Can Massless Photons Carry Momentum?

[MonstersFromTheId]

Do photons "carry momentum"?

I was just reading this article in the NY Times,..

http://www.nytimes.com/2007/03/13/s...tml?ex=1175918400&en=d898bf8d246a0844&ei=5070

And THIS sentence just doesn't make ANY sense to me...

"Particles of light, or photons, have no mass, but they carry momentum."

What? P=mv. If m=0, P=0. If something is massless, how in the hell could it possibly carry ANY momentum - at all?

 

[Doc Al]

What? P=mv. If m=0, P=0. If something is massless, how in the hell could it possibly carry ANY momentum - at all?

P = mv only applies to massive particles traveling at speeds slow compared to the speed of light. A more general relationship, good for any particle at any speed, is:
$$E^2 = p^2 c^2 + m^2 c^4$$

Where E is energy, p is momentum, and c is the speed of light. The massless photon has a momentum equal to: p = E/c.

 

[MonstersFromTheId]

Thank you SO much!

Someone also once told me that E=mc^2 is ALSO a special case where a second term drops out, ie. E=mc^2 + (sumpthin)?

Is that also true?

 

[Doc Al]

Yes, that comes from the same equation. E = mc^2 is the rest energy of a particle. Thus the momentum is zero and the p^2c^2 term drops out.

 

[MonstersFromTheId]

So the broader aplication would be...

E=mc^2 + pc or E=mc^2 + mvc?

 

[Doc Al]

So the broader aplication would be...

E=mc^2 + pc or E=mc^2 + mvc?

No. The broader equation is the one I gave above:

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

Remember: p doesn't equal mv! And the square root of a sum is not the sum of the square roots! (2 + 2)^2 does not equal 2^2 + 2^2!

 

[MonstersFromTheId]

How would temperature figure into all this?

For example; if you had, say, a one kilogram mass with a temperature of -270C (i.e. *really* cold), traveling at three quarter light speed, and another one kilogram mass, also traveling at three quarter light speed, but at a temperature of 900C, how would you compare the energy states of the two?

 

[MonstersFromTheId]

Monsters
(Smacks head)
Idiot!
Sorry for the Curly from the 3 stooges moment.
"Whoop-whoop-whoop-whoop-whoop!"
Got a cold and I'm a little buzzed on Nyquil and no sleep.

 

[Doc Al]

How would temperature figure into all this?

For example; if you had, say, a one kilogram mass with a temperature of -270C (i.e. *really* cold), traveling at three quarter light speed, and another one kilogram mass, also traveling at three quarter light speed, but at a temperature of 900C, how would you compare the energy states of the two?

Not sure what you are asking, but a hot object has more energy than a cold one. (By that I mean: Take two identical one kg masses at the same temperature. Now heat one to a higher temperature: its total energy will be greater.)

 

[MonstersFromTheId]

"Not sure what you are asking,..."

Honestly, neither am I, and frankly I'm just too "out of it" at the moment to think straight. Time to roll around in bed and pretend to sleep I guess.

;-).

I'll get my thoughts together and ask more cohierent q's after a few Z's.
Thanks SO much for your patience though Doc. 'Preciated, really do.

 

[robphy]

Compton Effect http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/comptint.html