What's Wrong With 'Relativity'?
    By Johannes Koelman | December 26th 2010 10:18 PM | 27 comments | Print | E-mail | Track Comments
    About Johannes

    I am a Dutchman, currently living in India. Following a PhD in theoretical physics (spin-polarized quantum systems*) I entered a Global Fortune


    View Johannes's Profile
    In his book "Everything's Relative - And Other Fables From Science And Technology" Tony Rothman writes:

     "[The term] 'special relativity' is probably the greatest misnomer in the history of science"

    I wholeheartedly agree. Amongst all scientific terms, the single word 'relativity' stands out as absolute record holder for triggering an astonishing amount of utter nonsense. 

    It was not Einstein but Max Planck, who introduced the term 'relativity theory'. That was in 1906, the year following Einstein's annus mirabilis. Despite Einstein's opposition, the name stuck. Years later Einstein surrendered, and from 1911 onward he started to use the term 'relativity theory' himself. But he never felt comfortable with the term, and in his writings he always put the words in quotes.

    'Relativity theory' deals with the description of physical phenomena in space-time, and the shadows these phenomena cast in space as well as in time. These shadows is what we tend to perceive, yet they are not absolute, but rather dependent on one's point of view. However, by quantifying these phenomena not in terms of these shadows, but in terms of an objective space-time formulation, an absolute description emerges. 

    So, the strength of 'relativity theory' is that it identifies space-time invariants, absolute values independent of point of view. It is for this reason that 'space-time invariants theory' would have been a much better description for Einstein's brainchild.*

    Sounds like hanky panky?

    Let's bring the issue into the realm of everyday phenomena. 

    Pythagoras - The First Relativist

    Imagine two persons, Alexios and Berenice, attempting to quantify the size of a straight fence. 

    Alexios makes the claim "If I take 20 steps sideway, I reach one end of the fence, and if I make 15 steps forward I reach the other end. The fence is 20 steps wide and 15 steps deep."

    "You are wrong", answers Berenice. "I carefully counted my steps: it takes 24 sidesteps to reach one end, and 7 steps forward to reach the other end. The fence is 24 steps wide and 7 steps deep."

    Along comes a guy named Pythagoras. "You are both right", he declares. "I happen to have studied this situation. The length of the fence is invariant and objective, but your measurement outcomes in terms of steps sideways and steps forward will depend on your orientation."

    "Wow, that's weird" Alexios remarks. "How can we both be right? Our numbers are different, Berenice is telling me the fence has shrunk in depth and dilated in width!""

    "Well" answers Pythagoras, "as strange as it might seem, there is no real contradiction. According to a theorem I derived, your descriptions of the fence are relative, yet the fence itself is absolute and.."

    ".. Ahh, it's all relative?" interjects Alexios.

    "I like that term!" exclaims Berenice. "Let's call his theorem on fence compression and dilation 'the relativity theorem'!"

    "Good idea", confirms Alexios. And off they went.

    Amazing Alignment

    Suppose this theorem you learned at math classes would have gone under the name Pythagoras' relativity theorem. Would that have triggered a whole industry of misapplication of this mathematical result ranging from simple crackpottery to straight abuse on moral matters?

    That seems very unlikely.

    As Hermann Minkowski clearly demonstrated, Einstein's theory is a straightforward extension of Pythagoras into the realm of space-time. And this in itself stresses a key difference between Einstein's results and plain-vanilla Pythagoras. The latter is intuitive as it refers to space only, while Einstein's theory applies to space-time and is highly counterintuitive.

    We are used to rotating yardsticks in space so as to conveniently measure the length of fences. Yet, we are much less used to rotating yardsticks in space-time. 

    Rotations in space-time correspond to changes in speed. So we are talking about measuring sizes when speeding along the object to be measured. And the issue is: in our daily lives we never speed. For all practical purposes we are at standstill compared to each other and compared to the objects around us. 

    In other words, referring again to the fence analogy that made it clear how orientations influence measurements: we take space-time measurements only in one orientation. This space-time orientation is common amongst all of us, and we refer to it as the orientation 'forward in time'. During our lifetime we typically move some seventy years in this direction. Yet, we hardly explore any of the orthogonal directions. The furthest some humans have gone away from other humans in these orthogonal directions is about a second. And we are talking here about the very few selected individuals who made it to the moon. A huge concerted effort and lots of tax money brought them about a second away from the seventy year long path that is provided to all of us free of charge. 

    We might have hugely different opinions and strongly orthogonal views, when it comes to our path in space-time we are better aligned than a laser beam. All seven billion of us, no exception!

    Space-Time Pythagoras

    Lacking the capability to freely orient ourselves in space-time, we also lack the intuitive notion of space-time rotations. We are like Alexios, but without the benefit of a Berenice who can challenge his point of view. 

    But there is one difference between us and Alexios and Berenice: for more than a century now, we have a consistent picture of space-time rotations, and we know exactly how to measure space-time distances despite the fact that we lack diversity in orientation. 

    Key is to measure both space and time directions just like Alexios and Berenice measured width and depth. Using these measurements, we reconstruct the true space-time size using Einstein's space-time Pythagorean theorem. Recalling Pythagoras for spatial measurements:


    the space-time Pythagorean theorem differs in one important aspect: time and space behave differently thereby causing opposite signs in the sum of squares on the right-hand side:


    Note that we have identified the space-time size as 'aging'. Where in the fence analogy the true size of the fence is the size measured along the direction of the fence, similarly in space-time true size is measured by orienting the measurement device in the same space-time direction as (i.e. moving along with) the object. As remarked earlier, this direction is the time direction common to the object and the observer. 

    What this equation tells us is that while different observers might measure different durations and different distances of a path in space-time, they will all agree on the difference between their squares, the aging along that space-time path.

    More Pythagorean Relations

    The beauty of Einstein's theory is that it applies more widely than just to distance and duration. Other physical parameters span similar four-dimensional spaces (referred to as Minkowski spaces) to which the same relativistic Pythagorean theorem applies. 

    A well- known example is provided by the physical parameters conjugate to time (energy) and conjugate to distance (momentum). So we have a relativistic Pythagorean theorem for energy-momentum space that reads:


    Again, the left-hand side and right-hand side of this equation are invariants: quantities independent of point of view. Mass is an objective quantity and so is the difference between the squares of the energy and momentum.

    For small relative velocities between object and observer (and as remarked above, we are invariably in a state of rest compared to all sizable objects around us), this reduces to:


    An equation most people are more familiar with when a conversion factor c^2 related to the use of clumsy units is included. 

    Relativistic Pythagorean theorems also extend to electromagnetism and are deeply rooted in quantum field theory. In fact, all of modern physics is formulated in a space-time description that unifies a huge range of physical concepts. 

    Whatever the name, 'relativity theory', 'theory of absolutes', 'invariants theory': modern physics is unthinkable without the Pythagorean space-time theorem. 


    * A proposal along these lines was actually made in 1910 by mathematician Felix Klein.

    The Hammock Physicist on: E=m.c2, Entropic Gravity, Entropic Force, Shut Down LHC?, Game Theory, Metric Vs Imperial, Big Bang, Dark Energy, Chaos And Time's Arrow, The Physics Arena, Square Root Of The Universe, Physics In A Nutshell, The Longest Path, Hotel Boltzmann, Quantum Telepathy, Quantum Viruses, QHD, Fibonacci Chaos, Counting A Black Hole, Entropic Everything, God, Godel, Gravity


    I don't think that the term is really responsible for the confusions and myths: people's oversimplified viewpoint on anything in science is the culprit. Relativity *does* imply that aside from many new absolute things - and new formulae for absolute things - some things such as motion and simultaneity become relative even though they may have been absolute at some point.
    Quantum mechanics is not called "spiritual mechanics" and some people still summarize it by saying that it makes the whole world controlled by ghosts, or whatever they say. ;-) The terminology is not the main culprit here.
    Johannes Koelman
    No one should be surprized that the advent of quantum physics led to an avalanche of myths and mystifications. Give that theory any name and exactly the same would have happened. Quantum physics is highly enigmatic in the sense that when approached with a classical physics mindset (a mindset that seems deeply rooted in our genes) it forces upon us the very question what is reality?

    But none of this applies to Einstein's theory. Relativity theory is a straightforward application of classical physics to a wider four-dimensional perspective. No enigmas. Yet, mystifications have caught on, also in the area of relativity theory.

    So I agree, there are some who always will prefer mystification over understanding: they simply don't want to get it. My point is that the term 'relativity theory' (as opposed to a term like 'invariants theory') has given those folks plenty of opportunity.
    Relativity theory recognizes the observer relatedness that is yet further made concrete by quantum mechanics, which in its most advanced form is Everett's relative state description plus decoherence. Any further advances are going to go yet more relative to a degree that can be justifiably called subjective (not just how the observer moves, not just how the observer observes, but what it believes). You focus on those aspects on which the relative can be described as such, the new substance that is underlying the relativity inside a description, the absolute that is in retreat like the god of the gaps. You like space-time to be the absolute thing, which is a big mistake (even if based on an Einstein ether, perceived space-time points would not be ontic) and maybe the multiverse underlying the relative state description is something absolute to you today (at least that is the gist of your post today - which is strangely conflicting with your usual emergent gravity agenda). I think the philosophically mature and scientifically most promising way is to get comfortable with relativity instead. It is called relativity theory for a good reason - even if the initial pioneer did not quite get it - but he did not get a lot of things that we know nowadays - physics has come a long way since and pioneers seldom quite grasp where it all ends up.
    I really like the way Minkowski spacetime is introduced here.  Now I’m trying to get my head around the squares of momentum and energy being of the same dimensions.  I must turn to G.Venkataraman’s At the Speed of Light (easiest to get hold of if you have a friend in India.)

    I’m glad you mentioned Felix Klein (1849 – 1925).  I first read seriously about him in Felix Klein and Sophus Lie by I.M.Yaglom, translated from the Russian (Birkhäuser, ISBN 0817633162).

    In later 19th century Germany, there were two main schools.  One was the highly formal, analytical Berlin school dominated by Karl Weierstrass (1815 – 1897), and it is their approach which still dominates university mathematics teaching to this day.  The other was the Göttingen school, headed by Klein, who were much more imaginative and intuitive.  They have proved much more productive for physics, for example the groups discovered by the Norwegian mathematician Sophus Lie (1842 – 1899) (pronounced “Lee”), are all over particle physics.  

    If you can get hold of the book, it is well worth reading.  The only mistake I found in it, which is rather relevant to the present context, is that he refers to Iamblichus (ca 245–325) as a Syrian Christian, whereas he was a leading Pythagorean, and it is his book On the Pythagorean Way of Life which is one of our main sources concerning Pythagoreanism.

    But it was searching for works by Felix Klein I came across Greek Mathematical Thought and the Origin of Algebra by Jacob Klein.  From this I extracted the following discovery by François Viète (1540 – 1603).


    Note Viète’s pre-Cartesian notation: B in F means B × F.  It was good in its time, but Fermat’s use of this pre-Cartesian notation did not help him in his struggle with Descartes.

    Here we have what could have led to an earlier grasping of complex arithmetic, if it had been followed up.

    Certainly this is a most excellent article.  Hammock time can be productive!
    Robert H. Olley / Quondam Physics Department / University of Reading / England
    Johannes Koelman
    "I’m trying to get my head around the squares of momentum and energy being of the same dimensions."

    Think about it like this: velocity is nothing more than a direction in space-time. And directions don't carry a physical dimension. And if velocity is dimensionless, it follows that space and time should be measured with the same yardstick. And similarly mass, energy and momentum.
    Time and space are often presented as kind of equals or peers, where time is a sort of the fourth musketeer. That is to say, we live in a four dimensional world and time is just one of the four dimensions. For some time now I have been convinced that time is not on the same level as space, but rather that time is more fundamental than space. To put is another way, I see space emerging either from time itself or from a common ancestor with time but at a later branch. I won't go into my reasoning here. I just bring it up to note an interesting variation on the Pythagorean relations Johannes so aptly presented here. In particular consider this one: AGING^2 = DURATION^2 - DISTANCE^2 Here it has been suggested that AGING is the invariant and therefore fundamental and that DURATION and DISTANCE are variable and relative. However, as Johannes points out and then dismisses, the equation is in the wrong format. The invariant hypotenuse is supposed to be sqrt of the SUM of the squares of the other two sides, not the DIFFERENCE. So now look what happens if we rearrange the equation to the correct form: DURATION^2 = AGING^2 + DISTANCE^2 Suddenly, when the equation is put into the correct form for the Pythagorean relationship, time becomes the invariant hypotenuse, leaving AGING and DISTANCE as our relative variables. Johannes chose the term AGING as the observers journey. I would prefer a word like STORY or HISTORY or LIFE EXPERIENCE. Whatever term we use for that third variable, it is interesting to consider time as the invariant which can present itself as different stories taking place in different locations. Likewise, take a look what happens to the MASS, ENERGY, MOMENTUM equation: MASS^2 = ENERGY^2 - MOMENTUM^2 As written, this equation suggests that mass is the invariant and is therefore more fundamental to energy and momentum. Rearranging to fit the Pythagorean formula we get: ENERGY^2 = MASS^2 + MOMENTUM^2 Here we see that when the equation is written in accordance to the Pythagorean relationship, energy is the invariant hypotenuse and that mass and momentum are relative. We know momentum is relative because it depends on velocity. Like time and space, mass and energy are often presented as equivalent. However, if you had to choose one to be the invariant hypotenuse, thereby identifying it as the fundamental, wouldn't you choose energy? I would. In summary, it seems to me that if you have a theory that identifies absolutes, which I think was the point of this article, I would have voted for Time and Energy as our winners, not Aging and Mass. But maybe that is just my bias :-)
    Citizen Philosopher / Science Tutor
    Johannes Koelman
    Steve -- the whole point of the Pythagorean theorem for space-time is that there has to be a minus sign associated with the time dimension. That is how time is different from the other dimensions.

    It is the space-time theorem that is more fundamental than the theorem we all learned at school. Not the other way around. When the space-time Pythagorean theorem is applied to spatial orthogonal directions only, you get all plus signs as a special case. But hidden in there, there still is this minus sign, albeit not visible as it multiplies a temporal distance of zero.

    When reshuffling terms so as to get all plus signs, you are morphing the equation into a special case that causes the invariants to evaporate from the equation...
    Johannes, I really like the way you showed that a theory of relativity is also a theory of absolutes, in that by identifying that which is variant, you also identify that which is invariant. It is not clear to me, however, if you see the same implications as I do that follow from that. As I see it, the variable you identify as invariant must be more fundamental than the other two. Do you see that as I do? Perhaps you disagree. I am coming from a perspective of evolution/emergence and I am constantly looking for evidence for the order of emergence. Seems to me that something you identify as invariant must be more fundamental than the set of orthogonal variables that compose its components.

    If you do buy into that implication, then that would make mass more fundamental than energy. Do see mass as more fundamental than energy? Perhaps you see mass and energy more as a duality like particle and wave, neither having preferred status. However, your equation does give one preferred status. That is what I am pointing out. What significance would you give to a property that is invariant in terms of being more or less fundamental? Does its preferred status in the equation say anything in this regard?
    Citizen Philosopher / Science Tutor
    Johannes Koelman
    "As I see it, the variable you identify as invariant must be more fundamental than the other two." Yes, and no. (There is always a 'but...') The invariant is obviously more fundamental than the individual components on the right hand side. However, the components on the right hand side combined into a space-time vector is as fundamental as the invariant on the left hand side. In other words: the length of a vector is as fundamental as the vector itself. The individual components of that vector are, however, observer dependent. This holds true for vectors in space as well as for vectors in space-time.
    Johannes, I see that you are right in saying that the hypotenuse cannot be more fundamental than the other two sides taken in combination, since they represent the same thing. Where I went astray, and I believe Robert as well, is in taking your equations to be as statement about the relationship among different properties. I should have known better, and Robert's post above should have reminded me. Of course all terms in the equation have to be in the same units. So for instance, we should point out to the casual reader, that you are not saying KG^2 = Joules^2 - (KG-M/S)^2. Your equations leave out, or rather imply, conversion factors. The fuller statement would be that MASS converted to energy then squared is equal to ENERGY squared minus MOMENTUM converted to energy, squared. Now I can see, of course, energy on the left is not more fundamental than energy on the right.

    That still leaves us with trying to understand the significance of the invariant as opposed to the observer dependent measurements. The equation involving time and distance is not so hard. It is usually presented as saying two observers will differ in their measurements of time between two events and distance between two events but will always agree on a SEPARATION between two events when time is converted to distance using the speed of light as the conversion factor and combining that with the distance measurement as the other orthogonal side. That is, the SEPARATION between two events is absolute, even if the separate measurements of time and distance vary with the observer.

    In the case of MASS, ENERGY and MOMENTUM, what are we saying? Is it rest mass converted to energy by c^2 is invariant but total energy and kinetic energy are observer dependent? Do I have that right? If not, what do these three terms represent when converted to common units, as they must be in your equations?
    Citizen Philosopher / Science Tutor
    Johannes Koelman
    "In the case of MASS, ENERGY and MOMENTUM, what are we saying? Is it rest mass converted to energy by c^2 is invariant but total energy and kinetic energy are observer dependent? Do I have that right? If not, what do these three terms represent when converted to common units, as they must be in your equations?"

    Steve -- there is much more to be said about the mass-energy- momentum relation. In one of my next blogs I will go in more detail on the meaning of this equation and discuss the implications of energy-momentum conservation. But a few words on the interpretation of the various terms: ENERGY is total energy, and MOMENTUM is total energy times velocity. If you are on a speeding train that passes by the platform where I am standing, we will disagree on the total energy of the train, and also we will disagree what is the momentum of the train. We will agree, however, on what is the root-square-difference of the total energy and momentum.

    On units: if you insist on working in non-rationalized units, just put in conversion factors c where needed.
    In the intended article, can you squeeze in an explanation of the potential energy of a mass at rest.
    Patrick and I were discussing this just yesterday, and both seem to agree that the teaching is wrong, since it is suggested that a body on the edge of a cliff has potential energy, but after it has fallen off, it has none....the question is, 'Surely the potential energy is just observer dependent, and a useful fiction for mechanical engineers and the like, but not really useful to physicists?'
    Another point is, that there is no instrument capable of measuring potential energy, since it is not stored within the atoms of the mass
    We both realise there is a connection with the 2nd law of thermodynamics at impact, and that kinetic and potential energies are different
    Interesting discussion with Steve, and an easily made misunderstanding - it seems to me that my old maths teacher's maxim of 'apples on one side of an equation never equate with oranges on the other' has stuck quite well

    Actually, Aitch, if I may jump in, potential energy if very real and useful to physicists, just as much as kinetic energy and mass energy. Think of potential energy as the energy stored in a stretched rubber band or spring. If you let go, the will be movement. You can measure the amount of potential energy released by measuring the amount of kinetic energy gained. Gravitational potential energy works the same way. Gravitational attraction is like a stretched spring. When released, two bodies will accelerate toward each other, gaining kinetic energy at the expense of potential energy. In other words, the potential energy is converted to kinetic energy. A simple pendulum also provides a nice illustration. When the bob is at its maximum height, it is momentarily at rest. It has zero kinetic energy at that moment and maximum potential energy. When the bob is at its lowest point it has the maximum kinetic energy and minimum potential energy. One has been converted to the other.

    Mechanical potential energy is not the only kind of potential energy. There is chemical potential energy stored in batteries and gasoline. Surely you would agree that in these cases potential energy has some real meaning. On an atomic level, this chemical energy is electrical potential energy between electrons and protons, and in the rearranging of these "stretched springs" much energy can be converted from potential to kinetic (making your car go, for instance).

    Hope that helps.
    Citizen Philosopher / Science Tutor
    Johannes Koelman
    Aitch -- you highlight a very fundamental issue: gravitational potential is not localized. But that doesn 't necessarily mean it is observer- dependent. I discussed this issue recently (see here) and elaborated on the idea that this potential energy is strictly holographic. Have a look and let me know in case of any remaining questions.
    All Bullsugar- Einstein should have stuck to playing the fiddle at coffee shops in Europe.
    "C" was flavour of the month back 100 years, combined with a NON existant entity-TIME.
    Any schoolboy Science 101 can show Time cannot exist by non equivalence of Units, the basic test in Any formula.
    Now turned in to a Giant Incestuos fantasy of Non truth.
    Get back to REAL Math & Physics, to advance.
    So Many errors in Physics- hard to know where to start to destroy.

    "...Bullsugar... back 100 years...Time cannot exist...So Many errors...hard to know where to start...."

    :-) That is so (unintentionally) funny.
    Citizen Philosopher / Science Tutor
    Johannes, I really appreciate your hanging in there with me. Things are getting clearer, especially the equation relating to the time between two events. It is often stated that there is no preferred frame of reference. However, your equation (well, Einstein's equation) shows that is not true. The observer who is present at both events is the preferred observer. He can directly witness both events and will always measure the invariant proper time between those two events. All others will "observe" one or both events only indirectly (that is, at a distance) and as a consequence measure a time that does not agree with the invariant proper time. However if they also measure the distance between the two events in their own frame of reference, they can use that distance measurement to make a correction to their measured time and calculate the actual invariant (dare we say absolute) proper time. In any case, I wholeheartedly agree with the main point of your article which is NOT EVERYTHING IS RELATIVE. This is such a persistent meme. I think it all goes back to the "God is dead", "there is no inherent purpose to life", "evolution has no direction", "the universe is winding down", existentialism, positivism, "everything is observer dependent", "we create our own realities", non-deterministic universe, randomness, entropy, chaos rules, "so let's party" and "don't tell me what to do", because "my truth is as good as your truth" culture that in my view is essentially just adolescent narcissism gone wild and mainstream. We need to grow out of that. Recognizing that some things are absolute is a good start. Thanks.
    Citizen Philosopher / Science Tutor
    Johannes Koelman
    Steve -- you're welcome, and I think you got the message I wanted to convey in this blogpost! :)

    An observer co-moving with the object under study indeed utilizes a 'natural' and 'preferred' frame of reference. However, this frame of reference is 'preferred' only in the sense that it leads to more convenient, less tedious computations. Typically, for this observer all spatial components of the various space-time vectors cancel out, and the single component (the time component) of the vector remaining can be identified with the invariant quantity.
    Other (non co-moving) observes have to work out some more math, but will arrive at exactly the same conclusions. So purely focussing on the outcomes of the calculations, there is no preferred frame of reference.
    Hi Steve, I think you are still a little bit confused. Relativity says that you cannot look at space or time alone - essentially these concepts have no 'absolute' meaning in themselves. This is because there is NO preferred reference frame.  
    Observers moving relative to one another (at sufficiently large velocities) will not agree on the space and time components between 2 events, but neither can say to the other that either one of their measurements about space and time are the CORRECT measurement. But the 2 observers do measure the same space-time interval. So space-time intervals are invariant and therefore fundamental to Einstein's conception of the universe. This is what I think Johannes was trying to convey with this post.
    OK, it may be about philosophy or emotional preferences but I would disagree with this interpretation, and if this interpretation were the point of the original text against the term "relativity", I disagree with the original text as well....

    There is nothing "incorrect" about measuring spatial and temporal coordinates in a specific reference frame. In fact, this procedure is pretty much necessary to describe the location of any event.

    Now, there are many reference frames one can use, and none of them is privileged relatively to others, but this multiplicity does *not* mean that one is not allowed to use any reference frame or that a particular reference frame is "incorrect".

    Clearly, *a* reference frame is needed to parameterize events. Coordinates themselves are not independent of the reference frame; the invariants such as the proper length or proper time - the actual length of a line in spacetime or area of a world sheet etc. -  are invariant.

    The more events - points in spacetime - one considers, the higher number of invariants one may construct. For N generic points in spacetime, with N being large enough, one may construct 4N-k invariants where k is small - essentially the dimension of the Poincare group, which is 6+4=10 in four dimensions.

    Most of the spacetime is real and most of the coordinates will numerically depend on the observer - they will be relative. This includes some things such as the time separation between pairs of events that used to be absolute in Newton's mechanics, but became relative i.e. observer-dependent in relativity. The velocities are relative i.e. observer-dependent as well - but this fact, underlying the notion of inertia, was already known to Galileo via his non-relativistic Newtonian principle of relativity. ;-) 

    (Funny to add adjectives Newtonian and non-relativistic to a principle of *relativity* by *Galileo*, but that's how the things actually were.)

    However, one may always reparameterize the coordinates into another system - most of which will be invariants if the number of points etc. is large.

    So I don't agree that the term "relativity" is totally wrong. It is as much oversimplifying the situation as the term Invariantentheorie would. Relativity is not all about invariants, either. Specific and convenient enough description of a generic object or process is mostly described by the data and observables that are relative.

    I actually think that many people - laymen as well as lousy theoretical physicists - misunderstand this point, too. This misunderstanding is, in some well-defined sense, the opposite one than the misunderstanding that the article above was trying to criticize. 

    The people I criticize now think that if a theory has a symmetry, they're or we're not allowed to use any concept that fails to be invariant under the symmetry; they think that only invariants are OK. But this is complete nonsense. Physics contains lots of things that are asymmetric with respect to the symmetry - and only the very product, when all objects and processes are correctly transformed, is invariant under the symmetry. To use non-invariant objects for any calculation - especially in the intermediate steps - is pretty much inevitable.  Objects spontaneously violate the symmetry.

    Many important physical properties of a physical system are best understood in a description that brutally violates some of the symmetries such as the Lorentz symmetry.

    Although gauge symmetries have a different status - they're redundances and observable objects have to be invariant - it's still true that the gauge-variant objects are important. They're the whole point of using the description with a gauge symmetry. If we could only use gauge-invariant objects in all intermediate calculations, all of the objects we would use would transform trivially and the gauge symmetry wouldn't really be there. ;-) A gauge symmetry is only "there" if we actually use some redundant degrees of freedom that transform nontrivially - i.e. objects that are not gauge-invariant.
    Hello, Siju, and thank you for your feedback. I do realize that relativity as you present it, is indeed how it is usually presented. That is to say that time and space must be taken as equal co-contributors to space-time. I am not confused by that. I am just disagreeing it, or at least with one small aspect of it. I do not see time and space as being equally fundamental, but rather that time is more fundamental than space. I think this is more in line with the Lorentz Theory (a competing theory that lost out to Einstein's) in which all the observer dependence was due to adjustments in space alone and not in time. For any two events, there is indeed a preferred reference frame and that is the frame in which both events take place in the same location. That observer and that observer alone measures the proper time between those two events.

    Other than that, I do completely agree with those here who say that some things really are relative and must be accepted as such. These include velocity, of course, position, length, some forms of energy and force, and many others. I also agree with Johannes's main point that just because some things are relative, NOT ALL THINGS ARE RELATIVE. I think we both lament how pervasive that meme has become in our culture. (See Steve Davis's articles for another example of a pervasive, destructive meme - the selfish gene or "selfishness as a virtue")
    Citizen Philosopher / Science Tutor
    Hi Steve, Could you explain what you mean when referring to the Lorentz Theory. I've read that Lorentz conjectured actual spacial contraction in the direction of motion to account for lack of aether measurements. Is this what you are referring to? I wasn't aware that he developed a theory around it. In any case, special relativity and what Lorentz proposed are essentially mathematically identical (if I remember correctly). 
    Yes, Siju, I am referring to Lorentz's explanation for the invariance in the measure of the speed of light in all directions. Perhaps "conjecture" is a better word than "theory". (I took my wording from David Bohm's book The Special Theory of Relativity, where he has two chapters devoted specifically to what he calls "The Lorentz Theory". ) We are talking about the same thing, and you are completely right that the mathematics are exactly the same. The data and the mathematics are not in dispute. The difference is in the interpretation of the data and the mathematics. It is the philosopher in me that seeks to find the most satisfying explanation for what we know to be true.

    Furthermore, I do not want to leave the impression that I agree with the details of the Lorentz explanation. Lorentz showed that there may, in fact, be an invariant background ether which would not be detected by any measurements on the speed of light, provided that objects and the rulers we use to measure object lengths both contracted or expanded to the same degree as we move with or against the background ether. The instruments we use to measure the speed of light would be affected in a way that would consistently give us the same measurement for the speed of light.

    I, myself, do not subscribe to the idea of an invariant background ether. However, I do think it is a brilliant insight of Lorentz to point out that, what may seem to be constant - the size of an object or the speed of light, for instance - may in fact be the result of a self-referring measuring system that is itself not invariant.

    The only reason I mentioned Lorentz in the context of Johannes's article was because Lorentz's conjecture depended only on lengths being variant and not time. The MEASUREMENT of time would be affected and therefore time would APPEAR to be variant/relative only because the lengths of the moving parts of our clocks would be affected in a way so as to give us a different reading of time. That is what I meant when I suggested that Lorentz and I somewhat agree that time and distance are not necessarily equals in space-time.
    Citizen Philosopher / Science Tutor
    Thank you Johannes!

    And a great deal of thanks goes out to all of the respondents to your thought provoking posts.

    I'm one of those, mostly, silent readers who you rarely hear from. And, I'm a layman to boot.

    Keep it up.

    I have wondered about something for a while, and this seems as good a place to ask as any.

    Do you think there's any evidence that time isn't a single dimension?

    What I've wondered about is if the time dimension is a sloped plane(if 2d), or maybe helical(3d)? And that inertia is the force of pushing matter up this slope, or of twisting the time dimension. Higher velocities have a larger slope or a larger twist. Also as your velocity increases, and you move up this slope(or time twists), you're moving at an angle to the 'normal' direction of time, this would explain time dilation, the time dimension isn't shrinking, you're move across it at a different angle.

    So this would be a 'physical' explanation for both inertia, and time dilation.

    Never is a long time.
    This particular Pythagorean Relation seems to be more significant than the others.


    Everyone seems to agree it is invariant, even the people who are trying to turn the constants of space time into variables.

    In recent times I've seen this equation offered as the basis for designing starships and opening worm holes.

    More down to Earth, the equation has been tested extensively in particle accelerators and found to be always valid.

    It was developed first by Paul Dirac on theoretical principles, and endorsed by Albert Einstein before it was tested experimentally. Dirac also developed a version for use in quantum mechanics with wave fund\stions and probabilities, so there is a chance that this equation will be the basis for uniting the theories of microscopic things with macroscopic nature.

    Why do you not have doubt about applicability Euclidean geometry to Planck length ?
    Thank you for advance.
    Yuri Danoyan