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.
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.