# Noether's theorem -- Time inversion

1. Nov 12, 2015

### LagrangeEuler

Noether's theorem said that because of homogeneity in time the law of conservation of energy exists. I am bit of confused and I am not sure is also time inversion some consequence of this. For example in the case of free fall we have symmetry $t \rightarrow -t$. I am sometimes confused of that. Symmetry $t \rightarrow -t$. is valid when we have conservation of energy and conservation of energy we have because of homogeneity in time. Could please give me some more insight on this problem. Thanks.

2. Nov 12, 2015

### Staff: Mentor

Noether's theorem applies to differential symmetries like time translation, and not to discrete symmetries like time reversal.

3. Nov 12, 2015

### LagrangeEuler

Yes but we will not have time reversal symmetry if we did not have symmetry under the time translations. Right?

4. Nov 12, 2015

### LagrangeEuler

Also when we have $t \rightarrow -t$ didn't we did translation of time $t$ of some kind?

5. Nov 12, 2015

### Staff: Mentor

No. Consider the function $\cos (t)$. It is symmetric under time reversal $\cos(t)=\cos(-t)$ but not time translations $\cos(t)\ne \cos(t+\delta t)$

6. Nov 12, 2015

### LagrangeEuler

Thanks Sir. Very nice example.