Suppose your reflector was insanely close to perfect. Light would lose a tiny amount of energy on every bounce. But the mirror is so good that it would take a million bounces before half was lost.

Suppose the ball is$10$ cm across. Light flows in, travels across the ball, bounces, travels across again, and so on. It reaches a million bounces after traveling$100,000$ meters, or$100$ km.

The speed of light is$300,000$ km/sec. So$100$ km takes$1/3$ of a millisecond. At this time, half the energy is still stored.

After another$1/3$ millisecond, there is$1/4$ of the light light. Another, and there is$1/8$ of it. Total time so far:$1$ millisecond.

You can't store light for any appreciable time with even an insanely good mirror.

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  $\begingroup$And of course the energy of the light would dissipate into heat.. Heating up the mirror and likely lowering it's reflective ratio even more$\endgroup$

  Tofandel

  – Tofandel

  2025-01-27 12:07:22 +00:00

  CommentedJan 27 at 12:07
• 2
  $\begingroup$That lost light at every bounce is, of course, energy that is of degrading photons at lower frequency and motion of the atoms/molecules of the containing structures crystal lattice due to the photon capture and releases. Start filling a metal tank with rapidly introduced balls and listen to the sound it makes and feel the vibration of its exterior wall as things become more quiet. As Tofandel also states.$\endgroup$

  civitas

  – civitas

  2025-01-27 18:02:15 +00:00

  CommentedJan 27 at 18:02
• $\begingroup$Hypothetically, if the properties of the inside of the mirrored sphere absorbed zero light, then what? The answer offered assumes that some light would be absorbed, or another response assumes that the light would dissipate into heat. Is the speed of light constant? Can it be reduced or made dormant altogether? Do different wavelengths travel at different speeds? If light is able to bend, might it be bent in such a way or to such an extent that it is effectively slowed in relationship with the transmission point to the reflection/reception point?$\endgroup$

  Christophilos Blu

  – Christophilos Blu

  2025-01-28 01:35:00 +00:00

  CommentedJan 28 at 1:35
• 2
  $\begingroup$Obviously we need the superconducting equivalent for a mirror - a super-reflecting mirror!$\endgroup$

  Michael

  – Michael

  2025-01-28 19:55:12 +00:00

  CommentedJan 28 at 19:55
• 3
  $\begingroup$@Michael The dc resistance is zero. The ac resistance isn't. The "physics of SRF cavities" section there has a good discussion of where this nonzero ac resistance comes from$\endgroup$

  llama

  – llama

  2025-01-29 13:59:48 +00:00

  CommentedJan 29 at 13:59

First of all, it is impossible to create a perfect mirror (although cavities ofvery high Q-factor exist – think tens of thousands of reflections within the cavity).

Classical electromagnetism is linear, so solutions just add up. Light can't "press" other light out of the ball (unless you reach intensities where you have to consider the quantum field theory effect ofphoton-photon scattering – but that would require incredibly intense field strengths).

But even long before you run into trouble: The light you shine in will always reach your aperture again after some time. You can see this from a simple ray optics argument: Assume you shine in a ray of light into the cavity. There will be a plane through the center of the sphere and the ray of light. All reflected rays will lie within that plane, because the surface of the sphere is perpendicular to a plane through the origin.

So it reduces to the 2d problem of a ray reflecting of a circle. Either the angle of incidence is commensurable with$2\pi$, then it will reach exactly the aperture after some time, or it is not – then it will come arbitrarily close to the aperture after some time (this is a basic property of the real numbers). As your aperture will have some finite size the ray will leave the aperture again.

In summary, there is simply no way to couple a ray into the sphere in a way, that keeps the light within the sphere beyond some finite time.

With wave-optics it gets even worse, since you have diffraction, so the smaller you get your aperture, the worse the ray optics approximation will get (but not in a way that helps your idea): The wave-front will spread and you can't keep a lot of your light close to such a "many-reflections" path.

So the average light intensity in the sphere will approach some limit point, where the same amount of radiation goes out as goes in. Not because the light pushes back, but simple due to the propagation of the light allowing no paths that keep the light within the sphere indefinitely.

The question also discusses the scenario of closing the aperture while some light is within the sphere. Assuming perfect conditions not achievable in nature when you open it again the light will exit again. The problem being that this doesn't work in reality as the mirrors won't be perfect and a switchable mirror even less so.

Similar setups to your sphere are used in real optical setups. They are called optical cavities. In some quantum optics experiments they are even used to store emitted photons for some time in a confined space (but not in the sense of putting them in and retrieving them later, rather in the sense of keeping them around and confined to increase the probability of some interaction).

A simple example of the application of optical cavities is aFabry-Pérot interferometer is a cavity where the mirrors allow partial transmission. By using multiple internal reflection you get a much narrower interference peaks compared to a setup where you split up the beam in two and let those interfere. So in a way, light stored in a cavity is use there to allow interference of multiple reflections of the same signal.

Lasers also use optical cavities (however the medium in the cavity emits light itself) and each emitted photon statistically makes several round trips in the cavity before it leaves through the partially reflective end.

• 5
  $\begingroup$Just one pedantic nitpick:Classical electromagnetism is linear. :)$\endgroup$

  hft

  – hft

  2025-01-27 00:29:24 +00:00

  CommentedJan 27 at 0:29
• 1
  $\begingroup$@Tofandel the orbits along the photon sphere are unstable. The light would not go around the black hole forever. That being said, the photon sphere only exists in the Schwarzschild spacetime, which is unphysical.$\endgroup$

  paulina

  – paulina

  2025-01-27 18:25:20 +00:00

  CommentedJan 27 at 18:25
• 1
  $\begingroup$@hft Fixed that with an edit to make it clearer.$\endgroup$

  Sebastian Riese

  – Sebastian Riese

  2025-01-27 19:14:52 +00:00

  CommentedJan 27 at 19:14
• 2
  $\begingroup$@ChristophilosBlu yes, impossible. Even superconductors aren't perfect reflectors. It is exceedingly rare that the physics of our universe allows perfection.physics.stackexchange.com/a/556329/11645$\endgroup$

  llama

  – llama

  2025-01-28 20:29:22 +00:00

  CommentedJan 28 at 20:29
• 2
  $\begingroup$@ChristophilosBlu"Do you believe in the possibility of discovery" Note that claims like these in physics are not "we haven't found a perfect mirror so one probably doesn't exist" but rather "the theory that explains amazingly well how light interacts says that perfect mirrors don't exist". Sure, the theorycan be wrong but the discovery would need to be something that completely breaks our current understanding but still agrees with our current understanding in most cases.$\endgroup$

  JiK

  – JiK

  2025-01-29 13:10:30 +00:00

  CommentedJan 29 at 13:10

Yes, in theory, the perfectly reflected sphere would eventually be filled with enough light that the backflow along the fiber would exactly equal the inflow. Or, if closed, have an electromagnetic field wobbling forever.

In practice, reflectance is usually below 99%, so after about a few bounces the light will be absorbed by the walls and just heat them up. This is really fast due to the high speed of light. In microwave resonators with superconducting walls the reflectance is really good and a wave can remain for nearly a second, but for visible light absorption is much much quicker.

• 3
  $\begingroup$You can buy mirrors that have reflectivity of 99.995% according to their specslaser2000.com/en/mirrors/82412-high-reflective-mirror.html . After 10000 bounces there would be 60% left.The question is of course hypothetical but 99% reflectivity is a bit strict.$\endgroup$

  AccidentalTaylorExpansion

  – AccidentalTaylorExpansion

  2025-01-27 17:15:32 +00:00

  CommentedJan 27 at 17:15
• 1
  $\begingroup$@AccidentalTaylorExpansion - Yes, those mirrors are great. But in a 1 meter cavity this means the light bounces just for 33 microseconds. Note that you can preserve light well in a big cavity or long waveguide; if you bounce against the moon and back you can keep the light a few hours.$\endgroup$

  Anders Sandberg

  – Anders Sandberg

  2025-01-28 13:53:22 +00:00

  CommentedJan 28 at 13:53
• $\begingroup$Would this be due to the Pauli exclusion principle? Or some other theory?$\endgroup$

  foolishmuse

  – foolishmuse

  2025-01-28 16:55:23 +00:00

  CommentedJan 28 at 16:55
• 1
  $\begingroup$@foolishmuse - Photons are bosons and don't obey the principle. You can stack as many as you want.$\endgroup$

  Anders Sandberg

  – Anders Sandberg

  2025-01-29 10:44:57 +00:00

  CommentedJan 29 at 10:44
• $\begingroup$Then why would there be a limit as to how many photons you could cram into that sphere? What is the principle behind your answer?$\endgroup$

  foolishmuse

  – foolishmuse

  2025-01-29 13:28:49 +00:00

  CommentedJan 29 at 13:28

If we stretch your scenario to the extreme imagining some kind of light valve at the entrance of the sphere and perfect reflection, then one can imagine the formation of aKugelblitz, that is a hypothetical black hole formed only by light.

• 3
  $\begingroup$Light exerts pressure. Unless your mirror is insanely strong mechanically, it will explode long before it reaches Kugelblitz.$\endgroup$

  fraxinus

  – fraxinus

  2025-01-27 17:44:54 +00:00

  CommentedJan 27 at 17:44
• $\begingroup$@fraxinus True, true... But again, extreme scenario :)$\endgroup$

  EPrivat

  – EPrivat

  2025-01-27 22:20:37 +00:00

  CommentedJan 27 at 22:20
• 1
  $\begingroup$Curious. Going to have to study up on this "Kugelblitz" idea.$\endgroup$

  Christophilos Blu

  – Christophilos Blu

  2025-01-28 01:39:43 +00:00

  CommentedJan 28 at 1:39
• 1
  $\begingroup$According tothis study: "If a beam of light gets too bright, space itself stops being transparent".$\endgroup$

  talex

  – talex

  2025-01-28 15:22:52 +00:00

  CommentedJan 28 at 15:22

After the light intensity inside this hypothetical sphere exceeds a certain limit, light back scattering might start, thereby some light coming out of the hole meant for adding light.

After the light intensity exceeds a certain (high) limit, nonlinear phenomena might start, thereby creating some additional holes in the sphere, wherefrom light of various wavelengths might come out.

In any case, it will not be possible to keep inputting light indefinitely.

• $\begingroup$Of course the practical application of such a feat would not be to keep adding light indefinitely... but only enough to ensure sufficient illumination throughout the night thoughts. Optimally, ideally, sun light could be collected and stored for up to 24hours, to be released over a period of 12 hours. A big ask. Yet, if possible, it would be a big deal. No need for photovoltaics cells, no need for electricity to be stored, to then be converted back into light. The application would be primarily very local; household illumination; workshops, caves, mines, etc.$\endgroup$

  Christophilos Blu

  – Christophilos Blu

  2025-01-28 01:46:09 +00:00

  CommentedJan 28 at 1:46

Basically your analysis is correct. Light will be stored in the sphere until an equilibrium is reached.

That happens when the amount of introduced light is equal to the light that is "lost". These losses can due to

1. reflection losses (if we have < 100% wall reflectivity)
2. light escape through the input hole.

Note: 2. is not the same as stopping light flow. It just means light is reflected back into the fiber. In fact the sphere will just appear as a mirror to the fiber. Just as if you would put a (diffuse) mirror in place of the sphere opening.

Another interesting fact is that light is indeed accumulated in the sphere, in the sense that the circulating light power can be very high, much higher than the input.

Example: If the only 1% of light currently inside the sphere is escaping the sphere, the power level inside the sphere is 100 times the input power (because at equilibrium the losses equal the input power). This 1% could be the ratio of the input hole to the whole sphere surface area for a perfect reflectivity.

Such a sphere is actually a technical device, it is calledintegrating sphere.

Losses are small, but still too high for storing light over significant times. Such spheres can have ring-down times in the order of 10s of µs. Larger spheres of course longer, smaller ones shorter.

• 1
  $\begingroup$Nit: Integrating spheres are a different beast, they don't optimize for reflectivity but uniformity (for photometric measurements – your link even says so: if the reflectivity is too high, the measurement of the total flux getsless accurate: "However, the more closely $\rho$ approaches unity, the larger is the influence of the ports, i.e., the less accurate the estimate is." – The reflectors used there arediffuse (and a diffuse reflector of very high reflectivity is technically much more challenging than a mirror).$\endgroup$

  Sebastian Riese

  – Sebastian Riese

  2025-01-29 15:55:02 +00:00

  CommentedJan 29 at 15:55

What you are describing already exists, and is called a"quantum memory" because it stores the light for some amount of time. (although these are typically done just by using two mirrors facing eachother)

While the theorists here are saying that such a device is useless because you can only "store" the light for a few milliseconds are incorrect in thinking this is useless. Light pulses can be made to be much much faster than milliseconds, so you have quite a large degree of control when working with these mirrors.

You are also correct that the light that is trapped inside the"cavity" will affect things:

1. The light will PUSH against the mirrors with each bounce. However, many many hits of photons is not typically enough to really cause a big pushing force.
2. while light will mostly reflect, it will sometimes get absorbed by the mirror and heat the mirror. Use too much light and you'll burn your chemical coatings which are made to help it reflect better.
3. The light that wants to come out, will constructively interfere with the light that is trying to enter. This happens even for a single photon, and you have to carefully choose the length of the mirrors such that the wavelength of light can fit inside the cavity. Otherwise the stuff entering will always cancel with the stuff exiting and you cant get anything inside.

• optics
• electromagnetic-radiation
• visible-light
• reflection
• dissipation