Photons have a size. Their diameter is broadly proportional to their wavelength. They also have a curious characteristic. The more energetic a photon, the smaller its wavelength. So they become more and more energy-dense.
This led me to question which energy would a photon have so much energy that the universe should form a black hole around it.
To estimate this, we need the equation for the Schwarzchild radius of a black hole. This equation is: R = 2GM/c^2. Given that we know that a photon's energy follows E = hc/λ = Mc^2, we can get that M = h/λc. Also, the radius of the photon is the radius of the black hole. So λ/2 = 2hG/λc^3. From which we can take λ^2 = 4hG/c^3. Given that, a Planck length is Lp^2= hG/(c^3*2π). From this we get that λ^2 = 8π Lp^2,
This is hard to estimate by hand, but the gist is that the Photon would be around 5 times a Plank length in diameter, or 8.10×10^−35 m big!
I wonder what would happen to the photon after it becomes a black hole. Technically, it should stop. But on which reference frame? Also, if it were just a bit more energetic, there would be a black hole with 5 Planck lengths in diameter moving around the universe.
What if, at some point during the inflationary universe, a large portion of photons had even higher energies, and as the universe cooled down, they coalesced into tiny black holes that roamed around and ate whatever got too close to them?
Overall, I like the idea of a super energetic photon stopping down into the life of a roaming black hole. Kind of like a retirement plan for photon superachievers.
PS: I need to learn how to write equations here.
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