Has the connection been noted between these two? I have been studying special relativity and in learning Minkowski diagrams I have noticed that as v approaches c, the relativity of simultaneity is so drastic that all of what any observer would call effects happen simultaneously with their causes. In other words, entropy can't be said to increase for that observer. This relationship between the relativity of simultaneity and entropy holds for all other velocities as well and after a little thought it seems obvious: time dilation occurs occurs with the relativity of simultaneity because a change in the order of events (rel of sim) is a change in the increase of entropy (second law of thermodynamics) for any observer, which defines the arrow of time. If entropy increases as events occur for any frame of reference, then if that frame experiences the relativistic effects of changes in the ordering of events, they will experience time dilation due to a lessening of entropy's increase (to the the extent of the relativistic effects of reordering of events). The relativity of simultaneity must cause time dilation due to the definition of the arrow of time in thermodynamics. I would like to express this mathematically, though I am just learning the math of relativity now. I am curious as to why I have not seen this point made yet. I can hardly imagine this connection would not be seen as interesting enough for anyone to mention in teaching these two fundamental ideas...?

Edit: because the question/idea has seemed unclear to many people I will state it like this. I believe there is a deep equivalence between relativity and thermodynamics. Viewing our universe as a system evolving toward higher entropy with time, I believe that any perspective which experiences less time (time dilation) must do so because they experience less entropy. Because entropy is defined by the most probable statistical evolution of events, an inertial frame which experiences time dilation (less entropy) must experience a less probable ordering of events, which happens via the relativity of simultaneity. Note that the probability of experiencing an increasingly highly relativistic perspective (for instance, from random natural accelerations) is increasingly rare exactly because it takes energy to do so, exactly as it is increasingly rare to find thermodynamic systems evolving toward states further and further from maximum entropy. I am not saying anything about violating causality, simply that (referring to thermodynamics) there are evolutions which at times momentarily shift away from maximum entropy, but don't violate the second law because they don't decrease entropy, just as there are relativistic frames that experience an ordering of events from the relativity of simultaneity that slow but do not reverse time.

  • $\begingroup$ Could you perhaps try to distill a clearer question out of this? I have honestly about half a dozen conflicting ideas about what you might mean, but basically I think you might be confused about what entropy actually means. As a general rule though, if you are just learning a subject that has been around for decades, it is pretty unlikely (though not impossible) that you have discovered some new fundamental insight in your first days or weeks. $\endgroup$ – ACuriousMind Jul 8 '14 at 23:09
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    $\begingroup$ what ACuriousMind said. Also, for timelike-related events, lorentz tranformations do not alter the order of events, only the interval between them. $\endgroup$ – Jerry Schirmer Jul 8 '14 at 23:25
  • $\begingroup$ So are you saying because of relativistic time dilation, the entropy arrow of time must change as well? I don't really understand what you're getting at. $\endgroup$ – user53089 Jul 9 '14 at 0:05
  • $\begingroup$ Thanks for the reply. Another way to express what I am saying is 'can time dilation be explained as being a result of the relativity of simultaneity (as opposed to analyzing the geometry of light clocks for instance)?' When we analyze light clocks and see how much longer a photon path traces on a 'moving clock' we are already making the assumption of the second law of thermodynamics (time has passed) just to analyze the situation. In trying to understand whether relativity or the second law is 'fundamental' I'd like to find a scenario to analyze relativity where the second law is absent... $\endgroup$ – JTT Jul 9 '14 at 1:18
  • $\begingroup$ which is only possible when relativistic effects are at a maximum. The second law(as usually experienced)disappears because of the relativity of simultaneity. Again, because the flow of time is dictated by the regular flow of events from any perspective, a moving observer will experience a change in that order due to the relativity of simultaneity and will experience time dilation to the extent that the relativistic effect changes the usual order which makes up what that observer would usually experience to be the increase of entropy (the second law). $\endgroup$ – JTT Jul 9 '14 at 1:26

The order of the events never changes in Special Relativity (as Jerry Schirmer stated above) to preserve causality. If you are thinking of Boltzmann entropy then I would guess its still increasing as the number of states after evolution (no matter how slow compared to a different reference frame) goes up just like in any other system.

  • $\begingroup$ Yes, as I said in response to Jerry, the causal order of events is never reversed as this would take infinite energy and is ruled out as impossible. I believe this is analogous to the impossibility of entropy decreasing. Again, notice the similarity between the two ideas (relativity and the second law) that the impossibility lies in the reversal of the course of causality. I'm saying that we can view different perspectives of spacetime as equivalent to different evolutions of a single macroscopic thermodynamic systems. Each(relativity and 2nd law) has a causal structure which can't be violated $\endgroup$ – JTT Jul 9 '14 at 5:42
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    $\begingroup$ @Jerry Schirmer, PhotonicBoom: Of course the order of two events can change (example: Einstein's train example with two simultaneous flashes in the front and the back of the train, you may retard one of the flashes by a small time lag so that the observer on the train will observe a different order than the observer on the platform). $\endgroup$ – Moonraker Jul 9 '14 at 7:04
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    $\begingroup$ The answer to the question: Only events which are separated by a spacelike interval may change order. Proof: Choose 2 events separated by a timelike interval. Now send a particle (electron) through both events. Now, according to SR, every observer will observe a different speed of the electron, but no observer will observe the electron flying backwards. As a result, there is no issue at all with thermodynamics nor with causality because the phenomenon is only concerning spacelike events. $\endgroup$ – Moonraker Jul 9 '14 at 7:04

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