# Tunnel-effect possible for massless particles?

1. May 22, 2005

### Max cohen

For the tunnel-effect, the relation between the transmissioncoefficent T and length of the barriere L is:

$T=e^{-2KL}$

in which:

$K=\sqrt{\frac{2m(U_0-E)}{\frac{h}{2\pi}^2}}$

Now, the tunnel-effect is possible for light right? But light means m=0, meaning K=0, meaningT=1!

I must be missing the point somewhere but I can't figure out where

2. May 22, 2005

### ZapperZ

Staff Emeritus
The major problem here is that you ignored is the nature of the "potential" that is providing the potential barrier for light to tunnel through. We know the nature of such barriers for charged particles, but what is this as far as light is concerned? It isn't the same barrier that charged particles are seeing.

You need to go back a bit and figure out if you're applying something that isn't valid to your situation.

Zz.

3. May 23, 2005

### Max cohen

I'm not sure I understand.

As for me, this situation is with two 45 degrees prisma closely located next to eachother so that some of the light goes thru and some is reflected. You can measure the reflecioncoefficient from the formula in my post so I thought it would be nice to calculate the energy of the barrier with this data, but as I it doens't work out. So then how exactly is this barrier different for a charged particle then for massless particles? How could I figure this out?

4. May 23, 2005

### ZapperZ

Staff Emeritus
What is U0 is in your equation? What is it supposed to be?

It is the Potential Energy that the particle is in. If it is a charge particle, this can be the electrostatic potential. If U0 is zero or constant throughout, you have a FREE particle. Thus, my question is, what is the potential field here for your photon? It can't be gravity because the warping of space-time manifold that causes gravity is naively the "geodesic" for the photon path. Thus, this is not the "potential" that is meant in a non-relativistic QM/Schrodinger equation.

So what is U0 in your equation as far as a photon is concerned?

Zz.

5. May 23, 2005

### Max cohen

Still not sure I'm getting this right. In the formula U0 is supposed to be the energy of the barrier and E is the potential energy of the photon (since if otherwise, K would be a complex number). Before the photon reaches the barrier, it's energy is E=hf (if the particle would be charged things would be different indeed). Since I know the frequency of the photon, this can be calculated. Now U0 is supposed to be the energy that it will take to get the photon thru this barrier, knowing that U0>E. In my situation, U0 would be the energy that it takes for a photon to get out of the prisma, get thru the air and make it into the other prisma though it's classicly seen really not supposed to.

I don't understand what this has to do with warping of spacetime :uhh:

6. May 23, 2005

### ZapperZ

Staff Emeritus
You need to double check what all those symbols you are using really mean.

E is the kinetic energy of the system (usually the total energy since the rest mass energy is ignored in typical cases such as this). U0 is the potential energy. But what is the potential energy OF A PHOTON? If this is a charged particle, the potential energy is the ELECTROSTATIC potential barrier! The particle could be in an electrostatic potential well, and it is trying to tunnel out of that well. In other words, it is the TYPE of potential that it can INTERACT with in the first place.

What you have studied is the GENERIC potential barrier of ANY kind. When you start applying it to a particle, then it DOES matter what kind of a barrier you are giving it. A particle with a mass will have a gravitational potential barrier. A charged particle will have an electrostatic potential barrier, etc.

So now you have to consider, what kind of a potential barrier is there for a photon? it doesn't interact with electrostatic and magnetic field (at least not for straightforward QM tunneling), and it doesn't interact with gravitational field (for non-relativistic case and that's why I mentioned the spacetime warping to make sure we don't include that). What possible barrier could you put in there? A dielectric material such as a glass? But is this really a tunneling phenomenon? It isn't!

Zz.