I have a question about photons. How can they have momentum but be massless. If they are massless, them they should have no momentum, and vice versa, right? p=mv. Or am I just applying classical mechanics laws to something I shouldn't?

Because with photons we are not talking classical momentum, you can work out momentum using p = hf/c and I think there's another one, possible h/f or something, I can't remember off by heart.

How does a photon have momentum? just because it's traveling fast?

Any moving object has a momentum, that's logic... however you are using a classical equation for a non-classical particle (a photon).

 

We know that (for a photon):

 

e^2 = (pc)^2 + (mc^2)^2

 

but for a photon we have no mass, this results in:

 

e^2 = (pc)^2

 

or for easier viewing but losing technicality

 

e=pc

 

which is rearranged as

 

p=e/c

 

but now we must define e, so we use the equation e=hf so we get

 

p=hf/c

Oh yeah, I looked it up... about when I mentioned the other formula, it is

 

[math]p = \frac{h}{\lambda}[/math]

p=mv. Or am I just applying classical mechanics laws to something I shouldn't?

 

Your reasoning does indeed go south for this reason. As we learn from quantum mechanics, [math]p= h / \lambda[/math], regardless of whether a particle has mass or not.

 

It's funny you bring this up because just minutes ago I was reading over a beautiful presentation of just this very thing in a free e-book:

 

http://www.geocities.com/zcphysicsms/chap3.htm

It's funny you bring this up because just minutes ago I was reading over a beautiful presentation of just this very thing in a free e-book:

 

http://www.geocities.com/zcphysicsms/chap3.htm

 

Grandfather paradox - nice...

If you use higher dimensional theory, is light not consider a vibration in the 4th Spatial Dimension (aka The 5th Dimension)? If you consider higher dimensional theory, look up when the kaluza-klein theory (which had flaws of course, but lead to the string theory).