# Time reversal invariant v.s. Time-independent systems

+ 1 like - 0 dislike
746 views
1. For classical systems, are time reversal invariant (T.R.I) and time-independent (T.I) necessarily the same thing?

2. For quantum systems, are time reversal invariant (T.R.I) and time-independent (T.I) the same thing?

Can one give examples for classical and quantum that are:

(1) T.R.I and T.I. systems

(2) T.R.I but not T.I. systems

(3) T.I but not T.R.I systems

(4) not T.R.I and not T.I. systems, but unitary.

This post imported from StackExchange Physics at 2020-11-05 13:27 (UTC), posted by SE-user annie marie heart

+ 0 like - 1 dislike

They are absolutely not the same thing. There are many time reversal invariant systems in classical mechanics, for example a planet orbiting a star, however nothing will ever be time independent. Imagine that you thought you had a system which is time independent, it consists of a bunch of things and none of them are moving. Relativity will tell you that you can move at a constant velocity and physics will be the same. In which case it will appear that everything in the system is moving uniformly and is not time independent.

Quantum mechanically, it's essentially the same, it is easy to come up with time reversal invariant systems, for example the quantum harmonic oscillator. And there are no time invariant systems in quantum mechanics because relativity still holds and you could use the previous argument.

This post imported from StackExchange Physics at 2020-11-05 13:27 (UTC), posted by SE-user yankyl
answered Dec 28, 2017 by (-10 points)
I am suspecting that you are confused with time-reversal symmetry transformation $T$ (the discrete transformations not within the continuous Lorentz group) and the Lorentz transformation $\Lambda_{1/2}$ (the 6 generators). They are not the same operations. (p.s. I did not vote in case someone willl vote later.)

This post imported from StackExchange Physics at 2020-11-05 13:27 (UTC), posted by SE-user wonderich

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysicsOverflo$\varnothing$Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). Please complete the anti-spam verification