My guess is that once you consider all of the symmetries that could exist (and there are many which have not yet been found; supersymmetry has long been posited but remains undiscovered), then our laws of physics are basically the only laws that can exist in a mathematically consistent way. Of course, that's just my hypothesis.
There's also the possibility that our universe is unnatural, which some physicists have recently been considering, but I'm skeptical. ("Unnatural" means that all of the constants in our universe that cannot be calculated from first principles are simply the result of random chance — i.e., only those universes with "finely-tuned" parameters capable of supporting life would have life in it to observe those parameters.)
>My guess is that once you consider all of the symmetries that could exist (and there are many which have not yet been found; supersymmetry has long been posited but remains undiscovered), then our laws of physics are basically the only laws that can exist in a mathematically consistent way.
If physical evolution is unitary, it may be phrased in terms of an S-matrix, and the possible symmetries of the S-matrix are well-known by the Coleman-Mandula theorem[0] and its supersymmetric generalization[1]. So, supersymmetry is possible, but, as you rightly point out, may or may not exist in the world. So mathematical consistency (unless what you mean is that quantum gravity might violate one of the assumptions of those theorems) is a lot less powerful than you guess.
My guess is that once you consider all of the symmetries that could exist (and there are many which have not yet been found; supersymmetry has long been posited but remains undiscovered), then our laws of physics are basically the only laws that can exist in a mathematically consistent way. Of course, that's just my hypothesis.
There's also the possibility that our universe is unnatural, which some physicists have recently been considering, but I'm skeptical. ("Unnatural" means that all of the constants in our universe that cannot be calculated from first principles are simply the result of random chance — i.e., only those universes with "finely-tuned" parameters capable of supporting life would have life in it to observe those parameters.)