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I'm starting to wrap my head around Feynman diagrams, and the idea of "real" vs. "virtual" particles, but one area where this distinction seems to break down is in describing Hawking radiation, where virtual particles become real particles through interaction with gravity.

How would one explain the difference between real and virtual particles in an interaction which produces one from the other? In the example of Feynman diagrams, are these on-shell or off-shell? When do they become real in the interaction? How is the fundamental "what-goes-in-must-come-out" rule allowed to be broken?

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    $\begingroup$ There is no clear-cut difference between real and virtual particles. One can find a smooth continuum of degrees of virtuality stretching between virtual and real. No interaction is ever exactly on-shell, although a lot of them come very, very close. $\endgroup$ – Peter Shor Aug 9 at 20:49
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    $\begingroup$ The virtual particle story of Hawking radiation is a simplification. Please see physics.stackexchange.com/a/252236/123208 $\endgroup$ – PM 2Ring Aug 9 at 21:01
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    $\begingroup$ I recommend looking at the post linked in @PM2Ring's comment, and I'll add one thing: Feynman diagrams are graphic representations of the terms in a small-interaction expansion, where a complicated theory is approximated by a series of corrections to a simpler theory. The "virtual particle" language also refers to that expansion. Hawking radiation is usually (and was originally) derived using non-interacting quantum fields, so the small-coupling expansion isn't needed. Quantum field theory isn't about Feynman diags or virtual ptcls. Those tools are useful for some things and not for others. $\endgroup$ – Chiral Anomaly Aug 10 at 3:16
  • $\begingroup$ For a qualitative answer see my answer here physics.stackexchange.com/q/451618 $\endgroup$ – anna v Aug 10 at 6:07
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The energy to create two particles (particle-antiparticle pair) is provided by the gravitational field of the black hole.

Now you can describe this classically (from a classical gravitation field) or from two gravitons (or one loop in effective quantum gravity).

You are asking about how virtual particles will transform into real particles.

Now you are saying that what goes in must come out, but only energy and momentum need to be conserved in this case.

Both energy and momentum are conserved. The energy of the particles reduces the energy of the black hole's gravitational field.

The energy of the gravitational field of the black hole is what is represented as a virtual graviton. That is what is emitted by the black hole.

This virtual graviton that goes into a loop creates a pair of real particles. This is when the energy is transformed into becoming real particles. One of the particles escapes, the other goes back into the hole.

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