Light and perfect mirrors.

[James Santoro]

So a friend asked me a question that I wasn't able to confidently answer. I figured I'd try here.

If we somehow trapped light in a box where all sides were perfectly reflective would it just bounce around inside the box indefinitely?

My answer was that yes, it would, but if the mirror was anything less than perfect the light would escape rather quickly because of how many times per second it would hit each side.

[swansont]

You can't have perfect reflection. When the photon bounces off of a mirror its momentum changes, which means that the mirror must likewise undergo a change in momentum. The mandates that energy be transferred. The photon would continually lose energy, under even the most ideal of circumstances.

[jgemmo]

Since light can't slow down in the transfer of energy does it just slowly red shift?

[Josh]

Moved to Q&A

[Cougar]

You can't have perfect reflection. When the photon bounces off of a mirror its momentum changes....

It's almost like, how technical do you want to get, James Santoro? Of course, photons don't just bounce off the surface of a mirror. They undergo a quantum interaction with one or more atoms that make up the mirror. There is no definite "angle of incidence, angle of reflection," only a set of probabilities for where the photon might end up. Billions of photons will end up where our common sense would expect, but a significant number of others will not. Occasionally, one will even tunnel through the mirror....

Richard Feynman's classic Quantum Electrodynamics (often referred to as QED) is largely about what's happening with these light interactions, and remarkably, it was written to be presented to a lay audience without any special knowledge of math or physics. Highly recommended.

[mugaliens]

You can't have perfect reflection. When the photon bounces off of a mirror its momentum changes, which means that the mirror must likewise undergo a change in momentum. The mandates that energy be transferred. The photon would continually lose energy, under even the most ideal of circumstances.

Not quite. The momentum imparted to one side of a rigid box whose insides were perfect mirrors would impart that momentum to the other side, which would then be moving towards the light. However, as Cougar said, QED realizes there are other avenues of entropy. For example, due to random variance in the wall's velocity at any given time, the frequency of a laser would rapidly disperse both up and down in wavelength.

[swansont]

Not quite. The momentum imparted to one side of a rigid box whose insides were perfect mirrors would impart that momentum to the other side, which would then be moving towards the light.

You can't have a rigid box that responds this way in a single pass, of course, as that violates principles of relativity.

[mugaliens]

You can't have a rigid box that responds this way in a single pass, of course, as that violates principles of relativity.

Naturally. However, any continuous light source inside such a box would be comprised of trillions of photons per femtosecond. Thus, the momentum imparted by one photon wouldn't cancel it out, but would instead impart energy to another, later photon impacting the opposite wall. While this process initially requires some energy to ramp it, it reaches equlibrium in the amount of time it takes sound waves to travel from one corner of the box to the other.

Yes, I meant "sound" waves. Remember, while light travels at c, the momentum imparted to one point of the box travels throughout the box no faster than the speed of sound through the box's material.

[JohnD]

THis perfectly mirrored box sounds very like a perfect gas inside a perfectly sealed box.
Sure, in the real world the gas will leak eventually, mainly through the walls.
But allow me my thought experiment, as you have the light one.

The impact of gas molecules would be an analogy for the interaction of photons and atoms, that would avereage throughout the box (unless extremely small - Brownian motion small). So this would stay at raised pressure, for ever?

Or is there a QED view?
John