It's weird that they had the idea of firewall just in 2012. I had this exact idea maybe ten years prior while being a school student. A fairly obvious one if you think of that - some photons will orbit the black hole.
Someone on Reddit asked a brilliant question a while back - what happens to quantum fields at the event horizon?
In QFT, fields are everywhere. But to support a field, you need a mechanism that allows causal propagation - which is exactly what isn't allowed across an event horizon.
So at the very least you have a discontinuity where three and possibly all four fundamental forces stop working, and which is separate to any hypothetical relativistic singularity.
Whatever is left is going to be some kind of unimaginably weird sub-quantum soup.
I don't know if that's the same firewall that was invented in 2012. But the takeaway is that relativity isn't complete enough to model black holes. You absolutely need to include quantum effects - and when you do, things get very strange indeed.
> to support a field, you need a mechanism that allows causal propagation - which is exactly what isn't allowed across an event horizon.
That's because the event horizon is a lightlike surface. Causal propagation isn't allowed across any lightlike surface. For example, there are lightlike surfaces that contain the event where you are right now. Causal propagation isn't allowed across them. Yet QFT works just fine in your vicinity.
What the Reddit questioner apparently did not realize is that the event horizon is defined globally, not locally. In other words, its location is defined in terms of the global properties of the spacetime, not in terms of any local properties. Locally, the EH is just a lightlike surface, and is no different, from a QFT point of view, from any other lightlike surface.
That's a neat way of putting it (at least broadly) in the first four pargaraphs. Thanks.
I'd add that the event horizon is the boundary below which the propagators of causality can only move further below the horizon itself.
The "unimaginably weird sub-quantum" part doesn't follow from those paragraphs, though, in the region outside the event horizon, or even a little ways inside. It is however a fair way of describing the problem of the singularity; the goal of nearly all quantum gravity research programmes is keeping the singularity from ever existing, and "weird microscopic behaviour" is a reasonable way of describing what that may entail.
I made some comments relevant to your last paragraph elsewhere in this discussion.
The fields in quantum field theory are mathematical tools, they are not physical entities.
But to support a field, you need a mechanism that allows causal propagation - which is exactly what isn't allowed across an event horizon.
But that is only a one-way thing - the future light cones of events inside the event horizon are contained inside the event horizon but the future light cones of events outside the event horizon certainly overlap the inside of the black hole.
> The fields in quantum field theory are mathematical tools, they are not physical entities.
If you mean that the world itself is not the mathematics then I can accept it (although I might resist, the philosophical rejection of things like Tegmark's Mathematical Universe Hypothesis), but if you mean that what we actually have is a bunch of particles doing one thing or another, I must object, because it is extremely difficult to explain nonperturbative phenomena like instantons or sphaelerons if you have that attitude.
Quantum fields have gauge symmetry so they do not have any definite values, you can assume them to have more or less any value as long as you are consistent. My views on this topic are heavily influenced by Nima Arkani-Hamed and here [1] are 30 seconds from a lecture where he is very explicit about this. But I am aware that this is not really a topic with universal agreement, at least this is what it looks to a non-physicist like me. And looking at your user profile I am pretty sure you are going to tell me that I am asking for to much realism.
Such as a singularity (e.g. gravitational)? I think in Physics (just as when analysing functions), the interesting things happen when you approach such limits.
> A fairly obvious one if you think of that - some photons will orbit the black hole.
That some photons would orbit black holes is fairly well-known. There's an "innermost stable circular orbit"[0] ("photon sphere" for rotating black holes [1]), inside which stable (circular) orbits do not exist. These are at larger radii than the event horizon and so would be unrelated to the firewall proposal.
Photons orbit the black hole in the photon sphere which is located outside of the event horizon, at 1.5 times the Schwarzschild radius in case of a Schwarzschild black hole. As far as I know such orbits are also usually not stable. For a photon to orbit the black hole in the photon sphere it has to move tangentially, to reach the photon sphere the photon needs to move with at least some radial component and a photon can of course not just fire its rockets when reaching the photon sphere to enter the orbit. The idea of the firewall is very different from the idea of photons orbiting a black hole which was studied a long time ago.
Wouldn't you get orbiting photons simply by having them emitted from falling bodies, i.e. hot gas?
Any photons emitted in the right direction by incoming material in the right place would enter an orbit; and given that hot material emits photons in all directions continuously, and there's a steady supply of infalling material, there's going to be a continuous source of orbiting photons.
IANAP so don't take my word for it, but I would assume the photons would have to be emitted EXACTLY tangentially at EXACTLY the photon sphere. Just a tiny bit earlier or later or with a tiny bit of radial momentum and the photon would eventually escape or fall into the black hole. And a real black hole is not a perfect Schwarzschild black hole, it will almost certainly have at least some charge or angular momentum, surrounding matter will change the metric somewhat. But I can not tell whether that makes it more or less likely for a photon to stay in orbit but I tend towards less likely because this seems to add more possibilities to randomly push the photon out of its orbit one way or another.
My understanding is that photons are uniquely unstable. By virtue of traveling at a constant (the speed of light), they lack the self-regulating orbital mechanics of matter (where going deeper into the gravity well speeds you up, and going farther away slows you down.)
Dealing with spherical cows, before accounting for drag, you can describe the possible space for valid orbits as a volume, and you could describe the bounds of the velocity vector via another volume, for all positions and velocities at those positions that describe - at least on paper - mathematically perfectly stable orbits.
Dealing with a photonic cow, before accounting for drag, you can describe the possible space for mathematically stable orbits as not a volume but an area - the surface of a sphere. The velocity vector has a very specific magnitude (c), and a very limited range of possible directions (exactly perpendicular to the normal of the sphere's surface). The shape you would use to describe the bounds of this velocity vector have 0 volume, 0 area. It only has a length.
Both cows can be further perturbed by drag, tidal effects, non-point gravity sources, etc. to further worsen the problem. Individual collisions with particles of space dust will push the spherical cow from one mathematically stable orbit to another, until eventually they add up enough to most likely deorbit it. Individual collisions with particles of space dust will instead take the photonic cow from one mathematically unstable orbit to another, with a decent chance of it ending up on an escape trajectory instead.
It's at 1.5 times the radius of the event horizon for a non-charged, non-rotating black hole. But it's more of a theoretical than practical construct. You wouldn't expect to actually find any photons there because the orbit is unstable and any deviance from a perfect orbit would accumulate exponentially.
