Recent content by md2perpe

Thus we can not just, as Dale did, say that ##E## and ##p## are the entities given by Noether's theorem by invariance under time and spatial translations. There is another condition that restricts the possible choices.

You seem to think that I am just changing for example 1 Joule to 2 half-Joules. That is *not* what I am doing. I am changing 1 Joule to 2 Joules. Noether's theorem just gives an expression ##h## (with a physical dimension!) that is conserved and doesn't say whether the correct energy to use is...

But it has been written that using different factors for ##E## and ##p## is just about units. It has also been suggested to put the unit conversion factors into the metric. That would change the metric. Or are people here just not clear about how they mean?

But if I use different factors for ##p_x##, ##p_y## and ##p_z## then will I not need to use different units in the different directions?

Replace ##p## with ##cp## which has same dimension as ##E## and use different factors for ##cp## and for ##E##. You don't seem to get the problem. You wrote that ##E## is the conserved quantity induced by time translation invariance and ##p## is the conserved quantity induced by spatial...

I don't understand why distances in spacetime would change just because I choose different factors for ##E## and ##p##.

So if I multiply ##E## with one constant and ##p## with another constant that will not be a problem, you think?

Does Noether's theorem really specify the value of the energy? Doesn't it just give an expression ##h(t,x,\dot{x})## that is conserved? I mean, if ##h## is conserved, then so are ##h+C## and ##Ch## where ##C## is a constant. Can you take ##E## to be any of these?

So it wasn't true that ##E## and ##p## are the total energy and total momentum?

Yes, the four-momentum is additive. But in the formula ##(mc^2)^2 = E^2 - (pc)^2## you just confirmed that ##E## is the total energy and ##p## the total momentum, so the formula shouldn't be used for the energy and momentum of individual bodies, however such things are defined.

If so, why is it used on individual particles in a multi-particle interaction? According to what you write such use is incorrect since it should only be used on the total energy and momentum.

So then ##E## is the total energy and ##p## is the total linear momentum, since those are the conserved quantities?

Do you mean that you use mass to compute energy? Is it through ##E=mc^2##? In ##(mc^2)^2 = E^2 - (pc)^2##, how are ##m##, ##E## and ##p## defined?

Mentors note: split from https://www.physicsforums.com/threads/energy-mass-equivalence.1003564/ How do you measure energy?

That's how I think about it.