Joho the Blog
An Entry from the Archives

I'd say technically b), with "imperceptibly" being an understatement. That is, it's literally true, and could be calculated, but the time difference is many, many, zeros after the decimal point.

Basically, on each reflection, some of the light gets absorbed by the mirrors and converted into heat, and at 186,000 miles per second, that happens *fast*.

Getting d) would be some sort of photon-superconductor phenomena, which would be very cool, but very hard to do.

Option d is a theoretical with a big IF. Natrually, in a closed system with no losses, the photons will keep going, but even then there'd probably be some kind of un-obvious quantum mechanical things happening.

If an actual experiment, you'd see a) behavior. You didn't say what kind of light bulb it is, but a "60 W" variety is probably incandescent. These things don't turn off instantaneously. From the moment the power is cut, the tungsten filament will gradually (on the order of say 10s or 100s of milliseconds) give off less and less light and blackbody radiation.

You'd have losses from the mirror, but probably even more from photons bouncing back into the dimming light bulb and any attached socket, wiring, etc. Compared with how long it would take the filiment to dim, the absorption losses would happen much, much quicker. Ergo, for all intents, it would dim as fast as any closet. -m

The interior would be dark as soon as you turned off the light.

Any interaction with a physical medium, even a mirror, with end with energy transfer to the medium.

There is no form of matter that we know of that does not interact with photons in some manner, therefore the energy will transfer to to the medium.

I think Micah has it, but IANAPhysicist.

Is there a dead cat in the box?

Option b).

Effectively keeping the filament hotter a weeny bit longer (less heat loss).

Why else does so much thermal insulation have silvered surfaces?

This question has a more mundane cousin:
"On average, at what time of day does a white T-shirt become warmer than a black T-shirt?"

Okay, a airtight box where the supposed source of illumination sits in the middle only to sense a reflection of his/her own brilliance from all sides without providing a useful radiance to the outside world.

Is this a new metaphor for blogging that's meant to replace the "echo chamber"? (Present company excluded, of course.)

It's really a case of obscurity through insignificance.

If you jump out of an aeroplane at 10,000 feet, your parachute fails, and land either on the concrete runway or the bottom of a dry well, is your impact velocity in the well:

a) the same - makes no difference
b) slightly faster - the steep sides accellerate your descent due to coriolis forces
c) slightly slower - cushion of air

One thing I noticed in the previous comments--nobody took in to account that the intensity (visible light energy) of the light bulb falls off with the square of the distance!

You've got a meter to cross before you hit a mirror--then 2m to reflect to the opposite mirror, and so on, and that's loss even if everything else is ideal... So by the time the light has gone down by 1/d^2 (I think that's it) so far that it is imperceptible, well, the speed of light is so fast that it is still *practically* "simultaneous", so you may as well say that the answer is a., since the difference between b. and a. is insignificant-- I'll leave the real math up to those who are better at it. :)
And oh yeah: of course there's absorption of energy by the mirrors since they're never "perfect"--AND the light bulb filament doesn't just instantly go black, it just dims down until it no longer radiates visible light (although it continues to give off IR (heat) for a little while longer than that (which means the answer is b. right off the bat if you take out the comparison to the closet's light.) And who knows what else is going to contibute to the dimming of the light after the current (energy) is no longer being supplied to the light's source?

How about this: let one of the mirrors actually BE the wall of one side of the cube. Make sure this mirror is only half-silvered. Then shine the light into the box from outside, through the back of the half-silvered mirror. This way, there is nothing inside the box getting in the way of the light. And, don't use a mere 60W bulb--get some kind of 500 million candle-power spotlight, and shine that into the box!
SO: *now* what happens? Still probably nothing, except that the material the box is made of will probably start melting-- but still, I *wonder*... ;)

b) says imperceptibly, but it does say slower.

The filament does not cool to below luminous temperature instantaneously, nor faster than it takes radiation to bounce off the mirrors and back.

If even one photon comes back to keep the filament hotter longer, it will dim more slowly.

It may even dim immeasurably slower, but that doesn't preclude being 'theoretically slower'.

And yes, in the right circumstances, the right sized and shaped room, the right contents, the right atmosphere, the right mirrors, the right initial illumination, we end up with something completely unexpected, i.e. a laser.

I used to think about this all the time in dull elementary-school classes. While (a) may be true, the premise provided a fascinating diversion, trying to engineer a solution that finessed entropy.