In response to falenas108′s “Ask an X” thread. I have a PhD in experimental particle physics; I’m currently working as a postdoc at the University of Cincinnati. Ask me anything, as the saying goes.
Since we are experimenting here… I have a PhD in theoretical physics (General Relativity), and I’d be happy to help out with any questions in my area.
And then the point goes out. All at once, as if God turned off the switch. You have crossed the event horizon of the black hole.
and:
But Alice cannot see Bob either, because in order to do so, she has to turn her head toward her own past. The distortion of spacetime is so great that the spatial direction in which Bob lies relative to her is actually in her past. In technical terms, any light that comes to her from Bob will fall perpendicular to her eyeballs, regardless of which direction she turns her head.
When I read this, I believed that it was wrong (but well-written, making it more dangerous!). (However, he described Gravity Probe B’s verification of the geodetic effect correctly.)
An observer crossing a black hole event horizon can calculate the moment they’ve crossed it, but will not actually see or feel anything special happen at that moment. In terms of visual appearance, observers who fall into the hole perceive the black region constituting the horizon as lying at some apparent distance below them, and never experience crossing this visual horizon.[7] Other objects that had entered the horizon along the same radial path but at an earlier time would appear below the observer but still above the visual position of the horizon, and if they had fallen in recently enough the observer could exchange messages with them before either one was destroyed by the gravitational singularity.[8] Increasing tidal forces (and eventual impact with the hole’s singularity) are the only locally noticeable effects.
Engulfed in blackness? NO!
It is a common misconception that if you fall inside the horizon of a black hole you will be engulfed in blackness. More specifically, the story is that as you fall towards the horizon, the image of the sky above concentrates into a smaller and smaller circular patch, which disappears altogether as you pass through the horizon. The misconception arises because if you lower yourself very slowly towards the horizon, firing your rockets like crazy just to stay put, then indeed your view of the outside universe will be concentrated into a small, bright circle above you. Click on the button to see what it looks like if you lower yourself slowly to the horizon. Physically, this happens because you are swimming like crazy through the inrushing flow of space (see Waterfall), and relativistic beaming concentrates and brightens the scene ahead of (above) you. See 4D Perspective for a tutorial on relativistic beaming. But this is a thoroughly unrealistic situation. You’d be daft to waste your rockets hovering just above the horizon of a black hole. If you had all that rocket power, why not do something useful with it, like take a trip across the Universe? If you nevertheless insist on hovering just above the horizon, and if by mistake you drop just slightly inside the horizon, then you can no longer stay at rest, however hard you fire your rockets: the faster-than-light flow of space into the black hole will pull you in. Whatever you choose to do, the view of the outside Universe will not disappear as you pass through the horizon.
This explanation agrees with everything I know (when hovering outside the event horizon, you are accelerating instead of being in free fall).
Can you confirm that the Reddit post was incorrect, and Wikipedia and its cited link are correct?
The last two quotes are indeed correct, and the reddit one is a mix of true and false statements.
To begin with, the conclusion subtly replaces the original premise of arbitrarily high velocity with arbitrarily high acceleration. (Confusing velocity and acceleration is a Grade 10 science error.) Given that one cannot accelerate to or past the speed of light, near-infinite acceleration engine is indeed of no use inside a black hole. However, arbitrarily high velocity is a different matter. It lets you escape from inside a black hole horizon. Of course, going faster than light brings a host of other problems (and no, time travel is not one of them).
As you continue to fall, the event horizon opens up beneath you, so you feel as if you’re descending into a featureless black bowl. Meanwhile, the stars become more and more crowded into a circular region of sky centered on the point immediately aft.
This is true if you hover above the horizon, but false if you fall freely. In the latter case you will see some distortion, but nothing as dramatic.
And then the point goes out. All at once, as if God turned off the switch.
This is false if you travel slower than light. You still see basically the same picture as outside, at least for a while longer.
If you have a magical FTL spaceship, what you see is not at all easy to describe. For example, in your own frame of reference, you don’t have mass or energy, only velocity/momentum, the exact opposite of what we describe as being stationary. Moreover, any photon that hits you is perceived as having negative energy. Yet it does not give or take any of your own energy (you don’t have any in your own frame), it “simply” changes your velocity.
I cannot comment on the Alice and Bob quote, as I did not find it in the link.
Actually, I can talk about black holes forever, feel free to ask.
I have a PhD in theoretical physics (General Relativity), and I’d be happy to help out with any questions in my area.
Excellent! That happens to be a subject I’m very interested in.
Here are two questions, to start:
1. Do you have a position in the philosophical debate about whether “general covariance” has a “physical” meaning, or is merely a property of the mathematical structure of the theory?
[I]f the whole universe was rotating around you while you stood still, you would feel a centrifugal force from the incoming gravitational waves, corresponding exactly to the centripetal force of spinning your arms while the universe stood still around you.
given that it implies that the electromagnetic force (which is what causes your voluntary movements, such as “spinning your arms around”) can be transformed into gravity by a change of coordinates? (Wouldn’t that make GR itself the “unified field theory” that Einstein legendarily spent the last few decades of his life searching for, supposedly in vain?)
Do you have a position in the philosophical debate about whether “general covariance” has a “physical” meaning, or is merely a property of the mathematical structure of the theory?
Yeah, I recall looking into this early in my grad studies. I eventually realized that the only content of it is diffeomorphism invariance, i.e. that one should be able to uniquely map tensor fields to spacetime points. The coordinate representation of these fields depends on the choice of coordinates, but the fields themselves do not. In that sense the principle simply states that the relation spacetime manifold → tensor field is a function (surjective map). For example, there is a unique metric tensor at each spacetime point (which, incidentally, precludes traveling into one’s past).
I would also like to mention that the debate “about whether “general covariance” has a “physical” meaning, or is merely a property of the mathematical structure of the theory” makes no sense to me as an instrumentalist (I consider the map-territory moniker an oft convenient model, not some deep ontological thing).
[I]f the whole universe was rotating around you while you stood still, you would feel a centrifugal force from the incoming gravitational waves, corresponding exactly to the centripetal force of spinning your arms while the universe stood still around you.
This is false, as far as I can tell. The frame dragging effect is not at all related to gravitational radiation. The Godel universe is an example of an extreme frame dragging due to being filled with spinning pressureless perfect fluid, and there are no gravitational waves in it.
it implies that the electromagnetic force (which is what causes your voluntary movements, such as “spinning your arms around”) can be transformed into gravity by a change of coordinates?
Well, yeah, this is an absurd conclusion. The only thing GR says that matter creates spacetime curvature. A spinning spacetime has to correspond to spinning matter. And spinning is not relative, but quite absolute, it cannot be removed by a choice of coordinates (for example, the vorticity tensor does not vanish no matter what coordinates you pick). So Mach is out of luck here.
May I ask you which is exactly your (preferred) subfield of work? What are the most important open problems in that field that you think could receive decisive insight (both theoretically and experimentally) in the next 10 years?
May I ask you which is exactly your (preferred) subfield of work?
My research was in a sense Abbott-like: how a multi-dimensional world would look to someone living in the lower dimensions. It is different from the standard string-theoretical approach of bulk-vs-brain, because it is non-perturbative. I can certainly go into the details of it, but probably not in this comment.
What are the most important open problems in that field that you think could receive decisive insight (both theoretically and experimentally) in the next 10 years?
Caveat: I’m not in academia at this point, so take this with a grain of salt.
Dark energy (not to be confused with Dark matter) is a major outstanding theoretical problem in GR. As it happens, it is also an ultimate existential risk, because it limits the amount of matter available to humanity to “only” a few galaxies, due to the accelerating expansion of the universe. The current puzzle is not that dark energy exists, but why there is so little of it. A model that explains dark energy and makes new predictions might even earn the first ever Nobel prize in theoretical GR, if such predictions are validated.
That the expansion of the universe is accelerating is a relatively new discovery (1998), so there is a non-negligible chance that there will be new insights into the issue on a time frame of decades, rather than, say, centuries.
In observations/experiments, it is likely that gravitational waves will be finally detected. There is also a chance that Hawking radiation will be detected in a laboratory setting from dumb holes or other black-hole analogs.
My research was in a sense Abbott-like: how a multi-dimensional world would look to someone living in the lower dimensions. It is different from the standard string-theoretical approach of bulk-vs-brain, because it isnon-perturbative. I can certainly go into the details of it, but probably not in this comment.
This looks really interesting, any material you can suggest on the subject? I was a particle physics phenomenologist until last year, so proper introductory academic paper should be ok.
There is also a chance that Hawking radiation will be detected in a laboratory setting from dumb holes or other black-hole analogs.
And this looks very fascinating, too. Thanks a lot for your answers.
I’ve never understood how going faster can make time go slower, thereby explaining why light always appears to have the same velocity.
If I’m moving in the opposite direction to light, and if there was no time slowing down, then the light would appear to go faster than normal from my perspective. Add in the effects of time slowing down, and light appears to be going at the same speed it always does. No problem yet.
But if I’m moving in the same direction as the light, and time doesn’t slow down, then it would appear to be going slower than normally, so the slowing down of time should make it look even slower, not give it the speed we always observe it in.
This Reddit comment giving a lay explanation for the constant lightspeed thing was linked around a lot a while ago. The very short version is to think of everything being only ever able to move at the exact single speed c in a four-dimensional space, so whenever something wants to have velocity along a space axis, they need to trade off some from along the the time axis to keep the total velocity vector magnitude unchanged.
The very short version is to think of everything being only ever able to move at the exact single speed c in a four-dimensional space, so whenever something wants to have velocity along a space axis, they need to trade off some from along the the time axis to keep the total velocity vector magnitude unchanged.
I like this way of thinking of it, so much simpler than the usual explanations.
That is a very good explanation for the workings of time, thank you very much for that.
But it doesn’t answer my real question. I’ll try to be a bit more clear.
Light is always observed at the same speed. I don’t think I’m so crazy that I imagined reading this all over the place on the internet. The explanation given for this is that the faster I go, the more I slow down through time, so from my reference frame, light decelerates (or accelerates? I’m not sure, but it actually doesn’t matter for my question, so if I’m wrong, just switch them around mentally as you read).
So let’s say I’m going in a direction, let’s call it “forward”. If a ball is going “backward”, then from my frame of reference, the ball would appear to go faster than it really is going, because its relative speed = its speed—my speed. This is also true for light, though the deceleration of time apparently counters that effect by making me observe it slower by the precise amount to make it still go at the same speed.
Now take this example again, but instead send the ball forward like me. From my frame of reference, the ball is going slower than it is in reality, again because its relative speed = its speed—my speed. The same would apply to light, but because time has slowed for me, so has the light from my perspective. But wait a second. Something isn’t right here. If light has slowed down from my point of view because of the equation “relative speed = its speed—my speed”, and time slowing down has also slowed it, then it should appear to be going slower than the speed of light. But it is in fact going precisely at the speed of light! This is a contradiction between the theory as I understand it and reality.
My god, that is probably extremely unclear. The number of times I use the words speed and time and synonyms… I wish I could use visual aids.
Also, I just thought of this, but how does light move through time if it’s going at the speed of light? That would give it a velocity of zero in the futureward direction (given the explanation you have linked to), which would be very peculiar.
The explanation given for this is that the faster I go, the more I slow down through time, so from my reference frame, light decelerates (or accelerates? I’m not sure, but it actually doesn’t matter for my question, so if I’m wrong, just switch them around mentally as you read).
Perhaps I’m reading this wrong, but it seems you’re assuming that time slowing down is an absolute, not a relative, effect. Do you think there is an absolute fact of the matter about how fast you’re moving? If you do, then this is a big mistake. You only have a velocity relative to some reference frame.
If you don’t think of velocity as absolute, what do you mean by statements like this one:
The same would apply to light, but because time has slowed for me, so has the light from my perspective.
There is no absolute fact of the matter about whether time has slowed for you. This is only true from certain perspectives. Crucially, it is not true from your own perspective. From your perspective, time always moves faster for you than it does for someone moving relative to you.
Maybe this angle will help: “relative speed = its speed—my speed” is an approximate equation. The true one is relative speed = (its speed—my speed)/(1-its speed * my speed / c^2). Let one of the two speeds = c, and the relative speed is also c.
Thanks for your answer, this equation will make it easier to explain my problem.
Let’s say a ball is going at the speed of c/4, and I’m going at a speed of c/2. According to the approximate equation, before the effects of time slowing down are taken into account, I would be going at a speed of -c/4. Now if you take into account time slowing down (divide -c/4 by the (1-its speed*...)), you get a speed of −2c/7.
So that was the example when I’m going in the same direction as the ball. Now let’s say the ball is still going at a speed of c/4, but I’m now going at a speed of -c/2. Using the approximate equation: 3c/4. Add in time slowing down: 2c/3.
So the two pairs are (-c/4, −2c/7) and (3c/4,2c/3). Let’s compare these values.
For the first tuple, when I’m going in the same direction as the ball, -c/4 > −2c/7. This means that −2c/7 is a faster speed in the negative direction (multiply both sides by −1 and you get c/4<2c/7), so from the c/2 reference frame, after the time slow effect, the observed speed of the ball is greater than it would be without the time slow down. So far so good.
For the second tuple, however, when I’m going in the opposite direction of the ball, 3c/4 > 2c/3. So from the -c/2 reference frame, after the time slow effect, the ball appears to be going slower than it would if time didn’t slow down.
But didn’t the first tuple show that the ball is supposed to appear to go faster given the time slow effect? Does this mean that time slows down when I’m going in the same direction as the ball, and it accelerates when I’m going in the opposite direction of the ball? Or does it mean that the modification of the approximate equation which gives the correct one is not in fact the effects of time slowing down? Or am I off my rocker here?
This might be just a confusion between speed and velocity. In one case relative velocity (not speed), in fractions of the speed of light, is −1/4 (classically) vs −2/7 (relativity). In the other case it is 3⁄4 vs 2⁄3. In both cases the classical value is higher than the relativistic value.
That the classical value is always higher than the time-slowed value is precisely what doesn’t make sense to me.
If −1/4 is the classical value, and −2/7 is the relativity value, −2/7 is a faster speed than −1/4, even though −1/4 is a bigger number. So the relativity speed is faster. However, if 3⁄4 is the classical value, and 2⁄3 is the relativity value, 3⁄4 is a faster speed relative to me than 2⁄3. So in this case, the classical speed is faster.
So when I have a speed of 1⁄2, time slowing down makes the relative speed of the ball greater. And when I have a speed of −1/2, time slowing down makes the relative speed of the ball smaller. More generally, this can be described by my direction relative to the ball. If I’m moving in the same direction as the ball, time slowing down makes it appear to go faster than the classical speed. However, if I’m going in the opposite direction of the ball, then it appears to go slower than the classical speed. And that doesn’t make sense. Time slowing down should always make the ball appear to go faster than the classical speed, and the effects of time slowing down should definitely should not depend on my direction relative to the ball.
If light has slowed down from my point of view because of the equation “relative speed = its speed—my speed”, and time slowing down has also slowed it, then it should appear to be going slower than the speed of light.
When your subjective time slows down, things around you seem to move faster relative to you, not slower. So your time slowing down would make the light seem to speed up for you.
Also, I just thought of this, but how does light move through time if it’s going at the speed of light? That would give it a velocity of zero in the futureward direction (given the explanation you have linked to), which would be very peculiar.
That’s right. From the point of view of the photon it is created and destroyed in the same instant.
To add to that, it is a relatively common classroom experiment to show trails in gas left by muons from cosmic radiation. These muons are travelling at about 99.94% of the speed of light, which is quite fast but the distance from the upper atmosphere where they originate to the classroom is long enough that it takes the muon several of its half-lives to reach the clasroom—by our measurement of time, at least. We should expect them to have decayed before the reach the classroom, but they don’t!
By doing the same experiment at multiple elevations we can see that the rate of muon decay is much lower than non-relativistic theories would suggest. However, if time dilation due to their large speed is taken into account then we get that the muons ‘experience’ a much shorter trip from their point of view—sufficiently short that they don’t decay! That they have reached the classroom is evidence (given a bunch of other knowledge about decay and formation of muons) that is easily observed for time dilation.
Also! Time dilation is surprisingly easy to derive. I recommend that you attempt to derive it yourself if you haven’t already! I give you this starting point: A) The speed of light is constant and independent of observers B) A simple way to analyze time is to consider a very simple clock: two mirrors facing towards each other with a photon bouncing back and forth between the two. The cycles of the photon denotes the passage of time. C) What if the clock is moving? D) Draw a diagram
Okay, but if it’s not moving through time, it only exists in the point in time in which it was created, no? So it would only be present for one moment in time where it would move constantly until it’s destruction. We would therefore observe it as moving at infinite speed.
Remember the thing from the Reddit comment about everything always moving at the constant speed c. The photon has its velocity at a 90° angle from the time axis of space-time, but that’s still just a velocity of magnitude c. Can’t get infinite velocity because of the rule that you can’t change your time-space speed ever.
Things get a bit confusing here, since the photon is not moving through time at all in its own frame of reference, but in the frame of reference of an outside observer, it’s zipping around at speed c. Your intuition seems to be not including the bit about time working differently in different frames of reference.
Sorry if I’m being annoying, but the light is not moving through time. So it should not appear at different points in time. If I’m not moving forward, and you are, and you’re looking directly to your side, then you’ll only see me while I’m next to you. And if I start moving from side to side, then I won’t impact you unless you’re right next to me. Change “forward” with “futureward” and “side” to “space”, and you get my problem with light having zero futureward speed.
My big assumption here is that even though things appear to behave differently from different frames of reference, there is in fact an absolute truth, an absolute way things are behaving. I don’t think that’s wrong, but if it is, I’ve got a long way to go before understanding relativity.
[...] but the light is not moving through time. So it should not appear at different points in time [...]
Since it’s not moving through time, light moves only through space. It never appears at different points in time. You can “see” this quite easily if you notice that you can’t encounter the same photon twice, even if you would have something that could detect its passing without changing it, unless you alter its path with mirrors or curved space, because you’d need to go faster than light to catch up with it after it passes you the first time.
In fact, if memory serves, in relativity two events are defined to be instantaneous if they are connected by a photon. For example, if a photon from your watch hits your eye and tells you it’s exactly 5 PM, and another photon hits your eye at the same time and tells you an atom decayed, then technically the atom decayed at exactly 5 PM. That is, in relativity, events happen exactly when you see them. On the other hand, the fact that two events are simultaneous for me may or may not (and usually aren’t) simultaneous for someone else, hence the word relativity.
(Even if you curve the photon, that just means that you pass twice through the same point in time. Think about it, if the photon can leave you and go back, it means you can see your “past you”, photons reflected off of your body into space and then coming back. Say the “loop” is three light-hours long. Since you can see the watch of the past you show 1PM at the same time you see your watch show 4PM, you simply conclude that the two events are simultaneous, from your point of view.)
I think what’s confusing is that we’re very often told things like “that star is N light years away, so since we’re seeing it now turning into a supernova, it happened N years ago”. That’s not quite a meaningless claim, but “ago” and “away” don’t quite mean the same thing they mean in relativistic equations. In relativity terms, for me it happened in 2012 because the events “I notice that the calendar shows 2012” and “the star blew up” are simultaneous from my point of view.
I don’t have good offhand ideas how to unpack this further, sorry. I’d have to go learn Minkowski spacetime diagrams or something to have a proper idea how you get from timeward-perpendicular spaceward movement into the 45 degree light cone edge, and probably wouldn’t end up with a very comprehensible explanation.
Hi again shminux, this is my second question. First, I’m sorry if it’s going to be long-winded, I just don’t know enough to make it shorter :-)
It might be helpful if you can get your hands on the August 3 issue of Science (since you’re working at a university perhaps you can find one laying around), the article on page 536 is kind of the backdrop for my questions.
[Note: In the following, unless specified, there are no non-gravitational charges/fields/interactions, nor any quantum effects.]
(1) If I understand correctly, when two black holes merge the gravity waves radiated carry the complete information about (a) the masses of the two BHs, (b) their spins, (c) the relative alignment of the spins, and (d) the spin and momentum of the system, i.e. the exact positions and trajectories before (and implicitly during and after) the collision.
This seems to conflict with the “no-hair” theorem as well as with the “information loss” problem. (“Conflict” in the sense that I, personally can’t see how to reconcile the two.)
For instance, the various simulations I’ve seen of BH coalescence clearly show an event horizon that is obviously not characterized only by mass and spin. They quite clearly show a peanut-shape event horizon turning gradually into an ellipsoid. (With even more complicated shapes before, although there always seem to be simulation artifacts around the point where two EHs become one in every simulation I saw.) The two “lobes” of the “peanut EH” seem to indicate “clearly” that there are two point masses moving inside, which seems to contradict the statement that you can discern no structure through an EH.
(In jocular terms, I’m pretty sure one can set-up a very complex scenario involving millions of small black-holes coalescing with a big one with just the right starting positions that the EH actually is shaped like hair at some point during the multi-merger. I realize that’s abusing the words, but still, what is the “no-hair theorem” talking about, given that we can have EHs with pretty much arbitrary shape?)
In the same way, I don’t quite get the “information loss paradox” either. Take the simple scenario of an electron and a positron annihilating: in come two particles (coincidentally, they don’t have “hair” either), out come two photons, in other words a “pair” of electromagnetic waves. (Presumably, gravity waves would be generated as well, though since most physics seems to ignore those I presume I’m allowed to, as well.) There are differences, but the scenario seem very similar to black hole merger. Nobody seems to worry about any information loss in that case—basically, there isn’t, as all the information is carried by the leaving EM waves—so why exactly is it a problem with black holes? That is, what is the relevant difference?
[Note: if electrons and annihilation pose problems because of quantum effects, one can make up a completely classical scenario with similar behavior, using concepts no more silly than point masses and rigid rods. I just picked this example because it’s easy to express, and people actually think about it so “why don’t they worry about information loss” makes sense.]
(2) As far as I understand, exactly what happens in (1) also happens when something that is not a black hole falls into one. Take a particle (an object with small mass, small size but too low density to have an EH of its own, no internal structure other than the mass distribution inside it) falling spirally into a BH. AFAIK, this will generate almost exactly the same kind of gravitational waves that would be generated by an in-falling (micro-) black-hole with the same mass, with the only difference being that the waves will have slightly different shape because the density of the falling particle is lower (thus the mass distribution is slightly fuzzier).
Even though the falling particle doesn’t have an EH of its own, AFAIK the effects will be similar, i.e. the black hole’s EH will also form a small bump where the particle hits it, and will then oscillate a bit and radiate gravitational waves until it settles. Like in case (1) above, all the information regarding the particle’s mass and spin should be carried by the gross amplitude and phase of the waves, and the information about the precise shape of the particle (how its mass distribution differs from a point-mass like a micro–black hole) should be carried in the small details of the wave shapes (the tiny differences from how the waves would look if it were a micro–black hole that fell).
(3) Even better, if the particle and/or black hole also has electric charge, as far as I can tell the electro-magnetic field should also contain waves, similar to the electron/positron annihilation mentioned above, that carries all relevant information about electro-magnetic state of the particles before, during and after the “merger” (well, accretion in this case) in the same way the gravitational waves carry information about mass and spin.
So, as far as I can tell, coalescence and accretion seem to behave very similarly to other phenomena where information loss isn’t (AFAIK) regarded as an issue, and do so even when other forces than gravity are involved. In other words, it seems like all the information is not lost, it’s just “reflected” back into space. I’m not saying that it’s not an issue and all physicists are idiots, I’m just asking what is the difference.
(I have seen explanations of the information loss paradox that don’t cause my brain to raise these questions, but they’re all expressed in very different terms—entropy and the like—and I couldn’t manage to translate in “usual” terms. It’s a bit like using energy conservation to determine the final state of a complex mechanical system. I don’t contradict the results, I just want help figuring out in general terms what actually happens to reach that state.)
I’ll quickly address the no-hair issue. The theorem states only that a single stationary electro-vacuum black hole in 3+1 dimensions can be completely described by just its mass, angular momentum and electric charge. It says nothing about non-stationary (i.e. evolving in time) black holes. After the dust settles and everything is emitted, the remaining black hole has “no hair”. Furthermore, this is a result in classical GR, with no accounting for quantum effects, such as the Hawking radiation.
The information loss problem for black holes is a quantum issue. If the Hawking radiation produced during black hole evaporation were truly thermal, then that would mean that the details of the black hole’s quantum state are being irreversibly lost, which would violate standard quantum time evolution. People now mostly think that the details of the state live on, in correlations in the Hawking radiation. But there are no microscopic models of a black hole which can show the mechanics of this. Even in string theory, where you can sometimes construct an exact description of a quantum black hole, e.g. as a collection of branes wrapped around the extra dimensions, with a gas of open strings attached to the branes, this still remains beyond reach.
If the Hawking radiation produced during black hole evaporation were truly thermal, then that would mean that the details of the black hole’s quantum state are being irreversibly lost, which would violate standard quantum time evolution.
OK, I know that’s a quite different situation, but just to clarify: how is that resolved for other things that radiate “thermally”? E.g., say we’re dealing with a cooling white dwarf, or even a black and relatively cold piece of coal. I imagine that part of what it radiates is clearly not thermal, but is all radiation “not truly thermal” when looked at in quantum terms? Is the only relevant distinction the fact that you can discern its internal composition if you look close enough, and can express the “thermal” radiation as a statistic result of individual quantum state transitions?
From a somewhat different direction: if all details about the quantum state of the matter before it falls into the black hole are “reflected” back into the universe by gravitational/electromagnetic waves (basically, particles) during formation and accretion, what part of QM prevents the BH to have no state other than mass+spin+temperature?
In fact, I think the part that bothers me is that I’ve seen no QM treatment of BH that looks at the formation and accretion, they all seem to sort of start with an existing BH and somehow assume that the entropy of something thrown into the BH was captured by it. The relevant Wikipedia page starts by saying
The only way to satisfy the second law of thermodynamics is to admit that black holes have entropy. If black holes carried no entropy, it would be possible to violate the second law by throwing mass into the black hole.
But nobody seems to mention the entropy carried by the radiation released during accretion. I’m not saying they don’t, just that I’ve never seen it discussed at all. Which seems weird, since all (non-QM) treatments of accretion I’ve seen suggest (as I’m saying above) that a lot of information (and as far as I can tell, all of it) is actually radiated before the matter ever reaches the EH. To a layman it sounds like discussing the “cow-loss paradox” from a barn without walls...
how is that resolved for other things that radiate “thermally”?
For something other than a black hole, quantum field theory provides a fundamental description of everything that happens, and yes, you could track the time evolution for an individual quantum state and see that the end result is not truly thermal in its details.
But Hawking evaporation lacked a microscopic description. Lots of matter falls into a small spatial volume; an event horizon forms. Inside the horizon, everything just keeps falling together and collapses into a singularity. Outside the horizon, over long periods of time the horizon shrinks away to nothing as Hawking radiation leaks out. But you only have a semiclassical description of the latter process.
The best candidate explanation is the “fuzzball” theory, which says that singularities, and even event horizons, do not exist in individual quantum states. A “black hole” is actually a big ball of string which extends out to where the event horizon is located in the classical theory. This ball of string has a temperature, its parts are in motion, and they can eventually shake loose and radiate away. But the phase space of a fuzzball is huge, which is why it has a high entropy, and why it takes exponentially long for the fuzzball to get into a state in which one part is moving violently enough to be ejected.
That’s the concept, and there’s been steady progress in realizing the concept. For example, this paper describes Hawking radiation from a specific fuzzball state. One thing about black hole calculations in string theory is that they reproduce semiclassical predictions for a quantum black hole in very technical ways. You’ll have all the extra fields that come with string theory, all the details of a particular black hole in a particular string vacuum, lots of algebra, and then you get back the result that you expected semiclassically. The fact that hard complicated calculations give you what you expect suggests that there is some truth here, but there also seems to be some further insight lacking, which would compactly explain why they work.
nobody seems to mention the entropy carried by the radiation released during accretion
The entropy of the collapsing object jumps enormously once the event horizon forms. Any entropy lost before that is just a detail.
From a string-theory perspective, the explanation of the jump in entropy would be something like this: In string theory, you have branes, and then strings between branes. Suppose you have a collection of point-branes (“D0-branes”) which are all far apart in space. In principle, string modes exist connecting any two of these branes, but in practice, the energy required to excite the long-range connections is enormous, so the only fluctuations of any significance will be strings that start and end on the same brane.
However, once the 0-branes are all close to each other, the energy required to excite an inter-brane string mode becomes much less. Energy can now move into these formerly unoccupied modes, so instead of having just N possibilities (N the number of branes), you now have N^2 (a string can start on any brane and end on any other brane). The number of dynamically accessible states increases dramatically, and thus so does the entropy.
nobody seems to mention the entropy carried by the radiation released during accretion
The entropy of the collapsing object jumps enormously once the event horizon forms. Any entropy lost before that is just a detail.
OK, that’s the part that gives me trouble. Could you point me towards something with more details about this jump? That is, how it was deduced that the entropy rises, that it is big rise, and that the radiation before it is negligible? An explanation would be nice (something like a manual), but even a technical paper will probably help me a lot (at least to learn what questions to ask). A list of a dozen incremental results—which is all I could find with my limited technical vocabulary—would help much less, I don’t think I could follow the implications between them well enough.
The conclusion comes from combining a standard entropy calculation for a star, and a standard entropy calculation for a black hole. I can’t find a good example where they are worked through together, but the last page here provides an example. Treat the sun as an ideal gas, and its entropy is proportional to the number of particles, so it’s ~ 10^57. Entropy of a solar-mass black hole is the square of solar mass in units of Planck mass, so it’s ~ 10^76. So when a star becomes a black hole, its entropy jumps by about 10^20.
What’s lacking is a common theoretical framework for both calculations. The calculation of stellar entropy comes from standard thermodynamics, the calculation of black hole entropy comes from study of event horizon properties in general relativity. To unify the two, you would need to have a common stat-mech framework in which the star and the black hole were just two thermodynamic phases of the same system. You can try to do that in string theory but it’s still a long way from real-world physics.
For what I was saying about 0-branes, try this. The “tachyon instability” is the point at which the inter-brane modes come to life.
I have some black hole questions I’ve been struggling with for a week (well, years actually, I just thought about it more than usual during the last week or so) that I couldn’t find a satisfactory explanation for. I don’t think I’m asking about really unknown things, rather all explanations I see are either pop-sci explanations that don’t go deep enough, or detailed descriptions in terms of tensor equations that are too deep for what math I remember from university. I’m hoping that you could hit closer to the sweet spot :-)
I’ll split this into two comments to simplify threading. This first one is sort of a meta question:
I think I understand the what of the image. What I don’t quite get is the when and where of the thing.
That is, given that time and space bend in weird and wonderful ways around the black holes, and more importantly, they bends differently at different spots around them, what exactly are the X, Y and Z coordinates that are projected to the image plane (and, in the case of the video, the T coordinate that is “projected” on the duration of the video), given that the object in the image(s) is supposed to display the shape of time and space?
The closest I got trying to find answers:
(1) I saw Penrose diagrams of matter falling into a black hole, though I couldn’t find one of merging black holes. I couldn’t manage to imagine what one would look like, and I’m not quite sure it makes sense to ask for one: Since the X coordinate in a Penrose diagram is supposed to be distance from the singularity, I don’t see how you can put two of those, closing to each other, in one picture. Also, my brain knotted itself when trying to imagine more than one “spot” where space turns into time, interacting. On the other hand, that does look a bit like the coalescence simulations I’ve seen, so I might not be that far from the truth.
(2) I suppose the images might be space-like slices through the event, perhaps separated by equal time-like intervals at infinity in the case of the video. I don’t want to speculate more, in case I’m really far from the mark, so I’ll wait for an answer first.
(In case it helps with the answer: I do know what an integral is (including path, surface, and volume integrals), though I probably can’t do much with a complicated one mathematically. Similarly for derivatives, gradient, curl and divergence, though I have to think quite carefully to interpret the last two. If you say “manifold” and don’t have a good picture my eyes tend to glaze over, though. I sort of understand space curvature and frame-dragging, when they’re not too “sharp”, qualitatively if not quantitatively. I can visualize either of them—again, as long as they’re not “sharp” enough to completely reverse space and time dimensions; i.e., I have an approximate idea of what happens when you’re close to an event horizon, but not what goes on as you “cross” one. (Actually, I’m not sure I understand what “crossing an EH” means, again it’s the “when” and “where” the seem to be the trouble rather than the “what”; most simple explanations tend to indicate that there’s not much of a “what”, as in “nothing much happens as you cross one that doesn’t happen just before or just after”.) I can’t quite visualize a general tensor field, but when you split the Riemann tensor into tidal and frame-dragging components I can interpret the tendex and vortex lines on a well-drawn diagram if I think carefully.)
I saw Penrose diagrams of matter falling into a black hole, though I couldn’t find one of merging black holes.
I’ll try to draw one and post it, might take some time, given that you need more dimensions than just 1 space + 1 time on the original Penrose diagram, because you lose spherical symmetry. The head-on collision process still retains cylindrical symmetry, so a 2+1 picture should do it, represented by a 3D Penrose diagram, which is going to take some work.
I can’t believe nobody needed to do that already. Even if people who can draw one don’t need it because they do just fine with the equations, I’d have expected someone to make one just for fun...
Now, if the Sun gets lighter, the planets do drift away so they have more (i.e. less negative) potential energy, but this is compensated by the kinetic energy of particles escaping the Sun… or something.
That’s right. The total energy of Sun+planets+escaped matter is classically conserved. Fortunately, the velocities and gravitational fields are small enough for the Newtonian gravity to be a very good approximation, so there are no relativistic complications.
I’m not an expert in general relativity, and I hear that it’s non-trivial to define the total energy of a system when gravity is non-negligible, but the local conservation of energy and momentum does still apply.
That’s true, the total energy in GR is only defined for a system with an “asymptotic time translation symmetry”, but most isolated systems are like that (what happens far away from massive objects is not significantly affected by the details of the orbital motion and such). There is a marginal quality wiki article on the subject.
Since we are experimenting here… I have a PhD in theoretical physics (General Relativity), and I’d be happy to help out with any questions in my area.
This Reddit post says things like:
and:
When I read this, I believed that it was wrong (but well-written, making it more dangerous!). (However, he described Gravity Probe B’s verification of the geodetic effect correctly.)
Wikipedia says:
And it cites http://jila.colorado.edu/~ajsh/insidebh/schw.html which says:
This explanation agrees with everything I know (when hovering outside the event horizon, you are accelerating instead of being in free fall).
Can you confirm that the Reddit post was incorrect, and Wikipedia and its cited link are correct?
The last two quotes are indeed correct, and the reddit one is a mix of true and false statements.
To begin with, the conclusion subtly replaces the original premise of arbitrarily high velocity with arbitrarily high acceleration. (Confusing velocity and acceleration is a Grade 10 science error.) Given that one cannot accelerate to or past the speed of light, near-infinite acceleration engine is indeed of no use inside a black hole. However, arbitrarily high velocity is a different matter. It lets you escape from inside a black hole horizon. Of course, going faster than light brings a host of other problems (and no, time travel is not one of them).
This is true if you hover above the horizon, but false if you fall freely. In the latter case you will see some distortion, but nothing as dramatic.
This is false if you travel slower than light. You still see basically the same picture as outside, at least for a while longer.
If you have a magical FTL spaceship, what you see is not at all easy to describe. For example, in your own frame of reference, you don’t have mass or energy, only velocity/momentum, the exact opposite of what we describe as being stationary. Moreover, any photon that hits you is perceived as having negative energy. Yet it does not give or take any of your own energy (you don’t have any in your own frame), it “simply” changes your velocity.
I cannot comment on the Alice and Bob quote, as I did not find it in the link.
Actually, I can talk about black holes forever, feel free to ask.
Awesome, thanks.
I swear it was there, but now I can’t find it either.
I’d be interested to hear your opinion of Gravity Probe B.
Excellent! That happens to be a subject I’m very interested in.
Here are two questions, to start:
1. Do you have a position in the philosophical debate about whether “general covariance” has a “physical” meaning, or is merely a property of the mathematical structure of the theory?
2. How can the following (from “Mach’s Principle: Anti-Epiphenomenal Physics”) be true:
given that it implies that the electromagnetic force (which is what causes your voluntary movements, such as “spinning your arms around”) can be transformed into gravity by a change of coordinates? (Wouldn’t that make GR itself the “unified field theory” that Einstein legendarily spent the last few decades of his life searching for, supposedly in vain?)
Yeah, I recall looking into this early in my grad studies. I eventually realized that the only content of it is diffeomorphism invariance, i.e. that one should be able to uniquely map tensor fields to spacetime points. The coordinate representation of these fields depends on the choice of coordinates, but the fields themselves do not. In that sense the principle simply states that the relation spacetime manifold → tensor field is a function (surjective map). For example, there is a unique metric tensor at each spacetime point (which, incidentally, precludes traveling into one’s past).
I would also like to mention that the debate “about whether “general covariance” has a “physical” meaning, or is merely a property of the mathematical structure of the theory” makes no sense to me as an instrumentalist (I consider the map-territory moniker an oft convenient model, not some deep ontological thing).
This is false, as far as I can tell. The frame dragging effect is not at all related to gravitational radiation. The Godel universe is an example of an extreme frame dragging due to being filled with spinning pressureless perfect fluid, and there are no gravitational waves in it.
Well, yeah, this is an absurd conclusion. The only thing GR says that matter creates spacetime curvature. A spinning spacetime has to correspond to spinning matter. And spinning is not relative, but quite absolute, it cannot be removed by a choice of coordinates (for example, the vorticity tensor does not vanish no matter what coordinates you pick). So Mach is out of luck here.
May I ask you which is exactly your (preferred) subfield of work? What are the most important open problems in that field that you think could receive decisive insight (both theoretically and experimentally) in the next 10 years?
My research was in a sense Abbott-like: how a multi-dimensional world would look to someone living in the lower dimensions. It is different from the standard string-theoretical approach of bulk-vs-brain, because it is non-perturbative. I can certainly go into the details of it, but probably not in this comment.
Caveat: I’m not in academia at this point, so take this with a grain of salt.
Dark energy (not to be confused with Dark matter) is a major outstanding theoretical problem in GR. As it happens, it is also an ultimate existential risk, because it limits the amount of matter available to humanity to “only” a few galaxies, due to the accelerating expansion of the universe. The current puzzle is not that dark energy exists, but why there is so little of it. A model that explains dark energy and makes new predictions might even earn the first ever Nobel prize in theoretical GR, if such predictions are validated.
That the expansion of the universe is accelerating is a relatively new discovery (1998), so there is a non-negligible chance that there will be new insights into the issue on a time frame of decades, rather than, say, centuries.
In observations/experiments, it is likely that gravitational waves will be finally detected. There is also a chance that Hawking radiation will be detected in a laboratory setting from dumb holes or other black-hole analogs.
This looks really interesting, any material you can suggest on the subject? I was a particle physics phenomenologist until last year, so proper introductory academic paper should be ok.
And this looks very fascinating, too. Thanks a lot for your answers.
One of the original papers, mostly the Killing reduction part. You can probably work your way through the citations to something you find interesting.
Thank you again, it looks like a good starting point.
I’ve never understood how going faster can make time go slower, thereby explaining why light always appears to have the same velocity.
If I’m moving in the opposite direction to light, and if there was no time slowing down, then the light would appear to go faster than normal from my perspective. Add in the effects of time slowing down, and light appears to be going at the same speed it always does. No problem yet. But if I’m moving in the same direction as the light, and time doesn’t slow down, then it would appear to be going slower than normally, so the slowing down of time should make it look even slower, not give it the speed we always observe it in.
What am I missing?
This Reddit comment giving a lay explanation for the constant lightspeed thing was linked around a lot a while ago. The very short version is to think of everything being only ever able to move at the exact single speed c in a four-dimensional space, so whenever something wants to have velocity along a space axis, they need to trade off some from along the the time axis to keep the total velocity vector magnitude unchanged.
I like this way of thinking of it, so much simpler than the usual explanations.
That is a very good explanation for the workings of time, thank you very much for that.
But it doesn’t answer my real question. I’ll try to be a bit more clear.
Light is always observed at the same speed. I don’t think I’m so crazy that I imagined reading this all over the place on the internet. The explanation given for this is that the faster I go, the more I slow down through time, so from my reference frame, light decelerates (or accelerates? I’m not sure, but it actually doesn’t matter for my question, so if I’m wrong, just switch them around mentally as you read).
So let’s say I’m going in a direction, let’s call it “forward”. If a ball is going “backward”, then from my frame of reference, the ball would appear to go faster than it really is going, because its relative speed = its speed—my speed. This is also true for light, though the deceleration of time apparently counters that effect by making me observe it slower by the precise amount to make it still go at the same speed.
Now take this example again, but instead send the ball forward like me. From my frame of reference, the ball is going slower than it is in reality, again because its relative speed = its speed—my speed. The same would apply to light, but because time has slowed for me, so has the light from my perspective. But wait a second. Something isn’t right here. If light has slowed down from my point of view because of the equation “relative speed = its speed—my speed”, and time slowing down has also slowed it, then it should appear to be going slower than the speed of light. But it is in fact going precisely at the speed of light! This is a contradiction between the theory as I understand it and reality.
My god, that is probably extremely unclear. The number of times I use the words speed and time and synonyms… I wish I could use visual aids.
Also, I just thought of this, but how does light move through time if it’s going at the speed of light? That would give it a velocity of zero in the futureward direction (given the explanation you have linked to), which would be very peculiar.
Anyway, thanks for your time.
Perhaps I’m reading this wrong, but it seems you’re assuming that time slowing down is an absolute, not a relative, effect. Do you think there is an absolute fact of the matter about how fast you’re moving? If you do, then this is a big mistake. You only have a velocity relative to some reference frame.
If you don’t think of velocity as absolute, what do you mean by statements like this one:
There is no absolute fact of the matter about whether time has slowed for you. This is only true from certain perspectives. Crucially, it is not true from your own perspective. From your perspective, time always moves faster for you than it does for someone moving relative to you.
I really encourage you to read the first few chapters of this: http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/index.html
It is simply written and should clear up some of your confusions.
Maybe this angle will help: “relative speed = its speed—my speed” is an approximate equation. The true one is relative speed = (its speed—my speed)/(1-its speed * my speed / c^2). Let one of the two speeds = c, and the relative speed is also c.
Thanks for your answer, this equation will make it easier to explain my problem.
Let’s say a ball is going at the speed of c/4, and I’m going at a speed of c/2. According to the approximate equation, before the effects of time slowing down are taken into account, I would be going at a speed of -c/4. Now if you take into account time slowing down (divide -c/4 by the (1-its speed*...)), you get a speed of −2c/7.
So that was the example when I’m going in the same direction as the ball. Now let’s say the ball is still going at a speed of c/4, but I’m now going at a speed of -c/2. Using the approximate equation: 3c/4. Add in time slowing down: 2c/3.
So the two pairs are (-c/4, −2c/7) and (3c/4,2c/3). Let’s compare these values.
For the first tuple, when I’m going in the same direction as the ball, -c/4 > −2c/7. This means that −2c/7 is a faster speed in the negative direction (multiply both sides by −1 and you get c/4<2c/7), so from the c/2 reference frame, after the time slow effect, the observed speed of the ball is greater than it would be without the time slow down. So far so good.
For the second tuple, however, when I’m going in the opposite direction of the ball, 3c/4 > 2c/3. So from the -c/2 reference frame, after the time slow effect, the ball appears to be going slower than it would if time didn’t slow down.
But didn’t the first tuple show that the ball is supposed to appear to go faster given the time slow effect? Does this mean that time slows down when I’m going in the same direction as the ball, and it accelerates when I’m going in the opposite direction of the ball? Or does it mean that the modification of the approximate equation which gives the correct one is not in fact the effects of time slowing down? Or am I off my rocker here?
This might be just a confusion between speed and velocity. In one case relative velocity (not speed), in fractions of the speed of light, is −1/4 (classically) vs −2/7 (relativity). In the other case it is 3⁄4 vs 2⁄3. In both cases the classical value is higher than the relativistic value.
That the classical value is always higher than the time-slowed value is precisely what doesn’t make sense to me.
If −1/4 is the classical value, and −2/7 is the relativity value, −2/7 is a faster speed than −1/4, even though −1/4 is a bigger number. So the relativity speed is faster. However, if 3⁄4 is the classical value, and 2⁄3 is the relativity value, 3⁄4 is a faster speed relative to me than 2⁄3. So in this case, the classical speed is faster.
So when I have a speed of 1⁄2, time slowing down makes the relative speed of the ball greater. And when I have a speed of −1/2, time slowing down makes the relative speed of the ball smaller. More generally, this can be described by my direction relative to the ball. If I’m moving in the same direction as the ball, time slowing down makes it appear to go faster than the classical speed. However, if I’m going in the opposite direction of the ball, then it appears to go slower than the classical speed. And that doesn’t make sense. Time slowing down should always make the ball appear to go faster than the classical speed, and the effects of time slowing down should definitely should not depend on my direction relative to the ball.
When your subjective time slows down, things around you seem to move faster relative to you, not slower. So your time slowing down would make the light seem to speed up for you.
That’s right. From the point of view of the photon it is created and destroyed in the same instant.
To add to that, it is a relatively common classroom experiment to show trails in gas left by muons from cosmic radiation. These muons are travelling at about 99.94% of the speed of light, which is quite fast but the distance from the upper atmosphere where they originate to the classroom is long enough that it takes the muon several of its half-lives to reach the clasroom—by our measurement of time, at least. We should expect them to have decayed before the reach the classroom, but they don’t!
By doing the same experiment at multiple elevations we can see that the rate of muon decay is much lower than non-relativistic theories would suggest. However, if time dilation due to their large speed is taken into account then we get that the muons ‘experience’ a much shorter trip from their point of view—sufficiently short that they don’t decay! That they have reached the classroom is evidence (given a bunch of other knowledge about decay and formation of muons) that is easily observed for time dilation.
Also! Time dilation is surprisingly easy to derive. I recommend that you attempt to derive it yourself if you haven’t already! I give you this starting point:
A) The speed of light is constant and independent of observers
B) A simple way to analyze time is to consider a very simple clock: two mirrors facing towards each other with a photon bouncing back and forth between the two. The cycles of the photon denotes the passage of time.
C) What if the clock is moving?
D) Draw a diagram
Okay, but if it’s not moving through time, it only exists in the point in time in which it was created, no? So it would only be present for one moment in time where it would move constantly until it’s destruction. We would therefore observe it as moving at infinite speed.
Remember the thing from the Reddit comment about everything always moving at the constant speed c. The photon has its velocity at a 90° angle from the time axis of space-time, but that’s still just a velocity of magnitude c. Can’t get infinite velocity because of the rule that you can’t change your time-space speed ever.
Things get a bit confusing here, since the photon is not moving through time at all in its own frame of reference, but in the frame of reference of an outside observer, it’s zipping around at speed c. Your intuition seems to be not including the bit about time working differently in different frames of reference.
Sorry if I’m being annoying, but the light is not moving through time. So it should not appear at different points in time. If I’m not moving forward, and you are, and you’re looking directly to your side, then you’ll only see me while I’m next to you. And if I start moving from side to side, then I won’t impact you unless you’re right next to me. Change “forward” with “futureward” and “side” to “space”, and you get my problem with light having zero futureward speed.
My big assumption here is that even though things appear to behave differently from different frames of reference, there is in fact an absolute truth, an absolute way things are behaving. I don’t think that’s wrong, but if it is, I’ve got a long way to go before understanding relativity.
Since it’s not moving through time, light moves only through space. It never appears at different points in time. You can “see” this quite easily if you notice that you can’t encounter the same photon twice, even if you would have something that could detect its passing without changing it, unless you alter its path with mirrors or curved space, because you’d need to go faster than light to catch up with it after it passes you the first time.
In fact, if memory serves, in relativity two events are defined to be instantaneous if they are connected by a photon. For example, if a photon from your watch hits your eye and tells you it’s exactly 5 PM, and another photon hits your eye at the same time and tells you an atom decayed, then technically the atom decayed at exactly 5 PM. That is, in relativity, events happen exactly when you see them. On the other hand, the fact that two events are simultaneous for me may or may not (and usually aren’t) simultaneous for someone else, hence the word relativity.
(Even if you curve the photon, that just means that you pass twice through the same point in time. Think about it, if the photon can leave you and go back, it means you can see your “past you”, photons reflected off of your body into space and then coming back. Say the “loop” is three light-hours long. Since you can see the watch of the past you show 1PM at the same time you see your watch show 4PM, you simply conclude that the two events are simultaneous, from your point of view.)
I think what’s confusing is that we’re very often told things like “that star is N light years away, so since we’re seeing it now turning into a supernova, it happened N years ago”. That’s not quite a meaningless claim, but “ago” and “away” don’t quite mean the same thing they mean in relativistic equations. In relativity terms, for me it happened in 2012 because the events “I notice that the calendar shows 2012” and “the star blew up” are simultaneous from my point of view.
I don’t have good offhand ideas how to unpack this further, sorry. I’d have to go learn Minkowski spacetime diagrams or something to have a proper idea how you get from timeward-perpendicular spaceward movement into the 45 degree light cone edge, and probably wouldn’t end up with a very comprehensible explanation.
Final question: Could you please comment a bit on
http://lesswrong.com/lw/cwq/ask_an_experimental_physicist/7ba5 ?
Hi again shminux, this is my second question. First, I’m sorry if it’s going to be long-winded, I just don’t know enough to make it shorter :-)
It might be helpful if you can get your hands on the August 3 issue of Science (since you’re working at a university perhaps you can find one laying around), the article on page 536 is kind of the backdrop for my questions.
[Note: In the following, unless specified, there are no non-gravitational charges/fields/interactions, nor any quantum effects.]
(1) If I understand correctly, when two black holes merge the gravity waves radiated carry the complete information about (a) the masses of the two BHs, (b) their spins, (c) the relative alignment of the spins, and (d) the spin and momentum of the system, i.e. the exact positions and trajectories before (and implicitly during and after) the collision.
This seems to conflict with the “no-hair” theorem as well as with the “information loss” problem. (“Conflict” in the sense that I, personally can’t see how to reconcile the two.)
For instance, the various simulations I’ve seen of BH coalescence clearly show an event horizon that is obviously not characterized only by mass and spin. They quite clearly show a peanut-shape event horizon turning gradually into an ellipsoid. (With even more complicated shapes before, although there always seem to be simulation artifacts around the point where two EHs become one in every simulation I saw.) The two “lobes” of the “peanut EH” seem to indicate “clearly” that there are two point masses moving inside, which seems to contradict the statement that you can discern no structure through an EH.
(In jocular terms, I’m pretty sure one can set-up a very complex scenario involving millions of small black-holes coalescing with a big one with just the right starting positions that the EH actually is shaped like hair at some point during the multi-merger. I realize that’s abusing the words, but still, what is the “no-hair theorem” talking about, given that we can have EHs with pretty much arbitrary shape?)
In the same way, I don’t quite get the “information loss paradox” either. Take the simple scenario of an electron and a positron annihilating: in come two particles (coincidentally, they don’t have “hair” either), out come two photons, in other words a “pair” of electromagnetic waves. (Presumably, gravity waves would be generated as well, though since most physics seems to ignore those I presume I’m allowed to, as well.) There are differences, but the scenario seem very similar to black hole merger. Nobody seems to worry about any information loss in that case—basically, there isn’t, as all the information is carried by the leaving EM waves—so why exactly is it a problem with black holes? That is, what is the relevant difference?
[Note: if electrons and annihilation pose problems because of quantum effects, one can make up a completely classical scenario with similar behavior, using concepts no more silly than point masses and rigid rods. I just picked this example because it’s easy to express, and people actually think about it so “why don’t they worry about information loss” makes sense.]
(2) As far as I understand, exactly what happens in (1) also happens when something that is not a black hole falls into one. Take a particle (an object with small mass, small size but too low density to have an EH of its own, no internal structure other than the mass distribution inside it) falling spirally into a BH. AFAIK, this will generate almost exactly the same kind of gravitational waves that would be generated by an in-falling (micro-) black-hole with the same mass, with the only difference being that the waves will have slightly different shape because the density of the falling particle is lower (thus the mass distribution is slightly fuzzier).
Even though the falling particle doesn’t have an EH of its own, AFAIK the effects will be similar, i.e. the black hole’s EH will also form a small bump where the particle hits it, and will then oscillate a bit and radiate gravitational waves until it settles. Like in case (1) above, all the information regarding the particle’s mass and spin should be carried by the gross amplitude and phase of the waves, and the information about the precise shape of the particle (how its mass distribution differs from a point-mass like a micro–black hole) should be carried in the small details of the wave shapes (the tiny differences from how the waves would look if it were a micro–black hole that fell).
(3) Even better, if the particle and/or black hole also has electric charge, as far as I can tell the electro-magnetic field should also contain waves, similar to the electron/positron annihilation mentioned above, that carries all relevant information about electro-magnetic state of the particles before, during and after the “merger” (well, accretion in this case) in the same way the gravitational waves carry information about mass and spin.
So, as far as I can tell, coalescence and accretion seem to behave very similarly to other phenomena where information loss isn’t (AFAIK) regarded as an issue, and do so even when other forces than gravity are involved. In other words, it seems like all the information is not lost, it’s just “reflected” back into space. I’m not saying that it’s not an issue and all physicists are idiots, I’m just asking what is the difference.
(I have seen explanations of the information loss paradox that don’t cause my brain to raise these questions, but they’re all expressed in very different terms—entropy and the like—and I couldn’t manage to translate in “usual” terms. It’s a bit like using energy conservation to determine the final state of a complex mechanical system. I don’t contradict the results, I just want help figuring out in general terms what actually happens to reach that state.)
I’ll quickly address the no-hair issue. The theorem states only that a single stationary electro-vacuum black hole in 3+1 dimensions can be completely described by just its mass, angular momentum and electric charge. It says nothing about non-stationary (i.e. evolving in time) black holes. After the dust settles and everything is emitted, the remaining black hole has “no hair”. Furthermore, this is a result in classical GR, with no accounting for quantum effects, such as the Hawking radiation.
The information loss problem for black holes is a quantum issue. If the Hawking radiation produced during black hole evaporation were truly thermal, then that would mean that the details of the black hole’s quantum state are being irreversibly lost, which would violate standard quantum time evolution. People now mostly think that the details of the state live on, in correlations in the Hawking radiation. But there are no microscopic models of a black hole which can show the mechanics of this. Even in string theory, where you can sometimes construct an exact description of a quantum black hole, e.g. as a collection of branes wrapped around the extra dimensions, with a gas of open strings attached to the branes, this still remains beyond reach.
OK, I know that’s a quite different situation, but just to clarify: how is that resolved for other things that radiate “thermally”? E.g., say we’re dealing with a cooling white dwarf, or even a black and relatively cold piece of coal. I imagine that part of what it radiates is clearly not thermal, but is all radiation “not truly thermal” when looked at in quantum terms? Is the only relevant distinction the fact that you can discern its internal composition if you look close enough, and can express the “thermal” radiation as a statistic result of individual quantum state transitions?
From a somewhat different direction: if all details about the quantum state of the matter before it falls into the black hole are “reflected” back into the universe by gravitational/electromagnetic waves (basically, particles) during formation and accretion, what part of QM prevents the BH to have no state other than mass+spin+temperature?
In fact, I think the part that bothers me is that I’ve seen no QM treatment of BH that looks at the formation and accretion, they all seem to sort of start with an existing BH and somehow assume that the entropy of something thrown into the BH was captured by it. The relevant Wikipedia page starts by saying
The only way to satisfy the second law of thermodynamics is to admit that black holes have entropy. If black holes carried no entropy, it would be possible to violate the second law by throwing mass into the black hole.
But nobody seems to mention the entropy carried by the radiation released during accretion. I’m not saying they don’t, just that I’ve never seen it discussed at all. Which seems weird, since all (non-QM) treatments of accretion I’ve seen suggest (as I’m saying above) that a lot of information (and as far as I can tell, all of it) is actually radiated before the matter ever reaches the EH. To a layman it sounds like discussing the “cow-loss paradox” from a barn without walls...
For something other than a black hole, quantum field theory provides a fundamental description of everything that happens, and yes, you could track the time evolution for an individual quantum state and see that the end result is not truly thermal in its details.
But Hawking evaporation lacked a microscopic description. Lots of matter falls into a small spatial volume; an event horizon forms. Inside the horizon, everything just keeps falling together and collapses into a singularity. Outside the horizon, over long periods of time the horizon shrinks away to nothing as Hawking radiation leaks out. But you only have a semiclassical description of the latter process.
The best candidate explanation is the “fuzzball” theory, which says that singularities, and even event horizons, do not exist in individual quantum states. A “black hole” is actually a big ball of string which extends out to where the event horizon is located in the classical theory. This ball of string has a temperature, its parts are in motion, and they can eventually shake loose and radiate away. But the phase space of a fuzzball is huge, which is why it has a high entropy, and why it takes exponentially long for the fuzzball to get into a state in which one part is moving violently enough to be ejected.
That’s the concept, and there’s been steady progress in realizing the concept. For example, this paper describes Hawking radiation from a specific fuzzball state. One thing about black hole calculations in string theory is that they reproduce semiclassical predictions for a quantum black hole in very technical ways. You’ll have all the extra fields that come with string theory, all the details of a particular black hole in a particular string vacuum, lots of algebra, and then you get back the result that you expected semiclassically. The fact that hard complicated calculations give you what you expect suggests that there is some truth here, but there also seems to be some further insight lacking, which would compactly explain why they work.
Here’s a talk about fuzzballs.
The entropy of the collapsing object jumps enormously once the event horizon forms. Any entropy lost before that is just a detail.
From a string-theory perspective, the explanation of the jump in entropy would be something like this: In string theory, you have branes, and then strings between branes. Suppose you have a collection of point-branes (“D0-branes”) which are all far apart in space. In principle, string modes exist connecting any two of these branes, but in practice, the energy required to excite the long-range connections is enormous, so the only fluctuations of any significance will be strings that start and end on the same brane.
However, once the 0-branes are all close to each other, the energy required to excite an inter-brane string mode becomes much less. Energy can now move into these formerly unoccupied modes, so instead of having just N possibilities (N the number of branes), you now have N^2 (a string can start on any brane and end on any other brane). The number of dynamically accessible states increases dramatically, and thus so does the entropy.
OK, that’s the part that gives me trouble. Could you point me towards something with more details about this jump? That is, how it was deduced that the entropy rises, that it is big rise, and that the radiation before it is negligible? An explanation would be nice (something like a manual), but even a technical paper will probably help me a lot (at least to learn what questions to ask). A list of a dozen incremental results—which is all I could find with my limited technical vocabulary—would help much less, I don’t think I could follow the implications between them well enough.
The conclusion comes from combining a standard entropy calculation for a star, and a standard entropy calculation for a black hole. I can’t find a good example where they are worked through together, but the last page here provides an example. Treat the sun as an ideal gas, and its entropy is proportional to the number of particles, so it’s ~ 10^57. Entropy of a solar-mass black hole is the square of solar mass in units of Planck mass, so it’s ~ 10^76. So when a star becomes a black hole, its entropy jumps by about 10^20.
What’s lacking is a common theoretical framework for both calculations. The calculation of stellar entropy comes from standard thermodynamics, the calculation of black hole entropy comes from study of event horizon properties in general relativity. To unify the two, you would need to have a common stat-mech framework in which the star and the black hole were just two thermodynamic phases of the same system. You can try to do that in string theory but it’s still a long way from real-world physics.
For what I was saying about 0-branes, try this. The “tachyon instability” is the point at which the inter-brane modes come to life.
Hi shminux, thanks for your offer!
I have some black hole questions I’ve been struggling with for a week (well, years actually, I just thought about it more than usual during the last week or so) that I couldn’t find a satisfactory explanation for. I don’t think I’m asking about really unknown things, rather all explanations I see are either pop-sci explanations that don’t go deep enough, or detailed descriptions in terms of tensor equations that are too deep for what math I remember from university. I’m hoping that you could hit closer to the sweet spot :-)
I’ll split this into two comments to simplify threading. This first one is sort of a meta question:
Take for instance FIG. 1 from http://arxiv.org/pdf/1012.4869v2.pdf or the video at http://www.sciencemag.org/content/suppl/2012/08/02/337.6094.536.DC1/1225474-s1.avi
I think I understand the what of the image. What I don’t quite get is the when and where of the thing.
That is, given that time and space bend in weird and wonderful ways around the black holes, and more importantly, they bends differently at different spots around them, what exactly are the X, Y and Z coordinates that are projected to the image plane (and, in the case of the video, the T coordinate that is “projected” on the duration of the video), given that the object in the image(s) is supposed to display the shape of time and space?
The closest I got trying to find answers:
(1) I saw Penrose diagrams of matter falling into a black hole, though I couldn’t find one of merging black holes. I couldn’t manage to imagine what one would look like, and I’m not quite sure it makes sense to ask for one: Since the X coordinate in a Penrose diagram is supposed to be distance from the singularity, I don’t see how you can put two of those, closing to each other, in one picture. Also, my brain knotted itself when trying to imagine more than one “spot” where space turns into time, interacting. On the other hand, that does look a bit like the coalescence simulations I’ve seen, so I might not be that far from the truth.
(2) I suppose the images might be space-like slices through the event, perhaps separated by equal time-like intervals at infinity in the case of the video. I don’t want to speculate more, in case I’m really far from the mark, so I’ll wait for an answer first.
(In case it helps with the answer: I do know what an integral is (including path, surface, and volume integrals), though I probably can’t do much with a complicated one mathematically. Similarly for derivatives, gradient, curl and divergence, though I have to think quite carefully to interpret the last two. If you say “manifold” and don’t have a good picture my eyes tend to glaze over, though. I sort of understand space curvature and frame-dragging, when they’re not too “sharp”, qualitatively if not quantitatively. I can visualize either of them—again, as long as they’re not “sharp” enough to completely reverse space and time dimensions; i.e., I have an approximate idea of what happens when you’re close to an event horizon, but not what goes on as you “cross” one. (Actually, I’m not sure I understand what “crossing an EH” means, again it’s the “when” and “where” the seem to be the trouble rather than the “what”; most simple explanations tend to indicate that there’s not much of a “what”, as in “nothing much happens as you cross one that doesn’t happen just before or just after”.) I can’t quite visualize a general tensor field, but when you split the Riemann tensor into tidal and frame-dragging components I can interpret the tendex and vortex lines on a well-drawn diagram if I think carefully.)
I’ll try to draw one and post it, might take some time, given that you need more dimensions than just 1 space + 1 time on the original Penrose diagram, because you lose spherical symmetry. The head-on collision process still retains cylindrical symmetry, so a 2+1 picture should do it, represented by a 3D Penrose diagram, which is going to take some work.
Oh, thank you very much for the effort!
I can’t believe nobody needed to do that already. Even if people who can draw one don’t need it because they do just fine with the equations, I’d have expected someone to make one just for fun...
See the end of the second-last paragraph of this.
That’s right. The total energy of Sun+planets+escaped matter is classically conserved. Fortunately, the velocities and gravitational fields are small enough for the Newtonian gravity to be a very good approximation, so there are no relativistic complications.
That’s true, the total energy in GR is only defined for a system with an “asymptotic time translation symmetry”, but most isolated systems are like that (what happens far away from massive objects is not significantly affected by the details of the orbital motion and such). There is a marginal quality wiki article on the subject.