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Sorry if this is a stupid question or if it's already been answered, but I struggled to find this answered anywhere:

I know that the equations and transformations etc etc show that, from two different perspectives (in different inertial reference frames? I guess is the word), two events could be perceived in one frame as having occurred simultaneously, and not simultaneously in the other frame. And that all the laws of physics are perfectly consistent with both points of view, and there's no way of measuring or determining that one frame was 'correct' and the other one was 'incorrect'.

What I'm unclear on is, even if there's no way of measuring or determining the 'correctness' of one frame over another, is it still possible that in reality, in the "source code of the universe" if you will, that everything really is being calculated from one particular inertial reference frame? Is it just that we can't find out what that 'objective' reference frame is, or is it categorically conceptually impossible for there to be an objective reference frame that underlies physics?

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    $\begingroup$ Although some on this site may disagree with what is a largely philosophical question being posed, I disagree with this consideration. However, as it is a philosophical question, I shall, in place of an answer, leave you with a list of questions that may help you ponder what the answers to such a question might be. Why should such an inertial frame exist? Indeed, what if this frame were to find itself within a black hole? Is the universe even being calculated, or is it simply that "things happen"? Is there even any meaning to a question which we cannot ever determine the answer to? $\endgroup$
    – FizzKicks
    Commented Jul 26, 2021 at 8:47
  • $\begingroup$ Perhaps it is also worth mentioning, that within the context of general relativity, there are no globally inertial frames - physics.stackexchange.com/questions/192128/… - which is another way of saying that we may choose coordinates that look inertial at any given point, but not everywhere. $\endgroup$
    – FizzKicks
    Commented Jul 26, 2021 at 8:53
  • $\begingroup$ Is the universe even being calculated, or is it simply that "things happen"? What I mean by this is that the future states of the universe apparently evolve from past states according to rules - this is true even in quantum physics, where the rules get a bit whacky and strange, but there are still rules. The evaluation of these rules to produce the next state is what I'm referring to as a 'calculation'. They are most likely being 'calculated' at a local level, but do they rely on a reference frame? $\endgroup$
    – TKoL
    Commented Jul 26, 2021 at 9:11

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... even if there's no way of measuring or determining the 'correctness' of one frame over another, is it still possible that in reality, in the "source code of the universe" if you will, that everything really is being calculated from one particular inertial reference frame ...

If there is no way even in principle to detect something, then in practice it does not physically exist. There's no reason to postulate undetectable things (like the "true" reference frame of the universe).

If that doesn't satisfy you, then consider this: the requirement that the laws of physics be the same for all choices of simultaneity is actually much stronger than assuming that there is some preferred "true" choice of simultaneity. Hence it is more useful in determining the laws -- it imposes an additional symmetry which isn't present in the "only one true simultaneity" situation. The "source code of the universe" is like a distributed program which must work correctly regardless of which system's clock is chosen as the reference. Writing a program that satisfies that requirement is much harder than writing a program that works on just one system (one choice of clock), and therefore there are fewer ways to do it.

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Your question assumes that there can be some measure of simultaneity that is somehow more absolute than others. That is quite an unnecessary assumption. All simultaneity means is that two or more events share the same t coordinate in some reference frame, no more and no less. It is rather like the concept of a horizontal level. Two points are level horizontally if they share the same z coordinate, which means they are level in some reference frames and not in others. You would not dream of wondering whether there is an absolute or objective sort of horizontal level- you would simply accept that it depends on the direction chosen for a z axis. You should apply the same thinking to time. There is no absolute direction for a t axis, and so there can be no sense in which one person's measure of simultaneity can be more significant than another's.

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  • $\begingroup$ I suppose my point of view is that I'm still thinking of the universe -- wrongly or rightly -- as a much more complex version of the 'game of life'. The game of life can also be entirely locally calculated - each pixel can be responsible for itself with only the knowledge of the surrounding pixels -- but it has a 'tick rate', so even though everything is local, there is still an objective fact about what two events happen simultaneously. $\endgroup$
    – TKoL
    Commented Jul 26, 2021 at 9:56
  • $\begingroup$ Now, my comparison of the universe to the game of life could be, and likely is, ENTIRELY off base, but I can't help but imagine that the rules that govern this universe also operate with a 'tick rate' of sorts. So for me, relativity of simultaneity might just mean "we can't TELL the objective fact about when two events are simultaneous" rather than "there is no objective fact about when two events are simultaneous" $\endgroup$
    – TKoL
    Commented Jul 26, 2021 at 9:58
  • $\begingroup$ If it's the second one, "there is no objective fact", then... I guess that's what I've come here to ask. I guess your answer is telling me that, there is no objective fact, right? It's not just that we can't tell, it's that the fundamental idea of there being an objective fact, discoverable or not, is incompatible with relativity? $\endgroup$
    – TKoL
    Commented Jul 26, 2021 at 9:59
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    $\begingroup$ It's not that there is no objective fact, it just means that the values of things such as position, speed, time are relative. Expecting there to be an absolute time is like expecting an absolute height- there is no such thing as it depends on which datum point you chose to measure it from. $\endgroup$
    – Professor Sushing
    Commented Jul 26, 2021 at 12:21
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Consider the same two high precision clocks, with a difference of altitude $h$, which can be as small as one or two centimeters. If at a moment you decide that they are synchronized, later you will observe a relative time shift of $1 + \frac{g h}{c^2}$, with the same synchronization protocol now and later (see for example https://doi.org/10.1038/s41566-020-0654-5).

If, because of the presence of the Earth with lab gravitation acceleration gravitation $g$ two synchronized clocks cannot give the same time, it is clear that the concept of simultaneity has no meaning other than mathematical, with the arbitrary choice of a $(t, x, y, z)$ coordinate system.

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