Is 2nd postulate of SR necessary?

[Arham]

D.J. Griffiths in his "Introduction to Electrodynamics" writes:

"Some authers consider Einstein's second postulate redundant - no more than a special case of the first. They maintain that the very existence of ether would violate the principle of relativity, in the sense that it would define a unique stationary reference frame. I think this is nonsense. The existence of air as a medium for sound does not invalidate the theory of relativity. Ether is no more an absolute rest system than the water in a goldfish bowl - which is a special system, if you happen to be the goldfish, but scarcely 'absolute.'"

I think Mr Griffiths' argument is not completely convincing. According to the 1st postulate of SR, the laws of physics apply in all inertial reference system. So in any inertial frame of reference, the Maxwell's equations and their direct results must be valid. In any given inertial frame of reference we can obtain the equation of a wave that propagates with speed c (which is a fundamental constant). In any other inertial reference system, the result is the same.

What's your opinion? Are the "some authors" right?

 

[JesseM]

There was a discussion of this a while back on this thread, if you're interested start with DrGreg's post #118 and follow the discussion for the next few pages. My basic position was that the second postulate should be independent of specific assumptions about the laws of electromagnetism (nowadays we know that Maxwell's laws are really only approximate anyway, that quantum electrodynamics is more accurate, although of course it also predicts light moves at c).

 

[Dale]

If you assume that all fundamental physical laws have the same form in any inertial frame and further assume that Maxwell's equations are a fundamental physical law then the second postulate can be derived. But I think that Einstein was trying to not assume any specific physical laws. In any case, what you consider a "postulate" or an "axiom" and what you consider to be derived is rather arbitrary.

 

[Naty1]

You also have to consider that Einstein was a theoretical genius, less so a mathematical one. In addition, the advanced mathematics of today was not even conceived when he developed special and general rerlativity...he was a founder of quantum theory, for example, one of the originators. So what was thought dependent versus independent back around 1905 likely has changed today.

His unique genius with relativity was to piece together pieces of a puzzle in a unique way combining Riemann curvature, Lozentz-Fitfgerald transofmorations,and a rejection of aether theory which was considered to underlie Maxwells equations in the early 20th century. His former professor, Marcell Grossman, discovered the Riemann math Einstein sought after several fruitless years...and made Einstein aware.

You can read Einstein's own account of special and general relativity at:
http://www.bartleby.com/173/

and download his book for free...I'm no math whiz by any means, but reading Einsteins account suggests to me maybe "some authors" have a point. Whether that was clear back when, may be a different question.

 

[Meir Achuz]

I agree with Arham and "some authors" The author of a UG text should not call more advanced texts "nonsense". The argument about the ether that G disputes is not the argument made by some authors. There are subtleties, but I won't go into them here.

 

[JustinLevy]

I agree with Arham and "some authors"

While you can agree with Arham with the opinion "Mr Griffiths' argument is not completely convincing", that does not make the other authors correct. Griffith's is indeed correct.

If you take the first postulate to be:
1] the laws of physics are the same in all inertial frames

then the second postulate
2] the speed of light is the same constant in all inertial frames
is an independent postulate

You cannot derive #2 from #1. To convince yourself of this, all you need to do is realize that statement #1 is Galilean relativity. What Einstein added was a finite speed limit for the propagation of information.

As Dalespam said, you have to "further assume Maxwell's equations" in #1 in order to get number two. In other words, the confusion is some people seem to incorrectly consider the first postulate to be:
1] the laws of physics are the same in all inertial frames and the laws of physics are (insert all laws here)

Again, that is not the case (otherwise relativity is not independent of what we state the laws of physics are, and we'd be constantly changing relativity itself as we learn more about nature).

The modern interpretation is usually to just consider special relativity as postulating: "the laws of physics have poincare symmetry"
This is more direct and to the point, as well as more precise... all contained in one postulate. Plus it is easier to see how this relates to GR, for the global symmetry of SR is still a local symmetry in GR. (I've even ran into some people that feel SR should be stated as local poincare symmetry, for it was clear to many what a "relativistic" metric theory of gravity meant long before GR was solidified. If you take that point of view, SR is always applicable, with Minkowski spacetime as just the simpliest example spacetime to work calculations in. I can see their points, but due to historical reasons I consider "SR" to imply global poincare symmetry, so applying it to a curved spacetime region valid only as a limiting approximation. It is my understanding this is how the majority use the term as well.)

 

[atyy]

Actually, are 1 or 2 axioms our only enumeration options? How about counting the axioms underlying logic, calculus, vector spaces etc. Sorry, I know this is a silly question, but I can't help myself.

 

[JustinLevy]

Actually, are 1 or 2 axioms our only enumeration options? How about counting the axioms underlying logic, calculus, vector spaces etc. Sorry, I know this is a silly question, but I can't help myself.

Physics is, in a not so well defined sense, more than just a mathematical structure. So it is difficult if not impossible to fully axiomize it. I believe in fact that this was one of Hilbert's famous unsolved 'questions for the century'.

Regardless though, relativity isn't an end-all. It is an ingredient to add or require of physical theories. So while we may need many other postulates or axioms to test things, I don't think it is really all that fair to say relativity depends on that much more. (I've seen some presentations of relativity that start with things like postulate 1: we can represent events as points on a four dimensional spacetime ... and so on, expanding out several assumed mathematical structure as multiple "pre" postulates of relativity.).

 

[dx]

The real content of special relativity is the Lorentz transformation and Lorentz invariance. Although it was motivated by light and electrodynamics, it is quite independent of them.

 

[Phrak]

Actually, are 1 or 2 axioms our only enumeration options? How about counting the axioms underlying logic, calculus, vector spaces etc. Sorry, I know this is a silly question, but I can't help myself.

It's turtles all the way down.

 

[Dale]

The modern interpretation is usually to just consider special relativity as postulating: "the laws of physics have poincare symmetry"

I like it since it gets directly to the geometrical interpretation. Is there a good reference for that specific formulation of the postulate(s)?

 

[atyy]

It's turtles all the way down.

Wouldn't that be a preferred reference frame consonant with GR and the CMB? But I think the OP wanted to limit the scope to SR?

 

[atyy]

In other words, the confusion is some people seem to incorrectly consider the first postulate to be:
1] the laws of physics are the same in all inertial frames and the laws of physics are (insert all laws here)

Again, that is not the case (otherwise relativity is not independent of what we state the laws of physics are, and we'd be constantly changing relativity itself as we learn more about nature).

Is this along the lines of the argument you consider incorrect?

Minkowski space-time: a glorious non-entity
Harvey R. Brown, Oliver Pooley
http://arxiv.org/abs/physics/0403088

 

[Fredrik]

Is this along the lines of the argument you consider incorrect?

Minkowski space-time: a glorious non-entity
Harvey R. Brown, Oliver Pooley
http://arxiv.org/abs/physics/0403088

Are you posting this because you've read it and think we could learn something from it? It seems to me that they just filled 18 pages with words that say very little. They don't even clearly define the "dynamical interpretation" that they're comparing with the standard formulation of SR. Yes, I could look at the references, but even if I did, it wouldn't tell me (clearly enough) how they have interpreted this "dynamical interetation".

One of their criticisms against Minkowski space is that it doesn't really explain why the laws of physics are Lorentz invariant. Duh. Of course it doesn't! It's not a theory's job to explain itself. Its job is to predict the results of experiments.

Why did I just say "itself"? What I mean is this: SR is the theory of physics that consists of a mathematical model (Minkowski space) and a set of postulates that tell us how to interpret the mathematics of Minkowski space as predictions about the results of experiments. It's a theory of space and time, not matter. But it's also a framework in which we can define theories of matter. We do this by postulating the principle of least action and writing down Lorentz invariant Lagrangians involving tensor fields on Minkowski space (also spinor fields, when we construct quantum theories of matter). To say that the laws of physics are Lorentz invariant is therefore the same thing as saying that this procedure has so far been successful! How could Minkowski space possibly explain that? It would have to explain itself...and then some! So its inability to do that can hardly be interpreted as a weakness of the theory.

One thing I would tell these authors if they were here, is that if you're going to compare two theories, or two formulations of the same theory, you should clearly define both theories. Write down the axioms of both. If they are mathematically equivalent, prove it. If they aren't, but still make the same predictions about the results of experiments, prove that. Then you would be in a much better position to compare the two, and to discuss what facts the theories can be said to explain.

 

[Vanadium 50]

Are you posting this because you've read it and think we could learn something from it? It seems to me that they just filled 18 pages with words that say very little.

Be fair. The only filled 15 pages with words that say very little. The rest are references. And besides, they are philosophers. It's their job to fill pages with words that say very little.

 

[atyy]

Are you posting this because you've read it and think we could learn something from it? It seems to me that they just filled 18 pages with words that say very little.

Sorry about that. I wanted to post this, but didn't find it online till now, and posted Brown and Pooley's article instead. Not that I think their article is bad, just haven't read all 18 pages, but scanned it enough to find it espousing a view similar to something I had read, but couldn't find:
Bell, How to teach special relativity, p67 of http://books.google.com.sg/books?id=FGnnHxh2YtQC&printsec=frontcover#PPA67,M1

Be fair. The only filled 15 pages with words that say very little. The rest are references. And besides, they are philosophers. It's their job to fill pages with words that say very little.

 

[Fredrik]

they are philosophers.

I actually didn't notice that. That actually explains a lot. I noticed that it had been placed in the category of "history of physics" but I assumed that it was written by physicists.

Bell, How to teach special relativity, p67 of http://books.google.com.sg/books?id=FGnnHxh2YtQC&printsec=frontcover#PPA67,M1

Now that's a much more interesting read. I'll have a closer look tomorrow.

 

[meopemuk]

Minkowski space-time: a glorious non-entity
Harvey R. Brown, Oliver Pooley
http://arxiv.org/abs/physics/0403088

The point made by Brown and Pooley is valid and non-trivial. They basically say this: if special relativity is correct, and if our dynamical theories indeed agree with special relativity, then we should be able to *calculate* the length contraction and time dilation effects within our dynamical theories, and the result should agree exactly with SR predictions.

For example, we could take a relativistic theory of inter-atomic forces and first calculate the equilibrium length of a rod in the reference frame at rest. Then repeat the same calculation in a moving reference frame. If everything is consistent, we should obtain *exactly* the length contraction predicted (but not explained) by SR. Unfortunately, as far as I know, there were no such convincing calculations for the length contraction and time dilation effects.

One may say that such consistency checks are not needed, because SR guarantees that they will be satisfied. However, I don't think that this guarantee is obvious. The 2nd postulate of special theory explicitly refers to the behavior of light or photons (the speed of light is the same in all frames). It does not say anything about other particles - protons, electrons, etc. It doesn't say anything about particles interacting with each other. So, in fact, if one wants to apply special relativity universally to all physical systems, one should introduce a 3rd postulate, which would say that all kinematical relations established in SR (Minkowksi space-time, 4-tensor calculus, etc.) are universally applicable to all physical systems without exceptions.

 

[dx]

Unfortunately, as far as I know, there were no such convincing calculations for the length contraction and time dilation effects.

That's how Lorentz originally calculated them.

 

[Fredrik]

The 2nd postulate of special theory explicitly refers to the behavior of light or photons (the speed of light is the same in all frames). It does not say anything about other particles - protons, electrons, etc. It doesn't say anything about particles interacting with each other. So, in fact, if one wants to apply special relativity universally to all physical systems, one should introduce a 3rd postulate, which would say that all kinematical relations established in SR (Minkowksi space-time, 4-tensor calculus, etc.) are universally applicable to all physical systems without exceptions.

I agree, but this is a weakness of Einstein's postulates, not of special relativity. Einstein's postulates are ill-defined and incomplete. They can't be taken as the starting point of a rigorous proof of anything, and they can't be taken as the definition of special relativity. They should be viewed as loosely stated guidelines that can help us guess what mathematical model we should use in a new (in 1905) theory of space and time.

That mathematical model is Minkowski space, and the only definition of special relativity that makes sense is the one I've been advocating in this forum. SR is defined by a set of postulates that tell us how to interpret mathematical statements as predictions about the results of experiments. Unfortunately, I have never seen a complete list of the postulates that are needed to define SR (remarkably, no physics book I've seen has even attempted to define what "special relativity" is), and I haven't worked it out myself. Well, not completely anyway, but I can tell you that the two most obvious postulates are:

1. Physical events are represented by points in Minkowski space. (Note that this implies that the motion of a classical object can be represented by a set of curves in Minkowski space, and that this suggests that we define a classical particle to be "a physical system whose motion can be represented by exactly one such curve").

2. A clock measures the proper time of the curve in Minkowski space that represents its motion.

It's clear that we also need to postulate something about measurements of length, but this is more difficult because of Lorentz contraction. There might be more than one OK way to do it, and one of them seems to be to postulate that lengths are measured by rulers, and that a solid object (like a ruler) that's accelerated gently undergoes Born rigid motion (which guarantees that if we slowly change its velocity, its measurements before and after the acceleration will be consistent with the Lorentz contraction formula).

Unfortunately, this postulate is inappropriate when we formulate theories of matter in this framework (as described in my previous post). It must be possible to possible to use those theories to prove the Born rigidity of an accelerating solid. However, that result isn't going to be a testable prediction of the theory unless we use something other than solid objects to perform length measurements.

If we can't use solids, it seems natural to use light instead. We can use radar to define distance. If we emit a signal at time t₁ (as measured by a clock attached to the radar device) and detect the signal coming back at time t₂, then the distance to the reflection event can be defined as (t₂-t₁)/2. But of course this only works as well as we'd like if the radar isn't accelerating. So we can take the third postulate to be that "lengths are measured by radar devices that move on geodesics", or that "infinitesimal lengths are measured by radar devices".

Hey, I learned something. Some of these things weren't perfectly clear to me before, in particular the reason why the postulate about length measurements should use radar instead of rulers.

The point made by Brown and Pooley is valid and non-trivial. They basically say this: if special relativity is correct, and if our dynamical theories indeed agree with special relativity, then we should be able to *calculate* the length contraction and time dilation effects within our dynamical theories, and the result should agree exactly with SR predictions.

For example, we could take a relativistic theory of inter-atomic forces and first calculate the equilibrium length of a rod in the reference frame at rest. Then repeat the same calculation in a moving reference frame. If everything is consistent, we should obtain *exactly* the length contraction predicted (but not explained) by SR. Unfortunately, as far as I know, there were no such convincing calculations for the length contraction and time dilation effects.

I'm not sure I understand what you're saying here. Are the "relativistic" "dynamical" theories you're talking about formulated in the framework of special relativity or not? (See my previous post for a clarification of what I mean by the "framework"). If they are, then this is all very trivial. One of the things that such a theory of inter-atomic forces would tell us is that the length of the moving rod can be calculated by calculating its rest length and doing a Lorentz transformation.

Actually, it seems equally trivial if you're talking about theories that aren't formulated in this framework (like a theory with Lorentz invariance and a spacetime that has a preferred frame). If the theory is Lorentz invariant, then it's only a matter of calculating its rest length and doing a Lorentz transformation.

Note also that these authors aren't criticizing those theories on the grounds that they can't be used for these calculations. They are criticizing the standard formulation of SR on the grounds that it doesn't explain why the moving rod has a different length than it did when it was stationary. (At least that's my interpretation, but maybe I read it too quickly).

I think you should be talking about a rod that's initially at rest (in some inertial frame) and then gently accelerated for a while, so that its velocity (in the same frame) when the acceleration period is over is v. Maybe that's what you meant. I would interpret what you said as involving two rods of the same material that have been moving at constant but different velocities forever. If the situation that concerns you is one rod moving at different velocities at different times, then I feel that what I said earlier in this post answers it pretty well. A theory of matter formulated in the framework of (a properly defined version of) SR does predict the Born rigidity that implies that if you change the velocity of a rod, its new measured length will be consistent with the Lorentz contraction formula.

 

[Max™]

I thought the second postulate was actually about the invariance of spacetime intervals, and was a rather deep statement about motion through Time.

 

[D H]

Be fair. The only filled 15 pages with words that say very little. The rest are references. And besides, they are philosophers. It's their job to fill pages with words that say very little.

Too bad we don't have a "Quote of the Month" award at PF. This would win the prize.

Some dead-giveaways that this paper is by philosophers:
- More (a lot more) scare quotes than equations.
- One equation, and a literally trivial one at that.
- 2 2/3 pages of references, including one published by Isaac Newton in 1962.

 

[Fredrik]

I thought the second postulate was actually about the invariance of spacetime intervals, and was a rather deep statement about motion through Time.

Einstein's postulates look like this:

1. The laws of physics are the same in all inertial frames.
2. The speed of light is the same in all inertial frames.

This isn't exactly how he said it, but it's close enough. Postulate 2 in my post above (#20) isn't meant to be a well-defined version of Einstein's 2nd. Actually, the well-defined versions of both of Einstein's postulates are contained in the 1st postulate in my post, but it's not so easy to see that.

 

[Max™]

Oh, I see what you're saying. I'm just saying that Einstein didn't say the speed of light is the same, he said it is measured to be the same. As I recall.

That is the key point which is overlooked, and why it is more correct to say the second postulate refers to the invariance of spacetime intervals.

 

[atyy]

Too bad we don't have a "Quote of the Month" award at PF. This would win the prize.

This seems to be a competitive month. Have you seen ZapperZ's post #9 at https://www.physicsforums.com/showthread.php?t=291087?

 

[meopemuk]

I'm not sure I understand what you're saying here. Are the "relativistic" "dynamical" theories you're talking about formulated in the framework of special relativity or not? (See my previous post for a clarification of what I mean by the "framework"). If they are, then this is all very trivial. One of the things that such a theory of inter-atomic forces would tell us is that the length of the moving rod can be calculated by calculating its rest length and doing a Lorentz transformation.

I am not sure that things are so simple. Let me take as an example the hydrogen molecule H2. Suppose that in the reference frame at rest I have a Hamiltonian H which describes interaction between 2 protons and 2 electrons. I can find the ground state of this Hamiltonian and calculate the equilibrium distance R between two protons. If my theory is fully relativistic, I should be able also to write the electron-proton Hamiltonian H', which is valid in the moving reference frame. (Note that H and H' must be different.) I can also find the ground state for H', and thus determine the equilibrium distance R' in the hydrogen molecule from the point of view of the moving observer. Now, your claim is that R and R' will be related exactly by the Einstein's length contraction formula. I am not convinced.

 

[JesseM]

I am not sure that things are so simple. Let me take as an example the hydrogen molecule H2. Suppose that in the reference frame at rest I have a Hamiltonian H which describes interaction between 2 protons and 2 electrons. I can find the ground state of this Hamiltonian and calculate the equilibrium distance R between two protons. If my theory is fully relativistic, I should be able also to write the electron-proton Hamiltonian H', which is valid in the moving reference frame. (Note that H and H' must be different.) I can also find the ground state for H', and thus determine the equilibrium distance R' in the hydrogen molecule from the point of view of the moving observer. Now, your claim is that R and R' will be related exactly by the Einstein's length contraction formula. I am not convinced.

Quantum field theories (the relativistic version of QM) are all Lorentz-invariant, which should mathematically guarantee that the predictions of different inertial frames are related by the Lorentz transformation.

 

[meopemuk]

Quantum field theories (the relativistic version of QM) are all Lorentz-invariant, which should mathematically guarantee that the predictions of different inertial frames are related by the Lorentz transformation.

If there is such a guarantee, then it should be not difficult to verify the transformations by direct calculations, as I described. Or perhaps, there should be a rigorous mathematical proof that direct calculations of equilibrium distances in different frames would yield exactly the length contraction formula. I haven't heard about such a proof.

I agree with you that Lorentz transformations are part of QFT. So, one possible approach is, as you said, just simply apply the length contraction formula. However, relativistic quantum theory gives us another approach: to find the ground state of the Hamiltonian H' in the moving frame. If the theory is self-consistent, then both approaches should yield the same result. If we, indeed, find that both results agree, then everything is great. The theory passed an important consistency check. But, what if the two results disagree?

 

[JesseM]

If there is such a guarantee, then it should be not difficult to verify the transformations by direct calculations, as I described. Or perhaps, there should be a rigorous mathematical proof that direct calculations of equilibrium distances in different frames would yield exactly the length contraction formula. I haven't heard about such a proof.

I agree with you that Lorentz transformations are part of QFT. So, one possible approach is, as you said, just simply apply the length contraction formula. However, relativistic quantum theory gives us another approach: to find the ground state of the Hamiltonian H' in the moving frame. If the theory is self-consistent, then both approaches should yield the same result. If we, indeed, find that both results agree, then everything is great. The theory passed an important consistency check. But, what if the two results disagree?

I don't know how to do quantum field theory calculations myself, but just based on the fact that the theory is Lorentz-symmetric, it's mathematically impossible that they could disagree. If you know the dynamical laws in one frame, all you have to do is perform a Lorentz transformation on these laws to find equations that give physically identical predictions in a different frame. If we don't assume Lorentz-symmetry, in general the equations might be different in different frames, but this is just a way of relabeling events so it can't give physically different predictions. And the very definition of Lorentz-symmetry implies that if you perform a Lorentz transformation on equations which are Lorentz-symmetric, the equations will be unchanged in the new frame, so you can use the same equations in different frames and get physically identical predictions.

 

[Meir Achuz]

I just came across some references that all dispense with the 2nd postulate:

[1] R. Weinstock: New approach to special relativity, Am. J. Phys. 33 (1965) 540-545.
[2] V. Mitavalsky: Special relativity without the postulate of constancy of light, Am. J. Phys. 34 (1966) 825.
[3] A. R. Lee, T. M. Kalotas: Lorentz transformations from the first postulate, Am. J. Phys. 43 (1975) 434-437.
[4] J.-M. Levy-Leblond: One more derivation of the Lorentz transformation, Am. J. Phys.
44 (1976) 271-277.
[5] A. M. Srivastava: Invariant speed in special relativity, Am. J. Phys. 49 (1981) 504-505.
[6] N. D. Mermin: Relativity without light, Am. J. Phys. 52 (1984) 119-124.
[7] H. M. Schwartz: Deduction of the general Lorentz transformations from a set of necessary assumptions, Am. J. Phys. 52 (1984) 346-350.
[8] H. M. Schwartz: A simple new approach to the deduction of the Lorentz transformations, Am. J. Phys. 53 (1985) 1007-1008.
[9] S. Singh: Lorentz transformations in Mermin’s relativity without light, Am. J. Phys. 54
(1986) 183-184.
[10] A. Sen: How Galileo could have derived the special theory of relativity, Am. J. Phys. 62 (1994) 157-162.
[11] M. J. Feigenbaum, N. D. Mermin: E = mc2, Am. J. Phys. 56 (1988

 

[meopemuk]

clem,

thanks for the references. I didn't read all of them, but I am familiar with some of them. They suffer from a common unjustified assumption, which, I think, is important.

For example, take Levy-Leblond's paper. In his eq. (1) he assumes that event's space-time coordinates (x', t') in the moving frame depend ONLY on its coordinates (x, t) in the frame at rest and on parameters {a}, which determine the relative velocity of the two frames. He doesn't entertain the possibility that x' and t' may also depend on the physical nature of the event.

Let me explain what I mean on the following example. Suppose that we are interested in the event of collision of two particles. This event is rather well localized in both space and time for both observers. So, coordinates (x, t) and (x', t') have clear meaning, and it makes sense to ask which transformation connects these two pairs of numbers. Consider two possibilities. In one case the particles are non-interacting. In the other case the particles interact with each other (for example, these are two opposite charges). Is there a good reason to assume a priori that the transformation laws (x, t) -> (x', t') will be exactly the same in these two cases? I don't think so.

I would be much happier if Levy-Leblond (and others) explicitly formulated their tacit postulate, which sounds roughly like this: "Transformations of space-time coordinates of events do not depend (i) on the physical nature of events; (ii) on the composition of the system in which the events occur; (iii) on the nature and strength of interactions in the system." This assumption lies in the foundation of all special relativity, but it is never (or rarely) mentioned.

 

[Fredrik]

My opinion is that people should care a lot less on Einstein's postulates (and possible alternatives to them) and a lot more about the details of how to interpret the mathematics of Minkwski space as predictions about the results of experiments. But I probably say that too often in this forum.

I decided to look up the original version of the postulates. I found a translation here (page 140) and the original german http://www.pro-physik.de/Phy/pdfs/ger_890_921.pdf . They are a bit different from what I said in #23. This is a better summary of what they say:

1. The laws of electrodynamics and optics are valid in any coordinate system where the equations of mechanics are valid.

2. In empty space, light always propagates at a definite velocity V which is independent of the motion of the light source.

These aren't exactly well-defined mathematical axioms either. Does the specification of what coordinate systems he's talking about in postulate 1 even make sense? (That's not a rhetorical question. I don't know what the answer is, but then I'm always a bit dumber the last hour before I go to sleep). Also, note that postulate 2 doesn't even mention coordinates.

 

[Meir Achuz]

Fred: I agree with your first paragraph, so I probably should stop right here but...
Neither postulate, as stated in that translation make much sense today.
For (1), the "equations of mechanics" as Einstein knew them at the time were mostly not valid.
For (2), isn't that completely compatible with an aether? That postulate holds for sound in air.
If anyone does want one or two basic postulates for SR, it can't be either one of those.

 

[robphy]

Be fair. The only filled 15 pages with words that say very little. The rest are references. And besides, they are philosophers. It's their job to fill pages with words that say very little.

In defense of some "philosophers [of science]",
there are some more-technical ones...
like Malament ( http://www.lps.uci.edu/home/fac-staff/faculty/malament/ )
who is interested in foundational aspects that most physicists gloss over in their treatment of the subject. (Foundational aspects are important, of course, in any search for a more fundamental theory.)

a review article "Classical General Relativity" http://arxiv.org/abs/gr-qc/0506065
and this famous paper: http://link.aip.org/link/?JMAPAQ/18/1399/1

 

[DrGreg]

I decided to look up the original version of the postulates. I found a translation here (page 140) and the original german http://www.pro-physik.de/Phy/pdfs/ger_890_921.pdf . They are a bit different from what I said in #23. This is a better summary of what they say:

1. The laws of electrodynamics and optics are valid in any coordinate system where the equations of mechanics are valid.

2. In empty space, light always propagates at a definite velocity V which is independent of the motion of the light source.

These aren't exactly well-defined mathematical axioms either. Does the specification of what coordinate systems he's talking about in postulate 1 even make sense? (That's not a rhetorical question. I don't know what the answer is, but then I'm always a bit dumber the last hour before I go to sleep). Also, note that postulate 2 doesn't even mention coordinates.

I would first paraphrase (1) as

1a. An inertial coordinate system is defined as one in which the equations of mechanics are valid.
1b. The laws of electrodynamics and optics are valid in any inertial coordinate system.

Then I would simplify (1a) to say "Newton's first law" instead of "the equations of mechanics", that is:

1a. An inertial coordinate system is defined as one in which every free-falling particle has constant coordinate velocity.

I would then generalise (1b) as

1b. Every law of physics takes the same form in every inertial coordinate system.

(In fact, that isn't technically quite good enough, because it makes no distinction between orthogonal and skew coordinates, so a bit more is needed to resolve that ambiguity. There is also an implicit assumption that inertial coordinate systems do actually exist, otherwise (1b) would be trivially true on an empty set of coordinate systems.)

Einstein's first postulate essentially extends the principle of relativity from Newtonian mechanics (where it was already known to be true -- "Galilean relativity") to all branches of physics.

Although (2) doesn't explicitly mention coordinates, velocity is implicitly defined in terms of coordinates. It can be interpreted as valid in any single frame where V might vary from one frame to another. Subsequent application of (1) would imply all frames have the same V.