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The first postulate of Special Relativity is that the laws of physics must be the same in all frames of reference i.e. invariant of coordinate transformations. I know this might be moot to ask but after reading a critique's paper on Special Relativity, I thought the question needs to be answered.

Is there any supportive evidence which suggests so other than the evidence of common sense and intuition?

As we know common sense and intuition are easily defied in most of the physics theories like Quantum Mechanics we should not rely upon such assertions to formulate an entire theory of Universe.

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  • $\begingroup$ It's a postulate. You start by assuming this is true (and from experimental evidence it seems to be), derive the ToR using the postulate, and then see if the results fit the real world by e.g. explaining the precession of Mercury. If the results match experimental evidence (and no simpler theory does), you've pretty much proved the postulate to be true. $\endgroup$ – jamesqf Jan 26 at 1:39
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    $\begingroup$ Does this answer your question? How do we know that the laws of physics are invariant in all inertial frames? $\endgroup$ – Milan Jan 26 at 9:49
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Is there any supportive evidence which suggests so other than the evidence of common sense and intuition?

Yes, there is quite a substantial body of experimental evidence supporting the two postulates of relativity. The best summary I know is this page:

http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

It is important to understand how these experiments are analyzed. Since you would like to test relativity you cannot assume it or its postulates. Instead, you create a test theory that is more general. It does not assume either of the postulates, but has one or more free parameters that can be adjusted. These free parameters have some specific setting which produces relativity, and any other combination of free parameters indicates a violation of relativity.

Then you use this test theory to develop experiments that measure the value of the free parameters. If the measured result of the experiment is equal to the relativity value (to within experimental error) then the experiment validates relativity. This approach is important because it allows you to test a theory without assuming it.

For special relativity Zhang (Special Relativity and Its Experimental Foundation https://doi.org/10.1142/3180 ) describes a general test theory, and for the standard model the Standard Model Extensions is a complete test theory including all possible relativity violating terms.

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  • $\begingroup$ Could you explicitly link to/cite the Zhang's test theory? $\endgroup$ – Ruslan Jan 26 at 7:51
  • $\begingroup$ Yes, I have added that $\endgroup$ – Dale Jan 26 at 12:59
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If special relativity were not true, the everyday world we experience would be very different, in very obvious ways. I will provide just one simple example:

Special relativity is embedded in Maxwell's equations and tells us (among other things) that if we insert a magnet into a coil of wire, so as to induce a current to flow in it, there will be no way to tell from looking at the meter measuring that current whether it was the coil that moved or the magnet that moved.

If this was not the case, then the output of an electric generator would depend on whether the armature inside it were rotating and the case was fixed in position, or the armature was fixed and the case were rotating. No such effect exists.

In addition, the output of an electric generator would depend on its state of motion relative to some fixed reference frame attached to the universe as a whole. As the generator, which is fixed to the surface of the (rotating) earth, moved relative to that frame, its output would vary according to its angle relative to that frame. This effect does not exist either.

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  • $\begingroup$ You just explained the consequences of Special Relativity which are stretched to agree with experimental observations. Since the starting point of the theory is that the Laws of Physics are same for all frames of references, there must exist a valid reason to state so. $\endgroup$ – Ajinkya Naik Jan 26 at 14:53
  • $\begingroup$ The entire formulation of Special and General Relativity is a series of thought experiments carefully and beautifully constructed one upon the other. Einstein's relativity was not discovered using empirical evidences, instead it is the other way around. Take quantum mechanics on the other hand which is constructed using empirical evidence and makes little to no sense. Yet, there is no reason to doubt its validity because the starting point of the theory is a fact and not a postulate unlike Relativity. $\endgroup$ – Ajinkya Naik Jan 26 at 14:57
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The laws of physics being the same in all inertial reference frames is an idea that originates not with Einstein but Galileo, who noted if you're in a sealed windowless room on a ship you can't tell whether the ship is moving (though you can tell if it's accelerating, such as when it bobs). Special relativity differs from Galilean relativity only in how we convert between inertial reference frames, claiming the transformation of spacetime coordinates to be Lorentzian instead of Galilean. With the right assumptions, you can show only that one of these transformations is correct. The Galilean case is then the special case $c^{-2}=0$, which is measurably incorrect. The positive empirical value of $c^{-2}$ is known precisely enough to define the metre in terms of the second.

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It's an observation that all laws of physics are the same (transform covariantly) in all inertial reference frames. If this wasn't the case, there would be some experiment that one can do to determine in which reference frame he is.

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Among all inertial frame of reference, clearly acceleration is zero and hence one can't experience any new resultant force. Alternatively, resultant force among various inertial frame of references are same. All laws of physics are directly or indirectly related to one or more forces.

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The laws of physics are same in all inertial frames of references. In fact, if it we find a "law" which is not so, we believe it is not a fundamental law.

To find the importance of an assumption, remove it and see the consequences. If the laws were different in distinct reference frames, that would be a terrible world to live in. Nobody would agree upon a measurement since they all could be potentially observing different things.

Just to give an example, suppose you are in a bus and you throw a ball upwards. If the bus is at rest, obviously the ball will fall straight down to your foot. But what if the bus is moving forwards at a constant speed (that is, “so long as the motion is uniform and not fluctuating this way and that”)?

One’s first guess might be that the ball will fall somewhere behind the foot or might as well hit the back of the bus. But it turns out not to be so; the ball will again fall at the foot. Had the laws been different, there would be no guarantee that the ball would fall back. But, of course that is not true.

In particular, this experimental verification of first law gives us enough confidence to assume the laws of physics to be same in all inertial frames. Since theory of relativity works well in explaining dynamics at higher velocities and subsumes to Newtonian regime as a low-velocity limit, this assumption is important and necessary. We have a strong reason to believe so.

In the end, these assumptions are tested time and again and you can find many useful references here.

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  • $\begingroup$ Why doesn't this same "importance" also apply to non-inertial frames? Suppose I am in a bus which is accelerating and I throw a ball upwards. The ball moves backwards (in my frame)! Oh no! It's the end of physics as we know it! ...or is it? We seem to have no trouble accepting that "the laws of physics are different" in accelerating frames. $\endgroup$ – user253751 Jan 25 at 23:29
  • $\begingroup$ the ball falls at your feet exactly because you are in an accelerating frame of reference. $\endgroup$ – Jasen Jan 25 at 23:38
  • $\begingroup$ @user253751 We have observed that the laws are different in accelerating frames, but we have not observed that the laws are different in inertial frames. (Setting aside general relativity, of course.) $\endgroup$ – Tanner Swett Jan 26 at 1:48
  • $\begingroup$ @TannerSwett So the reason we believe "the laws of physics are the same" in all inertial frames is because we observe that, not because "it would break physics if the laws were different in different frames." $\endgroup$ – user253751 Jan 26 at 14:00

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