Testing conservation laws experimentally

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

Well, I think that conservation laws are NOT independent of each other anyways. For example, the conservation of energy is derived by integrating Newton's second law (rewriting $\frac{dv}{dt}$ as $\frac{dv}{dx}\frac{dx}{dt}=v\frac{dv}{dx}$), whereas conservation of momentum (and by extension, angular momentum) is derived from the same equation. So we actually have to verify both simultaneously (as if one is false, the other is also most probably false). Note that I am not saying that they are conserved in equivalent situations, I am saying that the overall conservation laws are equivalent.

Conservation of charge can be proved from conservation of energy also, if we take Coulomb's law as a fundamental. So really, the question doesn't mean much as most of these laws are theoretically interdependent, and thus there is experimentally prove them independently.

The best way to go about this, IMHO, is to use a series of experiments. Prove energy and momentum together in one experiment (or separately if you can manage it). Now, use an experiment that takes these two conservation laws into account without having to deal with other conservation laws (make the system charge neutral for example); prove another law with this experiment.

I think really an example of sich an experiment would make the question clearer.

Answer 2

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.