Why don’t ordinary photons spontaneously collapse into black holes? You should get a singularity if the energy density in any region of space is high enough. But you can pick an inertial reference frame such that any given photon has arbitrarily high frequency (and thus energy) due to blueshift. Since any inertial reference frame is as valid as any other due to relativity, why don’t all photons collapse under their own weight?
But you can pick an inertial reference frame such that any given photon has arbitrarily high frequency (and thus energy) due to blueshift.
That applies to anything, not just photons. In any event, I’m not an expert in general relativity, but I think what matters is the energy of an object in its own center-of-mass frame (a.k.a. its mass). (And a single photon, or a collection of photons traveling in the same direction, doesn’t even have a center-of-mass frame.) Anyway, elementary particles (including photons) already are point-like so far as we know, so they couldn’t possibly collapse any further.
Quantum mechanics and relativity are not compatible. That’s one of the big problems (probably even the biggest) of modern physics. From each one’s point of view the other one is nonsense, the math breaks down.
I think I see where you’re going with this. If I can answer the question of how the universe would be different if photons did collapse, that might help explain why they don’t.
That applies to anything, not just photons.
What would the world look like if, say, electrons were actually black holes with an electric charge? I do think black holes can be electrically charged, that is, charge is still conserved even if charged particles fall into a black hole. Same with angular momentum etc. We would expect black holes of electron mass to spontaneously decay via Hawking radiation. Into a shower of particles that in sum obey the conservation laws… in other words, into another electron. Hmm. That didn’t really change anything did it? It might help to explain quantum tunneling though.
I would also expect electrons to have an event horizon of finite radius, rather than behaving as an infinitesimal point. I don’t know enough general relativity to calculate how big this should be for a black hole of electron mass, but perhaps it’s too small for us to have observed yet. (Edit: asking Wolfram Alpha yields 1.353E-57 meters. Plank Length is only 1.616E-35 meters, far too small to observe.) An event horizon means that light can be trapped by the gravity of the electron. Which would give the black hole enough extra mass to spontaneously decay into more than just an electron. In the case a low-energy photon, into another electron and photon (explains photon scattering), or if high-enough energy, into heavier particles that add up to zero charge and spin, plus the election again. Like positron/electron pair production. Which has also been observed. Hmm. That still didn’t change anything, did it?
Maybe electrons really are black holes?
Oh, I know! Neutrinos are as massive as electrons (edit: not really, but they do have positive rest mass), but lack charge. If electrons are black holes, then neutrinos are also. The effect of gravitationally scattering light as described above should work for neutrinos too, but to my knowledge, they don’t. (Do they?)
Why don’t ordinary photons spontaneously collapse into black holes? You should get a singularity if the energy density in any region of space is high enough. But you can pick an inertial reference frame such that any given photon has arbitrarily high frequency (and thus energy) due to blueshift. Since any inertial reference frame is as valid as any other due to relativity, why don’t all photons collapse under their own weight?
That applies to anything, not just photons. In any event, I’m not an expert in general relativity, but I think what matters is the energy of an object in its own center-of-mass frame (a.k.a. its mass). (And a single photon, or a collection of photons traveling in the same direction, doesn’t even have a center-of-mass frame.) Anyway, elementary particles (including photons) already are point-like so far as we know, so they couldn’t possibly collapse any further.
Quantum mechanics and relativity are not compatible. That’s one of the big problems (probably even the biggest) of modern physics. From each one’s point of view the other one is nonsense, the math breaks down.
How do you know that ordinary photons aren’t black holes?
I think I see where you’re going with this. If I can answer the question of how the universe would be different if photons did collapse, that might help explain why they don’t.
What would the world look like if, say, electrons were actually black holes with an electric charge? I do think black holes can be electrically charged, that is, charge is still conserved even if charged particles fall into a black hole. Same with angular momentum etc. We would expect black holes of electron mass to spontaneously decay via Hawking radiation. Into a shower of particles that in sum obey the conservation laws… in other words, into another electron. Hmm. That didn’t really change anything did it? It might help to explain quantum tunneling though.
I would also expect electrons to have an event horizon of finite radius, rather than behaving as an infinitesimal point. I don’t know enough general relativity to calculate how big this should be for a black hole of electron mass, but perhaps it’s too small for us to have observed yet. (Edit: asking Wolfram Alpha yields 1.353E-57 meters. Plank Length is only 1.616E-35 meters, far too small to observe.) An event horizon means that light can be trapped by the gravity of the electron. Which would give the black hole enough extra mass to spontaneously decay into more than just an electron. In the case a low-energy photon, into another electron and photon (explains photon scattering), or if high-enough energy, into heavier particles that add up to zero charge and spin, plus the election again. Like positron/electron pair production. Which has also been observed. Hmm. That still didn’t change anything, did it?
Maybe electrons really are black holes?
Oh, I know! Neutrinos are as massive as electrons (edit: not really, but they do have positive rest mass), but lack charge. If electrons are black holes, then neutrinos are also. The effect of gravitationally scattering light as described above should work for neutrinos too, but to my knowledge, they don’t. (Do they?)
Energy density is a function of mass, and photons have zero mass.
Zero rest mass. Photons certainly have energy.