Check invariance under time-reversal?

In summary, the conversation discusses the concept of time reversal in relation to the equation of motion for a 2D pointlike particle with a given potential. The potential in question is not time independent due to the inclusion of a time derivative term, which is argued to not be part of a true potential. This means that the potential is not invariant under time reversal. The conversation also touches on the concept of friction and its relationship to potential.
  • #1
FilipLand
52
3
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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  • #2
Your potential seems constant ...
 
  • #3
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?
 
  • #4
Something that is time independent is obviously invariant under time reversal.
 
  • #5
Orodruin said:
Your potential seems constant ...

There is a y-prime in it.
 
  • #6
Then it is not a potential.
 
  • #7
Vanadium 50 said:
There is a y-prime in it.
yes it is
 
  • #8
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.
 
  • #9
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.
 

FAQ: Check invariance under time-reversal?

What is check invariance under time-reversal?

Check invariance under time-reversal is a concept in science that refers to the ability of a system or phenomenon to remain unchanged when time is reversed. This means that the system or phenomenon will behave the same way regardless of whether time is moving forward or backward.

Why is check invariance under time-reversal important in scientific research?

Check invariance under time-reversal is important because it allows scientists to make accurate predictions and observations about the behavior of a system. It also helps to identify fundamental laws and principles that govern the behavior of the universe.

How do scientists test for check invariance under time-reversal?

Scientists test for check invariance under time-reversal by performing experiments and observations that involve reversing the direction of time. This can involve reversing the direction of motion, changing the direction of a magnetic field, or observing the decay of a radioactive substance in reverse.

What are some examples of systems that exhibit check invariance under time-reversal?

Some examples of systems that exhibit check invariance under time-reversal include Newton's laws of motion, Maxwell's equations of electromagnetism, and the laws of thermodynamics. These laws and principles hold true regardless of the direction of time.

Can check invariance under time-reversal be violated?

In some cases, check invariance under time-reversal can be violated. This is known as time-reversal asymmetry. Examples of this include certain subatomic particle interactions and the concept of entropy in thermodynamics. However, these violations are still subject to ongoing research and study.

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