The energy comes from virtual particles. You should think of it this way : anything has a certain chance of happening, but must follow conservation laws. Conservation of energy, conservation of mass, conservation of ... (the "real" conservation laws are more complex, but ... E.g. only mass+energy+entropy is constant, not mass, nor energy, nor entropy). But small, "short term" violations are possible.
Now imagine there are particle pairs that, when added together have zero mass, zero energy, zero ... These would pop into existence in pairs everywhere and be anihilated soon after. Same is true for triples, quadruplets, ... with different probabilities. Surprise : these particles "exist" (normally for very short times).
So particle a and particle b come into existence, both particles on a path that separates them from eachother. However, because opposite charges attract (and other effects related to other forces) they will fall back into eachother after a while, anihilating eachother and leaving nothing. These are generally referred to as "virtual" particles.
Except of course if something comes between them while flying on their path. This results in multiple effects, like the Casimir pressure, and hawking radiation.
The Casimir pressure is simpler. Suppose you have 2 straight plates, and you bring them close together. So close that these virtual particles have a good chance of impacting one but not the other. If the plates are metal, the particles will generally "merge" with it (like electrons). So a tiny percentage of the virtual particles between the plates become real.
This does not affect virtual particles that are not between the plates. So there is a clear differential between vacuum interactions outside of the plates and inside. This results in a massive pressure pushing the plates together, like removing gas particles in a container results in a pressure on the outside of the container (and, in an athmosphere of large molecules, if you move plates closer together than the size of the gas molecules, there will be a pressure that pushes the plates completely together).
Likewise, in black holes what comes between the particles is an event horizon. Event horizons "erase" quantum information, only the black hole as a whole has quantum information (the reason for is that black holes are physical, localized, manifestations of the end of time : they don't have an inside as far as anything outside the black hole can detect), no individual parts of a black hole have quantum state. So if an electron crosses the event horizon the charge of the entire black hole changes instantaneously, and the point charge of the electron disappears. That means the charge pulling the particles back together (assuming an e+ and e- virtual particle pair) becomes much more distant to the particle, and if it has enough speed and a convenient direction it will fly away from the black hole. Due to conservation laws the net result is that the black hole has eaten a somehow negative-mass charged particle, and the mass has decreased. A particle has been created outside of the black hole and is flying away to infinity.
The vast majority of these particles are photons of a specific frequency, and, surprisingly, the smaller the black hole, the larger the effect (and the higher the frequencies). So spaceships would have to carry "heavy" black holes to get a decent output and would have to "feed" the black holes to avoid exploding (millions of tonnes as least, and you have to shovel in matter at a rate of 10+ kg per second to keep it stable. Or you could reflect hawking radiation back in). And of course, large black holes have large inertia (plus : how do you hold on to one ? Electrical fields can do it, but it would have to be a field so huge it baffles the imagination ...).
A 1kg black hole would be converted into energy in less than a planck second by this effect and there is nothing, even theoretically, that can hold back that energy. Such an explosion might even do what people were "afraid" would happen with CERN's Higgs experiments and disrupt the Higgs field, causing a cascading conversion of the energy "powering" inertia into photons (the higgs field is something like a magnetic field that opposes all velocity changes in mass). If this were to happen, it would look one hell of a lot like a big bang.
>So a tiny percentage of the virtual particles between the plates become real.
Let's say you get a positron/electron emission, and happen to capture the electron. Won't that free positron eventually annihilate a "real" electron, resulting in the same net effect? You still aren't creating anything long-term.
>Event horizons "erase" quantum information
I was under the impression that this was theorized to not really be the case. See http://en.wikipedia.org/wiki/Black_hole_information_paradox . There are a number of proposed solution that involve the black hole not destroying quantum information.
>the reason for is that black holes are physical, localized, manifestations of the end of time
What does this statement mean?
>So spaceships would have to carry "heavy" black holes to get a decent output and would have to "feed" the black holes to avoid exploding
What causes the black holes to explode? By "explode", do you mean they emit hawking radiation so fast that they decay quickly? If not, why are large black holes stable?
>So spaceships would have to carry "heavy" black holes to get a decent output
Didn't you say the effect was more significant with small ones?
Thanks for the explanation. Hopefully you wouldn't mind helping me clear up my confusion.
Thanks a ton for explaining like that. I love people who can take super complex concepts and break them into bite size concepts. But do explain this (simply, if possible), do black holes only eat things INSIDE their event horizon? i thought they pulled everything towards them (like shown on tv) due to their immense gravity. But from your explanation it seemed as if one of the particles accidentally wandered into the black hole and got consumed. Also, if gravity is what causes black holes to pull, wouldn't that mean it pulls +ve mass particles and push -ve mass particles?
PS: Sorry if some of my questions are super dumb. Advanced Phy really is NOT my field
Well it's a matter of perspective. It is not possible to transmit information across an event horizon. So the position of the particle that has crossed the event horizon cannot be transmitted at all, so it has no position in space different from the black hole's own position. That's the quantummechanical view, very mathematical. It can only be expressed as X, so it must be X.
In relativity theory it is actually more complex than that. Think about what an outsider (like the particle that's about to become hawking radiation) sees when you fall into a black hole. Because space itself is falling into the black hole, it takes ever longer for light to cross the distance between you and the observer. So as you approach the event horizon, first, you appear to slow down. Now this slowdown will also produce a fading effect, and a redshift. The fading effect is what's important. Whatever process produces the light travelling from you to the observer will itself slow down, so the number of photons transmitted will decrease as you approach the event horizon. Then, at the crossing point, the time for any photon to reach the observer becomes infinite, which means the photon will never be received by the observer. So what happens to an electron is the same. As it approaches the event horizon, the magnetic field of the particle fades, and the field of the black hole itself strengthens at the same time. When the particle hits the event horizon, it's field is gone.
This is why one might refer to a black hole as a location where time ends.
You should not think of matter falling into a black hole as getting consumed. There is a difference of perspectives here. What's described above this line is what one sees if observing from a comfortable distance away from the black hole. For the person falling inside of the black hole, assuming the black hole is sufficiently large, nothing extraordinary would happen. The only real phenomenon you'd see is that the distance between you and any object (not just the ones outside of the black hole) would get larger by itself. Including the distance between you and the black hole itself.
An intriguing observation you can make is that if you look at galaxies' movements from earth, what do you see ? Well, the distances between all of them are getting bigger in all directions. Suppose you place dots on a balloon, then inflate it, the distance between all the dots increases. The same is happening in 3 dimensions to galaxies. And, guess what, the edge of the universe (as measured as being "just behind" the farthest object we can see, or alternatively where the redshift would turn infinite) is exactly where you'd expect to find an event horizon (we only have accuracy for that of half a billion light years, but still, pretty big coincidence). Do we exist inside a black hole ?
Since we have never seen negative mass particles, we don't actually know whether they exist or whether gravity attracts or repulses them. While it is true that electromagnetism can both attract and repulse, that is not a given for fundamental forces. The strong force only attracts, no matter the charges or any other property of the particles involved. Since we don't have a theory that has both gravity and the other forces we can't calculate this. Since we don't have any test material we can't simply test it out. Einstein's theories claim that gravity always attracts, even particles with negative masses. Now this theory doesn't have a good basis for that claim as it doesn't have negative mass particles, but historically it has been a mistake to bet against it.
We also don't know why there is an imbalance of "negative" mass virtual particles into the black hole. The reason black holes lose mass in this process is simply because of conservation laws. You'd expect 50-50 chances of losing mass but that doesn't happen in practice. Why ? No idea. Some explanations include that particles inside the black hole don't have to follow conservation laws, only the black hole itself and anything outside of it. This would mean that inside the black hole another hawking radiation particle came into existence, with positive mass and everything. Since this can never affect anything outside, this does not actually violate any laws of physics. It is a bit of a moot point though, like asking what happens to a number after it's been divided by zero. There is no answer, anything can happen.
Is there a similarly simplified explanation for why the black hole tends to 'eat' the negative-mass halves of the virtual particle pairs but not the (or at least more often than the) positive-mass ones? Just going by your explanation above, it seems just as likely that the positive-mass particle would be captured by the black hole, emitting the negative mass one, but since the black hole loses mass through this radiation, that must not be the case.
There is no "positive" or "negative" mass. They are both virtual. Their sum-total energy is zero.
Virtual pairs appear and disappear all the time. They are like water boiling in a pot making foam; there are virtual "bubbles" everywhere around you. As long as they disappear back into nothingness, everything about them is virtual.
It's only that the event horizon throws a snag into the mechanism, and swallows up one of the particles, thereby preventing recombination. The only way for that to happen is that if the other particle gets promoted from virtual to real. The only way that could happen is if the black hole itself provides the required energy to make that particle real.
Again, the BH does not pick "positive" vs "negative" mass. It just swallows up one random member of a virtual pair. The other member, left alone, cannot recombine; it sucks up some energy from the BH's gravitational field and becomes a real particle, with positive energy and mass.
To sum it up, it's the virtual pair "foam" that slowly sucks up energy from the BH.
well by his definition they HAVE to be negative mass. Because when these particles unite, they end up having ZERO mass, energy, entropy etc. So all of their properties must be inverses of each other, including mass
Now imagine there are particle pairs that, when added together have zero mass, zero energy, zero ... These would pop into existence in pairs everywhere and be anihilated soon after. Same is true for triples, quadruplets, ... with different probabilities. Surprise : these particles "exist" (normally for very short times).
So particle a and particle b come into existence, both particles on a path that separates them from eachother. However, because opposite charges attract (and other effects related to other forces) they will fall back into eachother after a while, anihilating eachother and leaving nothing. These are generally referred to as "virtual" particles.
Except of course if something comes between them while flying on their path. This results in multiple effects, like the Casimir pressure, and hawking radiation.
The Casimir pressure is simpler. Suppose you have 2 straight plates, and you bring them close together. So close that these virtual particles have a good chance of impacting one but not the other. If the plates are metal, the particles will generally "merge" with it (like electrons). So a tiny percentage of the virtual particles between the plates become real.
This does not affect virtual particles that are not between the plates. So there is a clear differential between vacuum interactions outside of the plates and inside. This results in a massive pressure pushing the plates together, like removing gas particles in a container results in a pressure on the outside of the container (and, in an athmosphere of large molecules, if you move plates closer together than the size of the gas molecules, there will be a pressure that pushes the plates completely together).
Likewise, in black holes what comes between the particles is an event horizon. Event horizons "erase" quantum information, only the black hole as a whole has quantum information (the reason for is that black holes are physical, localized, manifestations of the end of time : they don't have an inside as far as anything outside the black hole can detect), no individual parts of a black hole have quantum state. So if an electron crosses the event horizon the charge of the entire black hole changes instantaneously, and the point charge of the electron disappears. That means the charge pulling the particles back together (assuming an e+ and e- virtual particle pair) becomes much more distant to the particle, and if it has enough speed and a convenient direction it will fly away from the black hole. Due to conservation laws the net result is that the black hole has eaten a somehow negative-mass charged particle, and the mass has decreased. A particle has been created outside of the black hole and is flying away to infinity.
The vast majority of these particles are photons of a specific frequency, and, surprisingly, the smaller the black hole, the larger the effect (and the higher the frequencies). So spaceships would have to carry "heavy" black holes to get a decent output and would have to "feed" the black holes to avoid exploding (millions of tonnes as least, and you have to shovel in matter at a rate of 10+ kg per second to keep it stable. Or you could reflect hawking radiation back in). And of course, large black holes have large inertia (plus : how do you hold on to one ? Electrical fields can do it, but it would have to be a field so huge it baffles the imagination ...).
A 1kg black hole would be converted into energy in less than a planck second by this effect and there is nothing, even theoretically, that can hold back that energy. Such an explosion might even do what people were "afraid" would happen with CERN's Higgs experiments and disrupt the Higgs field, causing a cascading conversion of the energy "powering" inertia into photons (the higgs field is something like a magnetic field that opposes all velocity changes in mass). If this were to happen, it would look one hell of a lot like a big bang.