Can SR be derived from other postulates than the constancy of c

In summary, there are multiple ways to derive Special Relativity, with the usual foundation being the constancy of the speed of light. Other attempts have been made using different approaches, such as postulating the results of SR and deriving the constancy of c and equivalence of inertial frames. Some have also tried to use symmetries and the principle of relativity in their derivations. One example is a derivation by Tom Roberts called "A Physicist's Derivation of Special Relativity".
  • #1
lalbatros
1,256
2
The usual foundation for deriving SR is the constancy of the speed of light.
Are there other ways to derive SR, and eventually some more general?

Have you ever read something about that?

Thanks,

Michel
 
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  • #2
You could postulate some of the results of SR, i.e. that spacetime is described by a Minkowski metric, that transformations between reference frames are described by the Lorentz transformation, and then derive things like the constancy of c and the equivalence of inertial frames. I think that the constancy of c line of reasoning is more physical though.
 
  • #3
lalbatros said:
The usual foundation for deriving SR is the constancy of the speed of light.
Are there other ways to derive SR, and eventually some more general?

Have you ever read something about that?

Thanks,

Michel

There have been several attempts in this direction. They all failed due to errors (that were discovered later). I have a list of all the failures.
 
  • #4
Here's the basic program that Lorentz followed in 1904.

1.) Assume that all frames move with a velocity less than c.

2.) Do a Galilean transform on the equations of electrodynamics.

3.) Notice that they're not in their original form.

4.) Insert time dilation and length contraction by hand so that the original form of the equations is restored.
 
  • #5
Had sufficiently energetic particle accelerators existed back then or if we had precise enough timepieces [or if everyday speeds were at least a significant fraction of the speed of light], one could have experimentally observed many of the "relativistic effects" of SR. Then, one may have deduced the appropriate equations and possibly the existence of a finite limiting velocity.

Along another thread, one might have asked what symmetries underlie the usually-formulated Maxwell's Equations of electromagnetism. Among the symmetries one would find is a group of transformations that preserve it: the Lorentz group, whose eigenvectors in an appropriately defined space are directions corresponding to the lightlike vectors in spacetime.

In some sense, the postulate of the "constancy of the speed of light" [or better, "the existence of a finite limiting velocity of signal propagation"] could be regarded as a [fortunately simple] representative "law of physics" that must be included under the umbrella of the "principle of relativity".

In an earlier post (from an earlier thread), I included an attachment that diagrams numerous attempts which have appeared in the literature. Depending on your scientific philosophy, you may or may not like the various approaches. However, it's clear that [thanks to the numerous symmetries of Minkowski spacetime] there are numerous ways to get to SR.
 
  • #6
lalbatros said:
The usual foundation for deriving SR is the constancy of the speed of light.
Are there other ways to derive SR, and eventually some more general?

Have you ever read something about that?

Thanks,

Michel

If you do a google search on the usenet newsgroups you can find a derivation by Tom Roberts called "A Physicist's Derivation of Special Relativity"
 
  • #7
cosmik debris said:
If you do a google search on the usenet newsgroups you can find a derivation by Tom Roberts called "A Physicist's Derivation of Special Relativity"

Thanks for the tip. I just browsed through it
The first sentence of my linked-post above applies here: This is one of those "Lorentz Transformations without the speed of light" proofs where the value of the speed of light plays its role only in the last step.
 

1. Can Special Relativity be derived from other postulates besides the constancy of the speed of light?

Yes, Special Relativity can be derived from other postulates such as the principle of relativity and the principle of causality. However, the constancy of the speed of light is crucial to the theory and cannot be replaced entirely.

2. Why is the constancy of the speed of light important in Special Relativity?

The constancy of the speed of light is important because it is a fundamental aspect of the theory. It means that the speed of light is the same for all observers, regardless of their relative motion. This postulate is necessary for maintaining the principle of relativity, which states that the laws of physics should be the same for all inertial observers.

3. Are there any other postulates that are necessary for Special Relativity?

Yes, in addition to the constancy of the speed of light, the principle of relativity and the principle of causality are also necessary for Special Relativity. The principle of relativity states that the laws of physics should be the same for all inertial observers, while the principle of causality states that cause and effect must occur in a definite order.

4. Can Special Relativity be derived from the theory of general relativity?

No, Special Relativity and general relativity are two separate theories. Special Relativity deals with the behavior of objects in a flat, unchanging space-time, while general relativity deals with the behavior of objects in a curved, dynamic space-time. However, Special Relativity is a special case of general relativity when gravity is negligible.

5. How does the constancy of the speed of light lead to time dilation and length contraction in Special Relativity?

The constancy of the speed of light leads to time dilation and length contraction because it implies that the speed of light is the same for all observers, regardless of their relative motion. This means that the measurement of time and distance will be different for observers moving at different velocities, leading to the observed effects of time dilation and length contraction.

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