Question

How conservation laws are tested experimentally independently from each other? what do I mean by that question?

It seems that to test one conservation law experimentally, such as conservation of energy, we will have to assume other conservation laws are correct such as conservation of charge and conservation of momentum and angular momentum...etc.

But to really test any conservation law one has to check if one of them is valid independent from any other one. Is this possible experimentally? if not then how scientists check conservation laws?

Answer 1

Suppose I collide two billiard balls then I can measure the velocities before and after and check that momentum is conserved. I don't need to assume that energy is conserved. I just measure the velocities before and after.

Alternatively I can use the same system to check for conservation of energy, but again I don't have to assume conservation of momentum.

It would be possible for this experiment to conserve momentum but not energy. For example suppose I'm working in the centre of mass frame, so the net momentum is zero, and the two billard balls collide and stop dead. That would conserve momentum but not energy. Likewise suppose the billiard balls meet but then both move off together at a right angle. That would conserve energy but not momentum.

So it's hard to think of an experiment that doesn't simultaneously test more than one conservation law, but you don't need to assume other conservation laws hold when testing your selected conservation law.