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I learn through confusion, and something about molecular structure still very much confuses me.

A vibrating clock will ultimately run slower than your wristwatch, because of, for one, kinematic time dilation, as it spends a lot of its time moving. Secondly, there is also a non-inertial (accelerated) frame because vibration moves the velocity vector.

If this vibration frequency/amplitude is slow/small, the physicist will say "you can neglect the time dilation, it's too small", and if the speed/amplitude is big so that the Lorentz factor becomes meaningful, the clock's mechanism and structural integrity will suffer and the physicist will go on about how the clock explodes and turns into a supernova, etc. That's what physicists like doing, and I love them for it.

But that's not what interests me and what confuses me right now.

Molecules, as they vibrate, each have their own inertial or non-inertial frame, because they get accelerated through all the bouncing and buildup of motion, and "spend their time" in motion compared to other things. They might get "time dilated" compared to a neighbouring molecule because of kinematic time dilation and actually I believe as well because they are in an accelerated frame. The thing that still confuses me is that infinitesimally, while this all seems rather meaningless, doesn't it start mattering because of the very speed at which molecules react with the environment? Is a relativistic attitude to matter even a thing? I can imagine some topological reasons why some molecules would pass on sound waves or phonons differently because they are running "slower" or "faster" compared to other parts of the matter.

Another thing that confuses me, is that molecules are so small, and change directions so swiftly, that their "a" acceleration vector has to be huge, infinitesimally, and I don't quite understand how that may matter in the relativistic concept of "local time dilation" in matter.

Sorry for being long-winded, I'm hoping my confusion can settle somewhat with smarter people showing the way.

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  • $\begingroup$ This seems very relevant in considering the half-lives of intermediate isotopes in stars, for example nitrogen-15 in the CNO cycle. Interesting... $\endgroup$
    – Mike Serfas
    Commented Nov 13, 2021 at 22:57
  • $\begingroup$ @MikeSerfas I just received a paper called “On the theory of time dilation in chemical kinetics” that deals with the above subject. $\endgroup$
    – buddhabrot
    Commented May 6, 2022 at 15:55
  • $\begingroup$ If the observer is in thermal equilibrium with the vibrating molecules and in the same reference frame, wouldn't the time-dilation effects average out? $\endgroup$
    – Stevan V. Saban
    Commented Jun 4, 2022 at 15:11

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It would seem the answer would be dependent on how "big" local is. The time dilation of the molecule with respect to itself would of course be a net zero, but as you expand "local" to the adjacent "neighborhood" there are relativistic differences, and thus a dilation. Keep going, and there would be a point where it would start to cancel out.

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