A thought experiment: Light in a mirrored box?

[ellie.l]

There is a perfect box with with no gaps or cracks, with mirrors on the interior walls of the box. There is also a light bulb which can emit light but reflects any that goes upon it (with a super two-way mirrored surface, perhaps?).

If one switches the lightbulb on, then there is light in the box. What happenes when the light is switched off? As the walls will reflect it and there is nothing to absorb it, will it go on being reflected for a long period of time, or forever if the mirrors are perfect?


I was thinking about this for quite a while now, and I know there must be holes in the experiement, but if all the conditions are perfect, is there anything that will stop the light from bouncing around forever inside the box? Thanks!

 

[russ_watters]

Welcome to PF.

Correct, if the box were perfect, the light would bounce around forever. But the box can't be perfect: mirrors can never be perfect and the box has a light bulb in it.

 

[my_wan]

Laser construction depends on this, except takes less than perfect mirrors into account.

 

[Sybren]

the light will reflect forever by the definition you make about the properties of the system. there is no mistake in your reasoning.

 

[Galap]

If the experiment were perfect, yes, the light would continue forever. as far as we know, there is no inherent property of light that would affect its passage through space. So, if all external influences that would do so were removed, yes, it would continue to reflect forever.

 

[Glen Bartusch]

But light does possesses momentum; momentum of which will get transferred to the walls of the box. the ultimate effect being that the light would progressively gain a longer wavelength.

 

[Duncanstives]

Yep... Would bound around forever.

I have often wondered if it would be possible to make one perfect enough that it would still contain visible light after some amount of time that humans would preceive is significant. Say 10 seconds.

Kind of doubt it... Even air would attenuate it do some degree due to suspended particles.

 

[pallidin]

Yep... Would bound around forever.

I have often wondered if it would be possible to make one perfect enough that it would still contain visible light after some amount of time that humans would preceive is significant. Say 10 seconds.

Kind of doubt it... Even air would attenuate it do some degree due to suspended particles.

And it can get even more interesting. If you could pump 10 seconds of light in there, that's 1,860,000 miles of that light contained in a very small space.

 

[AlbertRenshaw]

schrodinger's cat...
There is really no way to prove that the light is bouncing around forever until you open the box... at that point though I guess the light would escape and you wouldn't see it hahah so nvm.
Anyways Yeah it should bounce forever but there is nothing in this life you can prove.. nothing.

 

[DaveC426913]

There is also a light bulb which can emit light but reflects any that goes upon it (with a super two-way mirrored surface, perhaps?).

If the bulb has a perfect mirror on it, then no light can be emitted from it, because it is opaque from the inside. In order for some light to get out, the mirror cannot be perfect, which means light can get back in and be absorbed and converted to heat.

Welcome to PF.

Correct, if the box were perfect, the light would bounce around forever. But the box can't be perfect: mirrors can never be perfect and the box has a light bulb in it.

I'll defer to you on this but it seems to me that even a "perfect" mirror will not do the trick. The atoms of the mirror will heat up as the photons reflect off it, so perfectly reflecting does not mean perfect conservation of energy in the light.

schrodinger's cat...
There is really no way to prove that the light is bouncing around forever until you open the box... at thaedt point though I guess the light would escape and you wouldn't see it hahah

Why would you not see it? It's light! You could open the box and have light come streaming out of it for an arbitrarily long time, depending on the shape of the box.

 

[Antiphon]

Superconducting walls with no cracks should do it if the box is evacuated.

This would be some kind of record Q for any passive resonator.

 

[dulrich]

But light does possesses momentum; momentum of which will get transferred to the walls of the box. the ultimate effect being that the light would progressively gain a longer wavelength.

Momentum is conserved in the system, so this should not happen. When it bounces off one wall, the momentum is transferred (and the wavelength changes), but when it hits the other wall, the momentum is gained back. So the box is just oscillating around its center of mass. (No different than an elastic bouncing ball trapped in a box).

 

[DaveC426913]

Momentum is conserved in the system, so this should not happen. When it bounces off one wall, the momentum is transferred (and the wavelength changes), but when it hits the other wall, the momentum is gained back. So the box is just oscillating around its center of mass. (No different than an elastic bouncing ball trapped in a box).

We're not talking about moving the box, we talking about the box heating up; no matter how perfect the mirror, the light will ultimately be converted to heat.

 

[dulrich]

Fair enough. I was just responding to the idea that there is a net transfer of momentum from the light to the box -- which won't happen whether the box heats up or not.

 

[kjl]

Yep... Would bound around forever.

I have often wondered if it would be possible to make one perfect enough that it would still contain visible light after some amount of time that humans would preceive is significant. Say 10 seconds.

Kind of doubt it... Even air would attenuate it do some degree due to suspended particles.

It should be possible, if not practical.

I have no idea what the best mirror that we can currently build is, but wikipedia says a http://en.wikipedia.org/wiki/Dielectric_mirror" [Broken] bounces 99.999% of light back.
Log base .99999 of .1 is ~230,000, which means if we bounce light off of these mirrors ~230,000 times we still have 10% of the light intensity.

Light travels 3,000,000,000 meters in 10 seconds, so if we have two mirrors pointed at each other ~13,000 meters apart, light bounces back and forth 230,000 times in 10 seconds.

So imagine:

Huge, giant tunnel in a vacuum, 13,000 meters long and 100 meters wide.
Mirrors of 99.999% efficiency at either end of the tunnel, pointed directly at each other.
Shine collimated light just over the edge of the first mirror, at the second mirror, at an angle of 3.333*10^-8 radians.
Light will bounce 230,000 times back and forth in a long, long zigzag path down the length of the mirrors, and emerge past the opposite edge of the mirrors having taken a path 3,000,000,000 meters long, 10 seconds later, at 10% brightness.


If you can make mirrors of 99.9999923% efficiency, you only need to put the mirrors 100 meters apart from each other.

If you can make the mirrors 99.9999992% efficient, you only need to put the mirrors 10 apart from each other.

If you have a 1 meter mirrored box made out of 99.999% efficient mirrors and let light bounce around it, the light should still be at 10% intensity after .00077 seconds, and 1% intensity after .0015 seconds (1.5 milliseconds is not bad! And sort of on timescale meaningful to humans).

 

[Glen Bartusch]

We're not talking about moving the box, we talking about the box heating up; no matter how perfect the mirror, the light will ultimately be converted to heat.

...But to add to the O/P's description of his gendanken experiment:
The box, lol, has a mirrored coating that reflects infrared with an efficiency of 100%. Likewise, his 'lightbulb' emits infrared... :tongue2:

 

[Glen Bartusch]

Momentum is conserved in the system, so this should not happen. When it bounces off one wall, the momentum is transferred (and the wavelength changes), but when it hits the other wall, the momentum is gained back. So the box is just oscillating around its center of mass. (No different than an elastic bouncing ball trapped in a box).

OK, thanks for your reply. I've been thinking about this and you seem to be correct. My problem was ignoring the light after its first reflection.
Thanks again! :)

 

[AlbertRenshaw]

If you left the light on for more then 10 seconds the glass from the mirrors would probably crack due to heat.

 

[Duncanstives]

It should be possible, if not practical.

I have no idea what the best mirror that we can currently build is, but wikipedia says a http://en.wikipedia.org/wiki/Dielectric_mirror" [Broken] bounces 99.999% of light back.
Log base .99999 of .1 is ~230,000, which means if we bounce light off of these mirrors ~230,000 times we still have 10% of the light intensity.

Light travels 3,000,000,000 meters in 10 seconds, so if we have two mirrors pointed at each other ~13,000 meters apart, light bounces back and forth 230,000 times in 10 seconds.

So imagine:

Huge, giant tunnel in a vacuum, 13,000 meters long and 100 meters wide.
Mirrors of 99.999% efficiency at either end of the tunnel, pointed directly at each other.
Shine collimated light just over the edge of the first mirror, at the second mirror, at an angle of 3.333*10^-8 radians.
Light will bounce 230,000 times back and forth in a long, long zigzag path down the length of the mirrors, and emerge past the opposite edge of the mirrors having taken a path 3,000,000,000 meters long, 10 seconds later, at 10% brightness.


If you can make mirrors of 99.9999923% efficiency, you only need to put the mirrors 100 meters apart from each other.

If you can make the mirrors 99.9999992% efficient, you only need to put the mirrors 10 apart from each other.

If you have a 1 meter mirrored box made out of 99.999% efficient mirrors and let light bounce around it, the light should still be at 10% intensity after .00077 seconds, and 1% intensity after .0015 seconds (1.5 milliseconds is not bad! And sort of on timescale meaningful to humans).

Not something one could build in there home but interesting none the less.
Of course building a sealed tunnel of that size and then evacuating all the air from it would be challenging and hardly seems worth doing for an experiment with fairly perdictable results no matter how much disposable income you may have.