- #1
Jerbearrrrrr
- 127
- 0
Basic 4 momentum questions. Trying to understand SR a bit better.
Suppose m is non zero for a particle (m being the rest mass of the particle). Then the 4-momentum is related to the 4-velocity by p=mu (in 4 coordinates).
The zeroth coordinate of p is therefore m*gamma(v) where v is the 3-velocity of the particle.
If we approximate this in the non-relativistic limit, we get mc²+½mv²+...
We call this quantity "E".
Why do we interpret (mc²+½mv²) as something's total energy?
Sure, the ½mv² term is some form of energy (and by dimensional analysis, the mc² term is also measured in energy units)...but why should this total thing be a useful quantity?
eg I can add two random things that happen to be measured in joules, and get a not-very-useful quantity.
I was going to ask why we call the zero'th component of 4-momentum "E" but I guess it's just because if we evaluate it in the rest frame, it turns out to be E (or E/c) and that let's us deal with the m=0 case.
Relativistically, mc² is a conserved quantity. Does this derive conservation of energy (for simple systems at least), or is it just consistent with it?
Thanks
Suppose m is non zero for a particle (m being the rest mass of the particle). Then the 4-momentum is related to the 4-velocity by p=mu (in 4 coordinates).
The zeroth coordinate of p is therefore m*gamma(v) where v is the 3-velocity of the particle.
If we approximate this in the non-relativistic limit, we get mc²+½mv²+...
We call this quantity "E".
Why do we interpret (mc²+½mv²) as something's total energy?
Sure, the ½mv² term is some form of energy (and by dimensional analysis, the mc² term is also measured in energy units)...but why should this total thing be a useful quantity?
eg I can add two random things that happen to be measured in joules, and get a not-very-useful quantity.
I was going to ask why we call the zero'th component of 4-momentum "E" but I guess it's just because if we evaluate it in the rest frame, it turns out to be E (or E/c) and that let's us deal with the m=0 case.
Relativistically, mc² is a conserved quantity. Does this derive conservation of energy (for simple systems at least), or is it just consistent with it?
Thanks