Over in the thread What’s up with the Law of Conservation? in GD I was starting to speculate on some of the following but it has gotten little response so I thought I’d give it a shot here.
In the past on this board people have speculated about travelling via wormholes in space. While fun to speculate about some posters (notably Chronos who has an excellent handle on this sort of thing) said that if you wanted to make one work you’d need negative mass (or energy but they are equivalent) to keep the mouth of the wormhole open and nobody has a clue if such a thing even exists (with the underlying assumption being it probably does not exist).
When speculating on the total energy of the Universe in the other thread I began talking about Hawking Radiation and black holes. Posters there basically said that total energy in the Universe remains constant via Hawking Radiation and black holes. A virtual particle pair winks into existence and the ‘positive’ particle flies away from the Black Hole (thus adding energy to the Universe) while the ‘negative’ particle enters the black hole and gets rid of some of its mass thus balancing the equation (I use quotes around those two terms since I do not know if that is the proper terminology but hopefully the distinction makes sense for this thread).
First off, if the negative particle acted like antimatter (which I do not think it is) then annihilating something inside the black hole would just convert mass to energy and the total mass of the black hole would increase (since nothing can escape). It seems reasonable to assume then that this negative particle ‘cancels’ anything it meets and they both wink out of existence (thus shrinking the black hole).
I also am unclear why Hawking Radiation should shrink a black hole. Shouldn’t there be a 50/50 chance as to whether the negative or positive of the virtual particle pair gets sucked inside the black hole? If so one would think the black hole would remain constant in size (lose some mass to the negative particle half the time and gain some mass back from the positive particle the other half the time). Is there some reason the negative particle would be more likely to enter the black hole?
So, is the negative piece of our virtual particle pair actually the negative energy Chronos and others alluded to? We can discuss the complexities of actually collecting the stuff from the event horizon of a black hole another time ;).
You bring up some good points about virtual particles and Hawking radiation. A Google search brings these links: (simple) and (advanced).
To summarize, it looks like Hawking radiation can’t really be described as the pair of particles, with one escaping and the other not. It appears the radiation is due to some strange causality going on near the event horizon. The spectrum is due to the accelerated frame of reference near the horizon.
Whack, let’s take the following setup. We have a pair of virtual particles which are both emitted right near the event horizon of the black hole. Remember that they want to recombine, and if they do, then there is no long time change in energy. Keeping this in mind, we have three possibilities:
Neither is absorbed by the black hole, so that in essence, nothing interesting happens.
Both are absorbed by the black hole, so that in essence, nothing interesting happens (recall that they recombine, offering no net change in mass).
One is absorbed, and one is not. Now they don’t recombine, so the particle that comes out must become real. And a real particle has positive mass, always.
Does that help clarify?
Note, by the way, that regardless of whether Hawking radiation is a real phenomenon or not, the energy and mass in the black hole are still part of the universe. We may not be able to get at them, but they still exist, and there’s no problem with energy conservation.
How are you keeping these black holes apart, jbird3000?
They should just merge and make one big one…
I think Whack-a-Mole had the wrong idea slightly- the virtual particles are not positive and negative mass but instead they are matter and anti-matter- both of which have positive mass.
The book-keeping of the universe is balanced by the creation of negative energy, which is normally destroyed when the pair recombine.
And the universe is full of negative energy-(as far as I can understand it)
a little drop more won’t hurt.
Ah well, I was being a bit optimistic trying to understand this anyway…
Perhaps you could syphon the negative energy out of the black hole by dropping a wormhole into it…
trouble is you need negative energy to create the wormhole in the first place.
Damn. Back to the drawing board…
All known particles have positive invariant mass. I think that it’s more accurate to say that in Hawking radiation the absorbed particle has a kinetic energy which is sufficiently negative that its total energy is negative.
In the mathematical treatment of quantum mechanics with which I am familiar, particles with negative kinetic energy do not have a well-defined velocity and do not propagate. As a result, they are not normally observed. Normal particles are confined to regions where their kinetic energy is positive – that is, where their potential energy is greater than the external potential, as is the case in classical physics. However, I can see how this might break down near a black hole event horizon.
A “quantum fluctuation” has some very small but finite chance of producing two particles, one with positive kinetic energy and one with negative kinetic energy. There would then be a very small but finite chance that the particle with positive kinetic energy has enough energy to escape from the black hole. The particle with negative kinetic energy would “fall” into the black hole, and its negative energy would be added to the mass seen by an external observer – a net reduction in mass for the hole.
This is my guess, but I don’t know how well it agrees with accepted theory. I’ve never seen a treatment of Hawking radiation that was neither too simplified to adequately explain the phenomena nor too mathematically intense for me to follow.
Okay, this is going to be confusing, I think. But a virtual particle is what is known as “not on mass-shell,” which means that generally speaking, it can have arbitrary energy, arbitrary momentum, and they needn’t be constrained to obey the usual E[sup]2[/sup] = p[sup]2[/sup]+m[sup]2[/sup] of a real particle. However, whenever we create a pair of virtual particles, energy and momentum are still conserved overall.
Thus, I think that what happens (I am not an expert on this, bear in mind) is that when the particle comes out and becomes a real particle, we get in the end a precisely defined momentum and energy, and the particle has to be on mass-shell to be a real particle; if you want, turning it into a real particle kills off the uncertainty in the mass. This particle will have positive energy, and the one that went in to the black hole will have negative energy and, I think, be on-shell as well, so that energy as a whole is conserved. But with negative energy, the energy of the black hole (and hence its mass) will decrease.
Virtual particles are not real particles. They exist on borrowed energy and must quickly annihilate and repay this energy. However, the extreme tidal gravitation of a BH can pull them apart with enough force that they gain enough energy to become real long lived particles, and at the same time pay back the energy debt to the nearby negative energy regions of space.
So when the hole captures one of these now real particles, it in effect radiates the other one. It has therefore supplied enough energy to create two particles, but only gets the energy of one back. Thus it loses mass.
I should probably add that neither particle has negative energy except in terms of potential energy with respect to the BH. There is no known material that has intrinsic negative energy.
I believe that if they are orbitting that close together, two black holes will rapidly spiral into each other due to loss of massive amounts of energy through gravitational waves. Unless Chronos, Ring, or g8rguy come along and say differently.
Yes, that’s what I meant. But before they crash horribly into one another, isn’t there a moment in time when their event horizons are so close that each virtual particle of a pair could pop up inside different event horizons?
Wow, I know that I officially have made it as a physicist on the SDMB when they mention my name with Chronos and Ring!
Let’s see… First off, I really hate the entire “borrowing energy from the vacuum” way of phrasing things, although it doesn’t really matter how precisely one says it because it’s a matter of interpretation. To me, it can be interpreted to mean that energy isn’t conserved on the short time scale, which is a little misleading in that even in the creation of a virtual pair, we enforce strict energy and momentum conservation. I’m not saying that Ring is wrong, just that one should understand that I’m also not saying that energy isn’t conserved even for virtual particles.
Now, as for gravitational radiation, it is true that they’ll radiate and spiral inwards, but I believe it takes a great deal of time for that to happen. On dimensional grounds, one can conclude that it looks like the time it takes is (apart from pure numbers) (R[sub]S[/sub]/R)[sup]x[/sup] (R/c)
where:
[ul]
[li]R[sub]S[/sub] is the Schwarzschild radius[/li][li]R is the separation we start with[/li][li]x is some power[/li][/ul]
If my analysis (which is not particularly interesting) is correct, x winds up being 3.
Using two solar-mass black holes separated by y Schwarzschild radii, I get something like 10[sup]-5[/sup]y[sup]4[/sup] seconds. I’ve no idea what y would be, but it doesn’t have to be that large for the time to become long. If, for instance, it’s the earth-sun distance of some 10[sup]7[/sup], we have an inordinately long time.
True, but I hardly think you’re going to have particle-antiparticle pair formation over that distance. Pair production is going to be taking place on less than centimeter scale (which I just pulled directly from my bum without bothering to do any math), by which time collision should be truly imminent, no?
Not to say that jbird3000’s situation couldn’t happen during that short interval of time. I have no real idea what the result would be, but my guess would be that it would be equivalent to both holes “radiating” a particle at the other; i.e., no change in mass.
Hmm. I was trying to get at the amount of time it would take two BHs to coalesce from any reasonable distance. Obviously, if they’re right on top of each other, they’ll be coalescing really darn fast.
Now, in Hawking radiation, we’re basically talking a pair created right at the event horizon. I suppose it’s possible that you’ll get a vacuum pair which each goes to a different black hole which are separated by, oh, a femtometer or so, but the black holes themselves would, as you say, in essence be radiating particles at each other.
