Conservation of momentum a universal truth

[stevmg]

This is a very nice post. Have you found a reference to the fact that m²c²=E²/c²-px²-py²-pz² holds for a system of particles also, not only for individual particles? I managed to prove it (the proof isn't trivial) but I haven't seen the proof in any book. (maybe in Griffiths' "Introduction to Particle Physics"? I don't have the book).

ETA: I found a proof in Rindler , pages 117-118. Takes him 1.5 pages of calculations to prove it. Interesting discussion on the fact that the total energy-momentum of the systm is not trivially a four-vector, one needs to sweat it out.

I like that m²c²=E²/c²-px²-py²-pz² - looks neat.

I looked this book up on Google Books and it got me to page 117 - just for grins - and that's just the start of the proof - The Zero Momentum Frame. The book is $97 somewhere. AbeBooks doesn't have it.

You're right... It isn't simple. We'll forgo that pleasure. I still like my old induction approach - if it's good for one, it's good for two, etc. all the way on up. I know that isn't right but at least I can conceptualize it. In AB French he sort of does an "induction" approach to justifying the concept verbally (no formal proof.) He uses the fact that the momenta are linearly related which allows for this "addition" or $$\sum$$ concept. I have used that before when we studied vectors in ejection bailout systems for jet aircraft. If the three-space vectors are not linear, you cannot add them up and get a good answer. Had to use the numerical solutions of calculating each minute step along the way.

My son lives a few blocks from UT Texas Dallas where Wolfgang Rindler teaches and if I really needed it I could get him to go the llibrary there and Xerox those pages.

 

[stevmg]

Is this the proof you saw in 2006 Rindler on page 117-18?

No way would I ever understand that. I would have to spend the last 50 years since high school getting it straight and even then wouldn't get it.

I'll accept the premise that one can find energy-momentum equations for systems of particles without understanding the proof.

The equation that DaleSpam gave (m²c²=E²/c²-px²-py²-pz²) is really another way of stating the AP French equation on page 213 of Special Relativity

-E₀²/c² = p_x² + p_y² + p_z² + (iE/c)²

That's good enough for me.

 

[starthaus]

Is this the proof you saw in 2006 Rindler on page 117-18?

Yes.

No way would I ever understand that. I would have to spend the last 50 years since high school getting it straight and even then wouldn't get it.

No one said that physics is easy. I have a more direct proof than Rindler's but it isn't trivial by any stretch of imagination.

I'll accept the premise that one can find energy-momentum equations for systems of particles without understanding the proof.

This is a bad idea, we need to strive to understand the proofs. Otherwise, we become robots that plug in numbers into equations that we don't understand. Or worse, we use equations that do not apply.

 

[stevmg]

OK, but if it takes me 50 more years to understand it, I will give you the derivation in the old soldiers' home.

I will first read space-time physics and then maybe invest in Rindler.

The price we pay for our intellectual curiosity.