Quantum Physics question

[Yllanes]

This is what I don't understand.

Who cares what en external observer sees? The particle DIDN'T come from the black hole, therefore the black hole can't lose energy.

I know I'm wrong, 'cause Hawking is right, but HOW am I wrong

Your question is a good one.

First of all, where does the Black Hole end? Its gravitational field extends to infinity. The external observer Cuddles mentioned is actually the asymptote, someone situated at infinity.

More importantly: the picture of a particle-antiparticle being created on the horizon is just a story. Actual calculations of Hawking radiation do not represent these pairs. The idea is often repeated because it is simple and we think that, once we get a full quantum description of the process, something similar will arise. But we lack a microscopic description. Our treatment of BH thermodynamics is only semiclassical at this point.

With more detail, to get particle creation you need quantum field theory. QFT is very well understood for flat spacetimes and we can handle it even for static curved spacetimes. With static I mean that the geometry is given and the processes we study do not change it (because they have too low an energy). Even static curved spacetimes are complicated. In them the concept of particle is not well defined, for example. But if we want to study things like BH evaporation, we will eventually reach a point were the quantum processes and the gravitational ones are both important, so we must handle dynamic curved spacetimes. We do not know how to do this.

 

[Beth]

This is what I don't understand.

Who cares what en external observer sees? The particle DIDN'T come from the black hole, therefore the black hole can't lose energy.

I know I'm wrong, 'cause Hawking is right, but HOW am I wrong

I don't know if I'm right, but this is how I think of it.

If one of a pair of virtual particles crosses the event horizon and the other didn't, then if the particle that crosses the event horizon is the anti-matter particle, I think of it as 'subtracting' from the total mass of the black hole. The particle that remains, that is perceived as 'emitted', is exactly the mass that's subtracted from the black hole. Thus, it is exactly the same as if the black hole had emitted the particle and it has lost energy.

What I don't understand is that since when the matter particle crosses the event horizon and the anitmatter particle remains, it would anniliate some other matter particle and the black hole would gain mass, why doesn't this effect cancel out and black holes remain stable? But perhaps my mental model isn't appropriate in some way that I don't understand yet.

 

[Yllanes]

As I said, things are more complicated than that. This sci.physics FAQ gives more details.

 

[Buckaroo]

What I don't understand is that since when the matter particle crosses the event horizon and the anitmatter particle remains, it would anniliate some other matter particle and the black hole would gain mass, why doesn't this effect cancel out and black holes remain stable? But perhaps my mental model isn't appropriate in some way that I don't understand yet.

Yeah, this has always been my problem with this explanation. I don't understand why just as many matter particles as antimatter aren't captured, statistically balancing each other out, unless antimatter particles are preferentially captured by the black hole. Is there some mechanism for this that I'm missing?

 

[ile]

matter - antimatter

Yeah, this has always been my problem with this explanation. I don't understand why just as many matter particles as antimatter aren't captured, statistically balancing each other out, unless antimatter particles are preferentially captured by the black hole. Is there some mechanism for this that I'm missing?

Yes, you are The point is that the particle / antiparticle in the argument are not the particle / antiparticle you have in mind related to usual matter / antimatter. What is called the particle in the BH argument might as well be an electron as a positron, if you will, and the antiparticle falling through the event horizon would then be the positron or the electron, resp.

So in fact you are right: there is no preferential capture of positrons, say.

The matter dominance in the Universe is not generated by this mechanism...

BTW, I followed up the link by Yllanes and found that John Baez made a reference to Robert Wald's textbook. So I took it down from its shelf and tried to refresh my mind. To think that at some point in my life I was under the delusion that I understood all this...

There is a footnote to some papers by Gary Gibbons and himself about the possible creation of single fermions, I'll have to look that up.

 

[Cuddles]

I don't know if I'm right, but this is how I think of it.

If one of a pair of virtual particles crosses the event horizon and the other didn't, then if the particle that crosses the event horizon is the anti-matter particle, I think of it as 'subtracting' from the total mass of the black hole. The particle that remains, that is perceived as 'emitted', is exactly the mass that's subtracted from the black hole. Thus, it is exactly the same as if the black hole had emitted the particle and it has lost energy.

What I don't understand is that since when the matter particle crosses the event horizon and the anitmatter particle remains, it would anniliate some other matter particle and the black hole would gain mass, why doesn't this effect cancel out and black holes remain stable? But perhaps my mental model isn't appropriate in some way that I don't understand yet.

It's not a question of matter and antimatter annihilating, since this would not result in a decrease in mass. Matter and antimatter both have positive mass, so whichever one falls into a black hole, the hole could be expected to gain weight.

The mechanism is to do with the uncertainty that results in the pair production in the first place. A certain amount of energy can effectively be created out of nothing, as long as it only exists for a very short time. It may make more sense as an analogy with semiconductors. In these, charge is carried by both electrons, and holes where the electrons are missing. In the case of pair production it is as if two electrons, each with charge +1, jump out of an atom leaving a hole with charge -2. In the normal course of events they would both quickly re-combine with the hole, with a net charge of 0. If one is removed, by falling into a black hole for instance, while the other escapes, the black hole will now attrack the hole and consume. Overall the black hole has overall lost a charge of +1, which is carried by the escaped electron.

I swapped the charge on the electron to positive so that if you replace the charges with energy you get a fair approximation of what happens to make black holes evaporate. This is by no means a perfect analogy, but hopefully it helps a little. As is probably apparent, even the best physicists around don't really understand what is happens around black holes, so trying to translate things to a layperson's understanding is a little tricky.

 

[Zygar]

You do not need anything, spontaneous pair production can happen in a true vacuum. This is an example of one of the uncertainty principles, that of time and energy. According to this E*t < h (E = energy, t = time, h = Placnk's constant). As long as the particles exist only for a short time there is no reason this cannot happen, and as Schneibster says, the Casimir effect is a very neat demonstration that it does.

Also, I'm not sure why you are talking about bosons. There are two different ways of classifying particles. The first is based on fundamental particles and is made up of hadrons, such as protons, which contain quarks, and leptons, which are not made of anything (that we know of), such as electrons. The other way of classifying them is as bosons or fermions. This is based on a particle's angular momentum, or spin. A fermion has half-integer spin, that is it's spin is always h*(2n-1)/2, while a boson has integer spin, h*n. All the fundamental particles (quarks and leptons) are fermions, while the force carriers (photons, gluons, etc.) are, so far, all bosons (although the graviton might confuse things if it exists). This is farily simple for fundamental particles, but it also applies to all other particles. For example, a deuterium nucleus is a boson while a tritium nucleus is a fermion. During pair production, any particles can be created (depending on the conditions), so it makes no sense to talk exclusively of bosons.

I think you misunderstood me, but it is not important. Reading the rest of this thread has cleared up the misconception I actually did have about the process.