- It’s usually held that Mechanics belongs to the Reversibility domain and the time-symmetry of dynamics’ second law would confirm this belief. Of course, it is maintained, the solution exhibited at the time “t” must show a reversible process. Otherwise the solution at time “-t” would cause the actual inversion of an irreversible process, which cannot happen in nature. In other words, the fact that both solutions are observable would confirm beyond any doubt Mechanics’ Reversibility.
- Unfortunately, the argument misses the point that solution “-t” might not violate any natural law simply because it exhibits the same irreversible process of solution “t”. As such, both solutions are again observable. An example will clarify that this is indeed the case.
- In a 1D elastic collision the two bodies move, say, from left to right. In this “t” solution we always observe the faster than average body slowing down and the slower than average one accelerating. This is an irreversible process in which kinetic energy flows spontaneously (since our system is isolated) from the faster body to the slower one, just like heat flows spontaneously from a hotter body to a colder one in contact. And the same irreversible process occurs when we observe the “-t” solution: now our colliding bodies will be moving from right to left, and it’s still true that the faster body slows down while the slower one accelerates.
- We meet the same situation with inertial forces when the motion of a material point along its path is considered. In a frame aboard the material point we detect the same inertial force for both, “t” and “-t”, solutions as stated by the dynamics’ second law. Here the classic example is the elevator in free fall: the inertial force is directed upwards compensating for “gravitational effects” of bodies inside. The “-t” solution shows a raising elevator, ascending at less rate in order to have the same inertial force still directed upwards.
- This is what, in my opinion, establishes a deep connection between Inertia and Irreversibility. By the way, the motion of an inertial frame would be reversible. But, does it really exist in nature a frame like that?
Tags: collision, inertia, irreversibility, symmetry
