Energy of photons vs classical physics energy

[PBTR3]

Relativity says photons have energy E=pc. Classical physics says E=1/2 pv. There seems to be a factor of 2 missing in one case or the other or does the energy formula change as the speed of light is reached? There must be a simple explanation but I have not found it yet. I did not know where to put this question-under classical physics of quantum physics. Thanks for any help.

hjr

 

[mfb]

Classical physics says E=1/2 pv

There are no photons in classical physics, so classical physics cannot say anything about them.

With the Maxwell equations and classical physics, you can derive E=pc for electromagnetic waves. There is no factor of 2.

 

[Bill_K]

The single relationship between energy and momentum that applies to both massive and massless particles is E = √(p²c² + m²c⁴). For a massless particle, set m = 0 and it reduces to E = pc. For a massive particle at rest, set p = 0 and it reduces to E = mc².

For a massive particle that's slowly moving, keep both terms and expand in a power series in p. The first two terms give you the usual Newonian expression, E = mc² + p²/2m.

 

[PBTR3]

Energy of photon vs classical physics energy

Thanks for the replys. I was trying to understand what happens to energy of a proton as a proton is accelerated from rest to almost the speed of light as in the LHA. I think I can calculate that now.

hjr