# Time reversal invariance of physical laws stated mathematically

There is a logical argument stated in many physics books that laws of physics obey time reversal invariance. A common example that is given is two colliding balls in a snooker game. If we observed that phenomenon and then reversed the time, we would conclude that both are equally 'real' scenarios and can happen within the axioms of mechanics. How can one state the above conclusions mathematically ? (for example in the second law of mechanics).

• I've edited to clarify you weren't referring to time translation invariance. – J.G. Mar 13 at 20:57
• Nice. So there is also a thing called time translation invariance. Cool. I guess this has to do with the laws of physics being the same at some time t + δt. – Unstoppable Tachyon Mar 13 at 21:04
• Exactly. What's more, they're two different kinds of symmetry. Translation invariance is continuous, so Noether's theorem relates it to a conservation law (in this case of energy). Reversal invariance is discrete, so doesn't have the same implication. – J.G. Mar 13 at 21:11