How can photons have momentum without mass?

[matt_crouch]

im confussed how a photon not have a mass. surly it has momentum as that's how it transfers energy to you (sun burn etc)
hasnt something got to have a mass to have energy?

someone help me

 

[Renge Ishyo]

A photon might have mass or it might not. The only thing that is clear is that if it does have mass the magnitude of it is going to be ridiculously small...perhaps due to the uncertainty principle it might be too small to even measure. To give an example, take this simple consideration of a single photon of blue light:

E=hv = (6.63x10^-34 Js)(7.5x10^14 Hz) = 5.0x10^-19 J

Converting energy to mass:

E = mc^2

m = (5.0x10^-19 J)/(3.0x10^8 m/s)^2 = 5.5x10^-36 kg

That is about one hundred thousand times smaller than the mass of an electron and about a billion times smaller than a proton (and blue light would have much more mass than less energetic light...). It's very difficult to measure a mass that small...there have been some projects where the experimenters are attempting to do just that (see here: http://www.weburbia.com/physics/photon_mass.html), but the results have not shown a non-zero rest mass yet (its still zero to the appropriate number of sig figs). It will also show that the above calculation of the mass using relativitistic principles is controversial, because there is no evidence of a photon at rest yet.

Of course there is other indirect evidence that light has mass...Einstein believed it did and he predicted that you could see the light "bend" as it traveled past the sun during an eclipse (showing that gravity was acting on it), and this was verified. I think the hesitance to consider light to have mass has to do with the nearly 100 years in physics where it was believed that light was "only" a wave and had no matter like properties. Modern physicists have cleverly dodged the issue by giving weights of particles in energy (typically eV). In this way everything gets treated the same (particle democracy!).

 

[matt_crouch]

ahh right i never thought to try and apply some maths
but ye your explanation explains a lot
cheers =]

 

[Renge Ishyo]

The math was just to illustrate a problem (that the size of the mass of a photon would be small and hard to measure)...the analysis fails because a blue photon is not "at rest" (so presumably this mass would be a sum of the rest mass + a kinetic energy term). See that website I linked to for more info on the problem if you are interested.

 

[adriank]

E = mc² only works when either (1) the particle is at rest (and photons never are), or (2) m is the so-called "relativistic mass", which isn't that useful anyway.

In general, in special relativity E² = (pc)² + (mc²)²; in the case of the photon, if m = 0, then you just end up with E = pc.

It's interesting how the original poster was fine with photons having momentum without mass (since this really is often defined as p = mv), but was not so sure about energy without mass.Also note: this equation in a sense proves that massless particles must move at speed c, for if the speed was less, then γ is finite, so p = γmv = 0 and E = pc = 0.