Physics is reversible, which means one can define a notion of “volume” which is conserved under the actual evolution of the system (this is much closer to a tautology than you would guess from the post).
In order for physics to be reversible, implementing your f would require making some other change, elsewhere in the system (or else some larger deviation from physics as we know it). Say, you would have to increment a counter somewhere marking “Number of times velocity has been halved: X”
If this were how physics worked, our notion of “volume” would just be changed (it would get multiplied by 2^X for each fixed X, and then added up across different values of X). And then notions of “entropy” and “temperature” would be changed as well, and order would be restored.
There are some conditions under which “temperature” and “entropy” correspond to other physical quantities, defined in terms of kinetic energy and so forth. This is not physical law, and this would just cease to be such a case.
Physics is reversible, which means one can define a notion of “volume” which is conserved under the actual evolution of the system (this is much closer to a tautology than you would guess from the post).
In order for physics to be reversible, implementing your f would require making some other change, elsewhere in the system (or else some larger deviation from physics as we know it). Say, you would have to increment a counter somewhere marking “Number of times velocity has been halved: X”
If this were how physics worked, our notion of “volume” would just be changed (it would get multiplied by 2^X for each fixed X, and then added up across different values of X). And then notions of “entropy” and “temperature” would be changed as well, and order would be restored.
There are some conditions under which “temperature” and “entropy” correspond to other physical quantities, defined in terms of kinetic energy and so forth. This is not physical law, and this would just cease to be such a case.