I am ready to describe a little how to replace Special Relativity with a better kinematics that discards the non-mathematical notions of ‘Observer’ and ‘Frame of Reference’. Instead one would use geometry both with and without coordinate systems, without the encumbrance of ‘physical’ interpretations.
The full power of mathematics would be available.
Without ‘Frames of Reference’, we should no longer call the kinematics ‘relativity’. Just ‘kinematics’.
Let us proceed...
As an example, imagine a burst from a flashbulb bouncing off a mirror and returning. This all occurs on a sled that is moving at a constant velocity normal to the direction from the bulb to the mirror.
In the new kinematics, c is no longer called ‘speed of light’ but just ‘c’. It was regarded as the ‘speed of light’ before Einstein but the trend probably has been away from that, anyway. It is a fundamental characteristic of electromagnetism that can be used to define the unit of velocity...
That c is constant means merely that an electromagnetic field is an ordinary object that you can move through without it becoming distorted, as long as you are neutrally charged and do not exude a significant electromagnetic field of your own.
This is why the Michelson-Morley experiment detected no differences in c.
There is no mystery and there is nothing weird about it...
Now suppose you are not on the sled. If you use galilean relativity you are likely to get a wrong answer to your question. If you use Einstein’s relativity you may get a correct answer to your question, but it is all very unintuitive and in more difficult problems you may make a mistake and get a wrong answer.
This has probably happened often, going back to Albert Einstein himself. One chooses the wrong line on the Minkowski diagram as measuring rod.
Let us take a new approach...
Say the sled is headed away from us. In this case, the waves from the flashbulb are striking the mirror at an angle and are stretched out. They are Doppler shifted towards a longer wavelength.
But we will be abstract and mathematical. So we are going to say simply that in this coordinate system there is a source of electromagnetic waves of that kind. We will not talk of it as ‘relativity’.
The problem of our kinematics, then, is to provide transformations between coordinate systems.▪️
Now we get to Part Two, which is the commentary on "So what changes?"
First, you can see that this is not simply galilean relativity, because you must calculate transformations of electromagnetic waveforms, or at least of parameters associated with them.
But also this is not Special Relativity, because you are dealing with two ordinary cartesian coordinate systems...
There is no attempt to involve "Observers". You simply have two coordinate systems of the same geometry. You wish to be able to transform between the two. Then from this tranformation you wish to be able to deduce facts.
Note also that there is no ether. I have not reintroduced the ether. It is the electromagnetic field itself we are immersed in and are, in fact, a part of. Apart from mass, we are mostly the field created by our electrons...
This observation explains, incidentally, why "faster than light travel" is an incredibly silly notion. You are demanding that things that are part of the electromagnetic field move faster than the electromagnetic field. That's really silly.
Many things in physics become a lot clearer if you look at the big picture. The idea behind this new kinematics is just that: to look at the big picture instead of the parochial views of "Observers".▫️
Barry Schwartz 🫖