Am I so far off on my explanations that they aren’t worth a reply?
If so, please correct me.
BioHazard, the key thing you missed is that it’s not the singularity which is relevant for Hawking radiation, but the event horizon. A quantum theory of gravity, for instance, need not have a singularity (so the mass of the hole wouldn’t be perfectly localized), but would almost have to have Hawking radiation. Even in “classical” (that is to say, non-quantum) GR, there are situations where one can get a horizon without a singularity, and in each case, you get an effect similar to Hawking radiation.
As for the virtual-real distinction, a pair of particles which would ordinarily be virtual can become real, provided that there’s an energy source available somewhere in the vicinity. As another example, if you have a very strong electric field, you end up with something called “polarization of the vacuum”: When (say) an electron-positron pair pops into existence, the electric field is strong enough to pull them apart (remember, electrons and positrons are pulled in opposite directions by an electric field) before they can re-combine, and you end up with a couple of real particles, whose mass came from the energy in the field. A similar thing can happen with the gravitational field, but it’s made more complicated by the fact that all particles react the same way to a gravitational field. So you can’t pull particles apart by a uniform field, but you can do it with a varying field, so the tidal forces pull the particles apart. This is approximately what happens in Hawking radiation.
Ok, I see. Thanks.
How can there be an Event Horizon without a singularity?
There are a variety of different sorts of horizons in GR. For instance, in a universe with a cosmological constant (such as ours, it would appear), there’s also a horizon at great distance from and surrounding any given observer. Anything beyond that horizon is receeding too quickly for light to reach the observer at the center. You’ll also observe a horizon if you travel at a constant acceleration for a long period of time. What’s interesting is that these horizons are observer dependent, and you’ll observe the radiation from them if and only if you’re in an appropriate frame to observe the horizon.
I don’t know of any way in classical GR to produce a globally-observable horizon without a singularity, but I’m reluctant to say that it’s impossible.
I looked this up in my book last night, and the reason the black hole loses mass is because the energy to “create” the pair of particles comes from the gravitational field of the black hole, so it is energy generated by the matter inside the event horizon. Even though light doesn’t escape, gravity does.
The pair of particles are a particle and an anti-particle. The particle has positive energy, and the anti-particle has negative energy. The postive particle is emitted out of the event horizon, and the negative anti-particle falls back in and when “reassorbed” removes energy from the black hole. Since e=mc^2 when energy is lost, matter is lost.
And because of something, something the Second Law is not violated.
FordPrefect, that is what I was trying to say, but not as well. (Not that I would mention the Second Law of Thermodynamics, because I would just :mumble: :mumble:) However, I object to the phrase “gravity escapes”. It doesn’t really have to. Before the black hole forms, the universe is curved around the “protohole”. When the hole forms, the curve changes, but nothing ever has to “escape” from the singularity - the curvature changes and stays that way.
In a quantum picture, something carries the gravitational field. That something, which is not understood yet, presumably behaves something like photons. Photons do not interact with each other in the sense that you could trap photons with photons. The same is true of the gravity carriers - they can not trap each other. So there is no problem with gravity “escaping”.
It’s not always the particle which escapes. Just as often, it’s the antiparticle. Of course, that’s partly moot, since a good bit of the energy radiated by black holes is in the form of photons and (presumably) gravitons, which are each their own antiparticle (this may also be true of neutrinos, which make up the rest of the radiation from a normal-sized hole, but that’s hotly debated).
Everyone, please re-read Chronos’ and BioHazard’s posts – they’re the only two showing an understanding of Hawking.
Here’s a step by step walk through of Hawking radiation:
Everywhere there is a vacuum (which is almost everwhere, including the space between particles in solid matter), there is a flurry of virtual particles appearing and dissappearing. Virtual photons, particle-antiparticle pairs, energy fields are constantly appearing and disappearing and transforming into one another.
The spontaneous creation of the particle-antiparticle pair (I’ll call it a PAP) is what we shall use to demonstrate Hawking radiation. PAPs are virtual not in the sense that they’re not real, but virtual in the sense that they’re not permanent. Although, given a strong enough source of energy, the virtual PAP can gain enough energy to become long lasting particles, i.e., ‘real’ particles with a stable mass.
Now, a virtual PAP that suddenly appears is on borrowed time, because it’s on borrowed energy it sucks up from quantum fluctuations in the void. After a short while, an incredibly short while, the PAP goes back to the void. Or perhaps, before blinking out of existence, either or both particles may interact with other virtual or real particles or some other energy source.
Now the creation of PAPs happen constantly outside the event horizon of a black hole and constantly inside the event horizon of a black hole. Ahhh, but what about a virtual PAP created just inside the event horizon. Perhaps it was so close to the event horizon that one of the pair borrowed enough energy to pop outside the even horizon (with a quantum-tunneling, faster-than-lightspeed energy). In that case, that virtual particle has escaped the clutches of the black hole and runs away, while the other one stays behind.
Now, here’s the thing – something, albeit a virtual particle with laughably tiny energy, has escaped a black hole!
Net loss for the hole. Whether you measure mass or energy or gravity – it’s all convertible in the end.
Eventually, Hawking theorizes, that a hole, if not fed with more matter, can radiate away enough energy to dissipate entirely. Probably with a big (little ‘b’) bang when there’s not enough gravitational mass left to support the (nearly?) infinite crushing of matter.
Peace.
“It’s radiation! Run for it!”
Except that the virtual particles come from just outside the hole, not just inside. The speed of light is not something that you can just tunnel past: It’s always just as far away, no matter how “almost there” you are. And the bang at the end is not due to the black hole ceasing to be a black hole; it’s caused by it becomming a very hot black hole. It might then cease to be a black hole, but we don’t know that, and that’s not necessary for the kaboom.
Papa Geppetto! I’m a real…
No. I can’t go on.
You are right SlowMindThinking the use of escaping for gravity was incorrect, but I was trying to explain where it is, as I understand it, where the energy the pair need to exist comes from.
Chronos the paragraph you quoted is a paraphrasement of what Hawking said. The idea that the anti-particle can escape had occurred to me as I read it, but I already put my neck out with the gravity escaping bit and I wasn’t about to misparaphrase Hawking as an encore.
Particles can (theoretically) get past the speed of light:
[list=1]
[li]Spooky action at a distance[/li][li]quantum tunneling or jumping (which creates a FTL speed on average[/li][li]particles going backward in time (another way to view antiparticles)[/li][li]tachyons! (no, I will not defend this one at all)[/li][/list=1]
But enough of my trying to defend my understanding from memory. Let me do some research… <working>…
Ahh, the USENET FAQ claims that the description of what’s happening is merely a hueristic device to explain what’s happening in some very complicated math. IOW, it’s a dumbed-down layman’s version which may or may not be right. <sigh>
However, this site Hawking Radiation provides a good explanation. It comes down on the side that the virtual PAP happens outside the event, but the one that gets sucked in doesn’t add to the mass of the hole because it has negative energy! Of course, it’s a virtual particle on borrowed time and it transfers its debt to the hole.
Peace.
“We’re in a black hole…run for it!”
Not quite. One of the spooky aspects of the action at a distance feature of quantum mechanics is that the information is transferred without some kind of particle carrying the information. A classical analogy would be pulling socks from a drawer. Suppose the drawer contained one black and one white sock. For no good reason, you blindfold yourself, pull both out, put one in a box, and ship one to mom. She looks in the package and asks you why mailed her a white sock. You instantly know that your sock is black. If they were quantum socks, neither sock would so much as have a color, until your mom looked at one. But, no particle transfer, and nothing ever moves FTL.
I don’t recall a situation in which quantum tunneling does implies FTL. “Tunneling” generally refers to energy barriers, which may or may not have a physical extent. Closer to FTL are the ramifications of quantum measurements. You can easily rig a scenario in which a photon could have travelled either, or both, of two paths that differ by light years. One measurement, and you suddenly know which path the photon took. Weird, but it only violates the speed of light if a mathematical function is, in some sense, “real”.
Backwards in time does not imply FTL. One of physic’s great mysteries is why time can be reveresed in all of the equations, and yet everything appears to be going forward in time. (Except, maybe antiparticles, which could be viewed as particles going backwards in time.)
Tachyons: Absolutely. And, of course, they are kind of difficult to detect, since they can’t be made to go slower than light.
There are things that can move FTL, by the way. Here is one from an old physics text. Picture a giant pair of scissors, about the size of the solar system. Close the scissors. The point at which the blades intersect can move faster than light - even though no particle exceeds c. That example was used to explain something called “phase velocity”, which can exceed c.
So I was at least partially right? Cool!
I remember reading Martin Gardner debunking this one in an issue of, I think it was, Popular Science (or was it Scientifc American?).
The point of intersection is an imaginary construct from the point of view of the observer and, yes, that construct can move FTL.
However, at no point do the blades themselves move FTL. A galaxy long piece of steel would bend when you tried to turn it at one end as the energy at one en propogates down the steel at less then the speed of light. The bonds between the atoms are not perfectly rigid. And by swinging this steel rod like a bat will not cause the other end to go FTL.
And, here’s the disappointing part… you can’t use that imaginary construct which, from your point of view, is traveling FTL to transmit information FTL.
Peace.
If I hit the knee of Orion with a hammer, how long would it take before Rigel kicks?
Sorry, I did not mean to imply that any part of the scissors exceed the speed of light. That is what I meant by “no particle exceeds c”. The point of intersection is not a physical object, and so can exceed the speed of light. That was my point, so to speak.
Phase velocity, which is a measurable property of waves, can exceed c, and I was using the scissors example as an analogy. Sorry if I was unclear.
Actually, if you try to close the scissors by pushing the handles together, then the intersection point won’t travel FTL, either. But if, say, you put a bunch of rocket engines on both blades, and put them on timers that you’ve set a long time before such that they all fire “at the same time”, then the intersection point can travel FTL.
To make things a little simpler: Shine a laser at the Moon, and there’ll be a little red spot on the Moon. Swing the laser over to the other side of the Moon, and that little red spot can also move FTL.
As for “backwards in time”, it depends on what you mean by that. An antiparticle can be viewed as a particle travelling backwards in time, but it still doesn’t carry information backwards in time (really, this is the same as saying that antimatter follows the same Second Law of Thermodynamics as matter). If you can get information to go back in time, though, then you can produce real FTL effects.