I have a question to a theoretical thought experiment to which I would dearly love an answer, I have asked many people about it and not received a definitive answer yet.
Imagine you had a perfect sphere which was mirrored on the inside and which was also a perfect vacuum, now imagine you managed to fire a string of photons or a beam of light into the inside of the sphere, what would happen to the light?
Would it bounce around forever randomly, or settle into some sort of “3D spirograph” effect or vanish as energy was lost to the mirror as heat, or some other answer, please also assume that the mirror was at least 500nm thick to prevent any “quantum tunnelling” effect as has been offered to me as an answer in the past.
Since there’s no such thing as a perfect mirror, the photons would eventually get absorbed by the mirror, and go into heat. “Eventually” would actually be pretty damned fast, on human time scales.
Incidentally, the “3D Spirograph” effect wouldn’t take on the interesting effects you think it would. There are optical devices that use opposing mirrors to "trap photons inside, but the only time they start to make interesting patterns on the walls are when you have aberrations in the shape of the mirrors. Lookk up “Herriot Cell” sometime – the interesting patterns occur when you have astigmatism or coma in the optics.
by the way, SF writer Spider Robinson says he’s been asking a similar question for years, without getting a satisfactory reply. what, he asks, would you see if you were yourself in the middle of such a sphere and the light was briefly turned on. He claims to have gotten lots of contradictory replies over the years, but nothing reliable.
the answer is that you’d get an all-too-brioef out-of-focus glimpse of your feet (or, more accurately, whatever happened to be the same distance from the center of the sphere as your eyes, going the other way). “Out of focus” because the apparent distance would place it directly in front of your eyes, and most people can’t focus on something that close. Being at the center of a sphere places you two focal lengths from the concave mirror that is the interior of the sphere, and you’ll see an inverte image of you. But it’ll be right on top of you.
If you put your eyes at the center of the sphere, you’ll get an upside-down image of your eyes. If you position yourself so that there’s nothing the same distance from the center as your eyes, then you’ll get an image of the image of the baxck of your head, right-side up this time, but still way out of focus.
but in any case, it’ll all go dark really quick, as the light is rapidly absorbed. since you’re in the cell this time, and you don’t have pervfect reflectivity, you’l probably absorb all the light.
The number of bounces inside a sphere of reflectivity R is typically about R/(1-R), so if the reflectivity is 1 - 10[sup]-n[/sup, then you’ll typically have 10[sup]n[/sup] bounces. Say R = 0.9999 (99.99%, which is damned good), then you’ll have on order of 10,000 bounces. If yiour sphere is 100 meters in diameter (a pretty bif sphere) and the transits are across the center, the widest part, that’s a total of 1,000,000 meters the light has to travel, which it’ll cover in 1/3 second.
CalMeacham answered the question in terms of what would happen if you’d try to perform the actual experiment. I’ll describe the idealized physics behind it.
In “simple” terms: we solve the Schroedinger Equation. The solution will be a set of eigenstates (equation (5) of the link has the equation for the lowest-energy eigenstate). An eigenstate is an standing waveform–if the photon you inserted into the system is corresponds exactly to an eigenstate, you’d not see any change over time in the system.
Of course, it’s unlikely your photon is exactly an eigenstate. Because the vaccum is a linear medium (waves add to together in the obvious way), we can describe the photon as a sum of eigenstates. Each eigenstate component of your photon does it own thing. But added together, the sum tells us what the actual photon does. This will produce your spirograph pattern.
Because photons can share the same state (unlike, for example, electrons), adding more photons doesn’t change the problem significantly. You just solve for each photon separately.
And welcome to the SDMB, Diablos. I hope we aren’t overwhelming you too much.
I don’t think you will get above around 95% to 98% without using dielectric mirrors. Once you start using those the angle of incidence starts to matter and that really messes up any spherical mirror uses.
