Sagittarius A-Star said:

@Ibix linked a related paper in posting #2. It does already, what you claim in the OP.
A general boost transformation in ##x##-direction between intertial frames in equation (27) is derived without using the 2^nd SR postulate:
$$\begin{pmatrix}
x' \\
t'
\end{pmatrix}
=
\frac{1}{\sqrt{1-Kv^2}}
\begin{pmatrix}
1 & -v \\
-Kv & 1
\end{pmatrix}
\begin{pmatrix}
x \\
t
\end{pmatrix}.$$
Source:
https://arxiv.org/abs/physics/0302045

Then 3 cases remain:
##K<0## is shown to be not self-consistent
##K=0## would mean that an absolute true time ##t=t'## exists (Newton) -> refuted by experiment
##K>0## would mean special relativity (##c## is invariant, Einstein) -> not refuted by experiment

It is difficult to explain my claim without saying what the assumptions actually are, but it is true, if you only change the Principle of Relativity, you wouldn't get anywhere.

Mind you, I have no problem showing the calculations, that's the whole point of my question. I am not sharing because, if I'm not mistaken, it is against the rules of the Forum. Just wanted to clarify this point.

That said, in experiments you measure time differently, but even inside Special Relativity there is a difference between what you can measure, and what the model implies is happening, as for example with the Andromeda paradox: everyone gets the same information at the same time, if they are in the same place at the same time, but what they calculate is the time at Andromeda is different, if they are moving at different speeds (even if they cannot receive that information).

That's what happens in what I've been studying. What can be directly observed is the same, until now, but what the model says is happening is different. Although, this raises a very interesting issue which I'm well aware of: if what I said is true, so far the model is not falsifiable. I believe it is, but perhaps it's a bit premature to discuss that if I can't even show the arguments in the first place

Matterwave said:

The postulate that the speed of light is constant and independent of frames is borne out by observation. Most famously by Michelson Morley and then subsequently over many experiments later on. It's probably one of the more well tested postulates of a physical theory since its result is quite unintuitive.

There might be some wrinkles in how you want to define "testing the principle of relativity" (I don't want to get into it here). But I think most physicists would say the principle of relativity is also very well tested.

It is somehow a bit dismissive of the body of experimental scientific work and literature to say "I violate no experiment, I only violate the postulates of SR" if those experimentalists spent all that effort to "validate the postulates of SR". Have you looked through all these experimental tests to see if they convince you of the postulates?

Certainly the problem could be theoretical. Maybe we haven't developed the theory of SR to "really be a consequence of the postulates". There, it might be useful to see some of Einstein's original work to see if his arguments convince you.

I feel like this basically exhausts the possibilities. If your claim is your theory is consistent, arising from postulates that contradict the postulates of SR, while still reproducing all of its observations, then you have a pretty uphill battle to climb.

The only thing I could say there is the overwhelming possibility is that there is an error in your calculations or chain of logic. If the error is purely calculational, maybe an AI would pick it up. If the error is logical, and it's non obvious, then it's very easy to deceive an AI into agreeing with you.

Note that other responders here have in their responses, as I read them, generally assumed your postulates don't contradict the SR ones, only that you chose a different initial set.

Well, I understand your frustration at yet another bizarre claim, but I'd like to point out I didn't contradict the constant and equal speed of light, I just said in this model that would be a consequence, not a principle. I contradict other things, but those can't be directly measured.

Interesting you mentioned Einstein's work. I did read "On the Electrodynamics of Moving Bodies." It's a wonderful work. Couldn't agree more with his arguments, just wish I were more used to the notation of the time.

I must say, I agree with all of the arguments that have been provided here, with the notable exception of

Matterwave said:

I feel like this basically exhausts the possibilities.

and

Matterwave said:

It is somehow a bit dismissive of the body of experimental scientific work and literature to say "I violate no experiment, I only violate the postulates of SR" if those experimentalists spent all that effort to "validate the postulates of SR". Have you looked through all these experimental tests to see if they convince you of the postulates?

The problem is I cannot discuss the content of my work here, as far as I can tell, and so the only thing I asked was what I should do about it.

I do claim it seems to be right, but I don't claim it is right. Whether it is right or wrong is what I want to find out.