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?

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.

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.