[greygrid19 (OP)]

Hello, I have a question about a possible revision of Einstein's theory of relativity. The fact is that its root error is indicated by the fact that at the initial moment of time, that is, when all three coordinates of the two systems coincide, we mistakenly decided at some point in time to take the speed as constant c instead of the variable dc, we got that at an infinitely small point in time, a constant final velocity was recorded — obviously, this does not happen. Therefore, when I typed the following expression in wolfram mathematica: {d (x ^ 2) + d (y ^ 2) + d (z ^ 2) == (dk) ^ 2 * (dt) ^ 2, d (w ^ 2 ) + d (y ^ 2) + d (z ^ 2) == (dk) ^ 2 * (df) ^ 2}, he in one of the solutions gave an answer that is quite suitable for the context of the problem in understanding the absolute time (with the Reduce command ) Please explain if it is possible in simple terms, do I have the right to such an interpretation as one of the interpretations, and maybe, if my reasoning is correct, I will incorrectly interpret the theory of relativity itself — but if it’s incorrect, how should I interpret it? Thank you very much!

[Colin2B]

when all three coordinates of the two systems coincide, we mistakenly decided at some point in time to take the speed as constant c instead of the variable dc,

It is quite difficult to understand what you are asking. Can you explain further what you mean.
When the coordinates of 2 frames coincide we can take t =0, x=0, etc. However, c is a constant as determined by Maxwell’s equations which describe the relationship between electric and magnetic fields and the propagation of electromagnetic radiation eg light/photons.

Therefore, when I typed the following expression in wolfram mathematica: {d (x ^ 2) + d (y ^ 2) + d (z ^ 2) == (dk) ^ 2 * (dt) ^ 2, d (w ^ 2 ) + d (y ^ 2) + d (z ^ 2) == (dk) ^ 2 * (df) ^ 2},

Why did you type that in?
Please explain what k, w and f represent and how you decided to use them in this form.

[greygrid19 (OP)]

k-speed of light, w-coordinate of the signal in the second system along the x axis, f-time of the second system. The logic is as follows. The speed of light does not propagate instantly - it takes a finite time to travel a constant path per unit time k, but both systems move relative to each other with a finite speed v, so it is already wrong to assume that when both observers notice k, then t = f = 0, nor equal to zero the derivatives of the times, leaving k a finite constant speed. That is, the question in my generalized equalities is not about the constancy of the speed of light itself (despite the fact that I do not deny its constancy), but about the constancy of the law by which it tends to zero in an infinitesimal period of time

[yor_on]

Are you asking about how one can define a infinitesimal amount of time to a system in where both 'observers' are moving? Relative some godlike frame of reference? I guess you started with a question in mind, before translating it into a formula? If you present the question you thought up then it will be easier.

[Colin2B]

If you present the question you thought up then it will be easier.

I think @yor_on is right, you are obscuring the question by not stating it clearly.
If you are trying to talk about infinitesimal time period then I don’t see it as a problem, each observer can happily talk about the proper time in their frame. It would be the same if they both wanted to discuss infinity.

[greygrid19 (OP)]

the question is whether I have the right to an even outdated, but in a sense clear interpretation, that time in both reference frames flows the same way, that is, always t = f

[Colin2B]

the question is whether I have the right to an even outdated, but in a sense clear interpretation,

I wouldn’t call it clear because your posts are still very unclear. However, you have the right to any interpretation even though it is wrong. We would classify it as a new theory.

that time in both reference frames flows the same way, that is, always t = f

For timelike and null event, observers in both frames will agree on the order of events, not always so for spacelike events.
Observers in each frame will measure their own elapsed time as t or f, but will disagree on the value of t or f in the other person’s frame.

If your interpretation agrees with this (and other SR and GR results) then your interpretation would be considered correct, otherwise it’s a new theory.

[yor_on]

Ahh, that one is interesting.  Do you mean locally equivalent? Now that depends on what you use. There is possibly no objective reality quantum mechanically, and in relativity you find frames of reference. Measurements use local definitions (cm, seconds, kg etc), and so do those 'frames' meaning that they always go out from a (local) observer to define other frames of reference relative their own. But Lorentz transformations is another thing, it's a construction from a 'mind space' representing another type of reality, the one we call the 'objective' universe. We presume that this must be correct, because we are all existing inside it, and we see the same universe and can agree on it.
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It is from this 'objective mindspace' we define time dilation's and LorentzFitzGerald contractions, using the local interpretation of what our clock and meterstick tells us. So locally defined, with a possibility of this soon finding itself in New Theories, you can define it as if 't' always will be 't' locally measured, becoming a local equivalence. 'Globally' or 'objectively' there is no such thing though, unless you are in a same frame of reference.
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Actually it's all connected to lights speed in a vacuum, our local definitions. And there you have the fact that this constant doesn't care about your speed, or mass. It's 'local' too.