Photon in a Box

[Mr Skeptic]

Since the box has no mass (nor momentum, I assume) but the photon has momentum, conservation of momentum would require that a single photon would push the box out of the way at the speed of light. This may result in your trapped photon interacting with cosmic background radiation. Anyhow, a very odd and non-physical result.

[Farsight]

Let's assume that the photon is in a hypothetical massless box that has perfectly reflecting mirrors so that the photon bounces around in the box forever without loss. My question is this: Could one accelerate the box-photon system to exactly the speed of light?

 

No. Let's assume that you let down the side of the box so the photon is free to get out. That means we're half way to our goal already, because the photon is moving at exactly the speed of light. All you had to do is stop accelerating it with those bounces. Just at that point you start pushing the box really really hard, to try to keep up with the photon. As swanson said, you can't actually have a massless box, so to simplify matters let's say the box is a single electron. It has a small mass, so it takes force to push it, and to get it up to something close to the speed of light you've got to keep on pushing hard and fast it for a long long way. But you can't push that electron all the way to c. You just can't. It's just not doable.

 

The reason why is crushingly simple. It's intimately related to the photon in the box, and the logic is utterly unassailable. But I can't tell you about it because the guys here will say it's pseudoscience. Sorry about that.

[Pete]

Einstein's "Photon in a Box " is fatally flawed.

I disagree. In the first place Einstein never discussed a photon in a box. Einstein's derivation centered on the emission of radiation. Although the radiation can be thought of as consisting of a stream of photons it is not neccesary to obtain this radiation from an atomic transition. The radiation could have been produced by accelerating charges. There is an approximation that Einstein used. I.e. he treated the box as if were a rigid body. However the non-rigidity of the box can be ignored.

There can be no recoil by the box when a photon is emitted.

If that were true the the pinciple of conservation of momentum would be violated.

The emitting electron simply drops to a lower energy level to lose (-e = -h) where (h) is Planck's Constant. The photon has an energy (e = h) and so energy is conserved at the atomic level with none left over for box momemtum change.

All that is required is that energy be conserved. There is no requirement which says that all the energy must be carried off by the photon. Some of the energy can go into the kinetic energy of the radiating atom. I.e. the change in energy equals the sum of the photon energy plus the atoms's kinetic energy.

 

Einstein's photo-in-a-box thought experiment has been analyzed by several physicists in the past. There is an article in the American Journal of Physics which explains the experiment from several points of view, including the radiating atom idea that you're talking about. The article is

 

Inertia of energy and the liberated photon by Adel F. Antippa. Am. J. Phys. Vol. 44, No. 9, September 1976

 

Section 7 is labeled The Radiating Atom

 

Pete

[Norman Albers]

Mass energy equivalence does NOT mean the photon has mass. The concept of relativistic mass isn't really used any more as it is missleading, it is generally considered that there is ONLY rest mass which is called mass (normally) and is a Lorentz invariant.

 

This has been discussed indepth in another thread including references....

 

I vote for Klaynos for whatever office he cares to assume...

[Pete]

I disagree. In the first place Einstein never discussed a photon in a box. Einstein's derivation centered on the emission of radiation. Although the radiation can be thought of as consisting of a stream of photons it is not neccesary to obtain this radiation from an atomic transition. The radiation could have been produced by accelerating charges. There is an approximation that Einstein used. I.e. he treated the box as if were a rigid body. However the non-rigidity of the box can be ignored.

 

If that were true the the pinciple of conservation of momentum would be violated.

 

All that is required is that energy be conserved. There is no requirement which says that all the energy must be carried off by the photon. Some of the energy can go into the kinetic energy of the radiating atom. I.e. the change in energy equals the sum of the photon energy plus the atoms's kinetic energy.

 

Einstein's photo-in-a-box thought experiment has been analyzed by several physicists in the past. There is an article in the American Journal of Physics which explains the experiment from several points of view, including the radiating atom idea that you're talking about. The article is

 

Inertia of energy and the liberated photon by Adel F. Antippa. Am. J. Phys. Vol. 44, No. 9, September 1976

 

Section 7 is labeled The Radiating Atom

 

Pete

 

I should also point out that Einstein defined the mass density of radiation to be proportional to the energy density. This was later seen to be an error in the general case.

 

Pete