# Best Understanding of the SR Postulate and the FAQ

#### Wes Tausend

Gold Member
...

I gained most of my elementary understanding of Special Relativity (SR) from books by Isaac Asimov. I made the continuing mistake on this forum, of either taking some things he may have said too literally, or misconstruing them altogether, and they are not entirely correct. In other words, I believe Asimov, along with other popular science authors, may have repeatedly used loose "literary (artistic) license" to enhance explanation of some physical events that may not stand up under "technical definitions" during discussion on this forum. In the future, definitions given on this forum must take precedence.

I was invited to, quote, "ask questions about the explanation itself if you did not understand the explanation", which I interpret as the FAQ. Either way, I would like to clarify my understanding of this "technical definition" in SR and on this forum.

Postulates of Special Relativity

Einstein said:
"1. First postulate (principle of relativity):
The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion. OR: The laws of physics are the same in all inertial frames of reference.

2. Second postulate (invariance of c):
As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body. OR: The speed of light in free space has the same value c in all inertial frames of reference.
FAQ: Rest frame of a photon

Physicsforums said:
I've read that in relativity the concept of the rest frame of a photon doesn't make sense. Why is that?

A rest frame of some object is a reference frame in which the object's velocity is zero. One of the key axioms of special relativity is that light moves at c in all reference frames. The rest frame of a photon would require the photon to be at rest (velocity=0) and moving at c (velocity=299792458 m/s). That of course is contradictory. In other words, the concept doesn't make sense.

Considering the Postulates of Special Relativity (above) that Einstein made, and the Physicsforums FAQ, Rest of a Photon, (above) the FAQ has apparently been constructed to be a nearly a word-for-word reference to the last sentence in the second postulate, and is firmly intended to be that way to serve the same purpose. The purpose is to establish a non-deviating foundation for SR. It is also this Physicsforums website's mission to discuss only established theories for clarity, all of which rely on some similar important foundation, and all welcome participants must try to strictly follow this mission and proper definitions.

1) It seems obvious to me that the above paragraph is essentially true, or is there a better way to say it?

Furthermore, when Einstein chose the wording of this SR postulate, he decided to base it on the basic supposition that all laws of physics always stayed the same for observers everywhere. In addition, he supposed earlier electromagnetic calculations by Maxwell hinted, and previous lightspeed measurements made by Michelson & Morley (M&M) indicated, light always traveled at an invariant speed in "free space" (a vacuum).

2) It seems obvious to me the above paragraph is also essentially true, or is there a better way to say it?

Concerning the importance of measurements, if some trustworthy individuals, including or other than M&M, later found any significant difference (other velocity) in "free space" lightspeed, Einstein knew that would immediately invalidate his SR postulate. So the words, "As measured", were carefully included in the SR postulate and are a necessary component. In other words, as were M&M, Einstein was aware most scientists were confounded by the invariance of lightspeed measured about eighteen years preceeding 1905 (1887), and as expected, M&M continued to make many re-measurements years after the 1905 SR Postulate, looking for a possible error. An error that has never been found to this day, and most likely never will be found... all because of the overwhelming success of this original SR Postulate.

3) It seems to me this last paragraph above is essentially true, or is there a better way to say it?

Thanks,
Wes
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Related Special and General Relativity News on Phys.org

#### Nugatory

Mentor
...
I gained most of my elementary understanding of Special Relativity (SR) from books by Isaac Asimov.
I loved Asimov dearly. The "Relativity of Wrong" should be mandatory in the high school science curriculum, and he is to some extent responsible for my lifelong and enormously rewarding fascination with science. But... Reading Asimov doesn't give you an understanding of SR, it gives you an understanding of what SR is about. It's not the same thing.
(Although to be fair Asimov was far better than the average populizer).

Furthermore, when Einstein chose the wording of this SR postulate, he decided to base it on the basic supposition that all laws of physics always stayed the same for observers everywhere. In addition, he supposed earlier electromagnetic calculations by Maxwell hinted, and previous lightspeed measurements made by Michelson & Morley (M&M) indicated, light always traveled at an invariant speed in "free space" (a vacuum).

2) It seems obvious to me the above paragraph is also essentially true, or is there a better way to say it?
We don't know exactly what was going on in Einstein's mind in the period leading up to the publication of the 1905 paper: the development of an idea is seldom along the linear stap-by-step no-wrong-turns path that we use to explain it after the development is done - but what you say above is a fair enough summary of the history.

Concerning the importance of measurements, if some trustworthy individuals, including or other than M&M, later found any significant difference (other velocity) in "free space" lightspeed, Einstein knew that would immediately invalidate his SR postulate. So the words, "As measured", were carefully included in the SR postulate and are a necessary component. In other words, as were M&M, Einstein was aware most scientists were confounded by the invariance of lightspeed measured about eighteen years preceeding 1905 (1887), and as expected, M&M continued to make many re-measurements years after the 1905 SR Postulate, looking for a possible error. An error that has never been found to this day, and most likely never will be found... all because of the overwhelming success of this original SR Postulate.

3) It seems to me this last paragraph above is essentially true, or is there a better way to say it?
Again, it's hard to know exactly what was going on in Einstein's mind.... But it seems overwhelmingly likely that Einstein put in the words "as measured" because he was a scientist not a philosopher.

#### ghwellsjr

Gold Member
...

2) It seems obvious to me the above paragraph is also essentially true, or is there a better way to say it?

Concerning the importance of measurements, if some trustworthy individuals, including or other than M&M, later found any significant difference (other velocity) in "free space" lightspeed, Einstein knew that would immediately invalidate his SR postulate. So the words, "As measured", were carefully included in the SR postulate and are a necessary component. In other words, as were M&M, Einstein was aware most scientists were confounded by the invariance of lightspeed measured about eighteen years preceeding 1905 (1887), and as expected, M&M continued to make many re-measurements years after the 1905 SR Postulate, looking for a possible error. An error that has never been found to this day, and most likely never will be found... all because of the overwhelming success of this original SR Postulate.

3) It seems to me this last paragraph above is essentially true, or is there a better way to say it?

Thanks,
Wes
...
Your quote of the second postulate is from wikipedia, not from Einstein. I don't believe he ever included the words "as measured" and if you look at his 1905 paper, they aren't there and the whole point of his explanation is that the propagation of light cannot be measured, it has to be assigned or defined and that's what his second postulate does.

#### Wes Tausend

Gold Member
I loved Asimov dearly. The "Relativity of Wrong" should be mandatory in the high school science curriculum, and he is to some extent responsible for my lifelong and enormously rewarding fascination with science. But... Reading Asimov doesn't give you an understanding of SR, it gives you an understanding of what SR is about. It's not the same thing.
(Although to be fair Asimov was far better than the average populizer).

We don't know exactly what was going on in Einstein's mind in the period leading up to the publication of the 1905 paper: the development of an idea is seldom along the linear stap-by-step no-wrong-turns path that we use to explain it after the development is done - but what you say above is a fair enough summary of the history.

Again, it's hard to know exactly what was going on in Einstein's mind.... But it seems overwhelmingly likely that Einstein put in the words "as measured" because he was a scientist not a philosopher.
Nugatory,

Well now a little wiser, I agree with everything you say and thanks for being kind.

I loved Asimov too. And Relativity of Wrong is my favorite. It shows that our most successful concepts are merely evolutions of previous foundations. Was it another Isaac, Isaac Newton who admitted, "If I have seen further it is by standing on ye sholders of Giants."

Thanks again,
Wes
...

#### Wes Tausend

Gold Member
Your quote of the second postulate is from wikipedia, not from Einstein. I don't believe he ever included the words "as measured" and if you look at his 1905 paper, they aren't there and the whole point of his explanation is that the propagation of light cannot be measured, it has to be assigned or defined and that's what his second postulate does.
George,

Thank you for pointing out the fallibility of my sources, sir.

This may be the correct wording copied and pasted from your link:

Einstein said:
...The following reflexions are based on the principle of relativity and on the principle of the constancy of the velocity of light. These two principles we define as follows:—

1.The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion.
2.Any ray of light moves in the “stationary” system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body. Hence

where time interval is to be taken in the sense of the definition in § 1...
I will re-think my adopted definition. I can see it may produce more questions.

Thanks again,
Wes
...

#### Wes Tausend

Gold Member
Your quote of the second postulate is from wikipedia, not from Einstein. I don't believe he ever included the words "as measured" and if you look at his 1905 paper, they aren't there and the whole point of his explanation is that the propagation of light cannot be measured, it has to be assigned or defined and that's what his second postulate does.
George,

I haven't recognized a direct reference to Einstein saying, "the propogation of light cannot be measured", and I find it confusing. Did you mean he knew it could not be measured perfectly or that it is futile or unnecessary to try, perhaps? In my thick-headedness, I would appreciate you elaborate a bit more.

I did recognize (I believe) the former "stationary" system (Galilean) of coordinates is no longer used, and therefore he may have considered the velocity of an electromagnetic wave might not be properly measured in that system.

I do need to read the 1905 Paper more thoroughly, but it is finally a nice work day outside, and my better half is giving me the evil eye again. I greatly appreciate the 1905 link, as I have not read it before. Thanks for your time, George.

Wes
=======================================================================
Just as a general question to anyone, may I use the wikipedia version of the postulate (in my first post) as a SR reference since the Physicsforums FAQ is so similar? I understand I may, or may not be able to take the "As measured" stipulation too seriously, just as Asimov may add iffy personal interpretations. Both wikipedia and the FAQ seem to be reasonably derived interpolations of Einstein's actual postulate if I scanned it correctly.

Thanks,
Wes
...

#### Dale

Mentor
I haven't recognized a direct reference to Einstein saying, "the propogation of light cannot be measured", and I find it confusing.
I suspect that ghwellsjr is refering to this part of the 1905 paper:

"We have not defined a common “time” for A and B, for the latter cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A."

This definition of the one way speed of light is a matter of convention, not measurement. The two way speed of light can be measured, but you could define your simultaneity so that light went instantaneously in one direction and at c/2 in the opposite direction. You would still wind up with a theory which is compatible with experimental measures of the two way speed of light as being c.

#### ghwellsjr

Gold Member
George,

I haven't recognized a direct reference to Einstein saying, "the propogation of light cannot be measured", and I find it confusing. Did you mean he knew it could not be measured perfectly or that it is futile or unnecessary to try, perhaps? In my thick-headedness, I would appreciate you elaborate a bit more.
It's not a matter of perfection, the propagation of light cannot be measured or determined by an experiment to any degree (except within the very broad limits mentioned by DaleSpam).

Near the end of article 1 of his 1905 paper, Einstein did say that the two-way speed of light can be measured:
In agreement with experience we further assume the quantity

to be a universal constant—the velocity of light in empty space.
If he had believed that about the one-way speed of light, he would have said so because if the one-way speed of light can be measured, then the two-way speed of light would have to be the same.

At the beginning of chapter 7 of his 1920 book, Einstein recounts two of the things we can measure about the propagation speed of light:

1) It is not dependent on frequency or color of the light.

2) It is not dependent on the speed of the source of the light.

Note that these two characteristics are also true for the ether theory of light which Einstein was arguing against.

But, Einstein says, the propagation (one-way) speed of light in all inertial reference frames can only be assumed.

I did recognize (I believe) the former "stationary" system (Galilean) of coordinates is no longer used, and therefore he may have considered the velocity of an electromagnetic wave might not be properly measured in that system.

I do need to read the 1905 Paper more thoroughly, but it is finally a nice work day outside, and my better half is giving me the evil eye again. I greatly appreciate the 1905 link, as I have not read it before. Thanks for your time, George.

Wes
=======================================================================
Just as a general question to anyone, may I use the wikipedia version of the postulate (in my first post) as a SR reference since the Physicsforums FAQ is so similar? I understand I may, or may not be able to take the "As measured" stipulation too seriously, just as Asimov may add iffy personal interpretations. Both wikipedia and the FAQ seem to be reasonably derived interpolations of Einstein's actual postulate if I scanned it correctly.

Thanks,
Wes
...
I don't think you should use an incorrect quote and attribute it to Einstein unless you can provide a direct reference to something he actually said.

Can you provide a link to the FAQ you are referring to?

#### abitslow

Other than pointing out how silly the contention is about two way speed (how about three, four, five-way,...) speed of light? LOL. I've not much to add. [ Either the Universe is conspiring to trick us, or the speed of light doesn't change based on direction. Think about a set up where the same pulse is split and travels in more than one path to the same target, the whole contention is a profound waste of time.]
Except one thing. Einstein wrote (and thought) in GERMAN. Although, based on my reading of the original German article and its English TRANSLATIONS, the translations are quite good, there can NOT be much confidence that a term in one language exactly translates into a term in a different language. There should be NO confidence in any determination of the authors intentions when dealing with translations, unless one has an extremely good understanding of the original language (in use at the time and place and context of the author).
Oh, also. In a frame of reference traveling at c, time and space would be on the same axis. That is, they would be only one thing. A frame of reference doesn't make observations, an observer in that frame of reference does. There can be no observer moving at velocity c, hence speaking about observations in that frame of reference is gibberish.

#### ghwellsjr

Gold Member
Other than pointing out how silly the contention is about two way speed (how about three, four, five-way,...) speed of light? LOL. I've not much to add. [ Either the Universe is conspiring to trick us, or the speed of light doesn't change based on direction. Think about a set up where the same pulse is split and travels in more than one path to the same target, the whole contention is a profound waste of time.]
Except one thing. Einstein wrote (and thought) in GERMAN. Although, based on my reading of the original German article and its English TRANSLATIONS, the translations are quite good, there can NOT be much confidence that a term in one language exactly translates into a term in a different language. There should be NO confidence in any determination of the authors intentions when dealing with translations, unless one has an extremely good understanding of the original language (in use at the time and place and context of the author).
Oh, also. In a frame of reference traveling at c, time and space would be on the same axis. That is, they would be only one thing. A frame of reference doesn't make observations, an observer in that frame of reference does. There can be no observer moving at velocity c, hence speaking about observations in that frame of reference is gibberish.
Silly? And then you talk about "a frame of reference traveling at c"???

#### Dale

Mentor
Other than pointing out how silly the contention is about two way speed (how about three, four, five-way,...) speed of light? LOL.
I don't think there is much contention. The definition is reasonable and extremely well accepted. Any alternative definition would be strange.

But the fact that it is a reasonable and well accepted definition doesn't make it stop being a definition.

#### Wes Tausend

Gold Member
I don't think you should use an incorrect quote and attribute it to Einstein unless you can provide a direct reference to something he actually said.
Thank you for the focused reply. I need the clear head of early morning to absorb much of your answer to measuring light, but the source of the misplaced quote suddenly dawns on me. My original intent was to simply html-box the link references and I later foolishly morphed the wiki version as a direct quote of Einstein and carried it on. Good catch. Thanks, George.

Can you provide a link to the FAQ you are referring to?
The FAQ link (and quote) was only in my first post and I should have included it again for clarity when I again referred to it. It is:

FAQ: Rest frame of a photon

This FAQ is very similar to the Wiki Postulate link. Both are boxed for comparison, above in the first post.

Silly? And then you talk about "a frame of reference traveling at c"???
Coincidental to the FAQ, I recently stubbed my toe on a similar comment to have "light in a rest frame" just as abitslow did, whom you retorted above. Like my errant quote, I found it surprisingly easy to write, but a "a frame of reference traveling at c" is not allowed within the confines of SR per the FAQ. This is a handy rule to remember, for both myself and abitslow.

Thanks again,
Wes
...

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#### ghwellsjr

Gold Member
Thank you for the focused reply. I need the clear head of early morning to absorb much of your answer to measuring light, but the source of the misplaced quote suddenly dawns on me. My original intent was to simply html-box the link references and I later foolishly morphed the wiki version as a direct quote of Einstein and carried it on. Good catch. Thanks, George.
You're very welcome.

The FAQ link (and quote) was only in my first post and I should have included it again for clarity when I again referred to it. It is:

FAQ: Rest frame of a photon

This FAQ is very similar to the Wiki Postulate link. Both are boxed for comparison, above in the first post.
The FAQ says:
One of the key axioms of special relativity is that light moves at c in all reference frames.
Note that word "axiom".

The wiki link says:
As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c...
Note that word "measured".

There's a big difference between "axiom" which means a stipulation, postulate, definition, or assumption and "measured" which means something which can be determined by experiment.

The two quotes are dissimilar in this very important aspect. The FAQ is good, the wiki is bad.

#### Wes Tausend

Gold Member
...

DaleSpam, ghwellsjr,

I think I understand the caution about measuring lightspeed in less than two directions. I'll offer a wordy Asimov style simplification and see if my intuition is in the ballpark.

These two equations are essentially the same form and the second defines the measurement of lightspeed in opposing directions:

...AND...

Einstein perhaps must do this because he wished to satisfy any remaining proponents of the hidden ether wind (no longer needed) which could possibly skew the one way measurement otherwise. As a "family" example, in other words, the refraction index of light in air is about 1.000293.
The determination is found by:

Where the ratio "c/v" equals "n" designating the "slowdown" of light speed as it passes through air.

Then it follows perhaps, if light travels against the wind (or ether) it encounters more *atoms of air (or ethereal obstruction) and measures slower than if it is measured with the wind (ether). This may be analogous to sound/air travel differences or the evidence of encountering more raindrops while walking against an unknown wind than not.

Partially, because the ether (invisible wind) effect was not, or could not be measured (detected) in either direction, Einstein was able to make a logical assumption that the directional speeds of light were always the same, at least in a vacuum. In reflection of DaleSpams note that differential measurements could be some irrational sort of average; i.e. he assumed moving objects always took their "calm" with them or better said, there simply was no ether and vacuum is inherently equivalent to a perfect calm that cannot be disturbed by motion. That was concerning measurement.

Separately he determined lightspeed:

1) It is not dependent on frequency or color of the light.

2) It is not dependent on the speed of the source of the light

This determination reaffirmed his assumption that lightspeed was constant in both directions.

It seems to me the above is essentially true, but a different way to say it. Would that be correct?

EDIT*: 2:48 PM 4-10-14
I stated I would try to use Physicsforums FAQs as preferential sources. The statement of "atoms of air" being the reason of light slowdown is not quite correct. I assume the accepted version here, is a physicsforums Physics FAQ called Do Photons Move Slower in a Solid Medium?. Essentially, I believe the "collected lattice" of the material (air in this case) is responsible for the accumulated delay of light moving through a nominal density of wind.

Wes
...

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#### bhobba

Mentor
I am a bit surprised people still think in terms of the speed of light thing. That's not relativity's real basis. Like so much of physics it's actually symmetry, and group theory is the natural language of symmetry so it's not surprising that is the most elegant derivation eg:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

That there exists an invariant speed naturally falls out of that approach.

There are all sorts of reasons it must be the speed of light but the one I like the best is to derive Maxwells equation from Coulombs law using it so just about any EM phenomena becomes proof it must be that very interesting constant that just happens to have the value of C:

IMHO it's a much clearer and more illuminating way of looking at it.

Thanks
Bill

#### ghwellsjr

Gold Member
...

DaleSpam, ghwellsjr,

I think I understand the caution about measuring lightspeed in less than two directions. I'll offer a wordy Asimov style simplification and see if my intuition is in the ballpark.

These two equations are essentially the same form and the second defines the measurement of lightspeed in opposing directions:

...AND...

Einstein perhaps must do this because he wished to satisfy any remaining proponents of the hidden ether wind (no longer needed) which could possibly skew the one way measurement otherwise.
I think maybe you're missing a big point here. Even if there were an ether wind and it was skewing the one way time for light in a round-trip measurement so that it took more time in one direction than the other, there would still be no way of making that measurement--there would be no way of knowing that the light was being skewed by the either wind.

As a "family" example, in other words, the refraction index of light in air is about 1.000293.
The determination is found by:

Where the ratio "c/v" equals "n" designating the "slowdown" of light speed as it passes through air.

Then it follows perhaps, if light travels against the wind (or ether) it encounters more *atoms of air (or ethereal obstruction) and measures slower than if it is measured with the wind (ether). This may be analogous to sound/air travel differences or the evidence of encountering more raindrops while walking against an unknown wind than not.
I don't know why you are bringing this up. The concept of the ether is that it undulates the light waves at c, relative to itself. If you are traveling with respect to it, any light that you emit would propagate at c with respect to the stationary state of the ether.

Partially, because the ether (invisible wind) effect was not, or could not be measured (detected) in either direction, Einstein was able to make a logical assumption that the directional speeds of light were always the same, at least in a vacuum. In reflection of DaleSpams note that differential measurements could be some irrational sort of average; i.e. he assumed moving objects always took their "calm" with them or better said, there simply was no ether and vacuum is inherently equivalent to a perfect calm that cannot be disturbed by motion. That was concerning measurement.

Separately he determined lightspeed:

1) It is not dependent on frequency or color of the light.

2) It is not dependent on the speed of the source of the light

This determination reaffirmed his assumption that lightspeed was constant in both directions.
Did you miss my comment that "these two characteristics are also true for the ether theory of light" in which the speed of light would not be constant in both directions for an observer traveling in the ether? I don't understand why you would say that they reaffirmed his assumption to the contrary.

It seems to me the above is essentially true, but a different way to say it. Would that be correct?
I think Einstein's way of saying it in chapter 8 of his 1920 book is perfectly adequate:
That light requires the same time to traverse the path A —> M as for the path B —> M is in reality neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make of my own freewill in order to arrive at a definition of simultaneity.”

#### ghwellsjr

Gold Member
I am a bit surprised people still think in terms of the speed of light thing. That's not relativity's real basis. Like so much of physics it's actually symmetry, and group theory is the natural language of symmetry so it's not surprising that is the most elegant derivation eg:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

That there exists an invariant speed naturally falls out of that approach.

There are all sorts of reasons it must be the speed of light but the one I like the best is to derive Maxwells equation from Coulombs law using it so just about any EM phenomena becomes proof it must be that very interesting constant that just happens to have the value of C:

IMHO it's a much clearer and more illuminating way of looking at it.

Thanks
Bill
Isn't postulating symmetry the same as postulating the equality of both halves of the roundtrip light propagation time?

And isn't that postulate also not a measurement?

#### Wes Tausend

Gold Member
I am a bit surprised people still think in terms of the speed of light thing. That's not relativity's real basis....

.....IMHO it's a much clearer and more illuminating way of looking at it.

Thanks
Bill
Bill,
Thanks for replying. We did get rather side-tracked with light in this post. My original intent was to learn to improve that I was on the same page with respondents on general language and definitions here. A key sentence from my post, #1 in this thread, is thus:
....I would like to clarify my understanding of this "technical definition" in SR and on this forum...
When discussing any subject, agreed upon definitions appear to be the key here. Note DaleSpams post #11 above us:
I don't think there is much contention. The definition is reasonable and extremely well accepted. Any alternative definition would be strange.

But the fact that it is a reasonable and well accepted definition doesn't make it stop being a definition.
I'm such an amateur at Physicsforums. It is a little like going to Rome and doing as the Roman's do. For a green outsider, one must try to learn Latin here. Your last sentence in your post #15, which I partially quoted, "IMHO it's a much clearer and more illuminating way of looking at it." is a good example of my original point and the principles at work here.

Besides an innate language and definition barrier to the uninitiated, I find this forum is much more formal and professional than others I have participated in. It may be a struggle, but this is the best place to find the most correct answers. Thanks again for your reply, Bill.

Wes
...

#### Wes Tausend

Gold Member
you're very welcome.

The faq says:
Note that word "axiom".

The wiki link says:
Note that word "measured".

There's a big difference between "axiom" which means a stipulation, postulate, definition, or assumption and "measured" which means something which can be determined by experiment.

The two quotes are dissimilar in this very important aspect. The faq is good, the wiki is bad.
Now I believe you are absolutely right, George. I agree, there is too much difference between the meanings and definition is nearly everything here.

Wikipedia used to be one of my best references in other forums. I am saddened as it slips from my grasp. It once seemed like a good idea, as I considered the truth of it's info as somewhat self-centering in consensus. But perhaps like most of the net, it is simultaneously top heavy with misconception, and may more easily tip from the truth.

Thanks,
Wes
...

#### bcrowell

Staff Emeritus
Gold Member
I am a bit surprised people still think in terms of the speed of light thing.
Yeah, I agree. There are many possible ways of axiomatizing SR, and I can find very little to say in favor of choosing Einstein's 1905 axiomatization. In ch. 2 of my SR book I give a sampling of some approaches: http://www.lightandmatter.com/sr/

#### bhobba

Mentor
Isn't postulating symmetry the same as postulating the equality of both halves of the roundtrip light propagation time? And isn't that postulate also not a measurement?
Symmetry implies the round trip must be the same - plus much more besides.

There are a number of ways of axiomatising relativity, and indeed many areas of physics, but I think for people exposed to it symmetry is the most elegant, not just in relativity, but in classical mechanics (see Landau - Mechanics) and QM (see Ballentine - QM - A Modern Development - Chapter 3). One of it's most striking aspects is the beautiful Noether's Theorem - if you don't know about it check it out.

Since Einstein's time a lot of work has been done on relativity, and of course many other areas of physics. It is now known symmetry is very fundamental and the thing that underpins much of physics:
http://www.pnas.org/content/93/25/14256.full

Einstein actually instigated this shift, but like so many revolutions at first he didn't appreciate exactly what was going on - that took a while to percolate so to speak. But from our vantage we view things differently - and I think that's the best way of looking at it rather than Einstein's original approach.

Thanks
Bill

#### vanhees71

Gold Member
For me the most convincing derivation of special relativistic is using only the postulates on the symmetries of space and time and the existence of an inertial frame of reference. This leads to either the Galileo or the Lorentz transformations between inertial frames, and then one can argue, which one is correct is an empirical question. The answer from many experiments is of course the Einstein-Minkowski spacetime is more accurate while the Galilei-Newton spacetime is an approximation. The Galilei group can be understood as a deformation of the Poincare group. Of course, General Relativity is even more accurate than Einstein-Minkowskian spacetime, and there the notion of an inertial frame is only valid locally rather than globally, but that's another issue.

V. Berzi and V. Gorini, Reciprocity Principle and the Lorentz Transformations, Jour. Math. Phys. 10, 1518 (1969).
http://dx.doi.org/10.1063/1.1665000

#### bhobba

Mentor
For me the most convincing derivation of special relativistic is using only the postulates on the symmetries of space and time and the existence of an inertial frame of reference.
Indeed.

One very interesting idea along those lines is Landau's definition of an inertial frame found in his classic - Mechanics. Its usually defined along the lines of a frame of reference in which Newton's laws of motion apply. However he defines it as a frame that is isotropic and homogeneous in space and time - which is pretty much the maximum symmetry a frame can have. He then shows they must all move at constant velocity relative to each other and from the PLA (Principle Of Least Action) that Newton's laws apply. It's symmetry that determiners everything really. Even relativistic mechanics follows in the same way from the most reasonable Lagrangian that is relativistic invariant. I remember when I first saw it I thought that's almost magical - its just so elegant.

The physical basis of relativity really lies in one almost trivial but very very important observation - frames, for all practical purposes, with this particular maximal symmetry, actually exist and conceptually assuming phenomena is contained in such frames is the correct way to proceed. That such exist is extremely intuitively appealing in the same way Euclid's axioms are, and that relativity has it as its basis is something I never cease to wonder at.

Thanks
Bill

#### Fredrik

Staff Emeritus
Gold Member
The set $\mathbb R$ was defined by mathematicians to have the properties that we intuitively associate with distances along a straight line in space. These are the same properties that we intuitively associate with time. So it's extremely natural to ask if there are any theories of physics in which $\mathbb R^3$ represents "space" and $\mathbb R$ represents "time". In any such theory, we can think of $\mathbb R^4$ as representing both space and time.

By 1905, physicists had found that in addition to the "obvious" theory of that kind (Newtonian mechanics), there's a less obvious one (SR). This raises the question of whether there are any more theories of this kind. This is the question that those symmetry-based arguments are answering. They show that the two theories that had already been found in 1905 are the only ones that are consistent with both the principle of relativity and rotation invariance. So if we want to find a third theory of space, time and motion, we have to abandon the idea that $\mathbb R^4$ is a good representation of space and time, or the idea that there's a group of global inertial coordinate systems on spacetime.

A "derivation" of the Lorentz transformation from Einsteins postulates serves another purpose. It tells us how someone who doesn't already know that there's a second theory that's consistent with the ideas mentioned above can guess how to define such a theory. It tells us more about how SR was found than about what SR is saying.

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#### strangerep

They show that the two theories that had already been found in 1905 are the only ones that are consistent with both the principle of relativity and rotation invariance.
At the risk of being an annoying nitpicker, I'll mention that one also needs a principle such as "a physically-meaningful transformation mapping (on velocity phase space) must be smooth in the physical variable". This allows one to resolve the ambiguity about the sign of $c^2$ that arises in the LT derivation.

(Of course there are other ways of doing this, such as invoking causality.)

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