What would happen if you could create a perfect two-way mirror into a sphere?

October 30, 2007 6:37 AM

What would happen if you could create a perfect two-way mirror into a sphere?

Imagine a hypothetical perfect two-way mirror. All light passes through one side, no light can penetrate the other.

Now, make it into a sphere with the mirrored surface on the inside.

What will happen as it collects light? Will it collect light forever? Will it fill up and burst like a supernova? How would it look to an outside observer?

posted by Lownotes to science & nature (12 comments total)

You seem to be thinking about a two-way mirror the wrong way. Light passes through the mirrored side, but not through the obverse, meaning that the inside of your sphere would be dark. Perfectly dark, given your hypothetical perfection. It wouldn't be reflective on the inside, even, because it would perfectly pass light. I think. Now you have me confused.
posted by OmieWise at 6:41 AM on October 30, 2007

Previously.
posted by These Premises Are Alarmed at 6:43 AM on October 30, 2007 [1 favorite]

...two-way mirror...

No such thing exists. Not even a little bit. The mirrors used in interrogation rooms, etc., are half-silvered. They behave symmetrically, i.e. reflects partially from both sides. The difference is the interrogation room is kept really bright, while the police room is kept really dark.
posted by fatllama at 6:45 AM on October 30, 2007

A two-way mirror doesn't actually behave differently from one side than from the other. It only works in practice because of bright light on one side of the mirror and little light on the other.

Ever look out of a window of a brightly-lit room at night, only to see a reflection of the room, and nothing at all of the world outside? That's basically what a two-way mirror is. An actual two-way mirror is partly silvered to enhance the effect, but the principle is the same: a two-way mirror doesn't inherently have a reflective side and a transmissive side; a viewer on the brightly lit side sees the reflection, and a viewer on the dimly lit side can see into the brightly lit side. Change the lighting on each side of the mirror, and you change which side appears reflective and which appears transparent. See here for a diagram.

A two-way mirror that acts the way you're thinking of would violate the second law of thermodynamics.

(On preview, what fatllama said.)
posted by DevilsAdvocate at 6:52 AM on October 30, 2007

But, if you could have a real two-way mirror, and made it into a perfect sphere such as you described...

It would be dark inside. Any light would convert from photons to heat energy as they hit the mirror's surface. So you'd get a slightly warm, dark glass sphere.
posted by bluejayk at 7:09 AM on October 30, 2007

bluejayk: I don't understand why you think this hypothetical two way mirror (which like DevilsAdvocate I think is impossible) would act that way. It seems to be contrary to the very definition of it.
posted by edd at 7:15 AM on October 30, 2007

What you are describing is very similar to the typical model used to introduce the concept of black-body radiation.

As the light bounces around in the sphere, it heats up the walls. The sphere itself then emits radiation due to its finite (as in non-zero) temperature. So, over time, the energy of the photons inside the cavity is radiated away.

For shits and giggles though, let's suppose that you could make a perfectly reflective material and make your sphere out of that. Then you'd just get an increasingly large density of photons inside the sphere. These come with an energy density and, because photons carry momentum, they also exert pressure on the walls of the cavity. So it becomes like trying to pump a gas into a bottle. At some point, it's going to blow.

Ok, so let's make it infinitely strong. Eventually (a long, long time from now), there would be a high enough energy density that you start to notice gravitational effects due to the energy density. And then, eventually, I would suppose you would get a black hole. But now you run into a problem, because black holes emit Hawking radiation, regardless of what you made them out of. So you're back to square one.

However, all's not lost. People do make slightly similar things for laser interferometers, such as the one at LIGO. Basically, you want a cavity with a very high number density of photons so that you get good statistics. So, they take two very, very shiny mirrors and bounce light between them, pumping it up with a laser to get the density higher and higher.
posted by dsword at 7:15 AM on October 30, 2007 [3 favorites]

edd, you're right. I was thinking of.. uh, something else?
posted by bluejayk at 7:22 AM on October 30, 2007

In Feynman's book, QED, there's a whole chapter about the odd way that light passes through a pane of glass. As the thickness of the pane is varied, light goes from not passing at all, to almost full passage. The percentage of light passing through behaves very interestingly due to quantum effects.
posted by odinsdream at 10:25 AM on October 30, 2007

Thanks dsword.

As I stated in the question, this is a HYPOTHETICAL and PERFECT mirror ball. Thus, a mind experiment and not something I'm planning to try and make as some answers seemed to suggest.
posted by Lownotes at 4:15 PM on October 30, 2007

We're aware it's hypothetical and perfect. However, it's not practical issues that stop you making this (in the same way that a question about a mile high skyscraper might be scuppered by practical issues), it's laws of physics issues. So by hypothesising this you're hypothesising changing the laws of physics, and you haven't told us which new ones we're supposed to be imagining this is in. It's a thought experiment we can't do, because we don't know the rules that apply to it.

dsword gives an excellent overview of what sorts issues come along to trip you up though.
posted by edd at 10:41 PM on October 30, 2007 [1 favorite]

Although this is a curious situation I'd never come across before.
posted by edd at 10:57 PM on October 30, 2007