- #1

giulio_hep

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One of the basic foundation of special relativity is that the speed of light is a constant, hence time is relative to the inertial framework reference. Usually GPS is also mentioned as a modern experimental evidence. My questions: if Maxwell's equations describe EM fields, how can we derive a more general notion of time (*)? It is said that lenght's contraction is measured by Einstein's convention between different points according to the reference framework and is not seen as "real" difference, how is time dilation interpreted in a more "paradoxical" (**) sense? Finally, in the experimental evidence (for instance the ticking of clocks on satellites) what is the mathematical tool used to separate the effect of acceleration/deceleration (***) from the mere inertial one?

[notes]

(*) with the term "more general" I mean the fact that (starting from an EM law, the constant light speed limit) we apply the spacetime diffeomorphism also to clocks not based on electromagnetic fields;

(**) I don't want to discuss the so called paradoxes, I'm simply focused on the fact, under Lorentzian signature, the spatial coordinates maintain a strict ordering while for the time coordinates only time-like events can be ordered, even though the invariant equations appear quite symmetric in space and time...

(***) my final question is the least important to me: maybe the clock postulate is already an answer, but I'm just wondering whether the effect of time dilation could be ascribed more to the past acceleration than to the current speed.

[meta-note]

Please, forgive me if my question seems too unclear or metaphysical... I would be happy to better clarify my doubts after your replies and I hope that can be considered enough to start a question or a dialog here.EDIT

I have to better clarify an important point that was unclear in my question but is maybe the main point I'd like to ask. If you look at the first lecture of Susskind about Special Relativity at 1:16:30 he says: "notice that we are really talking about two really different things" and he is speaking about the end of a meter stick in a moving reference frame compared to a rest one... What I'm asking is: if you can explain the length contraction as due to different points in different reference frames, couldn't you do the same with time, saying that the time dilation is due to different instants in different reference frames?

[notes]

(*) with the term "more general" I mean the fact that (starting from an EM law, the constant light speed limit) we apply the spacetime diffeomorphism also to clocks not based on electromagnetic fields;

(**) I don't want to discuss the so called paradoxes, I'm simply focused on the fact, under Lorentzian signature, the spatial coordinates maintain a strict ordering while for the time coordinates only time-like events can be ordered, even though the invariant equations appear quite symmetric in space and time...

(***) my final question is the least important to me: maybe the clock postulate is already an answer, but I'm just wondering whether the effect of time dilation could be ascribed more to the past acceleration than to the current speed.

[meta-note]

Please, forgive me if my question seems too unclear or metaphysical... I would be happy to better clarify my doubts after your replies and I hope that can be considered enough to start a question or a dialog here.EDIT

I have to better clarify an important point that was unclear in my question but is maybe the main point I'd like to ask. If you look at the first lecture of Susskind about Special Relativity at 1:16:30 he says: "notice that we are really talking about two really different things" and he is speaking about the end of a meter stick in a moving reference frame compared to a rest one... What I'm asking is: if you can explain the length contraction as due to different points in different reference frames, couldn't you do the same with time, saying that the time dilation is due to different instants in different reference frames?

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