According to Hawking, those particle-antiparticle pairs which are constantly appearing in space and after a short time, annihilating each other, which happen to be in the vicinity of the event horizon of the black hole, can't do that, because one will get sucked into the black hole, and the other escapes.

My question is: the gravitational forces in the vicinity of the event horizon of a black hole are immense. Where does the particle which does not get trapped by the black hole, get the needed escape velocity to get away?

It is a requirement of the radiation that the particles that escape have enough energy to escape, so the kinetic energy is part of the creation process. Dosent take a whole lot of extra energy to make particles screamingly fast. 1 MeV energy loss can give you an electron moving better than .5c.

I wonder if quantum foam even exists.

We know the problems GR and QM have at the Planck length. Doesn't this arise from QM modeling the fundamental particles as 0 dimensional points? String theory gets around this problem, by saying the length of the 1 dimensional string is that of the Planck length.

Strings cannot probe distances smaller that themselves, so they cannot even reach sub-Planckian distances. One cannot probe sub-Planckian distances if strings are the fundamental units of the universe. If something must be measurable in order to exist, it can be said that this quantum foam does not actually exist. It is simply a mathematical artifact arising out of an imprecisely formulated theory (QM).

Quantum foam is a theoretical construct (devised by John Wheeler in 1955) based on fairly straightforward inference:

As the scale of time and space being discussed shrinks, the energy of the virtual particles increases (due to Heisenberg Uncertainty). Since energy curves spacetime according to Einstein's theory of general relativity, this suggests that at sufficiently small scales the energy of the fluctuations would be large enough to cause significant departures from the smooth spacetime seen at larger scales, giving spacetime a "foamy" character.

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Everyone is entitled to his own opinion, but not his own facts.

No, it's a problem with GR. As Cougar points out, at small enough scales, there are significant departures from the smooth spacetime. GR models spacetime as a pseudo-Riemannian manifold, which by definition, is smooth. If, in GR, you can identify a difference between gravity and acceleration, you have to find a smaller volume of space to work with. This is due to the equivalence principle. When you get to small enough scales, the manifold is no longer smooth and the equations of GR no longer work. In the case of String Theory, spacetime doesn't matter. Gravity is modeled as a particle interaction, the same as the other three forces.

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Some try to tell me, thoughts they cannot defend,... - Moody Blues.

Neptune- The original Dark Matter.

The author feels that this technique of deliberately lying will actually make it easier for you to learn the ideas. - Donald Knuth

I'll soon be helping my father replace some of his current windows with Quantum Foam Insulation.

gzhpcu, I believe that quantum foam does exist, just as we've been able to image matter at the atomic level. The Planckian level for spacetime is incredibly smaller, but we've indirect evident of quantum effects observed in the behavior of Bose-Einstein condensates.

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If I set the budget, we'd have Ares and more. Unfortunately, I don't set the budget, and Ares is just too expensive and too far out for us to accomplish our goals within the budget we were given.

If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.

But doesn't this situation arise from QM using a mathematical model of 0 dimensional points for the elementary particles? If the size of the elementary particle is increased to that of the Planck length, don't we eleminate this effect?

Despite the fact that it's the only length obtainable from the constants c, G, and h-bar (the reduced Planck constant, or Dirac's constant), we still don't know a heck of a lot about it, or even if it's a real limit, or merely a theoretical one.

It may play a role in quantum gravity, although there's no evidence that exists, either.

Here's a col thing, from Wikipedia: "The task is to measure an object's position by bouncing electromagnetic radiation, namely photons, off it. The shorter the wavelength of the photons, and hence the higher their energy, the more accurate the measurement. If the photons are sufficiently energetic to make possible a measurement more precise than a Planck length, their collision with the object would, in theory, create a minuscule black hole."

Naturally, such a black hole would evaporate nearly instantaneously.

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If I set the budget, we'd have Ares and more. Unfortunately, I don't set the budget, and Ares is just too expensive and too far out for us to accomplish our goals within the budget we were given.

If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.

You're under a slight misunderstanding here. In QM, particles don't have a specific size as they do in classical mechanics (CM). Particles are described by wave packets. Each point in space has a value that corresponds to the probability of finding a particular particle, based on the values in the wave packets. That might seem a rather subtle difference, I admit, but it is a difference.

Another problem comes, not from the size, but from the background. GR is background independent. Meaning simply that the background (in this case spacetime) can change. Distances between points change, depending on how the mass is moving through it. In the case of QM, it is background dependent. Spacetime is unchanging in QM. (There is some discussion within physics circles whether this is an actual problem or not with string theory and Loop Quantum Gravity).

Another way of looking at this. GR requires knowing exactly where a particle is, so as to define its gravitational field. With a wavepacket, since it's "location" is spread out based on probability, there is no way to specify it's gravitational field, until we know exactly where it is.

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Some try to tell me, thoughts they cannot defend,... - Moody Blues.

Neptune- The original Dark Matter.

The author feels that this technique of deliberately lying will actually make it easier for you to learn the ideas. - Donald Knuth

Correct me if I am wrong: I was under the impression that we are dealing with wave/particle duality. The Schrödinger equation shows the probability distribution of where the particle could be. A measurement causes the Schrödinger equation to collapse (if it does collapse...), and results in the particle being "located". This particle, according to QM, is modeled as a 0 dimensional point.

I had thought the conflict arose from the fact that GR depends on a smooth spacetime, whereas at the Planck level, the Heisenberg Uncertainty Principle results in a quantum foam. This cause spacetime at this level to be extremely wavy and distorted, which causes GR a problem..

Well, wave particle duality has more to do with trying to fit QM concepts into classical concepts.

Nope. In QM there are no particles as classical mechanics thinks of them. The wavepackets contain values for momentum, position, spin, etc. The Schrodinger equation shows how the system evovles over time, just not the location of the particle. Remember, by the Uncertainty principle, if you locate the particle precisely, you then have the problem of not knowing what the momentum of the particle is. That's a problem for GR as the stress-energy tensor (which determines the curvature (or gravity of a particle)) uses the total energy of the particle. It's mass (times c²) and it's momentum. If you don't know the momentum, you don't know the total energy of the particle, and you can't calculate the curvature.

There are actually several different problems. Which theory has the problem depends on how you want to approach it. As above, there is a problem with quantum foam and the smooth manifold required by GR. Or, the problem with position and momentum of the particle. If you want to ignore GR and try to just use QM, there is a problem with the guage boson required for gravity, the problematic Graviton. It has to massless, due to the speed of propagation (c) and its range (infinite), much like the photon. It has to have spin 2 because gravity is only attractive, where the photon is spin 1 (either attractive or repulsive). The problem with the Graviton is that the techniques used to get rid of the infinities in QM (renormalization) don't work with spin 2 particles. The answers you get can be any value, which isn't very predictive.

As you can see, there is a bit more to the problem than just point particles and smooth manifolds.

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Some try to tell me, thoughts they cannot defend,... - Moody Blues.

Neptune- The original Dark Matter.

The author feels that this technique of deliberately lying will actually make it easier for you to learn the ideas. - Donald Knuth

Thanks tensor, however, I still thought that the Standard model of QM does use pointlike particles:

http://en.wikipedia.org/wiki/Point_particle

Note the last sentence (which I've bolded). It can be used as a shorthand or classical explanation, but in QFT, "particle" as a little hard ball, really has no meaning. Also note my second signature. It happens a lot when some concepts in physics are explained. Then you have to unlearn those concepts, when faced with the actual model.

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Some try to tell me, thoughts they cannot defend,... - Moody Blues.

Neptune- The original Dark Matter.

The author feels that this technique of deliberately lying will actually make it easier for you to learn the ideas. - Donald Knuth

Still struggling here... Take the two slit experiment: when the particle impacts the screen, a discrete particle is detected isn't it?

That's due to the difficult concepts (read that as me reaching and exceeding my level of being able to explain it) .

The particle aspect of a wavepacket is detected. That type of experiment is designed to detect the particle aspect. We design our experiments to detect either the wave or particle aspect of the wavepacket. The position, after all, is still only approximate (the phosphor point on the screen is much larger than the "classical size" of the particle). Remember, the pattern that forms, and thus what rules the individual wavepackets (or particles) is based on the Schrodinger equation, and that is a wave equation. There are no particle equations in QFT.

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Some try to tell me, thoughts they cannot defend,... - Moody Blues.

Neptune- The original Dark Matter.

The author feels that this technique of deliberately lying will actually make it easier for you to learn the ideas. - Donald Knuth

Thanks for the explanations, Tensor!

Yes, GR can handle an evolving or expanding spacetime. So is the smooth manifold problem due to GR's breakdown at the center of black holes, or is it that the background manifold (?) can change in time, but must do so in a mathematically continuous fashion?

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Everyone is entitled to his own opinion, but not his own facts.

Thanks tensor, I was not aware that QFT dealt purely with the wave aspect and did not include any equations on the particle (point) aspect.

Quantum tunneling needs explanation here also. Quantum tunneling violates classical physics. To throw a baseball and clear it from the gravitational field of the earth one must throw it at the escape speed, 7 miles/sec., of the earth. An electron can escape at 2 miles/hour via quantum tunneling. So the electron does not need escape velocity to get away.

When short-lived particle-antiparticle pairs pop up and quickly annihilate themselves, do they have high repulsion speed? Near the event horizon of the black hole, where allegedly one gets sucked into the black hole and the other escapes, causing the leak, they must have been created with a high velocity separating each other. If they have a high repulsion speed, how come leaking in normal space doesn't occur? Or could it, even if with an extremely low probability?

Since we have calculated the position of the event, we cannot calculate the speed. It seems that, perhaps, the concept of quantum tunneling and wave packets are a touch foggy to you. Also, spacetime is extemely warped near a black hole and creation/annihilation events have very short durations. Billions of such events take place each second between the electron and nucleus of a hydrogen atom.

A continuous wave differs from a wave packet. One measures speed quite accurately while the other measures position quite accurately. One can calculate the speed of ocean waves by measuring the displacement of the wave crests verses time as the walls of energy head for shore. The probability of the electron's location lies somewhere along that wall's crest that can stretch for quite a distance. When a continous light wave is shined on an electron to locate it, that is what occurs. We can measure its speed but not location.

A wave packet, however, does not have consistency of wave lengths nor are the waves all the same amplitude. The distance between the crests has many possibilities so the speed cannot be determined. But this wave packet operates akin to a periscope peeking out of the still waters. One can locate it easily. But what is its speed?

Remember, when it comes to quantum physics, we have to look at the experimental results and adjust our language to fit those results. If the results suggest something that does not make sense, then accept it. Quantum physics does not make sense and trying to make sense out of it is to fail to understand it. Richard Feynman took a part of ancient Greek math, the mechanical geometric displacements of old hand clocks along with some vector addition to butcher them all together to describe quantum electrodynamics. Mathematicians cringed and called him "insane". Those diagrams are accurate to 12 decimal places and they do not describe anything else but QED.

Thanks blueshift. Actually, I am familar with both the Heisenberg Uncertainty principle as the tunneling effect, as well as the Feynmann diagrams.

It seemed strange to me that near the black hole's event horizon, one of the particle-antiparticles could even manage to escape.

As far as the Schrödinger Equation is concerned, Heisenberg didn't like it. He wrote to Pauli in 1936:

He came up with Matrix mechanics which allows no attempt at visualization.

It's the ultra-high tidal gravity that can quickly separate them and, like a rich uncle, it can also pay back the energy loan to the vacuum, letting the escaping virtual particle become real, leaving the BH a tiny bit less massive.

This is something that is thought to happen but, to my knowledge, has not been seen to happen.

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Everyone is entitled to his own opinion, but not his own facts.

No problem. I try.

Neither. It's becase the denominator of the equations (which is the radius) goes to zero. As you are aware, division by zero is undefined. Actually, once the radius gets below the Planck length, the manifold is no longer smooth, and that's where the breakdown happens.

__________________
Some try to tell me, thoughts they cannot defend,... - Moody Blues.

Neptune- The original Dark Matter.

The author feels that this technique of deliberately lying will actually make it easier for you to learn the ideas. - Donald Knuth

Isn't this where string theory gets around the problem by defining the radius of the elementary particle (string) to be that of the Planck length?