Relativity, time, and quantum mechanics

[anuttarasammyak]

[Mentors’ note: Spun off from this thread]
I understand that you are interested in the concept of time in quantum mechanics. Here are examples of my questions, in case they may be of reference.

１.How can one calculate the proper time of an electron in the 1s orbital of a hydrogen atom? How should the Lorentz factor be applied to motion that is not classical?　Would that result in a superposition of different proper times?

2. To determine the invariant spacetime interval between events associated with a particle, one would obtain the spacetime coordinates (t, x, y, z). However, due to the uncertainty principle, measuring the spatial coordinates x, y, z imparts momentum to the particle, so its rest frame changes from the original one. It would be a mess. Since there is no measurement operator for t, does time play the role of reconciling this inconsistency?

3. It appears that, with respect to a measurement at time zero, when collapse takes place in interaction with apparatus or environment, the state before measurement and the state after measurement are asymmetric, e.g. entangled and disentangled. Could this be the origin of thermodynamic or arrow of time?

 

[Nugatory]

１.How can one calculate the proper time of an electron in the 1s orbital of a hydrogen atom?

How should the Lorentz factor be applied to motion that is not classical?[/quote]We don’t. Proper time is the length of a path through spacetime between two events; the electron has no path or position so the notion “the proper time of an electron” is meaningless. Instead we work with the time measured by our lab clock between observation events.

2. To determine the invariant spacetime interval between events associated with a particle, one would obtain the spacetime coordinates (t, x, y, z). However, due to the uncertainty principle, measuring the spatial coordinates x, y, z imparts momentum to the particle, so its rest frame changes from the original one.

X,y,z,t are the coordinates of the observation event using the frame in which the lab is at rest. The “rest frame of the electron” never enters into the calculation (unsurprisingly, because it’s not defined).

3. It appears that, with respect to a measurement at time zero, when collapse takes place in interaction with apparatus or environment, the state before measurement and the state after measurement are asymmetric, e.g. entangled and disentangled.

The global collapse interpretation you are trying to use here is non-relativistic so cannot be applicable here. Instead we have to use the methods of quantum field theory, in which there is no global collapse.

Could this be the origin of thermodynamic or arrow of time?

We’ll find that in statistical mechanics.