Black Holes
There is something obviously wrong with the way most if not all physicists think about black holes.
The story usually goes that stuff can fall into a black hole but can't come out again. This is fishy for a number of reasons: it causes an ``information paradox,'' as information about the stuff that falls in seems to be lost from the universe, something that doesn't happen under any other known circumstances. It also seems to violate time symmetry, the principle that if you watch a video of the universe backwards, everything you see is physically possible (though not necessarily probable).
There's also the ``singularity,'' that big bad infinity that lurks inside the event horizon, waiting to be experienced by anyone who has the bad luck to fall in. This is one of the big motivating factors for trying to develop a quantum theory of gravity: it is hoped that this infinity will be avoided for esoteric quantum reasons.
But it turns out that both the information paradox and the singularity problem can be avoided by a bit of layman's-terms back-of-the-envelope thinking, without using any quantum mechanics, based on a level of knowledge of general relativity that's available from pop science books. It goes like this:
Imagine you are at a safe distance from a black hole, watching something fall in. Let's say it's a clock. As everyone who's ever read about black holes knows, the hands of the clock will slow down as it approaches the event horizon, approaching a certain time (let's call it 12:00) ever more slowly, but never passing it. From the clock's own point of view, times after 12:00 do exist. This is because (and this is something they don't always tell you in pop science books) the event horizon is not at a fixed position in space but actually moves if you accelerate towards it. So if you were falling into the black hole behind the clock, the event horizon would be further away and the clock's hands would approach a later time than 12:00 (say, 12:05).
But here's the thing: no matter what you do you can never watch the clock go past the event horizon. At all points in time, from your point of view, the clock is always in front of the horizon, never beyond it. You can also never experience passing the horizon yourself: if you're falling feet-first into a black hole then you can never watch your feet pass the event horizon, which means you can never experience any other part of you being beyond it either. The horizon is like a rainbow, moving away whenever you move (or rather, accelerate) towards it. Until the moment you hit the singularity, that is, but we'll come to that in a moment.
Incidentally, this seems to apply to the formation of a black hole as well: as a giant star collapses at the end of its life, the event horizon forms at a point (or points) and spreads outwards, and the matter that makes up the star falls towards it. But from our point of view, outside the star, none of that matter can end up inside the event horizon. We must surely experience it as sort of stuck to the edge, always falling further in but doing so ever more slowly, never quite passing the horizon. At this point we can see a hint about how the ``information paradox'' might be resolved: if all the matter that ever fell into the black hole is stuck to the edge, outside of the event horizon, then photons from all that matter can still reach us, and information about it is not impossible to access at all.
Now let's imagine watching the clock fall into the black hole again. Let's imagine that we sit and watch it for countless billions of years. These days everybody knows that black holes emit photons in a process known as Hawking radiation. As they do so they shrink, emitting radiation faster as they do and eventually they evaporate entirely in an enormous flash of electromagnetic radiation. The point is that although this won't happen for billions, maybe trillions of years, when it does happen the clock will still be outside the event horizon. It never hit the singularity because the black hole exploded before it could happen.
From our point of view it took aeons, but from the clock's point of view it was all over rather quickly. It experienced all those billions of years' worth of Hawking radiation in the space of a few minutes, from 12:00 to about 12:06, at which time the black hole exploded, depositing the remains of the clock in empty space. Of course there's no question that all that radiation would completely destroy the clock, but as it did so all those photons would carry information about it back into the outside universe. So there's no information paradox after all. Everything that falls in eventually comes back out.
There's also no singularity. If the black hole existed for an infinite time (as observed from the outside) then the clock would have experienced the singularity at 12:06 in its time frame (which is infinitely far into the future in our time frame), but it didn't because the black hole evaporated before then. So the singularity problem has actually already been solved by the existence of Hawking radiation, it's just that nobody else seems to have noticed.
Another of black holes' mysterious weirdnesses is that their entropy (a quantity that is, roughly speaking, the opposite of information) is proportional to their surface area. But if all the stuff that's ever fallen into them is still hanging around just outside then that doesn't seem anywhere near as surprising.
One objection to what I'm saying here is something called the ``no hair theorem,'' which one often finds in popular science books. This states that all black holes are perfectly smooth spheres or ellipsoids, and that once you know their mass, spin and charge you know everything that can possibly be known about them. This seems to contradict the idea that a black hole can store any information. It took a little bit of research to find out that the no hair theorem only applies after an infinite amount of time. It basically says that, given eternity, a black hole will eventually settle down into a perfect featureless sphere. But we now know that black holes never last forever because of Hawking radiation, so there will never be a time at which the theorem applies. All black holes must always have at least a little bit of ``hair.''
So anyway that's all I have to say about black holes for now. Nothing ever really falls into them before they explode, and once you take that into account all the paradoxes disappear. Hope you enjoyed :)
The story usually goes that stuff can fall into a black hole but can't come out again. This is fishy for a number of reasons: it causes an ``information paradox,'' as information about the stuff that falls in seems to be lost from the universe, something that doesn't happen under any other known circumstances. It also seems to violate time symmetry, the principle that if you watch a video of the universe backwards, everything you see is physically possible (though not necessarily probable).
There's also the ``singularity,'' that big bad infinity that lurks inside the event horizon, waiting to be experienced by anyone who has the bad luck to fall in. This is one of the big motivating factors for trying to develop a quantum theory of gravity: it is hoped that this infinity will be avoided for esoteric quantum reasons.
But it turns out that both the information paradox and the singularity problem can be avoided by a bit of layman's-terms back-of-the-envelope thinking, without using any quantum mechanics, based on a level of knowledge of general relativity that's available from pop science books. It goes like this:
Imagine you are at a safe distance from a black hole, watching something fall in. Let's say it's a clock. As everyone who's ever read about black holes knows, the hands of the clock will slow down as it approaches the event horizon, approaching a certain time (let's call it 12:00) ever more slowly, but never passing it. From the clock's own point of view, times after 12:00 do exist. This is because (and this is something they don't always tell you in pop science books) the event horizon is not at a fixed position in space but actually moves if you accelerate towards it. So if you were falling into the black hole behind the clock, the event horizon would be further away and the clock's hands would approach a later time than 12:00 (say, 12:05).
But here's the thing: no matter what you do you can never watch the clock go past the event horizon. At all points in time, from your point of view, the clock is always in front of the horizon, never beyond it. You can also never experience passing the horizon yourself: if you're falling feet-first into a black hole then you can never watch your feet pass the event horizon, which means you can never experience any other part of you being beyond it either. The horizon is like a rainbow, moving away whenever you move (or rather, accelerate) towards it. Until the moment you hit the singularity, that is, but we'll come to that in a moment.
Incidentally, this seems to apply to the formation of a black hole as well: as a giant star collapses at the end of its life, the event horizon forms at a point (or points) and spreads outwards, and the matter that makes up the star falls towards it. But from our point of view, outside the star, none of that matter can end up inside the event horizon. We must surely experience it as sort of stuck to the edge, always falling further in but doing so ever more slowly, never quite passing the horizon. At this point we can see a hint about how the ``information paradox'' might be resolved: if all the matter that ever fell into the black hole is stuck to the edge, outside of the event horizon, then photons from all that matter can still reach us, and information about it is not impossible to access at all.
Now let's imagine watching the clock fall into the black hole again. Let's imagine that we sit and watch it for countless billions of years. These days everybody knows that black holes emit photons in a process known as Hawking radiation. As they do so they shrink, emitting radiation faster as they do and eventually they evaporate entirely in an enormous flash of electromagnetic radiation. The point is that although this won't happen for billions, maybe trillions of years, when it does happen the clock will still be outside the event horizon. It never hit the singularity because the black hole exploded before it could happen.
From our point of view it took aeons, but from the clock's point of view it was all over rather quickly. It experienced all those billions of years' worth of Hawking radiation in the space of a few minutes, from 12:00 to about 12:06, at which time the black hole exploded, depositing the remains of the clock in empty space. Of course there's no question that all that radiation would completely destroy the clock, but as it did so all those photons would carry information about it back into the outside universe. So there's no information paradox after all. Everything that falls in eventually comes back out.
There's also no singularity. If the black hole existed for an infinite time (as observed from the outside) then the clock would have experienced the singularity at 12:06 in its time frame (which is infinitely far into the future in our time frame), but it didn't because the black hole evaporated before then. So the singularity problem has actually already been solved by the existence of Hawking radiation, it's just that nobody else seems to have noticed.
Another of black holes' mysterious weirdnesses is that their entropy (a quantity that is, roughly speaking, the opposite of information) is proportional to their surface area. But if all the stuff that's ever fallen into them is still hanging around just outside then that doesn't seem anywhere near as surprising.
One objection to what I'm saying here is something called the ``no hair theorem,'' which one often finds in popular science books. This states that all black holes are perfectly smooth spheres or ellipsoids, and that once you know their mass, spin and charge you know everything that can possibly be known about them. This seems to contradict the idea that a black hole can store any information. It took a little bit of research to find out that the no hair theorem only applies after an infinite amount of time. It basically says that, given eternity, a black hole will eventually settle down into a perfect featureless sphere. But we now know that black holes never last forever because of Hawking radiation, so there will never be a time at which the theorem applies. All black holes must always have at least a little bit of ``hair.''
So anyway that's all I have to say about black holes for now. Nothing ever really falls into them before they explode, and once you take that into account all the paradoxes disappear. Hope you enjoyed :)