# Deductively proving the conservation of momentum

1. Nov 7, 2012

### Mektrik

I won't go into all the details but, to summarize, I'm planning on writing something on the philosophy of science and I was wondering if it's possible to deductively prove, that is without the use of observation or experience, the conservation of momentum. I know that it's possible to prove it using Newton's third law, but that itself requires induction.

As a side note, without meaning to sound too pretentious, is it possible to prove Newton's third law using Pauli's exclusion principle? If so, is the exclusion principle deductive?

Anyway, apologies for my naivety and I look forward to seeing your responses.

2. Nov 7, 2012

### dipole

Yes, it's called Noether's theorem. If you make the assumption that the laws of physics are invariant under translations in space - that is the laws of physics are the same here as they are in China or on the moon or in another galaxy, then the quantity we define as $m\vec{v}$ in classical mechanics is conserved.

Pauli exclusion principle is purely quantum mechanical, and has nothing to do with Newton's third law. The whole concept of a force is a purely classical idea.

3. Nov 7, 2012

### Mektrik

Ahh, for reasons which I won't go into, is there a way to do it without using Noether's theorem? Sorry for not mentioning this earlier and thanks for the reply!

4. Nov 7, 2012

### jbriggs444

Is there a way to prove conservation of momentum based on the pure force of logic along the lines of "cogito ergo sum" without recourse to experiment? Nope, certainly not.

One can conceive of a universe in which reactionless drives exist. Science fiction is full of such creations.

5. Nov 7, 2012

### sophiecentaur

One could 'conceive' the Moon being made of green cheese but is it relevant to Science?

6. Nov 7, 2012

### jbriggs444

Certainly not. But the question that was posed was not about science. It specifically repudiated the use of observation and experience.

7. Nov 7, 2012

### sophiecentaur

I have to ask what the point is of considering deliberately non-Science questions* in a Science Forum.
*questions / hypotheses that are not testable.