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What happens to light in a perfect reflective sphere?

I was working on my toy ray tracer when I pondered on this:

Say we build a hollow sphere big enough to fit a person. The internal surface is perfect mirror, with no cracks or holes. We place an invisible observer with an invisible flashlight, just for the sake of argument, inside the sphere. The flashlight is turned on for, say, 1 second. What does the observer continue to see after the flashlight has been turned off, and why?

  1. it is pitch black, so he can't see anything.
  2. there is just as much light as when the flashlight was on, but it dims and eventually becomes pitch black?
  3. it isn't pitch black, and he can see.
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Arlen
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2 Answers2

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(Note: This answer treats photons as if they were classical point particles; I am ignoring effects such as diffraction.)

An invisible observer is a contradiction, because something is invisible if it does not interact with photons, and if it does not interact with photons then it cannot observe them. An invisible flashlight is similarly impossible, but we can hypothetically assume we shine some light into the sphere from an opening and then slam the (perfectly mirrored) hatch shut, since light travels at a finite speed.

First, assuming a perfect reflector and nothing in the sphere (not even air, since that will interact slightly), then what we have is a volume full of electromagnetic radiation bouncing around. It contains a (nearly) fixed amount of energy and will continue to do so indefinitely (except for this effect).

If we introduce an observer, then the observer absorbs some of the light. If we assume the observer absorbs no light that it does not also observe (a bodiless perfect retina?), then it will observe an (exponentially) decreasing brightness. The photons have essentially random tracks through the sphere, so at any given moment some of them will be absorbed, and as the population of photons (amount of energy) reduces there will be fewer of them to be absorbed. (Some of the photons may be on paths which will never intersect the observer, but they can be just ignored.)

If we additionally grant your invisible flashlight — it doesn't actually have to be invisible, just to emit more light than it absorbs — then this simply adds to the photons in the sphere at some fixed rate. With both the flashlight and the observer, assuming that 1 second is sufficient time, then the amount of photons in the sphere will increase until the observer's absorption rate equals the flashlight's emission rate (or until the flashlight is turned off before then). When the flashlight is turned off, the photons will be absorbed as discussed above.

So, your option 2 is correct, but you have to think carefully about what kind of impossibilities your “ideal” objects are introducing.

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Kevin Reid
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Since there is nothing to disperse and diffract the light in the dome, and the curvature of sphere ,its concave nature (from the inside) will converge light and diverge depending the position of light wrt to the sphere.

and one might see an ray of light travelling in random directions, getting converged or diverged from time to time,

But to see light one will definitely have t absorb photons, which will be impossible for our invisible friend,

Tomarinator
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