

Hawking Radiation and Pair Annihilation
Name: Christopher
Status: student
Age: N/A
Location: N/A
Country: N/A
Date: N/A
Question:
Regarding Hawking Radiation, the usual
description is that one member of a virtual particle pair enters a
black hole, leaving it's orphaned partner roaming our universe,
appearing to have been radiated out of the black hole. If two such
processes take place, the first orphaning the virtual matter
particle while the second orphans the virtual antimatter particle,
can these two orphans meet and annihilate each other? If your answer
is "yes" this suggests Hawking Radiation is only a temporary
phenomenon, awaiting only sufficient time for all orphan /
antiorphan particles to either: meet and vanish, or vanish into a
black hole which need not be the same black hole into which its
original pair creation particle vanished.
Replies:
Christopher,
The one fault in your analysis lies in your interpretation of
probabilities. Your analysis assumes that every particle, given enough
time, will eventually meet up with every other particle in the universe.
If a virtual antiparticle exists, it will eventually meet up with a
virtual particle of the same kind. It is quite possible for an event to
have less than 100% chance of occurring over infinite time. If not,
then one could conclude that EVERYTHING has a 100% chance of occurring,
given enough time. This then leads to the conclusion that everything
that CAN happen eventually WILL happen.
A simple example that such an interpretation is incorrect lies in
radioactive decay and halflives. Within a second's time, a radioactive
particle has a certain probability that it will decay. If this is 50%
per second, we cannot say that the probability is 100% after 2 seconds.
Should the particle survive one second, then there is only a 50%
probability that it will decay during the next second. Should it
survive the 2nd second, there is only a 50% probability that it will
decay during the 3rd second. This continues on. A radioactive particle
does not ever have to decay. If you have 100 million such particles,
the odds are quite high that half of them (50 million) will decay during
the first second. It is quite likely that half of what remain (25
million) will decay during the 2nd second, and so on. This pattern
continues so long as there are a very large number of particles present.
There is always a chance that no particles will decay in the first
second, but it is not likely to occur. When you get down to the level
of individual particles, probability behaves quite differently. It is
truly random.
One can never say that something with less than 100% chance of happening
will definitely happen. This is one of the properties of quantum
physics that Albert Einstein could not bring himself to accept. You
cannot say that the antiparticle will meet a corresponding particle.
You cannot say that it won't. And even if they do come close together,
you cannot say that they will interact. That too is based only on
probability.
Dr. Ken Mellendorf
Physics Instructor
Illinois Central College
This is not my area of expertise, but your propositions seem reasonable.
The probability of virtual antimatter particle and a matter particle
meeting in spacetime, while not zero, would be quite small it would seem.
The same is true, I would think, for the virtual antiparticle encountering a
star, another black hole, etc. would also be very small. What is unknown is
whether matter particles, e.g. electron itself, has a finite lifetime. Yes
it is long, but it may not be infinite. These very fundamental questions
await answers.
Vince Calder
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Update: June 2012

