hawkings radiation

[Galo Aguirre]

http://www.straightdope.com/mailbag/mhawkingradiation.html

Reading the above article on hawkings radiation, I got the distinct inpression that what the guy was saying was that a black hole even though it is a black hole it still is made of either completely matter or antimatter and that by adding antimatter you could "evaporate" it. Am I understanding this correctly.

Lets say that in the future we are able to produce antimatter by the mega tons and if we fed it to a black hole could we create a naked singularity? If so could we create end the universe? What about if you fed it only anti protons or antineutrons or positons (perhaps misassuming that matter in a black hole still exists in these states) would we create like a unbalanced black hole? like a black hole that is made completely of electrons?

[Exapno Mapcase]

The whole point of calling the core of a black hole a "singularity" is that our current physics cannot explain what is happening there. When Chronos says that speculation about a "naked singularity" bringing about the end of the universe is a job for quantum gravity, he means that until such a comprehensive theory of physics exists nothing meaningful can be said about what will happen. All you can do is speculate wildly, with no real justification behind it.

But I'm sure that in a few minutes there will be any numbers of Dopers flocking here, ready and eager to do just that. :)

[Chronos]

The passage to which you're referring to was added by Ed Zotti, based on his reading of an encyclopedia article. The answer is currently being revised (or will be, as soon as Ed reads his e-mail). The best source you can get on the subject is Hawking's book A Brief History of Time, where he's able to go into much more detail than I had room for.

But to answer the question, black holes don't care what they're made of. The matter-antimatter distinction is meaningless for a black hole. All that a black hole has is mass, angular momentum, electric charge, and (if it exists) possibly magnetic charge. So if you feed a black hole a bunch of electrons, you'll get a negatively charged black hole (but as you put them in, it would eventually become more difficult or even impossible to add more electrons). If you then added protons, the charge would be neutralized again. The result would be identical if you instead added the same amount of positrons (antielectrons) and antiprotons.

And the part about a naked singulariy causing Big Problems is pretty well accepted; the part that calls for quantum gravity is deciding whether there would be a naked singularity in the first place.

[Lumpy]

Originally posted by Galo Aguirre
I got the distinct inpression that what the guy was saying was that a black hole even though it is a black hole it still is made of either completely matter or antimatter and that by adding antimatter you could "evaporate" it. Am I understanding this correctly.Not antimatter, which despite it's somewhat misleading name has mass just like ordinary matter.1

What you might be thinking of is that theoretically you could unmake a black hole if you could feed enough negative mass or energy into it. Which is one reason some physicists are pretty certain that negative energy can't be produced except as temporary and limited quantum fluctuations.

1. As far as we know anyway. Physicists are trying hard to obtain enough antimatter to be able to directly measure it's response to gravity, to make sure of this.

[Chronos]

Antimatter's indirect response to gravity has been thoroughly measured, though, and it behaves exactly like matter. And unmaking a black hole is the least of one's worries concerning negative matter. You could also use negative matter to construct a time machine or FTL drive. Which, of course, raises its own questions.

[ftg]

Can a black hole's charge or magnetic field extend outside the Swartzchild radius? After all, it's just an electromagnetic field and photons are made of the same stuff.

[C K Dexter Haven]

<< You could also use negative matter to construct a time machine or FTL drive. >>

If God had meant us to invent time machines, He wouldn't have given us clocks.

[Q.E.D.]

Originally posted by ftg
Can a black hole's charge or magnetic field extend outside the Swartzchild radius? After all, it's just an electromagnetic field and photons are made of the same stuff.
No, since the escape velocity of a black hole is greater than c.

[Galo Aguirre]

Chronos: (and every one else too) I'm not sure i quite understood your explanation about black holes. You said that in a black hole the matter=antimatter distinction did occur in a black hole, right? The way you explained it didn't make sense to me because you were talking about electrons and protons. But electrons are not the antiparticles to protons.

So what would happen if you injected, if you will, a lot of say antiprotons in a black hole that mostly consist of normal matter. Would the matter and the antimatter coexist? Is there a line that when crossed the matter antimatter distinction no longer occurs or matters? like say the event horizon? And lets say matter and antimatter met just before that line and the two particles anihilated each other, would the energy still be sucked in?

Anyway getting back to your explanation, what Q.E.D said above changed my perspective a bit about what you said concerning protons and electrons which have opposite charges. He (or she) said that the electric field could not escape the black hole. But if this is true how would the lets say necgative charge of a black hole, no matter how intense prevent more negatively charged electrons from entering?

If the electric field cannot escape, any electrical repulsion would not occur until said electron was completely absorbed by the black hole, way past the event horizon. So no matter the charge inside the black hole, the electron would not be able to escape unless the repulsion inside would sent the elctron flying out of the black hole at +c. But +c is not possible at least in normal space. would it be possible inside a black hole?

I really apreciate all your input. I guess a good thing to do intead of bugging you guys, is buying Hawkings book as you suggested. But I still would apreciate a responce, thanks.

[Galo Aguirre]

[i] You said that in a black hole the matter=antimatter distinction did occur in a black hole, right? [/B]

I meant not, does not occur. How come one can't edit his or her own posts?

[Chronos]

The electromagnetic field of a black hole can, in fact, extend beyond the event horizon. Real photons can't escape, but virtual photons can. However, the only information that the virtual photons can carry is how much charge there is inside. If the possibility that electric fields can escape disturbs you, consider that the gravitational field most definitely is able to escape, and gravity and electromagnetism aren't really all that different.

And black holes really don't care about the matter-antimatter distinction. If you make a black hole out of, say, three solar masses worth of hydrogen, and then add three more solar masses of antihydrogen, you'll get a six solar mass black hole. You'd get the exact same thing if you started with six solar masses of hydrogen, or with six solar masses of antihydrogen.

[Q.E.D.]

Originally posted by Chronos
...and gravity and electromagnetism aren't really all that different.
We don't know that. It has been posited that the force of gravity is transmitted by particles called gravitons in the same manner that the electromagnetic force is transmitted by photons, but to date no empirical evidence exists to demostrate their existence.

Also, virtual photons are emitted in photon-antiphoton pairs, which annihilate before being able to be detected. Which is why Hawking theorized that very tiny micro black holes would be able to evaporate away.

[C K Dexter Haven]

<< How come one can't edit his or her own posts? <>>
Because we've had problems in the past when we permitted this, with people making some absurd statement, waiting for responses, then editing their post to say something different. It's more of a problem with the other forums, but we decided not to allow this feature.

If you've made a real bonehead typo and would like a Moderator or Administrator to fix it, you can email and ask pretty-please and we'll do our best to comply.

[Galo Aguirre]

Thanks ck dexter, I'll keep that in mind for later. Although, I asked the webmaster if I could change my user name and I got no response.

QED: I just read an article this weekend of how they had proven that gravity travels at the speed of light. They measured how Jupiter affected the light from a quasar. Should we not (more specifically wouldn't you) consider this empirical evidence?

My guess why it physicists could not measure the speed of gravity fields as easily as we can measure say an electromagnetic field is because you cannot control a gravity field. We cannot just turn on or off a gravity field as we might be able to do with an electromagnetic field.

To whoever may read this, can any of you recommend or know of any online physics books or articles? I figure my knowledge of physics is pretty basic and i figure if i find one, I wouldn't have to bug this board with every detail. Those that are free I would be more intrested in, although I wouln't mind paying some sort of fee.

[NE Texan]

I want to thank Chronos for his excellent report. I find the subject of black holes fascinating, although there are a few things I still don't quite get. This question is about one of them.

I'm trying to understand how a black hole would lose mass through Hawking's radiation. So you have a black hole. Virtual particle/anti-particle pairs appear randomly throughout vacuum, including near the event horizon of this black hole. One set appears too close, and one particle goes into the event horizon, and the other goes away. [Say, for the sake of argument, the one that goes in is a positron - an anti-electron.] If I understand what Chronos said in his post above:

Originally posted by Chronos
And black holes really don't care about the matter-antimatter distinction. If you make a black hole out of, say, three solar masses worth of hydrogen, and then add three more solar masses of antihydrogen, you'll get a six solar mass black hole. You'd get the exact same thing if you started with six solar masses of hydrogen, or with six solar masses of antihydrogen.

... then it doesn't matter that it was a positron; the mass of the black hole is now [Old mass of black hole] + [mass of positron], which is greater (not less) than before. Even if it interacts with an electron within the black hole (assuming that interaction even makes sense in a black hole), then the released energy (which still has an equivalent mass) isn't going to leave the event horizon, so the mass increase is still the same.

How can any particle appearing there lead to a reduction in mass (no matter how small) of the black hole? Obviously, I'm missing something basic, can someone tell me what?

[SlowMindThinking]

How can any particle appearing there lead to a reduction in mass (no matter how small) of the black hole?

Well, back when I was in grad school, and we had to make our water by hand, I could explain this. Let me see if I can now.

You can think of matter as a form of energy, and energy as a form of matter. The relationship is specified by Einstein's famous E= m c^2 (that is "m c-squared). So when energy is radiated out from the black hole, the black hole has lost the amount of mass specified in that equation.

I have a question about the charge of a black hole. For some reason, I was pondering this very question a few days ago, and how convenient for someone else to ask it. First, to me the "existence" of virtual photons is somewhat nebulous. The arise in what are called "perturbation expansions" in quantum field theory. Basically, you start with an exact solution, and consider small deviations, or perturbations, from that. So they definitely exist as mathematical entities, but I really don't know what it means to exist.

Consider, though, that every electron is emanating an electric (and gravitational) field as it crosses the event horizon. Any photon carrying the electrostatic field, that is leaving the electron, as it crosses the event horizon, is infinitely red shifted. But, a static field has no time dependence anyway, so what does the red shift mean? Is the electric field carried by photons that were emanated when the electron crossed the event horizon really the carriers of the electric field? Or are virtual photons crossing the event horizon and propagating to infinity (and beyond! - sorry Toy Story humor)???

[bruntilda]

A virtual particle pair zaps into existence, and one of the particles falls into the black hole while the other flies away. That is Hawking radiation. While the black hole does absorb one particle, the net effect is that a new particle flew away from the black hole, and its mass has to come from somewhere.

[Xerxes]

I'm still with NE Texan on this one, brunthilda - both the virtual particles have mass, correct? Now, if one flies away and the other gets eaten. The one which flew away gives the effect of the black hole radiating, and apparently losing mass (I might not be right on that one), but the one which disappeared across the event horizon has added mass to the BH.

Actually, thinking further about it I wonder if the problem here is that I'm imagining the virtual particles to be different (or behave differently) from how they really are.

[bup]

I've got a much more basic question about the column. I get that it answered the basic question - if a black hole loses mass, does it un-become a black hole? The answer was a clear no - it remains a black hole.

I didn't see anything that explained why that is, though. Gravity is directly proportional to the amount of mass - if mass decreases, won't the gravitational pull be decreased until the escape velocity is less than the speed of light? In other words, why won't light start escaping?

[Galo Aguirre]

SlowMindThinking: you are thinking that the virtual photon is created inside the black hole and radiates away, but it's not. It's created just before the event horizon by space.

+ bruntilda: You are thinking in terms of conservation of mass + energy. How ever virtual photos are supposed to be a violation of the principle of conservation of mass and energy. They really are created out of nothing. So the creation of the virtual photon does not(or should not as far as my thinking goes) take away from the black holes mass. If anything it should add to it, since one particle falls into the bh.

[Galo Aguirre]

One of us should really go out and buy hawking's book and quote a few passages for the sake of the rest of us to put this matter to rest.

[White Lightning]

Originally posted by SlowMindThinking
You can think of matter as a form of energy, and energy as a form of matter. The relationship is specified by Einstein's famous E= m c^2 (that is "m c-squared). So when energy is radiated out from the black hole, the black hole has lost the amount of mass specified in that equation.How does energy radiate out from a black hole? Isn't that the whole idea of a black hole, that that's not possible?

I'm fairly certain I'm suffering from the same problem Xerxes mentions. Galo Aguirre, I did read A Brief History, and I didn't get it then either.

At any rate, though, I also wanted to commend Chronos on a very interesting and well-written Staff report.

[Mielikki]

I also have a very simple question.

The column stated that the Sun has a Schwarzschild radius of 3km. So closer than that to the Sun, no light escapes? So if you're standing on the Sun, what does it look like? My 'Starry Nights' program shows that it looks yellow and shiny, but now I'm skeptical.

Also, is there a Schwarzschild radius for the Earth? I'd do the math, but I have a liberal arts degree. I get the feeling that below a certain mass, there is no Schwarzschild radius, or the Schwarzschild radius is smaller across than an atom, or something like that. I wonder what that mass is?

[SlowMindThinking]

Galo Aguirre and White Lightning: The gravitational field stores energy, much like an electric field. Quantum field theory says that energy can spontaneously create particles. The created particles are not virtual. For example, a gamma ray, which is a form of electromagnetic energy, can spontaneously create an electron, and it's antiparticle - the positron. Likewise the electron and positron can annihilate each other and form a gamma ray.

Near the event horizon of a black hole, the gravitational energy density is high enough to create particle pairs in this manner, as Hawking showed. (One of his claims to fame.) Sometimes one particle falls into the black hole, but one escapes. (That conserves momentum.) Note that neither particle was ever inside the event horizon. The escaping particle carries mass, and energy, so the black hole loses the amount of mass necessary to account for that mass and the energy. Correspondingly, the gravitational field is reduced, so it all works out neatly.

Mielikki, if the sun were a black hole, then it's event horizon would be at the Schwarzschild radius. Since most of the sun is outside of that radius, there is no black hole there. The same with the earth. There is no intrinsic mass below which you can not form a black hole. (Unless, of course, some unknown quantum gravity theory says there is.) You can do the math to figure out what mass forms an atom sized Schwarzschild radius. Take the radius to be 1 angstrom, and use that GM/c squared
formula.

I still don't understand the static electric field that a charged black hole exerts, however.

[bup]

Originally posted by Mielikki
I also have a very simple question.

The column stated that the Sun has a Schwarzschild radius of 3km. So closer than that to the Sun, no light escapes? So if you're standing on the Sun, what does it look like? My 'Starry Nights' program shows that it looks yellow and shiny, but now I'm skeptical.

Also, is there a Schwarzschild radius for the Earth? I'd do the math, but I have a liberal arts degree. I get the feeling that below a certain mass, there is no Schwarzschild radius, or the Schwarzschild radius is smaller across than an atom, or something like that. I wonder what that mass is?

1) 3 km from the center of the sun. The sun would only be a black hole if the matter was so dense that it all fit within a 3 km radius sphere. And the event horizon would occur at the 3 km point. If your mass doesn't fit within the Schwarzschild radius, you don't have a black hole.

2) Sure, there's a Schwarzchild radius for the Earth. Its radius would probably be measured in centimeters. You'd need to pack the Earth pretty tight for it to be a (very small) black hole.

[Saltire]

You've mistaken the meaning of the Schwartzchild radius. It is the radius into which any given mass must be compressed in order to collapse into a black hole. It is also the radius of the event horizon.

So when Chronos said the sun's Schwartzchild radius is 3 km, he was telling us that if you were to somehow mash the sun down to a ball 6000 meters in diameter, it would become a black hole. With the sun at its present size, the Schwartzchild radius has no effect.

[BioHazard]

This is the way I understand it.

According to the Hesienbergh Uncertainty Principle, you can never know the Position and Velocity of a particle. If there are particles inside the singularity, you DO know there position and velocity (the same as the singularity) Hawking Radiation compensates for this. You can not really define a particle as being anywhere, only that it has a % chance of being somewhere, a % chance of being somewhere else, a % chance of being yet another place. This is like the electrons in the electron cloud of an atom. For a black hole, some of these places the particle may be are outside the black hole, so the particle pretty much appears outside and escapes. It's the same as the Quantum Barrier Principle (I think thats whats its called), where an electron apears to go through an un passable barrier.

Another way to think of it is that the particle speeds to a speed higher than c, crosses the Event Horizon and escapes. This is because we know where all the particles are, therefore we cannot know their velocity, so it could be faster than c.

What it REALLY comes down to is that our physics can't say whats going on inside a Black Hole yet.

[BioHazard]

I have a question, IIRC a naked singularity is a singularity with no event horizon. Why would this destroy the universe?

[NE Texan]

To answer Mielikki's question, just for grins, let's figure out the mass of a black hole with an event horizon 1 Angstrom in radius. I'm doing this from old memory, and showing my work so that someone can come along and correct my errors.

Let's see, if something is travelling in orbit, then it needs a force inwards on it which is

F = mv2/2r

... where v is the orbital velocity, and m is the mass of the object. This is provided by gravity, which is

F = mMG/r2,

... where M is the mass of the object it's orbiting, and G is the gravitational constant. Oh, yes, and r is the distance between the centers of the 2 objects both times. So,

mv2/2r = mMG/r2, or

v2r = 2MG,

... for a normal orbit. Where the event horizon comes in, is when the escape velocity is the speed of light, so that even light can't escape, so v = c.

So, looking up a few constants on the web, in consistent units, without too much precision:
G = 6.67 * 10-8 cm3/g * s2,
c = 3 * 1010 cm/s,

and our 1 Angstrom radius becomes
r = 1 * 10-8 cm.

M = c2r/2G = 6.75 * 1019 g, or 6.75 * 1016 kg

The Earth has a mass of 5.98 * 1024 kg, so I suppose it would be larger than an Angstrom. Actually, we can figure that out, too:

r = 2GM/c2 = 0.886 cm, or just under a centimeter.

(I'm still not very clear on the mass leaving the black hole, though. While I see BioHazard's post on preview, I don't think his explanation is consistent with the original report.)

[Chronos]

The thing with the Sun, is that the Schwarzschild radius is measured from the center of the mass, not from the surface. And you can't get within 3 km of the center of the Sun, because you run into the surface a long time before then. If we assume that you have some amazing heat-resistant spacecraft which can fly down into the core of the Sun, then it's still not a problem, because it's only the mass closer to the center than you that matters, and very little of the mass of the Sun is within 3 km of the center. So the Schwarzschild radius of that amount of mass is that much smaller.

Every mass has a Schwarzschild radius, and it is quite possible for that radius to be smaller than an atom. There's some question as to what, if anything, is the significance of, say, the S. radius of an electron, but we can calculate it (it's an insanely small distance, even by physics standards).

As for the mechanism of Hawking radiation: Hawking spends a whole chapter on it, and I'm not sure that it's possible to give a complete and accurate explanation of it in much less space than that (and we can't just copy that chapter over onto the board, because it's copyrighted). If you try to make the explanation too simple, it ends up just being wrong. The simplest non-wrong explanation I can give is this: Due to virtual particle pairs being separated, some particles manage to go from the vicinity of the black hole to great distances away. Since these particles have energy, that energy must have come from somewhere, and the only place for it to come from is the mass of the hole.

On preview, I see that others have already covered a lot of this, but I started typing a couple of hours ago, so I'll leave it in.

[NE Texan]

Originally posted by Chronos
As for the mechanism of Hawking radiation: Hawking spends a whole chapter on it, and I'm not sure that it's possible to give a complete and accurate explanation of it in much less space than that (and we can't just copy that chapter over onto the board, because it's copyrighted). If you try to make the explanation too simple, it ends up just being wrong.
That's okay, and thanks for stopping by to say that much. I have no problem with the answer being "it's really complicated". In fact, that's somewhat comforting, since it keeps me from feeling quite so ignorant for not understanding it immediately.

I shall strive to do some reading on the topic when I have time.

[BioHazard]

Originally posted by NE Texan
(I'm still not very clear on the mass leaving the black hole, though. While I see BioHazard's post on preview, I don't think his explanation is consistent with the original report.)

It may not be consistent with the original report but it is still valid. I'm pretty sure that Hawking gave an explanation like mine in that book, or another one, but it could have been a different writer.

What I said is just as valid, it describes the same thing, but any/all of the explanations are physical descriptions of what the math says, so they don't neccesarily relate to the real universe.


I have another question. The report didn't mention anything about Hawkings Theory that the event horizon can never decrease in size due to the Law of Increasing Entropy, it can only increase. If that theory is true, then a Black Hole would eventually explode.

[SPOOFE]

both the virtual particles have mass, correct? Now, if one flies away and the other gets eaten. The one which flew away gives the effect of the black hole radiating, and apparently losing mass (I might not be right on that one), but the one which disappeared across the event horizon has added mass to the BH.
All right, you can apparently grasp the notion that the one virtual particle that "got away" had a mass that had to come from somewhere, yes? And that somewhere would be the black hole.

So where's the confusion? The other virtual particle - of the virtual particle pair - also had a mass that had to come from somewhere. That somewhere was also the black hole. It's just that, in the case of the virtual particle that didn't get away, that mass was almost instantly returned to the black hole, resulting in no net gain from the one "re-absorbed" virtual particle, and a net loss from the escaped virtual particle.

[bup]

Yeah, but why does the thing forever remain a black hole?

I'm going to guess that as the black hole goes down in mass, it must get denser, so that you keep that high gravity.

But what would make it do that?

Or, if they don't know that, why do they think it will stay a black hole?

[FordPrefect]

Originally posted by Galo Aguirre
+ bruntilda: You are thinking in terms of conservation of mass + energy. How ever virtual photos are supposed to be a violation of the principle of conservation of mass and energy. They really are created out of nothing. So the creation of the virtual photon does not(or should not as far as my thinking goes) take away from the black holes mass. If anything it should add to it, since one particle falls into the bh.

Having just finished the book a few weeks ago (xmas present from Mrs. Prefect) and not being a physicist all I can do is parrot from memory and confused recollection...

<WAG>

The creation of the particle-antiparticle pair do not come from nothing, but by borrowing energy from the universe. This happens all over the cosmos all the time. Most occurrences will take place away from an event horizon and will quickly collapse upon themselves and be annihilated. However, if the energy that creates the pair of particle pairs comes from the black hole and only one particle is returned, you would have a net loss of energy. This could reduce the energy keeping the black hole from collapsing further on itself and prevent one less particle pair to form resulting in less potential mass.

</WAG>

[FordPrefect]

Crap. Somehow I missed SPOOFE's post, which was what I was trying to say.

[SlowMindThinking]

I believe you are mistaken to assume that particles must be virtual. If my memory serves me, virtual particles can not be directly detected. There is nothing, in principle, preventing one from detecting the escaping particle.

Within General Relativity - so ignoring quantum effects - you can think of the black hole as not disappearing because the matter is no longer within the universe. You describe the universe with a set of points called a manifold. The singularity is not part of the manifold. That "point" is not part of the set. "Unsingularlizing" the black hole would be required to get rid of the black hole. So, you take mass out, the Schwarschild radius shrinks, but the black hole never goes away. Again, I'm ingnoring all things quantum, and quantum physics is necessary to make the holes lose mass, but so it goes.

I used quotes because the singularity persists in time, so it is not a point, but at least a one-dimensional object. Relying on my shakey memory, I believe the it is actually two dimensional, but that is complicated to show. (Look up the the Kruskal extension if you must.)

[Xerxes]

So where's the confusion? The other virtual particle - of the virtual particle pair - also had a mass that had to come from somewhere. That somewhere was also the black hole. It's just that, in the case of the virtual particle that didn't get away, that mass was almost instantly returned to the black hole, resulting in no net gain from the one "re-absorbed" virtual particle, and a net loss from the escaped virtual particle.

The confusion is that at the time when the virtual pair zapped into being, their mass didn't come from the black hole. That's the point - they are created outside it, so the idea that mass is 'returned' can't (in my admittedly incomplete and probably mostly wrong understanding of this) be right. I could go with the idea that somehow the 2nd particle (the one that got swallowed) somehow had some property that was the inverse of the one that got away, and in that sense the cosmic ledger book is squared up, but I've still yet to hear an explanation which really resonates with me.

That this is my problem and not a problem with reality goes without saying, of course.

[SlowMindThinking]

Xerxes, I think your problem is thinking of the black hole as an object made of particles. Without a quantum theory of gravity, no one really knows what a black hole is made of. According to "classical" General Relativity, which admittedly is something of an oxymoron, you can look at all of the "mass" as residing in the gravitational field. There is no "point" in the universe in which the black hole's particles can reside. It is this incomprehensibility, caused by all sorts of 1/0 in the equations, that a quantum theory would, presumably, solve.

Quantum field theory has virtual particles popping in an out of the vacuum. This does not violate conservation of energy, because the virtual particles do not last long enough - the Heisenberg principle. This effect has actually been measured.

In the case of the black hole, the particles can hang around and become "real", because they take energy from the black hole's gravitational field. The energy of the field is lessened, and by the equivalence of energy and mass mentioned above, the mass of the black hole is lessened.

If you think about it, the only way you know the mass of something is either by its gravitational field, or its behavior in some other gravitational field. Fling a piece of the earth out into space. You suddenly weigh less, which you know because the gravitational pull of the earth is lessened.

It would seem the same logic would permit you to do equally well by waiting for some particles to be created out of the earth's gravitational field and throwing them out into space. No, I really don't understand how that works. No particles left the earth, but suddenly it weighs less. Probably looks like quantum tunneling, but I have no idea.

[Xerxes]

SlowMindThinking; Thanks!

In the case of the black hole, the particles can hang around and become "real", because they take energy from the black hole's gravitational field

While I might not understand how they *do* become real, this is the key thing I was missing.

[BioHazard]

Am I so far off on my explanations that they aren't worth a reply?

If so, please correct me.

[Chronos]

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.

[BioHazard]

Ok, I see. Thanks.

How can there be an Event Horizon without a singularity?

[Chronos]

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.

[FordPrefect]

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.

[SlowMindThinking]

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".

[Chronos]

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.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).

[moriah]

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!"

[Chronos]

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.

[Nametag]

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.Papa Geppetto! I'm a real...

No. I can't go on.

[FordPrefect]

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.

[moriah]

Originally posted by Chronos
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.
Particles can (theoretically) get past the speed of light:
[list=1]
Spooky action at a distance
quantum tunneling or jumping (which creates a FTL speed on average
particles going backward in time (another way to view antiparticles)
tachyons! (no, I will not defend this one at all)
[/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 (http://www.rdrop.com/users/green/school/radiatin.htm) 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!"

[SlowMindThinking]

Particles can (theoretically) get past the speed of light: Spooky action at a distance

quantum tunneling or jumping (which creates a FTL speed on average

particles going backward in time (another way to view antiparticles)

tachyons! (no, I will not defend this one at all)



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.

[BioHazard]

So I was at least partially right? Cool!

[moriah]

Originally posted by SlowMindThinking
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.

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?

[SlowMindThinking]

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.

[Chronos]

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.