Unruhs Law and how part of a photon pair disappears beyond a Rindler horizon?

Question

Unruhs Law says that "an accelerating observers in empty space will see themselves embedded in a gas of hot photons at a temperature proportional to their acceleration."

Tell me if I have this wrong, but as I understand, this is because empty space is full of virtual particles popping into existence and immediately annihilating, so you cannot detect them until you begin to accelerate. This is because an accelerating observer has an effective horizon (a Rindler horizon) which they cannot see beyond, so if one of these particles drifts out of their view and into their hidden region, they only see one of the particles (lets say they're photons) and will be able to detect it and interpret it as heat.

How is this possible? Shouldn't a photon still annihilate with its partner regardless of which side of some arbitrary horizon it's on? And is this photon pair entangled?

Answer 1

Yes, it is possible, and although never observed (you'd have to be accelerating fast) it is theoretically on firm ground. The idea is very similar to Hawking gravity from Black Holes (BHs), and the equations are equivalent.

There's the view and explanation you mentioned, and there are others more rigorous explanations. Hawking derived his result differently. I am not sure how Unruh did it, but all are equivalent. On your explanation, it is seen as more of a conceptual explanation than a physical result, if there's a horizon if one heads out the other one will head in by conservation of momentum. Another way to do it is by assuming a quantum field outside the horizon, and calculating the field in that gravitational field, or equivalently as seen by an accelerated observer, and it'll turn out that it emits particle pairs (positive and negative freqs, one going out one in), and even for the ground state it still does that. Another way is calculated as quantum tunneling from the other side. All equivalent explanations, but some people don't like the virtual particle explanation because virtual particles are not real, and can be thought of as really mathematical fictions. But the math works out right.

On your explanation, the thought is that if there was no gravitational field, or equivalently an accelerated frame, they would indeed annihilate, so you need the acceleration or gravitational field to try to separate them, and you need the horizon to keep them separate.

They could be thought of as entangled, conservation of momentum, charge etc makes their states fully entangled. However the one going in is virtual, not really a particle, and has negative mass and energy, so that's all arguable.