What is a joule, when you calculate relativistic energy?

[Dgonzo15]

Energy is E=γmc^2, but when I calculate this, will my result be in joules? I am unsure what the units are when I calculate it, and I keep hearing people saying joules.
Also, what is PJ and MJ?

 

[PAllen]

Energy is E=γmc^2, but when I calculate this, will my result be in joules? I am unsure what the units are when I calculate it, and I keep hearing people saying joules.
Also, what is PJ and MJ?

Relativity doesn't change the units of anything. If you use kg, meters, seconds you get joules for energy. Most commonly, I would guess PJ is petajoule and MJ megajoule, but these are ambiguous out of context: MJ could be millijoule or microjoule; PJ could be picojoule or the founder of groklaw.

 

[Dgonzo15]

So how would I calculate the energy of a photon? Since a photon travels at c, gamma (in E=γmc^2) would be undefined, so it doesn't make any sense to calculate the energy of a photon.
Also, are photons considered to have mass, because mass is also a factor in E=γmc^2.

 

[PeterDonis]

So how would I calculate the energy of a photon? Since a photon travels at c, gamma (in E=γmc^2) would be undefined, so it doesn't make any sense to calculate the energy of a photon.

Not if you use an incorrect formula for a photon, no.

The correct formula, valid for any object, timelike (nonzero rest mass, moves slower than light) or lightlike (zero rest mass, moves at speed of light) is:

$$E^2 = p^2 c^2 + m^2 c^4$$

where $E$ is the energy, $p$ is the momentum, and $m$ is the rest mass. A photon has $m = 0$, so the formula reduces to $E = pc$.

 

[PAllen]

So how would I calculate the energy of a photon? Since a photon travels at c, gamma (in E=γmc^2) would be undefined, so it doesn't make any sense to calculate the energy of a photon.
Also, are photons considered to have mass, because mass is also a factor in E=γmc^2.

You need to use the more general formula: E^2 = (mc^2)^2 + p^2 c^2 [p is momentum]

For massless particles you get E=pc. For a photon, E = h$\nu$, p=E/c.

Note, if you plug in p = $\gamma$mv, you will get the special formula for massive particles.

 

[PeterDonis]

Also, are photons considered to have mass, because mass is also a factor in E=γmc^2.

Photons have zero rest mass. Some people use the term "relativistic mass", but that's really just another term for "energy"; a photon certainly has energy, so it does have relativistic mass, but as in my previous post, you can't define its relativistic mass/energy using $\gamma$, so you have to use the more general formula I posted.

 

[Dgonzo15]

OK, so the formula E^2=P^2... reduces to E=pc for photons since photons have zero REST mass. Since they have zero REST mass, what is their mass when they are moving at c? You would need to know their mass in order to calculate p so you can calculate E when they are moving, right?

 

[PAllen]

OK, so the formula E^2=P^2... reduces to E=pc for photons since photons have zero REST mass. Since they have zero REST mass, what is their mass when they are moving at c? You would need to know their mass in order to calculate p so you can calculate E when they are moving, right?

No, you directly measure momentum via interaction (using conservation of momentum). There is not mass distinguishable from energy (which is also directly measurable). For light, relevant formulas use only E and p not mass.

Note, this does not imply photons are not affected by gravity. In GR energy is a source of gravity and is affected by gravity.

Really, what distinguishes mass from energy is the existence of a frame where p=0, and KE=0. Without that, there is no meaningful way to distinguish mass from energy.