Check invariance under time-reversal?

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Discussion Overview

The discussion revolves around checking the invariance of a particle's equation of motion under time reversal, specifically in the context of a given potential function. Participants explore the implications of including time derivatives in the potential and whether such terms can be considered part of a potential energy function.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant inquires about checking time reversal invariance for a specific potential function, questioning if it can be done through reasoning rather than computation.
  • Several participants express confusion regarding the nature of the potential, suggesting it appears constant and questioning the implications of that in the context of time reversal.
  • Some participants argue that a time-independent potential is invariant under time reversal, while others challenge this by pointing out the presence of a time derivative in the potential.
  • There is a contention about whether a term involving a time derivative can be classified as a potential, with some asserting it cannot due to the nature of potential energy being a function of coordinates only.
  • Participants discuss the implications of including a friction term, with one stating that friction is not conservative and thus misleading to include in potential terms.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the given potential can be classified as a potential energy function due to the presence of a time derivative. There are competing views on the implications of time independence and the inclusion of friction terms.

Contextual Notes

There are unresolved assumptions regarding the definitions of potential energy and the role of time derivatives in determining time reversal invariance. The discussion reflects varying interpretations of these concepts.

FilipLand
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Hi!

How do I check if the equation of motion of the particle, with a given potential, is invariant under time reversal?

For a 2D pointlike particle with potential that is e.g $$V(x) = ae^(-x^2) + b (x^2 + y^2) +cy', where a,b,c >0$$

Can it be done by arguing rather then computing?

Thanks!
 
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Your potential seems constant ...
 
Orodruin said:
Your potential seems constant ...

How come? And what would that mean in this context? That we can tell if the particle move back or forward in time since potential is constant?
 
Something that is time independent is obviously invariant under time reversal.
 
Orodruin said:
Your potential seems constant ...

There is a y-prime in it.
 
Then it is not a potential.
 
Vanadium 50 said:
There is a y-prime in it.
yes it is
 
Orodruin said:
Then it is not a potential.

I get your point, that it's not a function of time. Thanks. But FYI it's wrong to say something is not a potential due to time independency.
 
FilipLand said:
But FYI it's wrong to say something is not a potential due to time independency.
I never said that. I said that it is not a potential because it contains a time derivative of the coordinates.
 
  • #10
Orodruin said:
I never said that. I said that it is not a potential because it contains a time derivative of the coordinates.

Why wouldn't it be? I have an example exercise where that is the potential we work with?
 
  • #11
FilipLand said:
Why wouldn't it be? I have an example exercise where that is the potential we work with?
Because the potential is a function of the coordinates only. Not of time derivatives of the coordinates. Please give more details of what you are reading.
 
  • #12
Orodruin said:
Because the potential is a function of the coordinates only. Not of time derivatives of the coordinates. Please give more details of what you are reading.

The statement was not true in this case, you can notice in which direction time flows! The time derivative term is a friction term which is not time reversible.
 
  • #13
FilipLand said:
The statement was not true in this case, you can notice in which direction time flows! The time derivative term is a friction term which is not time reversible.
A friction term is not part of any potential because friction is not conservative. It is misleading to include friction terms as "potential" terms.
 

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