B A little logical doubt on Hawking radiation

Summary
As hawking radiation is based on quantum fluctuations, can they cancel out each other due to equal probabilities of a particle remaining in or drifting away?
Summary: As hawking radiation is based on quantum fluctuations, can they cancel out each other due to equal probabilities of a particle remaining in or drifting away?

I recently learned how hawking radiation actually works. It is based on quantum fluctuations which happen randomly in space. So when one of them happens on the edge of a black hole's event horizon, there is a chance that the anti-particle drifts away and the particle stays inside or gets pulled inside the black hole, and the opposite can happen too. This results in an extra particle or anti-particle which annihilates the opposite part inside the black hole.

So, shouldn't there be an equal chance of a particle drifting away or getting pulled in by the black hole? In each case, the opposite would happen to the anti-particle. So, suppose that in an instance two fluctuations happened at the edge of event horizon. In the first one the particle drifted away and in the second one, the anti-particle drifted away. So that leaves one particle and anti-particle outside the black hole, and one set inside. So, both sets can cancel out each other and the particle or anti-particle inside the black hole won't annihilate an extra particle or anti-particle.

This means that hawking radiation shouldn't happen, logically.

I might have made a big error in this, as I don't know a lot about physics. But, please correct me if you find any mistake (which there surely must be). Thanks for reading!
 
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You have made TWO big errors in this. The first error is thinking that the particle-antiparticle pair explanation of Hawking Radiation is the actual explanation. It is not. It is a heuristic that Hawking came up with because, as he described it, he could not find any simpler way using English to describe something that really can only be described with math. It is not to be taken literally (although it always is by pop-science presentations)

Second, you have misunderstood even the heuristic. I can't explain it well myself but there are dozens (probably hundreds) of threads here on PF in which it is explained that in the heuristic, whichever particle falls in adds to the mass of the BH and the escaping particle just, well, escapes.
 
That's where I learned that
I don't know how I misunderstood it,

Edit: yes, I get my mistake, thanks a lot for the answer.
 
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