What is the maximum amount of light that can fit inside a mirrored sphere?

[Uhh]

I just joined to ask this question...

I was imagining a sphere made of mirrors inside it and shooting a light to the inside (assuming none of it would escape back through the same hole). Once light enters, it will forever bounce inside the sphere. So my question is, will there be a limit of the amount of light that can 'fit' the sphere?

In other words, as light has no volume, is there a limit of the amount of light that can fit inside a given volume or is it potentially infinite?

 

[24forChromium]

I just joined to ask this question...

I was imagining a sphere made of mirrors inside it and shooting a light to the inside (assuming none of it would escape back through the same hole). Once light enters, it will forever bounce inside the sphere. So my question is, will there be a limit of the amount of light that can 'fit' the sphere?

In other words, as light has no volume, is there a limit of the amount of light that can fit inside a given volume or is it potentially infinite?

I am not an expert on quantum mechanics, but I know that a reason why someone may get the idea that there is a capacity to light is due to the conceptualization of photons being flying little balls. The most I can say is that light is a disturbance is electromagnetic field (may not be precise terminology), and in a sense, it's like waves in a bath tub, you can stir at two different points and get two ripples, you can also stir and a hundred points and have a wavy bath tub, but there isn't a moment in time when you can say that the bath tub can't get any wavier, partly because waves can pass right through each other, both light and water waves, also, one formation of waves can be understood as the combination of many constituent waves. Heck, you can say that a waveless surface of water is actually a pool where all the waves cancel each other out exactly.

However, if you line up the light beam that you shot into the sphere perfectly, the photons may resonate and the energy stored in the waves get so strong that it forms a Kugelblitz--a black hole made of energy, because energy has mass--but I assume that was not what you were looking for.

feel free to ask for clarification if my wordings are incomprehensible anywhere.

 

[davenn]

hi there uhh
welcome to PF

I was imagining a sphere made of mirrors inside it and shooting a light to the inside (assuming none of it would escape back through the same hole). Once light enters, it will forever bounce inside the sphere. So my question is, will there be a limit of the amount of light that can 'fit' the sphere?

since there are no perfect mirrors the light will be absorbed into the mirror surface very quickly so there will be nothing left to contain

Dave

 

[Uhh]

I am not an expert on quantum mechanics, but I know that a reason why someone may get the idea that there is a capacity to light is due to the conceptualization of photons being flying little balls. The most I can say is that light is a disturbance is electromagnetic field (may not be precise terminology), and in a sense, it's like waves in a bath tub, you can stir at two different points and get two ripples, you can also stir and a hundred points and have a wavy bath tub, but there isn't a moment in time when you can say that the bath tub can't get any wavier, partly because waves can pass right through each other, both light and water waves, also, one formation of waves can be understood as the combination of many constituent waves. Heck, you can say that a waveless surface of water is actually a pool where all the waves cancel each other out exactly.

However, if you line up the light beam that you shot into the sphere perfectly, the photons may resonate and the energy stored in the waves get so strong that it forms a Kugelblitz--a black hole made of energy, because energy has mass--but I assume that was not what you were looking for.

feel free to ask for clarification if my wordings are incomprehensible anywhere.

Interesting but I thought two light beams don't interact with each other.

 

[Uhh]

hi there uhh
welcome to PF
since there are no perfect mirrors the light will be absorbed into the mirror surface very quickly so there will be nothing left to contain

Dave

My question was more on the hypothetical side where mirrors are perfect etc.

 

[davenn]

My question was more on the hypothetical side where mirrors are perfect etc.

even then I suspect there's still going to be EM energy absorbed and it's just going to take a fraction longer to disappear

we don't live in a universe where everything is perfect ... its better to stick to reality
rather than speculate about impossibilitiesDave

 

[Dale]

In other words, as light has no volume, is there a limit of the amount of light that can fit inside a given volume or is it potentially infinite?

Hi Uhh!

I have no problem with a perfectly reflective material. It is an idealization that is not achievable, but is often used for simplicity. Like a frictionless bearing or whatever.

So in principle you could cram a lot of light into a sphere. However, light carries momentum and when light gets reflected that change in momentum produces a pressure on the container. So the reflective container would need to be a pressure vessel. The amount of pressure is actually quite substantial if you want to contain large amounts of energy. You are usually better off just storing a compressed gas.

 

[Khashishi]

As DaleSpam indicated, there's a certain radiation pressure due to the momentum of light. So the walls of the sphere would need to contain this pressure. But the pressure of light is small for lab-achievable light levels, important only for some pulsed laser applications. I would be more worried about the heat flux lost on the walls. Assuming you reach some kind of steady state of energy in-energy out, then you have all the light energy you pump into the vessel heating up the walls of the chamber, which will eventually melt.

If you are able to overcome all the material limits, and several other limits, then eventually you will create a black hole if you keep putting energy into a volume of space. The limit is given by the Scwarzschild radius $r_s = \frac{2GM}{c^2}$

 

[24forChromium]

Interesting but I thought two light beams don't interact with each other.

They do, waves are fundamentally unlike other objects, a wave can be seen as multiple waves occupying the same space, like I said. Also, an example of light waves interacting is the production of laser, which involves the amplification of light waves that are in phase of one another.

 

[Khashishi]

A laser isn't formed by light beams interacting with each other, but from light interacting with an excited medium with a population inversion.

As far as I know, there's no experimental evidence for light beams interacting with each other in a vacuum, although they are theoretically predicted to do so in minute amounts. Light can interact gravitationally with other light, but this effect is teeny-weeny.