# Check invariance under time-reversal?

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## Main Question or Discussion Point

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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Orodruin
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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?

Orodruin
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Something that is time independent is obviously invariant under time reversal.

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There is a y-prime in it.

Orodruin
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Then it is not a potential.

There is a y-prime in it.
yes it is

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.

Orodruin
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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.

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?

Orodruin
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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.

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.

Orodruin
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