Are Lorentz transformations exact and universal?
- Postulate 1 (the principle of relativity): All inertial frames of reference are equivalent.
- Postulate 2 (the invariance of the speed of light): The speed of light is the same for all observers and does not depend of the speed of the source.
Then the textbook discusses various physical events usually associated with light pulses. For such events one can use the Postulate 2 and derive the beautiful results of special relativity: the time dilation, the length contraction, the relativity of simultaneity, etc. All these results are summarized in the Lorentz transformations for the time and position of events. All this is fine and good.
The problems begin when one wants to extend the Lorentz transformations and other special-relativistic formulas to events associated not with light pulses, but with systems of interacting particles. How can we do that? There is no Postulate telling us anything about interacting particles. So, when we say that Lorentz transformations apply universally to all events and phenomena in the world, we make a huge leap of faith. Actually, we introduce into special relativity a third Postulate
- Postulate 3 (the universality of Lorentz transformations) The Lorentz transformations of special relativity apply to all events independent on their nature and involved interactions.
Only after this Postulate is introduced, we can notice the suspicious symmetry between spatial and temporal coordinates of events and how they transform to the moving frame of reference. Only then we can follow Einstein and Minkowski and boldly introduce the idea of space-time unification into one 4-dimensional continuum.
The question I would like to ask is this: What is the reason for introducing this third (hidden) Postulate? Yes, I know how well special relativity agrees with experiment. However, it could be possible that one can abandon Postulate 3 and still keep this perfect agreement with experiment. Actually, this is possible. One can construct a theory in which Postulates 1 and 2 are respected, but Postulate 3 is not. In this theory, therefore, there is no place for the 4D Minkowski space-time. In this theory, the Lorentz transformations are violated by a tiny amount that depends on the strength of interaction acting in the physical system. These violations are, in principle, observable. However, they are a few orders of magnitude less than the resolution of modern instruments. More about that in later posts.