Black holes do not exist where space and time do not exist, says new theory(phys.org)
phys.org
Black holes do not exist where space and time do not exist, says new theory
http://phys.org/news/2015-01-black-holes-space-theory.html
9 comments
This isn't a "fringe" variation in any but the sociological sense. I hadn't heard of either of these ideas until today, but my first thought was, "Yeah, that makes sense" (I'm a physicist, but not a gravity person.)
If you believe in the Planck scale (and almost everyone does) then incorporating it into SR as an "observer independent maximum energy" that is comparable to the usual "observer independent maximum velocity" is a very natural thing to do.
The theory might not have got much play, but this result will definitely increase interest because the black hole information paradox is a pain. However: the amount of interest a theory gets does not reflect the likelihood that it is correct. Caloric was once a very popular idea. Currently string theory is. Tomorrow maybe "extra special relativity" will be.
If you believe in the Planck scale (and almost everyone does) then incorporating it into SR as an "observer independent maximum energy" that is comparable to the usual "observer independent maximum velocity" is a very natural thing to do.
The theory might not have got much play, but this result will definitely increase interest because the black hole information paradox is a pain. However: the amount of interest a theory gets does not reflect the likelihood that it is correct. Caloric was once a very popular idea. Currently string theory is. Tomorrow maybe "extra special relativity" will be.
>If you believe in the Planck scale (and almost everyone does)
What? The idea that spacetime is quantized is most definitely not widely accepted. Spacetime is presumed to be continuous by basically every mainstream physicist (though most will admit that we don't have conclusive evidence either way, we only know that spacetime is not quantized down to a certain scale (which is short of the planck length by a good deal)). I personally think spacetime is quantized, but the only physicists pursuing the consequences of such an idea tend to be the fringe ones...
What? The idea that spacetime is quantized is most definitely not widely accepted. Spacetime is presumed to be continuous by basically every mainstream physicist (though most will admit that we don't have conclusive evidence either way, we only know that spacetime is not quantized down to a certain scale (which is short of the planck length by a good deal)). I personally think spacetime is quantized, but the only physicists pursuing the consequences of such an idea tend to be the fringe ones...
I should have said "take seriously" rather than "believe in". Most people take the notion seriously, for some value of "seriously". It's not a binary state.
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Perhaps people don't take it seriously because it sounds a lot like "double secret probation"?
As a physics PhD I feel like an idiot for accepting the theory of the classical black hole.
If you write the equations for the space around a black hole in the straightforward way you see a singularity at the event horizon. You can make a coordinate change that makes this singularity go away, but then you get the classical black hole singularity where there is either an "end of time" or an infinitely dense point or ring.
Physicists believed that this coordinate transformation was valid but it is not because it infinitely stretches space/time which at some point will blow up the Planck scale to be visible, at which point something completely indescribable happens -- it might be something like DSR or it might be different, but you void any warranty on the space time continuation, so the classical black hole is science fiction.
The obvious semiclasicalization is for the infinitely dense singularity to become a highly dense object which has some dimensions on the length of the Planck scale, but no model of quantum black hole using actual quantum gravity looks like that at all.
We don't have a "complete" theory of quantum gravity but we do have a number of competing partial theories, and we can already make some strong conclusions, such as holography, that are generic to many or any QG models. Underlying this are principles such as unitarity (unitarity is pretty much the one thing you need to make QM work) that means no information is lost when stuff falls in a black hole and that can't be reconciled with the mass being concentrated all in one place.
If you write the equations for the space around a black hole in the straightforward way you see a singularity at the event horizon. You can make a coordinate change that makes this singularity go away, but then you get the classical black hole singularity where there is either an "end of time" or an infinitely dense point or ring.
Physicists believed that this coordinate transformation was valid but it is not because it infinitely stretches space/time which at some point will blow up the Planck scale to be visible, at which point something completely indescribable happens -- it might be something like DSR or it might be different, but you void any warranty on the space time continuation, so the classical black hole is science fiction.
The obvious semiclasicalization is for the infinitely dense singularity to become a highly dense object which has some dimensions on the length of the Planck scale, but no model of quantum black hole using actual quantum gravity looks like that at all.
We don't have a "complete" theory of quantum gravity but we do have a number of competing partial theories, and we can already make some strong conclusions, such as holography, that are generic to many or any QG models. Underlying this are principles such as unitarity (unitarity is pretty much the one thing you need to make QM work) that means no information is lost when stuff falls in a black hole and that can't be reconciled with the mass being concentrated all in one place.
Counterargument to "the Planck scale is blown up to be visible": The expanding universe itself has (or very probably has) stretched by a factor starting to push into "practical infinity" territory since the Big Bang. (As I recall, common models of cosmic inflation require a minimum of 60 "e-foldings" of expansion in the first moments of the universe's existence: a factor of 10^26 or so, not counting the considerable expansion since then.) By that argument, we ought to be dangerously close to "voiding the warranty" on spacetime already, everywhere in the universe.
As far as I know, the notion that curved space can "enlarge the Planck-scale granularity of spacetime" is not a universal feature of quantum gravity theories. It's not even clear to me what that would mean. (I've only seen one or two string theory talks that suggested such a thing, for instance, and most of the experts in the audience seemed fairly convinced that the idea had no compelling basis in our context. I don't recall whether that's a feature of LQG.)
As far as I know, the notion that curved space can "enlarge the Planck-scale granularity of spacetime" is not a universal feature of quantum gravity theories. It's not even clear to me what that would mean. (I've only seen one or two string theory talks that suggested such a thing, for instance, and most of the experts in the audience seemed fairly convinced that the idea had no compelling basis in our context. I don't recall whether that's a feature of LQG.)
Well, any funny business that happened at the Planck scale during the big bang is hidden from us by an ionized cloud of gas. Maybe there is some trace left in the CMB, but there could be other physics in the way.
People have often said that "physics breaks down" at a gravitational singularity, but it is right to say that the theory of GR breaks down. Singularities generally are a sign that your theory is incomplete and aren't something that occurs in nature.
My argument is that the coordinate transformation and analytic continuation of the schwarzchild singularity is invalid, not that anything specific happens because of high curvature. The semiclassical view is that the event horizon is a quantum object, and if that is the case why believe the classical theory of the interior.
There is also the classical story that an outside observer sees it take forever for something to hit the event horizon but that the semiclassical theory says the black hole decays so presumably an outside observer sees the in falling object get burned up by hawking radiation or otherwise destroyed by something that happens at the eh.
Somehow the physics establishment denies there is a contradiction too and it is certainly true that the wall of fire has it's own problems, but that is because our current theories don't entirely work.
People have often said that "physics breaks down" at a gravitational singularity, but it is right to say that the theory of GR breaks down. Singularities generally are a sign that your theory is incomplete and aren't something that occurs in nature.
My argument is that the coordinate transformation and analytic continuation of the schwarzchild singularity is invalid, not that anything specific happens because of high curvature. The semiclassical view is that the event horizon is a quantum object, and if that is the case why believe the classical theory of the interior.
There is also the classical story that an outside observer sees it take forever for something to hit the event horizon but that the semiclassical theory says the black hole decays so presumably an outside observer sees the in falling object get burned up by hawking radiation or otherwise destroyed by something that happens at the eh.
Somehow the physics establishment denies there is a contradiction too and it is certainly true that the wall of fire has it's own problems, but that is because our current theories don't entirely work.
When I'm talking about the Planck scale being "blown up" to observable size during the Big Bang, I'm not talking about any need to look past the CMB, I'm talking about right here, where we're sitting. If there's some issue in which significant "stretching" of spacetime (as via a coordinate transformation) can make Planck scale effects important even in regions of finite curvature, then we ought to be sitting in such a region right now, here on Earth.
Based just on what you've said here, you seem to be conflating the notion of a true curvature singularity (where "physics breaks down") with a mere coordinate singularity (like the event horizon of a Schwarzchild black hole in asymptotically flat spherical coordinates, or the north/south poles of the earth in latitude/longitude coordinates: there's an "infinitely stretched coordinate transformation" required to resolve the latter, too). Specifically, it sounds like you're worried about the coordinate transformation that's necessary to eliminate the infinity that shows up at the event horizon in "normal" spherical coordinates. But why should I think that those coordinates (which are optimized to describe the flat space infinitely far from the black hole) reflect any special physical "truth"? Just for instance, if you set up a local coordinate system based on the proper time and length as measured by a freely-falling infalling observer, there's no trace of any infinity in the coordinates or metric at the event horizon. And there's no coordinate-independent quantity in classical GR that diverges at the event horizon. This is why most physicists aren't worried about the event horizon being a meaningful singularity in classical GR.
Now, bringing in a semiclassical analysis (or presumably a full quantum analysis, if you've got one; also, call Stockholm) does lead to interesting effects related to the event horizon. But that has nothing to do with coordinate singularities in classical GR and everything to do with the causal structure of spacetime. (Personally, I do harbor some significant doubts about whether we should trust the classical description of the black hole interior once we have a full quantum theory, so I've been quite interested to see the recent firewall questions come up. But the arguments casting doubt on those conclusions are pretty strong, too.) But regardless of my hunches about what will be true in a "final" theory, semiclassical theory is really quite clearly in agreement with classical GR that a local observer won't see anything special as they cross the event horizon.
Based just on what you've said here, you seem to be conflating the notion of a true curvature singularity (where "physics breaks down") with a mere coordinate singularity (like the event horizon of a Schwarzchild black hole in asymptotically flat spherical coordinates, or the north/south poles of the earth in latitude/longitude coordinates: there's an "infinitely stretched coordinate transformation" required to resolve the latter, too). Specifically, it sounds like you're worried about the coordinate transformation that's necessary to eliminate the infinity that shows up at the event horizon in "normal" spherical coordinates. But why should I think that those coordinates (which are optimized to describe the flat space infinitely far from the black hole) reflect any special physical "truth"? Just for instance, if you set up a local coordinate system based on the proper time and length as measured by a freely-falling infalling observer, there's no trace of any infinity in the coordinates or metric at the event horizon. And there's no coordinate-independent quantity in classical GR that diverges at the event horizon. This is why most physicists aren't worried about the event horizon being a meaningful singularity in classical GR.
Now, bringing in a semiclassical analysis (or presumably a full quantum analysis, if you've got one; also, call Stockholm) does lead to interesting effects related to the event horizon. But that has nothing to do with coordinate singularities in classical GR and everything to do with the causal structure of spacetime. (Personally, I do harbor some significant doubts about whether we should trust the classical description of the black hole interior once we have a full quantum theory, so I've been quite interested to see the recent firewall questions come up. But the arguments casting doubt on those conclusions are pretty strong, too.) But regardless of my hunches about what will be true in a "final" theory, semiclassical theory is really quite clearly in agreement with classical GR that a local observer won't see anything special as they cross the event horizon.
As not a physics PhD it seems so much easier to realize that GR's equivalence principle fails at the event horizon, in which case black holes are a mistake of GR. (Let downvotes commence since I must be a crackpot.)
Let a particle be above the horizon and escaping to infinity, as GR allows. By definition of a black hole, a signal can't be sent from below the horizon to the escaping particle. In an inertial frame, signals can be sent between any two points in the frame. Then an inertial frame relative to which the escaping particle is at rest can't extend below the horizon. That's a violation of the equivalence principle, because (we'll call this law of physics K:) inertial frames can wholly contain other inertial frames, and the inner frames can be extended to fill all of the outer frame. But as we've proven, a frame falling through the horizon of a black hole violates law K. An inertial frame relative to which the escaping particle is at rest cannot be extended to fill all of a frame falling through the horizon. Texts on GR tell us that an inertial frame can fall through the horizon, but we've just proven that such frame cannot be inertial without violating the equivalence principle. That principle is the core of GR, so black holes need be rejected as a mistake of the theory.
Black holes are predicted by the Schwarzschild metric. That metric can be tweaked to not predict black holes, while still agreeing with all physical experiments of Schwarzschild geometry to date. In the tweaked metric the escape velocity is always less than the speed of light (including at r < 2M), so that escape is always possible in principle. Singularities vanish (with escape always possible, no body need implode to one), so no quantum gravity is needed to make GR compatible with QM, and much better agreement to Occam's razor. Also solves the black hole information loss paradox.
Please downvote this major advance of physics if you haven't already.
Let a particle be above the horizon and escaping to infinity, as GR allows. By definition of a black hole, a signal can't be sent from below the horizon to the escaping particle. In an inertial frame, signals can be sent between any two points in the frame. Then an inertial frame relative to which the escaping particle is at rest can't extend below the horizon. That's a violation of the equivalence principle, because (we'll call this law of physics K:) inertial frames can wholly contain other inertial frames, and the inner frames can be extended to fill all of the outer frame. But as we've proven, a frame falling through the horizon of a black hole violates law K. An inertial frame relative to which the escaping particle is at rest cannot be extended to fill all of a frame falling through the horizon. Texts on GR tell us that an inertial frame can fall through the horizon, but we've just proven that such frame cannot be inertial without violating the equivalence principle. That principle is the core of GR, so black holes need be rejected as a mistake of the theory.
Black holes are predicted by the Schwarzschild metric. That metric can be tweaked to not predict black holes, while still agreeing with all physical experiments of Schwarzschild geometry to date. In the tweaked metric the escape velocity is always less than the speed of light (including at r < 2M), so that escape is always possible in principle. Singularities vanish (with escape always possible, no body need implode to one), so no quantum gravity is needed to make GR compatible with QM, and much better agreement to Occam's razor. Also solves the black hole information loss paradox.
Please downvote this major advance of physics if you haven't already.
I don't completely understand the argument you're making, so please correct me if I'm misunderstanding you, but I think I see the problem.
It is true that in an inertial frame you can send a signal between two points. But if you have an inertial frame which is falling into a black hole any signal sent from beneath the event horizon will not reach any other point until that point has also fallen beneath the event horizon.
Remember that the inertial frame is in free fall, so points which are fixed in the inertial frame are moving according to a distant observer.
It is true that in an inertial frame you can send a signal between two points. But if you have an inertial frame which is falling into a black hole any signal sent from beneath the event horizon will not reach any other point until that point has also fallen beneath the event horizon.
Remember that the inertial frame is in free fall, so points which are fixed in the inertial frame are moving according to a distant observer.
> But if you have an inertial frame which is falling into a black hole any signal sent from beneath the event horizon will not reach any other point until that point has also fallen beneath the event horizon.
Problem is, the escaping particle never falls beneath the horizon. So an inertial frame in which that particle is at rest cannot extend below the horizon at all. That's a violation of law K for a frame falling into a black hole. By violating law K, the latter frame cannot be inertial. Note that law K is about allowing inner frames be extended to fill all of an outer frame.
Let a cloud of particles straddle the horizon. Let all the particles above the horizon be escaping to infinity. According to GR, such cloud must be splitting apart. The particles below the horizon must move inexorably inward, toward the singularity at the center of the black hole, whilst the particles above the horizon move ever outward, away from the black hole. Then a frame falling through the horizon of a black hole cannot be inertial, for in an inertial frame the cloud needn't be splitting apart (since law K applies). For example, in an inertial frame in Earth's atmosphere you can have a cloud of particles in which half the particles are given to be escaping to infinity, and the cloud needn't be splitting apart (just let all the particles escape in formation).
Problem is, the escaping particle never falls beneath the horizon. So an inertial frame in which that particle is at rest cannot extend below the horizon at all. That's a violation of law K for a frame falling into a black hole. By violating law K, the latter frame cannot be inertial. Note that law K is about allowing inner frames be extended to fill all of an outer frame.
Let a cloud of particles straddle the horizon. Let all the particles above the horizon be escaping to infinity. According to GR, such cloud must be splitting apart. The particles below the horizon must move inexorably inward, toward the singularity at the center of the black hole, whilst the particles above the horizon move ever outward, away from the black hole. Then a frame falling through the horizon of a black hole cannot be inertial, for in an inertial frame the cloud needn't be splitting apart (since law K applies). For example, in an inertial frame in Earth's atmosphere you can have a cloud of particles in which half the particles are given to be escaping to infinity, and the cloud needn't be splitting apart (just let all the particles escape in formation).
Elaborate on said "tweak" to the Schwarzschild metric?
See https://finbot.wordpress.com/2010/01/02/toward-a-new-theory/. It's not my blog.
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Where is it that space does not exist? The headline seems like a contradiction in terms.
Your question, actually, is self-contradictory. "Where" already assumes space.
I believe that was the point. The article title makes the same mistake.
It's probably just a 'dumbing down for journalism' title.
"In gravity's rainbow, space does not exist below a certain minimum length, and time does not exist below a certain minimum time interval"
I'm definitely not an expert, but I was under the impression that both space and time are already thought to be discrete and have minimum quanta, Planck length (10^-36 m) and Planck time (10^-44 s). I guess this new theorem suggests that not only do they have minimum values, they don't exist between these points. Sort of like how pixels aren't really sized objects, but they sort of fill the space between them -- this might be a terrible analogy.
I thought that it was the opposite - you can't draw half a pixel on a screen. (Perhaps a better analogy would be that you can't represent every real number as a floating point integer.)
I had never head of anything like this. Does that mean that space and time are somehow discrete instead of continuous?
They have a scale. They are not "discrete" in the sense that pixels are discrete because there is no grid (no orientation, no preferred direction, etc).
Think of it like the resolution of a microscope: you can only see objects down to scales of 1 micron, say. That doesn't make what you are looking at discrete at the 1 micron level. It makes it blurry (invisible, or in the case of space and time, non-existent) below that level.
Think of it like the resolution of a microscope: you can only see objects down to scales of 1 micron, say. That doesn't make what you are looking at discrete at the 1 micron level. It makes it blurry (invisible, or in the case of space and time, non-existent) below that level.
How it shows up depends on the model. Superstrings are objects of (usually) Planckian size, so if the particles are the size of the "grain" then that is one way a scale could manifest.
In other models like loops quantum gravity you can only ask questions about loops in space and not about points so that is another way the scale manigests.
In other models like loops quantum gravity you can only ask questions about loops in space and not about points so that is another way the scale manigests.
Discrete is probably not the best way of looking at it; instead, think of it as the smallest scale across which space can change. From this perspective, it's not possible to discern between a quantized and continuous spacetime.
For all practical purposes, they kind of appear to be:
https://en.wikipedia.org/wiki/Planck_length
https://en.wikipedia.org/wiki/Planck_time
https://en.wikipedia.org/wiki/Planck_length
https://en.wikipedia.org/wiki/Planck_time
This idea kind of ties into the idea of a 'computable' universe: I'm no expert but this article gives some ideas[1].
[1] http://en.wikipedia.org/wiki/Digital_physics#Criticism
[1] http://en.wikipedia.org/wiki/Digital_physics#Criticism
So does discrete space and time also solve zenos paradox? (or was that already solved classically?)
Yes.
But Zenos paradox has a simple solution; Time. It takes k(1) * 1/x time to reach k(2) * 1/x location assuming constant velocity. Basically moving an infinitely small distance takes an infinitely small unit of time.
But Zenos paradox has a simple solution; Time. It takes k(1) * 1/x time to reach k(2) * 1/x location assuming constant velocity. Basically moving an infinitely small distance takes an infinitely small unit of time.
Zeno's paradox assumes less than "constant velocity". It assumes that there is a minimum finite velocity, or that an infinite number of moments in time must be experienced, not skipped over.
Zeno's paradox is about our casual/informal passing between the continuous and the discrete.
If in reality there is some planck-length-like discrete grid structure to the universe, there is no paradox.
Zeno's paradox is about our casual/informal passing between the continuous and the discrete.
If in reality there is some planck-length-like discrete grid structure to the universe, there is no paradox.
There are two options that are intuitively acceptable.
Discrete space, or continuous space and time. You can travel through infinite points in finite time iff time is infinitely divisible.
Discrete space, or continuous space and time. You can travel through infinite points in finite time iff time is infinitely divisible.
Having so little evidence and information about the phenomena http://en.wikipedia.org/wiki/Black_hole#Observational_eviden... the entire theory around black holes is a mathematical model that probably has nothing to do with the real phenomena.
Absence of information in Wikipedia isn't very good evidence that there isn't very much evidence.
Black holes can be observed in multiple ways:
1) radiation from infalling matter 2) gravitational lensing 3) dynamics of orbiting objects
Remember: we not see the moon by its own light. We see the moon by the light it reflects from the sun. That reflected light is a direct causal consequence of the moon's existence, and we quite properly take it as such... even though the moon emits no light of its own.
No one, to the best of my knowledge, has ever suggested we ought to treat the evidence for the Moon as scanty or inadequate on this basis. So the fact that the radiation we see from black holes originates from the heat of infalling matter, which is a direct causal consequence of the black hole's existence, should constitute similarly strong evidence.
Lensing and dynamical measurements are also quite direct, strong and compelling. There exist compact bodies with more than 1.4 solar masses, which is the limit for nuclear matter (we would have to be wrong about quite a lot of nuclear physics for this to be otherwise.)
The question is: what is the best theory to describe black holes, given we know based on this deep and broad evidence that they exist? Currently we have a rough combination of GR and quantum theory, and while the theory has issues, the claim it "probably has nothing to do with the real phenomenon" is minimally plausible.
Black holes can be observed in multiple ways:
1) radiation from infalling matter 2) gravitational lensing 3) dynamics of orbiting objects
Remember: we not see the moon by its own light. We see the moon by the light it reflects from the sun. That reflected light is a direct causal consequence of the moon's existence, and we quite properly take it as such... even though the moon emits no light of its own.
No one, to the best of my knowledge, has ever suggested we ought to treat the evidence for the Moon as scanty or inadequate on this basis. So the fact that the radiation we see from black holes originates from the heat of infalling matter, which is a direct causal consequence of the black hole's existence, should constitute similarly strong evidence.
Lensing and dynamical measurements are also quite direct, strong and compelling. There exist compact bodies with more than 1.4 solar masses, which is the limit for nuclear matter (we would have to be wrong about quite a lot of nuclear physics for this to be otherwise.)
The question is: what is the best theory to describe black holes, given we know based on this deep and broad evidence that they exist? Currently we have a rough combination of GR and quantum theory, and while the theory has issues, the claim it "probably has nothing to do with the real phenomenon" is minimally plausible.
Wouldn't something like the uncertaintity principle mean information is destroyed all the time?
I don't see how you can find an earlier state from knowing the current state since you can't know position and momentum, right?
I don't see how you can find an earlier state from knowing the current state since you can't know position and momentum, right?
The uncertainty principle doesn't imply that any information is being destroyed, it implies that there is a limit to the amount of information you have. Position and momentum are things that you derive from the available information. You just can't use the same limited pool of information to derive the both in a way that would use more information than you have.
>I don't see how you can find an earlier state from knowing the current state since you can't know position and momentum, right?
State has little to do with position and momentum directly, but the underlying information. We use those concepts to indirectly refer to state, but state is more fundamental. Information arises from a correlation between states, and position and momentum are different measures of this correlation.
>I don't see how you can find an earlier state from knowing the current state since you can't know position and momentum, right?
State has little to do with position and momentum directly, but the underlying information. We use those concepts to indirectly refer to state, but state is more fundamental. Information arises from a correlation between states, and position and momentum are different measures of this correlation.
Could it be that when space and time get stretched beyond the Planck interval, then the black hole ceases to exist at all beyond that point? In other words, the center of a black hole is non-existence itself.
Looking at it from the time angle, we all blink in and out of existence constantly. But when time and space gets stretched too far, it becomes impossible to blink back into existence, as if the process runs out of gas if the out-of-existence time period is too long.
Looking at it from the time angle, we all blink in and out of existence constantly. But when time and space gets stretched too far, it becomes impossible to blink back into existence, as if the process runs out of gas if the out-of-existence time period is too long.
Would this imply hawking radiation doesn't exist? Can we no longer use black holes as a potential energy source?
On a quick read before I've entirely finished my morning coffee, Hawking radiation will still exist.
The argument seems to go like this:
1) the event horizon in GR is infinitely sharp 2) gravity's rainbow implies nothing can be infinitely sharp (because that requires space and time to exist on scales below the Planck scale) 3) therefore gravity's rainbow implies the event horizon does not exist at those scales
Above those scales, something that looks very much like the event horizon still exists. The time taken to fall into a black hole will still be very long, just not infinite. Presumably the details of the theory show how this happens, which is the interesting bit. It's one thing to say "Hey, maybe the horizon is smooth or doesn't exist at small scales!" but to be useful the theory has to show how reality will actually behave if that is the case.
With regard to using black holes as power sources: if we have the technology to do that we'd be unlikely to need black holes as power sources.
The argument seems to go like this:
1) the event horizon in GR is infinitely sharp 2) gravity's rainbow implies nothing can be infinitely sharp (because that requires space and time to exist on scales below the Planck scale) 3) therefore gravity's rainbow implies the event horizon does not exist at those scales
Above those scales, something that looks very much like the event horizon still exists. The time taken to fall into a black hole will still be very long, just not infinite. Presumably the details of the theory show how this happens, which is the interesting bit. It's one thing to say "Hey, maybe the horizon is smooth or doesn't exist at small scales!" but to be useful the theory has to show how reality will actually behave if that is the case.
With regard to using black holes as power sources: if we have the technology to do that we'd be unlikely to need black holes as power sources.
Re power source, I think the idea is you have a small, quickly evaporating black hole (electrically charge so you can hold it in place?)
And you feed matter into it, and immediately get radiation back due to hawking radiation equivalent to e=mc^2 of the matter you dropped in?
And you feed matter into it, and immediately get radiation back due to hawking radiation equivalent to e=mc^2 of the matter you dropped in?
I didn't see what about your explanation says why hawking radiation would still exist? It's caused by particle-anti particle pairs being created with one on each side of the event horizon, no?
When I first posted that response I was thinking that the scale that mattered was the compton wavelength of the particles being emitted, but having actually finished my coffee now I'm no longer so sure. My point was that so long as the horizon is sufficiently fine on the scale of the particle's compton wavelength then hawking radiation can still be emitted, even granted the horizon is not infinitely fine. This may be correct, or not.
For using black holes as a potential energy source, we have to find it first. There are a lot of potential candidates for black holes (binary stars, center of our galaxy), but we still haven't seen any direct evidence of their existence.
It isn't clear what "direct evidence" would be. We have the kind of perfectly ordinary evidence that is used to infer the existence of everything from the Higgs to neutrons: we see consequences of an entity that fits with a particular theoretical description.
The fundamental piece of evidence for black holes is the existence of compact objects with more than 1.4 solar masses. This is direct evidence. These things exist.
We know they can't be neutron stars because there is an upper limit on their mass due to nuclear physics. We therefore infer they are black holes (fully gravitationally collapsed objects) because "maybe the aren't" is not a compelling counter-argument.
If you're going to ask for "direct evidence" you need to be extremely clear what you mean, and your definition really should be such that the evidence we have for the existence of neutrons or muons counts as "direct". Otherwise, you will be in a position of insisting that we have a kind of evidence for black holes that we don't have for almost anything else, which is not something anyone is going to take seriously.
The fundamental piece of evidence for black holes is the existence of compact objects with more than 1.4 solar masses. This is direct evidence. These things exist.
We know they can't be neutron stars because there is an upper limit on their mass due to nuclear physics. We therefore infer they are black holes (fully gravitationally collapsed objects) because "maybe the aren't" is not a compelling counter-argument.
If you're going to ask for "direct evidence" you need to be extremely clear what you mean, and your definition really should be such that the evidence we have for the existence of neutrons or muons counts as "direct". Otherwise, you will be in a position of insisting that we have a kind of evidence for black holes that we don't have for almost anything else, which is not something anyone is going to take seriously.
This article looks like one big paradox that shouldn't actually exist.
http://en.wikipedia.org/wiki/Doubly_special_relativity
It seems to have been around for at least ten years but perhaps never gained much traction. In short, this seems like it may be an interesting result that only applies in a fringe variation of accepted modern theory. Perhaps someone with actual training in physics can comment in more detail.