Tunnel-effect possible for massless particles?

In summary: 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
  • #1
Max cohen
13
0
For the tunnel-effect, the relation between the transmissioncoefficent T and length of the barriere L is:

[itex]T=e^{-2KL}[/itex]

in which:

[itex]K=\sqrt{\frac{2m(U_0-E)}{\frac{h}{2\pi}^2}}[/itex]

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 :confused:
 
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  • #2
Max cohen said:
For the tunnel-effect, the relation between the transmissioncoefficent T and length of the barriere L is:

[itex]T=e^{-2KL}[/itex]

in which:

[itex]K=\sqrt{\frac{2m(U_0-E)}{\frac{h}{2\pi}^2}}[/itex]

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 :confused:

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
ZapperZ said:
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.
I'm not sure I understand.

As for me, this situation is with two 45 degrees prisma closely located next to each other 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
Max cohen said:
I'm not sure I understand.

As for me, this situation is with two 45 degrees prisma closely located next to each other 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?

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
ZapperZ said:
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.
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
Max cohen said:
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:

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.
 

1. What is the tunnel-effect for massless particles?

The tunnel-effect for massless particles refers to the phenomenon in which a massless particle, such as a photon, can pass through a potential barrier that would be impenetrable for a particle with mass. This is due to the wave-like nature of massless particles, which allows them to exist in multiple places at once and therefore have a probability of passing through a barrier.

2. How is the tunnel-effect possible for massless particles?

The tunnel-effect is possible for massless particles because they do not have a rest mass, meaning they are not bound by the same laws of physics as particles with mass. In quantum mechanics, particles with no rest mass are described by wave equations, which allow them to pass through potential barriers and exist in multiple locations simultaneously.

3. What are some real-life examples of the tunnel-effect for massless particles?

One real-life example of the tunnel-effect for massless particles is the photoelectric effect, in which photons (massless particles) can pass through a potential barrier and cause the ejection of electrons from a metal surface. Another example is the emission of alpha particles from a radioactive nucleus, in which the alpha particles (massive particles) must tunnel through the nuclear potential barrier to escape.

4. Is the tunnel-effect for massless particles only applicable to quantum mechanics?

No, the tunnel-effect for massless particles is also applicable in other fields of physics, such as optics and nuclear physics. In optics, it is known as total internal reflection and is used in fiber optics and other light-based technologies. In nuclear physics, it is involved in processes such as alpha decay and nuclear fusion.

5. Can particles with mass also exhibit the tunnel-effect?

Yes, particles with mass can also exhibit the tunnel-effect under certain conditions. However, the probability of tunneling decreases as the mass of the particle increases, and it becomes much more difficult for particles with significant mass to tunnel through potential barriers compared to massless particles.

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