# Can quantum entangled particles be split and sent into a black hole

• B
Benfield
TL;DR Summary
Virtual particles
I am new here so apologies in advance. When a virtual particle and anti particle appear at the event horizon of a black hole, before they destroy each other, they are split with one being sucked into the black hole and the other becoming exhaust. Are these the same particles as the quantum entangled ones, with one corresponding to the other, or if not is it possible to send one half of a quantum entangled particle into a black hole?
Thanks sorry to those who are shaking heads.

Staff Emeritus
When a virtual particle and anti particle appear at the event horizon of a black hole, before they destroy each other,

That doesn't happen. It's a pop-science myth. That renders the rest of your question moot.

Heikki Tuuri
Heikki Tuuri
The myth of a virtual particle pair, one falling to the horizon, was started by Stephen Hawking himself in his 1975 paper. Later he commented that "no one has been able to give a mathematical description of that hypothetical process."

https://arxiv.org/abs/hep-th/9907001

The famous 1999 paper by Parikh and Wilczek describes a model where a quantum tunnels from behind the horizon. The paper contains some assumptions which are not obvious to me.

Gold Member
The famous 1999 paper by Parikh and Wilczek describes a model where a quantum tunnels from behind the horizon. The paper contains some assumptions which are not obvious to me.
What assumptions?

Heikki Tuuri
What assumptions?

Parikh and Wilczek assume that a spherical electromagnetic wave, which travels radially outward, can spontaneously form just behind the horizon and the horizon can contract because the mass-energy omega of that wave is not to be counted in the mass M of the black hole when the wave travels outward.

We do not know if any of the above assumptions are true in nature.

Classically, such a wave cannot form spontaneously. Why can we use classical general relativity to argue about the radius of the horizon then?

What controls the rate at which various quanta are produced?

Gold Member
Parikh and Wilczek assume that a spherical electromagnetic wave, which travels radially outward, can spontaneously form just behind the horizon
They don't assume that it forms spontaneously. They assume that it appears there throught the process of quantum tunneling. The probability of tunneling is computed via the standard WKB formula.

But I have a different reservation about their approach. The principal value of the integral in (6) is real, so the imaginary part is zero, implying that the probability of tunneling is zero. But they choose not to take the principal value, but a value obtained with a deformed contour of integration which results in the non-zero result (7). It looks quite ad hoc to me.

Another deficiency of their approach is that they do not compute the quantum state after (or even before) the tunneling. In this way they cannot say much about the information paradox.

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Heikki Tuuri
They don't assume that it forms spontaneously. They assume that it appears there throught the process of quantum tunneling. The probability of tunneling is computed via the standard WKB formula.

Maybe I did not understand something in the paper.

Parikh and Wilczek write above equation (5):
The imaginary part of the action for an s-wave outgoing positive energy particle which crosses the horizon outwards from into out can be expressed as

The imaginary part of the action, I am S, tells the probability that the particle tunnels through the potential wall. That is the WKB approximation.

I understood the paper like this: a virtual photon representing the outgoing spherical wave appears spontaneously behind the horizon.

After tunneling through the horizon the photon has stolen some energy from the black hole, and it leaves as a real particle.

Let us compare this to how a real photon is born in ordinary quantum physics. There is an electric charge in an accelerating motion. Classically, there would be electromagnetic radiation. If quantum mechanics allows the system of charges to fall into a lower energy state, then a quantum of energy, a photon, may leave.

The emission of a photon from a black hole does not have a classical counterpart. That is one of the reasons why I do not see the assumptions of Parikh and Wilczek as obvious.

EDIT:
Can we draw a Feynman diagram style description of the process? We may assume that in a collision experiment, a large number of particles create a bound state, a black hole. Then a virtual photon steals energy from this bound state and becomes real. Unfortunately, Feynman diagrams do not allow bound states.

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Gold Member
I understood the paper like this: a virtual photon representing the outgoing spherical wave appears spontaneously behind the horizon.
They never said that the photon behind the horizon was virtual. They did not say how exactly it appeared there, but it could have been created by some "ordinary" non-gravitational mechanisms.

Heikki Tuuri
I have spent quite some time analyzing the Parikh and Wilczek paper. I will do more analysis some time in the future. A theory of quantum gravity should clarify which assumptions in the paper are correct.

A few other points: the radiation in the Hawking 1975 paper is not visible to a freely falling observer. The Parikh and Wilczek radiation is probably visible.

In an idealized case, the black hole is spherically symmetric. Can it create transverse radiation? The symmetry would be broken.

Keith_McClary