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https://www.livescience.com/65113-fastest-camera-captures-speed-of-light.html

This is what light looks like when captured by a camera at 10 trillion fps. Interesting.  You can find this YouTube video in many other places (Planet Slow Mo). Please pay attention to the section between minute 6, 40 seconds, to minute 7, 25  seconds into the video. It looks like the old Pong game. This is a pulse of laser light (multiple photons), exciting atoms and molecules in a reflection cavity, that generate photons in an orthogonal direction (compared to the direction of the initial laser pulse) , that reach our eye.

And here is  formulation of the question.  You can design a special reflection cavity (an Archimedes spiral maze is just an example, many other designs are possible), so that the pulse spends more time in a very small region. If you have many, many pulses of laser light entering this reflection cavity ( simultaneously,  or properly timed, in an empty cavity), you could have, at a certain moment in time, a lot of pulses concentrated in a very small region. In other words, with high probability,  at a certain moment in time (and not after eons, if the reflection cavity is properly designed ), you could have a region of space with extremely high energy density. You probably know by now what I am leading to, little black holes, or something close. The problem is that with each reflection,  some photons will be lost ( this requires some though, the emitted photons go in the wrong direction  ),  but with proper timing of the pulses (and the right design of the reflection cavity), I think that you can guarantee that a high energy density region will emerge in reasonable time, this is a problem of probability , Markov  chains modeling. 

A way of creating small regions of high energy density? A way of creating little black holes? Probably not the latter (and is probably recommended not to create any mezoscale black holes close to Earth anyway ), but I think it's worth some thought, exremely high energy density regions of space could open the way to new phenomena 

The question, in a nutshell, is the following.

Is is possible to design such  a system?. Would it be feasible, in principle? Am I missing any facts that would make such a design impossible?

Edit. After receiving an answer, I will reformulate the question, without changing the original question (even if I realise now I am off orders of magnitude ).

What is the maximum energy density achievable with such a design (and current technology ) , keeping in mind the fact that it must depend on the design of the reflection cavity , the power and the timing of the laser pulses?

Edit 2. If one puts a White -Juday warp field interferometer inside the reflection cavity, would it lead to any measurable effects? A proper design should lead to regions of high energy density inside the reflection cavity. This is a more down to Earth question , after realizing that the original question was orders of magnitude off reality.

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A black hole is profoundly difficult to create artificially. This applies even to creating a black hole with light alone - a so-called "kugelblitz" - instead of matter which requires a high degree of compression.

And this is the reason why. The lightest-mass black hole that is believed to be possible (i.e. ignoring some speculative theories of quantum gravity that do not appear to have panned out) is somewhere around the Planck mass,

$$M_\mbox{min BH} = m_P := \sqrt{\frac{\hbar c}{G}}$$

which in terms of mass units is about 22 micrograms, which may not seem like a lot, but in terms of energy, is around 2 gigajoules - roughly the energy released by detonating half a megagram (500 kg) of TNT. While generating that energy is thus eminently possible, confining it to the requisite small space is as hard as ever: the space required is on the order of a Planck length, about $10^{-35}$ metre. Even if you are using light, the extent to which you can "confine" a ball of light photons is limited by their wavelength: you cannot make a light pulse that's tighter than the wavelength of the individual photons. For ordinary light, that means a distance of around 500 nm, while the Planck length is on the order of $10^{-26}$ nm, about 28 orders of magnitude smaller. If you could generate light at that short a wavelength, its individual photons would already have about Planck energy and so you are already there, and moreover if we could get that kind of energy in a single subatomic particle of any sort, we'd have the answer to quantum gravity by now :)

Alternatively, we can take it the other way around. If we want to consider making a black hole from 500 nm light, then we must give enough energy in an about 500 nm-radius spherical region so that that radius equals the Schwarzschild radius. From

$$r_S := \sqrt{\frac{2GM}{c^2}}$$

we get that $$M = \frac{r_S^2 c^2}{2G}$$ and hence taking $r_S = 500\ \mathrm{nm} = 500 \times 10^{-9}\ \mathrm{m}$, we get the mass as around 168 Pg - which is petagrams - of mass equivalent in light. That means you need even more mass than that in raw fuel simply to generate the needed light. To get an idea of the size of that mass unit, one Pg is about the mass of a small mountain, and thus you can tell this is also quite infeasible indeed.

ADD: You ask about the energy density. This can be found simply by dividing the energy by the volume of the region in question. For the Planck mass black hole, the volume will be on the order of Planck volume, density will thus be around the Planck energy density, which is equal to the Planck pressure: hence about $10^{113}\ \mathrm{J/m^3}$. Yes, that's ten trillion googols of joules - vastly more than in the entire observable Universe - per cubic metre. For the optical case, the region has volume $\frac{4}{3} \pi \left(500\ \mathrm{nm}\right)^3 \approx 5.24 \times 10^8\ \mathrm{nm}^3$ or $5.24 \times 10^{-19}\ \mathrm{m}^3$ and so the energy density is $\frac{1.68 \times 10^{14}\ \mathrm{kg} \cdot c^2}{5.24 \times 10^{-19} \mathrm{m^3}} \approx 2.9 \times 10^{49}\ \mathrm{J/m^3}$, or about 290,000 supernovae (1 FOE standard) per cubic metre :) Please keep in mind that all black holes with "reachable" energy densities are formed by collapsing entire stars. Making black holes is NOT easy!

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  • $\begingroup$ Thank you @Tthe_Sympathizer, I suspected I was off orders of magnitude, no surprise there. Could you please estimate how high that energy density might be? I know it must depend on the design of the reflection cavity and the timing of the laser pulses. $\endgroup$ – Cristian Dumitrescu Apr 1 at 4:13
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    $\begingroup$ @Cristian Dumitrescu : Added. It's beyond insanity :) $\endgroup$ – The_Sympathizer Apr 1 at 4:24
  • $\begingroup$ OK, forget about black holes. What is the estimated maximum energy density achievable in such a design, with current technology? $\endgroup$ – Cristian Dumitrescu Apr 1 at 4:35
  • $\begingroup$ Observation @The_Sympathizer Once again, forget about black holes. What is the estimated maximum energy density achievable with sucha z design? $\endgroup$ – Cristian Dumitrescu Apr 1 at 4:40
  • $\begingroup$ Anyway, thank you for your answer @The_Sympathizer, I appreciate it. I just thought interesting physical phenomena could occur even before the energy densities related to black holes. $\endgroup$ – Cristian Dumitrescu Apr 1 at 4:46

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