasoning" is flawed.
    Check the math if you don't believe me.  Like charges attract in that theory.
    This proposal is logically inconsistent, so is ruled out before any experiments need to be done.
    The only thing that is inconsistent is your expectations due to your brand of reasoning, and what I am claiming the equations say.  Check the mathematical consequences of that Lagrangian and see who is correct.

    When you meet a result that conflicts with your intuition and expectations, its a sign that there is something to be learned there.

    It seems that more than once, you've realized there is a problem in your theory, but instead of learning what is actually going on, you latch onto something else.  So you realize you made a mistake, but fail to learn from it.  This is not a good habit to have.  You seem to be getting a stronger foundation for classical theories, and you are not presenting your theory as a quantum theory, so why not just abandon these things like "spin" and gauge groups of the standard model?  It is these faulty notions that keep leading you astray, and they have nothing to do with analyzing your theories at the level you present them here.
    There needs to be a hand to have handedness.
    Then it sounds like you are saying the matter has handedness, not space-time.
    Wherever there is a curl, there is a handedness.
    EM is invariant to parity changes.  So there is no handedness there.


    Some signs are arbitrary.  Maybe I could define moving to the west as positive y direction, or I could define it as the negative y direction.  Is this what you mean by spacetime has handedness?


    Those signs are just arbitrary.  As is the arbitrary sign choice in the curl in Maxwell's equations.  Change the sign, and particles still move the same.  It is merely a redefinition B -> (- B' ). Can you measure some effect of this redefinition? No.


    Now consider the standard model.  Setup a situation and watch how everything evolves.  Now setup the initial situation except with a parity change.  Is it possible to measure some effect of this parity change? Yes.  Because there IS handedness in the standard model.

    So when you say something like:
    Answer
    There is a handedness to spacetime, all of the handedness coming from space.
    there doesn't seem to be anyway to make sense of it.

    If the handedness come from space itself, then we should be able to measure it somehow.  Are you saying the equations for your gravity theory should violate parity to meet your expectations?
    The Stand-Up Physicist
    NO!

    I gather we are still in disagreement.

    In your proposal, I all ready agreed the solution to the field equation, plugged into the force equations indicates that like charges attract for the action you wrote. That does not mean the proposal is free of internal inconsistencies. One needs to look at a proposal from other angles.

    What you appear to ignore is the issue of spin.

    I know when I am quoting from authorities, and when I am struggling to make something a little bit new. This is quoting from authorities. I take it you do not own "Feynman Lectures on Gravitation". It looks like Amazon is no longer offering the "peek inside" feature which used to provide enough access to learn the point (pages 29-39). I did scan it for my grad student friend, so if you want the pages in question, send me a private email for a pdf.

    This isn't about any proposal I have made. This is about the action of EM, an utterly consistent theory. In the Feynman book, it is equation 3.2.10 which concerns the spin 1 projection operators as a result of relativistic corrections to a current-current interaction. This is what is built into the standard, Doug-free, EM interaction term JuAu: it is spin 1.

    The second rank field strength tensor Fuv=-Fvu is also mediated by an odd integral spin particle. If it were even, then the sign would not flip on the exchange of the indices. That too is standard, Doug-free EM. One can spot issue concerning spin in standard actions with a little training since no one is born with the skill.

    If you remain steadfast in your belief that one cannot identify any issues about spin by looking at the action, then we will remain at odds on this technical issue. If you start to see spin 1 fields in both the interaction and field terms, the discussion can go forward. If not, it is a stalemate because we agree the force equation for your proposal shows like charges attract.

    Maybe I could define moving to the west as positive y direction, or I could define it as the negative y direction.  Is this what you mean by spacetime has handedness?

    That is essentially it. The description involves arbitrary decisions about handedness. Such arbitrary decisions are not made about time. Another event can be in the past, the present, or the future. There is no basis choice to make for time. There are plenty of options for space: Euclidean, cylindrical, spherical, or something even fancier.

    HenryB
    When you've made incorrect claims before, I and others have taken the time to explain it mathematically for you, and have even given many explicit examples.  Now you are claiming something that I can't counter with math, since your answer is essentially 'yes Henry, I agree your example has a JA coupling and like charges attract, but I am dismissing your counter-example because it is disagreeing with my understanding '

    You've setup a situation that is intractable in the current state.  This reminds me of a crackpot I met once that was fascinating, because he considered himself a defender of relativity but he didn't understand relativity, and there was no convincing him that he was wrong because he took everything that was counter to his understanding as an attack on relativity which he would always remind everyone was well backed by experiment.  To him, relativity was experimentally verified, so anyone that disagreed with him was, in his mind at least, disagreeing with mainstream physics.  It was amazing to watch the combination of stubbornness and contortions he would go through to make his hodge-podge of misapplied tidbits fit.  (This nut also harassed the physics department off and on for two years, so the "fun" wore off after awhile.)

    Anyway, the point is that when two reasonable people get in a situation like this, it seems like to move forward we need to abandon preconceptions (we'll both consider the possibility that we are wrong) and work everything out ourselves (starting at common ground to save time, but not resort to arguing or debating by authority).

    So let's work this out.
    Currently I don't understand what your complaints are, since it sounds to me like you are combining snippets of things you read in an incorrect manner.  So let's start by figuring out exactly what you mean by "inconsistent".

    There are a bunch of easy checks which may be useful later, that I assume we can agree on as common ground:
    1) it has time invariance --> energy is conserved, 
    2) similarly, it also has symmetry for momentum, angular momentum, 
    3) the equations of motion are invariant to the same gauge transformation as EM, 
    4) charge is conserved


    To me an inconsistent "theory" is one which is mathematically contradictory, so it is not always possible to predict the evolution of the system.

    Can we agree that we can solve for the equations of motion from the Lagrangian, and they are consistent in the sense above: there is no ambiguity in the evolution of the system?


    If you don't agree, can you give a specific example to explain your point? 
    I think this is only a fair request after all the examples commenters have taken the time to give to explain their points.

    Use the books and passages to help you or inspire you to come up with an example if you want, but don't refer to them to make your argument.  Make your argument with a simple setup where anyone can work out the math to check if indeed the theory is inconsistent as you claim.
    The Stand-Up Physicist
    Can we agree that we can solve for the equations of motion from the Lagrangian, and they are consistent in the sense above: there is no ambiguity in the evolution of the system?
    I thought I had said I agree with all those points already, but I will say again, yup.


    Here are my additional "areas of agreement" questions:


    1) Do we agree that a spin 1 particle is used to mediate a force where like charges repel?

    2) Do we agree that a spin 2 particle is used to mediate a force where like charges attract?
    HenryB
    I thought I had said I agree with all those points already, but I will say again, yup.
    You can't agree it is consistent, and then claim it is inconsistent due to some misunderstanding you will not explain.  How can I possibly work with that?
    Are you claiming there is a different way to derive equations of motion from the Lagrangian, in some vague way involving spins?  Ultimately, you are claiming you can somehow get to a different mathematical answer.  Are you claiming the action principle doesn't give a unique answer here?  What exactly are you claiming?
    1) Do we agree that a spin 1 particle is used to mediate a force where like charges repel?
    2) Do we agree that a spin 2 particle is used to mediate a force where like charges attract?
    I feel these are very loaded questions since you won't even explain why my counter-example doesn't disprove your claims.  Which means we don't agree on what your claims are or what you are even trying to imply with those statements.  So I will not agree to answers to those as a "common ground", since your understanding of those questions is the very same "misunderstanding ground" that we are trying to address.


    Above you seem to analyze spin 1 as:
    1) a vector coupling, as in j^\mu A_\mu
    2) the field tensor F^\mu\nu is antisymmetric (changes sign when indices are swapped)

    As a classical theory, in EM or this counter-example Lagrangian, neither the matter nor the electromagnetic fields are quantized, and nothing has intrinsic quanta of angular momentum. So I feel it is incredibly inappropriate for you to grab snippets from something else and misapply it while trying to argue by authority.

    If you want to define the above two things as "spin 1", well ... we still have those properties there, and like charges interact.

    Either accept the counter-example or, 
    Explain mathematically why this isn't a counter-example to your claims.
    Give a concrete example.
    The Stand-Up Physicist
    So I will not agree to answers to those as a "common ground", since your understanding of those questions is the very same "misunderstanding ground" that we are trying to address.

    Then this is where we part ways.

    I can imagine the following scenario. A fringe physicist emails me to look into his work. This fellow actually has equations (about half do not). What he is most excited about is his idea he calls "double-working photons". These photons have the ability to do both gravity and EM.

    I would tell such a person to read Brian Hatfield's introduction to the Feynman book (I prefer to argue from authority whenever possible). In there, he talks about scattering calculations for static fields. He says plainly that odd integral spin particles mediate forces where like charges repel. He says plainly that even integral spin particles mediate forces where like charges attract. Those are in not loaded answers. He goes on to discuss spin 0, spin 2, and spin 4 possibilities for the graviton.

    I think an additional constraint has been added: the analysis of an action must be entirely classical and cannot broach any issues that arise in quantum field theory. With that additional constraint, as I have said before, I would be 100% on the same page as you. The thing I have been calling "your proposal" really is the action for gravitomagnetism. So gravitomagnetism as a purely classical theory is a consistent proposal.

    I don't think one is obligated to have a completely worked out quantization scheme and show the proposal is renormalizable before one can bring up issues in quantum field theory. A scattering calculation of a force with spin 1 gives a different message than the classical analysis of the action. That was an issue I brought up directly with someone who did a review on gravitomagnetism. He knew the issue, and how to work around it. In his papers, he did talk explicitly about two signs for charges in mass (I was surprised, but it is still there on the preprint server).

    I cannot give a classical counter-example because there is no classical counter-example, as a classical theory you are right. I cannot give a quantum field theory explanation either, at least that appears to be a requirement of yours. Looks like a stalemate to me.

    As an outsider to this discussion, is the solution as simple as:

    Doug, did Feynman analyze the Lagrangian for EM, showing that it involves spin one mediators and like charges repel ... or did he analyze an entire class of Lagrangians involving spin one mediators (which encompasses Henry's example Lagrangian) and claim that they all result in like charges repelling?

    I assume it is the first, because it is straight forward enough to check that Henry's counter-example does have the properties you claim are "spin one" as well as having like charges attract. So the solution may be as straightforward as Feynman said something which you are taking out of context to apply to theories he was not discussing.

    Maybe try working through Feynman's math with Henry's Lagrangian, and see how that change of sign propagates through.

    A Lagrangian, after applying the action principle, gives an equation of motion. It is currently unclear what other way you are trying to extract an equation of motion from the Lagrangian to claim the like charges will move to repel. It really does appear that the misunderstanding is on your side, since the counter-example is so straight forward.

    The Stand-Up Physicist
    This time, the software trusts you :-)

    Sorry, but Feynman did not analyze the Lagrangian for EM. He investigated the interaction term JuAu. His analysis would apply to any proposal that has a JuAu coupling term.

    This is not about the equations of motions. It is not the Lorentz invariant JuAu even. It is about the phase of JuAu, the virtual currents (Jx Jy). Feynman approached problems differently, this being yet another example.

    I was bitch slapped by someone for this very flaw, writing an action that contained JuAu, hoping it would deal with gravity. He told me to read and understand Feynman's message. I have done that. I didn't have a viable proposal for gravity for a year because of that issue. Henry has insisted I should only use classical analysis. That would wipe out this lesson.


    HenryB
    I cannot give a classical counter-example because there is no classical counter-example, as a classical theory you are right.
    Good. So the issue then rests firmly in your understanding of quantum mechanics. You are essentially claiming that if we quantize this theory, that suddenly particles that once attracted, will now repel.
    (I prefer to argue from authority whenever possible)
    I truly hate this attitude. Hate is a strong word, but this willingness to ignore any contradictions to continue believing a mish-mash of snippets is incredibly frustrating.

    I admit I have made this error myself before. When I was in undergrad I remember having a (series of) discussion where I kept dismissing something that was contradicting my expectations, because I equated it with contradicting a solid mainstream theory. In retrospect, maybe I thought my understanding of the mainstream stance was a bit too weak and so somehow the contradiction was "covered" by some subtly I was missing, but regardless of why, the issue was I remained confident I was correct just because of this "nugget" I had about the theory. Someone finally gave me a counter-example so sweet and simple that it forced me to sit down and figure out what I was misunderstanding. Looking back it seems so obvious: it is possible that both the "contradiction" is correct as well as the mainstream theory, if my understanding of the "nugget" I was parrotting or grabbing from the theory was mistaken.

    You need to accept the possibility that you are wrong in order to learn. If you are being confronted with a clear counter example, don't dismiss it "by authority". For the real issue may be that you are not understanding "the authority" in the first place!
    So I will not agree to answers to those as a "common ground", since your understanding of those questions is the very same "misunderstanding ground" that we are trying to address.
    Then this is where we part ways.
    I'm not saying we cannot discuss beyond classical. I AM saying it is not very relevant here, but now that you agree the theory is consistent classically, but still refuse to accept it as a counter-example to your expectations ... we might as well move onto a little quantum (I don't want to get side tracked into this too much).

    So we know where most of the common ground is now. I was hoping you'd actually take the time to try to make your claims mathematical, since you'd probably see the flaw just writing it down. Especially since if you force ME to go first, I have to guess what your misunderstanding is, potentially just causing more issues. Since you seem timid to go first, let me try a paraphrasing of what Feynman and others probably actually mean, that you are misinterpreting.

    In EM we have an interaction like:
           
    For the purposes of this discussion, for the quantized theory we'll just read the spin off of the index terms. The field A has no spinor index, and one spacetime index. It is spin 1. And because the interaction is linear, the interaction "sign" will change if the charge changes.

    Now let's look at some kind of coupling to a spin 2 field:
            
    The field h has two spacetime indices, and will be symmetric to their exchange. Because the interaction is quadratic in the currents, the interaction "sign" will not change if the "charge" changes.

    With odd integral spin, we can have both "signs" of the interaction, while for even integral spin the interaction will be the same regardless of the "charge sign".

    This is about as close as you can get to your interpretation of the snippets you read.

    Up to this point, discussing purely on spins, it should be clear there is nothing that sets the overall sign. This should also be obvious if you've gained anything from the previous discussions regarding field and force equations ... the sign of the JA term alone is not enough information to figure out if the interaction is attractive or repulsive.

    So to have a theory that ONLY can allow attractive interactions, you'd need an even integral spin field. But the interaction between like charges can be attractive for either type. If you are willing to require everything only have charges of one sign (which you have been doing), then that is not an issue.

    Of course there are other reasons to reject this theory. But I don't want to get into the quantum stuff further, or details on why this theory is not worth it (I'm also not sure I can consistently restrict the charge signs like you wanted to do, which could then lead to a vacuum catastrophe when I look at the energy in the quantum version), because that is not the important issue here. What I want you to get out of this is two things, in order of importance:
    1) You need to stop rejecting concrete math, in favor of "talking points" you've built up or grabbed from various sources over time (especially if you can't reduce these snippets to actual math to check things with yourself, otherwise you can get stuck in an unresolvable situation)
    2) Your various "spin" claims are severely misleading you, and you should just drop them (J \boxtimes A does not give you a spin 2 interaction and is just as linear in J as is J \normaltimes A... grabbing little chunks from the details of a calculation and putting it on a pedestal as some wonderful general definition you can use as a hammer on everything is not a good learning strategy.)
    The Stand-Up Physicist
    I truly hate this attitude.

    Too bad about that. If someone said there was a book that was particularly good about vector bundles and all that jazz, I would probably buy the book tonight. I am aggressive about getting the best sources of information on difficult subjects.

    You need to accept the possibility that you are wrong in order to learn.

    It would be nice to see some indication that you would accept the possibility too. Read ten pages of the relevant book. Oh no, you won't. You just guess at what Feynman said, and well, go figure, you guessed wrong (looks like you were closest to the Hatfield introduction).

    >>So I will not agree to answers to those as a "common ground", since your >>understanding of those questions is the very same "misunderstanding ground" that we >>are trying to address.
    >Then this is where we part ways.
    I'm not saying we cannot discuss beyond classical. I AM saying it is not very relevant here, ...

    My reading comprehension is horseshit. Not agreeing = not very relevant?

    So we know where most of the common ground is now. I was hoping you'd actually take the time to try to make your claims mathematical, since you'd probably see the flaw just writing it down.

    The math was in the previous blog, under spin. I was trying to follow what is better written in chapter three of that book you won't read.

    So to have a theory that ONLY can allow attractive interactions, you'd need an even integral spin field.

    Stop the presses. Isn't that a direct answer to this question:

    2) Do we agree that a spin 2 particle is used to mediate a force where like charges attract?

    All this upset tummy so you finally answered the question after doing your own thinking, the only sort you trust, and we agree. The statement, "a theory that ONLY can allow attractive interactions, you'd need an even integral spin field" sounds extremely relevant. You add the nice touch that both charges could be positive, or both could be negative, but they will end up being attractive. This is progress.

    So what about spin 1?

    For the purposes of this discussion, for the quantized theory we'll just read the spin off of the index terms. The field A has no spinor index, and one spacetime index. It is spin 1. And because the interaction is linear, the interaction "sign" will change if the charge changes.

    So there is a plus and a minus. I will call that progress. I bet in a few lines you might be able to say like charges - whether they are positive or negative - will repel each other. It works that way in EM with the spin 1 photon mediating the force between positively and negatively charged particles.

    This was suppose to be an exercise in seeing where we agree. What I want you to get out of this is two things

    1) I agreed to your four points that the classical action has equations of motion where like charges attract.

    2) You agreed to one and half points on the even spin/odd spin observation.

    Sweetser wrote:
    "The thing I have been calling "your proposal" really is the action for gravitomagnetism. So gravitomagnetism as a purely classical theory is a consistent proposal."

    No, Henry's example Lagrangian is not gravitomagnetism. Gravitomagnetism comes from a non-relativistic limit, of a linearized limit, of GR. There are still remnants of the original rank 2 tensor that show up even after all this (usually as various factors of 2 relative to Maxwell's equations). I don't think there is any way to write a Lagrangian that would give you gravitomagnetism. It would at least look very strange, with Lorentz breaking terms to zero out some tensor components or something.

    Before posting, I checked if there was anything good at wikipedia, and noticed you posted there. You seriously have a hang up on these spin misunderstandings.

    Sweetser also wrote:
    "A scattering calculation of a force with spin 1 gives a different message than the classical analysis of the action. That was an issue I brought up directly with someone who did a review on gravitomagnetism."

    So tell me, what "action" were you using for gravitomagnetism? And how did you analyze it quantum mechanically? I'm betting all that actually happened is you saw something that reminded you of a vector potential, and then you just made leap after leap of your spin misunderstandings from there.

    I'm not sure Henry's example can be a consistent quantum field theory (maybe as a non-relativistic field theory?), but for the level of discussion here I hope it at least makes you realize you should stop trying to jump way ahead into quantum considerations and making all kinds of incorrect claims about identifying spins in various theories (your comments on gravitomagnetism, and your comments on your hypercomplex multiplication giving you a spin two interaction, are two examples). Drop the spin stuff, and get the hang of classical physics first.

    The Stand-Up Physicist

    The gravitomagnetism Lagrange density can be found in "Gravitoelectromagnetism: A Brief Review", equation 1.10. He wrote that with the matter and interaction terms only. The field term has to be inferred from equation 1.7 which as you wrote, has to have factors of two sprinkled in the right places. It is doable, and has been done. Henry's example was not written out in detail. If we infer that Henry meant an exact replica of the EM action with one sign flip on the field term, than I did make an error. It does have the same structure, but factors of 2 and of 2 only are the difference between Henry's action and the one for gravitomagnetism.

    Before posting, I checked if there was anything good at wikipedia, and noticed you posted there. You seriously have a hang up on these spin misunderstandings.

    WTF? I recall once writing something about Schrödinger's cats. I don't think I ever contributed to an article, not even one on quaternions (other people added links to my web site). I "posted" there? Posting sounds like something that happens in forums. I have had discussion in forums, nothing wrong with that. Wikipedia articles get written and edited and fought over. I have not been such a participant. Odd claim there guy. Send me the URL, I am curious.

    So tell me, what "action" were you using for gravitomagnetism?

    The Lagrangian in the paper.

    And how did you analyze it quantum mechanically?

    I wrote the author and asked him. He was quite polite and pleasant. I bet his answers are correct. I will add your name to the list of people who prefer not to read Feynman. I though he was popular.

    HenryB
    This was suppose to be an exercise in seeing where we agree.
    We disagree on some physics and math.  To find out where we agree is just a start, then we should work out the result from there to resolve the misunderstanding of the physics and/or math.  I don't want you arguing by authority, because I feel that is what is leading to this problem in the first place.  I take the time again and again to present examples, explain with math, and give follow up information.  As I've pleaded before, please actually address the counter-example with math. Why do I have to do this song and dance every single time?  Drop your misleading talking points and let's get to the math to resolve this.
    It would be nice to see some indication that you would accept the possibility too. Read ten pages of the relevant book. Oh no, you won't. You just guess at what Feynman said, and well, go figure, you guessed wrong (looks like you were closest to the Hatfield introduction).
    You refused to take the first step, so I started by showing some of math and explaining some logic behind what you can and cannot say about the properties of a theory solely from those coupling terms.  It wasn't what you claimed (even though you seem to think I agreed to 1 1/2 of your statements).


    What if I just responded to everything you said with "Go read book XYZ".  And if you read that, then I said "nope, you are still wrong, read book QRS".  That is the problem with arguing by authority.  It ultimately doesn't matter what they said, or more importantly how we interpret them.  Because we can actually check the math, work it out ourselves, and see if we are actually understanding.

    Imagine for a moment you are wrong.  If your way of resolving a situation is to just argue by authority, then if you are misunderstanding what you are parroting, it is impossible to resolve the misunderstanding.

    Sure I'll consider the possibility that I am wrong, so go ahead and join in by explaining with some logic and math. Stop arguing by third party. This should be very straight-forward stuff. Just spell it out. I don't want to get into an argument over what some other set of people thought and said, which is just another layer of confusion. The math says what it says, and I want to cut directly to your understanding and claims.

    As a sign of good faith, I'll even read your book scans if you want, but I do not want to end up arguing about our different interpretations of the applicability or implicit assumptions used in the analogies and conclusions Feynman makes.  So don't just refer to the book and argue by your understanding of authority.


    Now it is your turn.

    Show how you take a Lagrangian, and determine if like charges attract or repel based solely on the interaction term.  If you do have to refer to the free-matter or free-field terms, then clearly you need to add some qualifiers and state assumptions to modify your claim that a JA coupling means spin 1 which necessarily means like charges repel.
    Henry,
    I think there are a couple issues that are too freely being mingled.
    Layer 1) How do you both define spin, and how do you extract that from a classical theory (especially when Lorentz symmetry may not be relied on, as that appears relevant here)
    Layer 2) Misunderstandings of what can then be said about these spins.

    You seem to be trying to get Doug to realize he is misunderstanding the spin issues with a counter-example to one of his Layer 2 claims. I'm not sure it is even the most appropriate one to go after, since as you and LagrangiansForBreakfast seem to be able to sniff out based on some off hand comments you both gave, there is probably a severe problem with your example Lagrangian as a quantum mechanical theory. (Some searching seems to suggest Lorentz symmetry + Unitarity is probably enough to fix the signs, and therefore give a definitive answer. If that simplistic summary does hold, then if analyzed as a relativistic field theory, I guess the issue is Untarity. As LagrangiansForBreakfast mentions, maybe everything still works okay as a non-relativistic field theory, I'm not sure.) A search also brought up this (only read abstract)
    http://prd.aps.org/abstract/PRD/v33/i8/p2475_1
    which may be interesting as it mentions some other counter-examples.

    Also, GR can have repulsive interactions. I'm pretty sure some energy conditions need to be assumed to get only attractive. So spin-2 can have BOTH attractive AND repulsive interactions in the same theory (instead of just one XOR the other as you concluded). Something in your analysis is overly simplistic.

    My personal opinion / gut feeling, is that nothing is worth discussing here until you resolve the layer 1 issue. There are some serious issues there, since Doug wants to consider terms that cannot be written in geometric notation. Even your simplistic rule of count the space-time indices will fail there.

    The articles don't contain much useful, but I've been following for awhile due to all the interesting information in the comments. Sometimes you and David write out enough that it could make several columns. Keep it up, and don't lose your cool. (If you or David could explain how Unitarity fixes any of the signs, that would be great.)

    I feel compelled to say something too.
    Henry,
    I agree it is clear Doug is misunderstanding a lot about spins, but I think you chose a truly awful avenue to approach this. As you mentioned yourself:
    "But I don't want to get into the quantum stuff further, or details on why this theory is not worth it (I'm also not sure I can consistently restrict the charge signs like you wanted to do, which could then lead to a vacuum catastrophe when I look at the energy in the quantum version), because that is not the important issue here."

    It is indeed very possibly your theory isn't consistent, as Doug said, but because it is lacking a Hamiltonian lower bound and not because of some spin argument. Is the suggestion regarding using a non-relativistic field theory just to avoid anti-particles and pair production? I'm not sure that is a valid leap, but even so would this really prevent ill fate to the theory? You run the serious serious risk of Doug taking away from this that his statement that your theory is inconsistent is correct, but thinking that this means his understanding of spins is also correct.

    You showed a JA coupling can classically attract like charges, everything beyond this I don't think will really be fruitful. Yes you need additional assumptions to make the claims he's making about force dependence on mediated forces, but just give him that lesson and state it all, instead of trying to lead him there. I was enjoying most of the comments up until this thread.

    *force dependence on spin of mediated fields

    The Stand-Up Physicist
    I am calling for a truce/blog devoted to this subject.
    I agree, citing "Read this book" is not a good thing. As I was writing up a "mathy" reply, it required too much content. So I will devote next weeks blog to the interaction term, what one can and cannot say based on taking the classical term, and looking at what one can and cannot say about its spin.
    HenryB
    I didn't realize so many people were following the comments.
    And yes, I did see the Hamiltonian bound issue and that is indeed why I made those comments (I wasn't the one that suggested treating it as a non-relativistic theory though).  I was hoping we could just look only deep enough to see that like charges still attract.  Perhaps by some current-current argument or however Feynman did it.  Or maybe by looking at the energy of a static field configuration such that we can see the energy is lower when like charges are closer.  I frankly could care less if this state is unstable, or about the general fate of the theory, which probably does have a vacuum catastrophe as mentioned.  I don't think even a non-relativistic treatment will save it, but as I said in that quote, I don't really care to waste time with that.

    So yes, I hear your criticisms that I probably chose a horrible approach on this one, and it may just confuse Doug more.  But I really felt a necessary first step was to get Doug in the mode of actually working these things out himself, and break him from the habit of arguing by authority.  I think that is the real common thread in all his confusion here: he takes snippets from things, and to borrow a phrase, "babbles" by stringing them together in a sometimes incoherent collage.

    I mean look at his spin 2 stuff, he claims:
    rho phi - j_x A_x - j_y A_y - j_z A_z  
    in a Lagrangian can mean two different things for spin depending on the notation he used to write that.  This is truly the ultimate in believing some misguided analogy to a snippet over what the math says.  It is so nonsensical, it is not even clear where to start.  You guys are all complaining I should have chosen a different path, fine.  Suggest one.  But I maintain that no path will be fruitful until Doug is willing to trust math over some random "talking point" that he stripped of the context and assumptions that are needed for the point to be useful.  As far as I'm concerned this spin stuff is just the topic de jour, showing a symptom of this same problem that anyone showing some math or logic countering his claims had to face previously.

    If you guys have a better approach, then please suggest another way.
    Maybe focus instead on issues with his interpretation of spin in Gravitomagnetism?  I didn't want to touch that one because his arguing by authority there is even less accessible.

    I'll read doug's scans if he sends them, but I'm taking a break for the next few days.  You guys have made this start to sound like a game of strategy or something.  I don't like thinking like that, so I should step back for awhile.  Why don't one of you nameless try your hand at some nice explanations for everyone.  Good luck.
    sweetser wrote:
    "Wikipedia articles get written and edited and fought over. I have not been such a participant. Odd claim there guy. Send me the URL, I am curious."

    From the gravitomagnetism discussion page
    http://en.wikipedia.org/wiki/Talk:Gravitomagnetism#Equations_are_not_con...
    posted by a user named Sweetser, with the same misunderstanding that you have, is too coincidental. The user wrote:
    "Because the field strength tensor is anti-symmetric, the interaction must be described by a spin 1 field where like charges repel. From the article, I did not get a sense that professionals take the subject with a large grain of salt because gravitomagnetism is inconsistent particularly with regard to spin. ... Maxwell's equations are a spin 1 field and so is gravitomagnetism, which is the source of the problem with the approach."

    As I said before, Gravitomagnetism comes from a non-relativistic limit, of a linearized limit, of GR. It is an approximation of GR, but you seem to be taking it as a proposed replacement of GR. If you are claiming it is fundamentally flawed, you are either:
    1) claiming GR is flawed
    or
    2) making claims that have nothing to do with gravitomagnetism (probably because you are not understanding the approximation)

    Currently it appears #2. If it is actually #1 (which is possible, since you seem to think GR started on a wrong foot or something weird), please let us know.

    Consider the approximations in order. If we linearize gravity, do you still consider this a spin-2 theory? If we now take the non-relativistic limit, this let's us ignore a lot of terms. Is this where you think it magically becomes a spin-1 theory?

    Sweetser wrote:
    "I wrote the author and asked him. He was quite polite and pleasant. I bet his answers are correct. I will add your name to the list of people who prefer not to read Feynman. I thought he was popular."

    From your discussion on spin, it is clear you misread/misunderstood something from Feynman. So you can't really blame us for not trusting your reading and understanding of a discussion from someone else that we can't check ourselves. And truthfully it shouldn't matter what anyone said. You shouldn't argue by authority. If you didn't take the attitude "I bet his answers are correct", and actually try to work out the math yourself, you'd hopefully figure out a lot of your mistakes yourself (mistakes that may be solely in your interpretation of what the 'authority' said, and not mistakes 'the authority' actually made).

    Currently you have this bizarre method of learning by random walk -- where you babble in physics terms, and watch what people write in response. You then adjust your babbling to better fit the expected pattern, and move on before learning any meaning. In a bizarre way, even your _learning_ seems to be a 'by authority' method devoid of thinking. It's like watching a machine learning program try to get through a spam filter. You are a conscious thinking human, so snap out of it and _choose_ to go on the path of actually learning the physics.

    I'm hoping you don't post again on Monday ... a sign that you are finally taking the time to learn before you write the next collumn. I wish you luck if you choose the journey of learning.

    The Stand-Up Physicist
    As I said before, Gravitomagnetism comes from a non-relativistic limit, of a linearized limit, of GR.
    I have written the same thing. I also cited the paper where he says explicitly that he treats the test masses as having a negative rest mass. The reason I requested you look in the paper is because I understand you trust nothing I say. You could have checked that fact yourself. I will respect your wish and not post on Monday. It is Tuesday, so I will post soon enough.
    "I forget what assumptions are needed to set the constant C equal to zero"-http://www.cs.uaf.edu/~bueler/M611heaviside.pdf which assumptions are,please?