The firewall puzzle is the claim that, if information is ultimately conserved as black holes evaporate via Hawking radiation, then an infalling observer sees a ferocious wall of high-energy radiation as they fall through the event horizon. This is contrary to everything we’ve ever believed about black holes based on classical and semi-classical reasoning, so if it’s true it’s kind of a big deal.
The argument in favor of firewalls is based on everyone’s favorite spooky physical phenomenon, quantum entanglement. Think of a Hawking photon near the event horizon of a very old (mostly-evaporated) black hole, about to sneak out to the outside world. If there is no firewall, the quantum state near the horizon is (pretty close to) the vacuum, which is unique. Therefore, the outgoing photon will be completely entangled with a partner ingoing photon — the negative-energy guy who is ultimately responsible for the black hole losing mass. However, if information is conserved, that outgoing photon must also be entangled with the radiation that left the hole much earlier. This is a problem because quantum entanglement is “monogamous” — one photon can’t be maximally entangled with two other photons at the same time. (Awww.) The simplest way out, so the story goes, is to break the entanglement between the ingoing and outgoing photons, which means the state is not close to the vacuum. Poof: firewall.
You folks read about this some time ago in a guest post by Joe Polchinski, one of the authors (with Ahmed Almheiri, Don Marolf, and James Sully, thus “AMPS”) of the original paper. I’m just updating now to let you know: almost a year later, the controversy has not gone away.
You can read about some of the current state of play in An Apologia for Firewalls, by the above authors plus Douglas Stanford. (Those of us with good Catholic educations understand that “apologia” means “defense,” not “apology.”) We also had a physics colloquium by Joe at Caltech last week, where he masterfully explained the basics of the black hole information paradox as well as the recent firewall brouhaha. Caltech is not very good at technology (don’t let the name fool you), so we don’t record our talks, but Joe did agree to put his slides up on the web, which you can now all enjoy. Aimed at physics students, so there might be an equation or two in there.
Just to point out a couple of intriguing ideas that have come along in response to the AMPS proposal, one paper that has deservedly received a lot of attention is An Infalling Observer in AdS/CFT by Kyriakos Papadodimas and Suvrat Raju. They consider the AdS/CFT correspondence, which relates a theory of gravity in anti-de Sitter space to a non-gravitational field theory on its boundary. One can model black holes in such a theory, and see what the boundary field theory has to say about them. Papadodimas and Raju argue that they don’t see any evidence of firewalls. It’s suggestive, but like many AdS/CFT constructions, comes across as a bit of a black box; even if there aren’t any firewalls, it’s hard to pinpoint exactly what part of the original AMPS argument is at fault.
More radically, there was just a new paper by Juan Maldacena and Lenny Susskind, Cool Horizons for Entangled Black Holes. These guys have tenure, so they aren’t afraid of putting forward some crazy-sounding ideas, which is what they’ve done here. (Note the enormous difference between “crazy-sounding” and “actually crazy.”) They are proposing that, when two particles are entangled, there is actually a tiny wormhole connecting them through spacetime. This seems bizarre from a classical general-relativity standpoint, since such wormholes would instantly collapse upon themselves; but they point out that their wormholes are “highly quantum objects.” They claim there is evidence that such a conjecture makes sense, although they can’t confidently argue that it gets rid of the firewalls.
I suspect further work is required. Good times.
You’re still not seeing the big picture, Marko. Remember NIST have demonstrated optical clocks running at different rates at different elevations. Idealise that with parallel-mirror light clocks. The elephant isn’t “in two places at once when it goes to the end of time and back”, it’s in the room, and more and more people have spotted it. Look at those parallel-mirror light clocks. Once you learn to step out of your frame and look at all frames at once, everything changes. Go back to the equatorial light clocks. The speed of the infalling observer relates to clock rate differences, and his speed at some location cannot exceed the speed of light at that location. So if he makes it to the event horizon he isn’t moving, his light isn’t moving, and he can’t verify anything. Go back to SR and try claiming that the gedanken observer moving at c with respect to us sees his clock ticking normally because all frames are equally valid.
Shame you didn’t like the QG sketch. IMHO a well-defined mathematical formulation needs something like this to get off the ground. LQG has rambled on for decades going nowhere because its adherents don’t have any concept of how electromagnetism and gravity fit together.
Nice to talk to you Marko. I suspect though we’ll have to agree to differ. Such is life: if we all agreed about everything life would be very dull.
I read Space against Time in New Scientist.
“This does point to the fact that we may be missing something in our conceptual description”. says Steve Giddings.
You betchya.
“This allowed him, for example, to relax the restriction that nothing can travel through space-time faster than light”.
Red flag. Nothing travels through space-time. It’s a static all-times-at-once mathematical model. It’s an artefact that doesn’t actually exist. We draw worldlines in it to represent motion through space. We “time” this motion using something that… moves through space. Motion is king*.
“A lot of people have this intuition that in some sense the existence of these null directions might be more fundamental than space or time”
Those null directions don’t actually exist. Light moves. Only when it doesn’t, such as at the black hole event horizon, then there is no more space, and there is more time.
* You can use repeated Compton scattering to turn a photon into the motion of electrons. Keep doing it, and in the limit you have no wave energy and so no photon left. It has been completely converted into the motion of electrons. But you could have put that photon through pair production instead, and made an electron (and a positron). The bottom line is that the electron is made of motion. Ergo motion is king.
John Duffield wrote:
“The locally-measured speed of light is only constant because we use the local motion of light to define the second and the metre, which we then use… to measure the speed of light.”
It’s not just a matter of circular definitions–by the equivalence principle, a free-falling observer in a small region of spacetime should be able to define length and time using any method that can be used in an inertial frame in flat SR spacetime (for example, multiples of cesium oscillations for time and multiples of interatomic spacing in some crystalline solid for distance), and the speed of light should still work out to c when measured by this method, a prediction that obviously isn’t just trivially true by definition.
The crystal solid doesn’t help because metre doesn’t change Jesse. It’s “the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second.” When the light goes slower, the slower light and the bigger second cancel each other out, and the metre stays the same.
The free-falling observer always measures c to be 299,792,458 m/s, but we know that the coordinate speed of light varies in a non-inertial reference frame. We know that one 299,792,458 m/s is not the same as another. And we also know about the wave nature of matter. The free-falling observer doesn’t measure any change because whatever the wave speed is, he uses it to calibrate the clock he uses to measure wave speed. He might convince himself that time is going slower and waves aren’t, but his clock is not literally measuring “the flow of time”. He cannot open up his clock and see time flowing within it. All he sees is regular cyclic motion, of a crystal, or cogs, or hyperfine spin flips creating microwaves. So when the clock goes slower, it’s because that motion goes slower, not because of anything else.
“The crystal solid doesn’t help because metre doesn’t change Jesse. It’s “the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second.””
This is merely the latest conventional definition, it wasn’t defined this way at the time Einstein formulated his theory, and the fundamental physics doesn’t say anything about which definition you “should” use. And even if you do choose to define the speed of light this way, then it is still a nontrivial prediction that the freefalling observer will not see any changes in any local physical observations in her local inertial frame; for example, the theory predicts she’ll always get the same answer if she measures the number of cesium atom oscillations between the time a light ray departs from the cesium clock and the time it traverses X number of atoms in the crystal lattice, hits a mirror, and returns to the clock (assuming the time and distance are small so that the observations can be considered “local”).
Agreed, Jesse.
The problem comes when you take it to the limit. Imagine you have a gedanken telescope panning to keep the infalling observer in view. You see her and her light and her measurements going slower and slower, much as you would if she was an SR observer going faster and faster. In the limit she and her light and her measurements grind to a halt. She will not see any changes because she sees nothing.
Apply that to your MTW page and hopefully you’ll appreciate that going to the end of time and back is a fantasy that leads to an elephant in two places at once. And that a new time coordinate is another fantasy. When a clock is stopped, you cannot make it start ticking again by changing your coordinate system. Like I said, it’s like putting a stopped observer in front of a stopped clock and pretending that for her, everything carries on as normal. It doesn’t. She’s stopped, her clock is stopped, and that’s the way it’s going to stay, forever.
“Imagine you have a gedanken telescope panning to keep the infalling observer in view. You see her and her light and her measurements going slower and slower, much as you would if she was an SR observer going faster and faster. In the limit she and her light and her measurements grind to a halt. She will not see any changes because she sees nothing.”
OK, now imagine you are carrying a telescope in flat SR spacetime and using a rocket to experience constant proper acceleration, so that you have a Rindler horizon. As you watch an inertial observer “falling” towards the Rindler horizon, it is likewise true that “You see her and her light and her measurements going slower and slower”, so that she never actually appears to reach it no matter how long you wait, but presumably you don’t therefore conclude that in the limit as her distance from your Rindler horizon approaches zero, her measurements “grind to a halt” in some objective sense, or that she no longer continues to perceive things after she crosses it (but the only way you or anyone else can see what happened to her after she crossed the horizon is to cross it yourself, just like with a black hole event horizon). Your pet theories aside, do you have any actual physical or logical argument for why others should agree with you that the slowdown is any more objective in the case of a black hole event horizon than it is in the case of a Rindler horizon? (assuming classical GR, leaving aside quantum arguments for firewalls)
The Rindler horizon is a mere artefact. I’m not the accelerating observer, I’m watching her through my gedanken telescope, and there is no cone of darkness following her. It just isn’t in the same league as a black hole.
Re: Your pet theories aside, do you have any actual physical or logical argument for why others should agree with you that the slowdown is any more objective in the case of a black hole event horizon than it is in the case of a Rindler horizon?
This is not some pet theory, this is general relativity. The slowdown is objective. Check out the NIST optical clock, see this and this where you can read this: “if one clock in one lab is 30 centimeters higher than the clock in the other lab, we can see the difference in the rates they run at”. All observers agree that the lower clock goes slower. Oh, and it’s an optical clock. Parallel-mirror light-clocks will do the same. This gif is idealised and exaggerated, but it is not misleading:
parallel-mirror light-clocks
Look at the gif, Jesse. Do not fool yourself that those two light pulses are moving at the same speed, because they’re not. There is no time flowing through this or any other clock. Ellis was wrong, Einstein was right. The speed of light varies with gravitational potential. A light clock can’t go slower than stopped. And you cannot make a stopped clock tick by adopting a fantasy coordinate system that does a hop skippity jump over the end of time.
The Rindler horizon is a mere artefact. I’m not the accelerating observer, I’m watching her through my gedanken telescope, and there is no cone of darkness following her.
My gedanken was that you (and the telescope) were the accelerating observer, not the inertial one. Remember, in this analogy the accelerating observer is analogous to the observer hovering above the event horizon (so neither one crosses the relevant horizon, and both must experience continual proper acceleration to avoid falling in), the inertial observer is analogous to the observer in freefall approaching it (so both experience zero proper acceleration, and both should experience crossing the horizon according to SR/GR). So this is a non-response to my scenario, like if I had responded to your black hole question by saying “I’m not the observer hovering above the horizon, I’m the falling observer watching the hovering one through the telescope, there is no cone of darkness following her”.
This is not some pet theory, this is general relativity. The slowdown is objective. Check out the NIST optical clock, see this and this where you can read this: “if one clock in one lab is 30 centimeters higher than the clock in the other lab, we can see the difference in the rates they run at”. All observers agree that the lower clock goes slower.
The ratio between the rates the clocks are ticking at any given moment is not objective, since that depends on the simultaneity convention. In general relativity, the only objective comparisons are local ones like “what does clock A read at the moment it receives the signal from clock B saying that clock B has elapsed 200 nanoseconds”. And by the standard of local comparisons like this, it’s equally “objective” that clocks that maintain different constant Rindler distances from the Rindler horizon (which require that they have different proper accelerations) tick differently, with the clock closer to the horizon elapsing less time than the clock farther from the horizon over any given interval (for example, if the closer one sends one signal when it reads 0 seconds and another when it reads 10, the farther one might elapse 20 seconds between receiving those two signals, then if the closer one sent a third signal 10 seconds after the second the farther one would have to wait another 20 seconds to receive it, etc.). So again, you have failed to explain why your argument couldn’t equally well be applied to make the case that time objectively stops at the Rindler horizon–saying the Rindler horizon is a “mere artefact” is not a physical argument, it’s just a denigrating rhetorical phrase, unless you can provide a precise physical definition of when a horizon is an “artefact” and when it isn’t.
“Ellis was wrong, Einstein was right. The speed of light varies with gravitational potential. ”
Ellis and Einstein would have no real physical disagreement, this is only a matter of the convention of how you choose to define the phrase “speed of light”. I’m sure both would agree that if you define it in terms of the coordinate speed of a light beam in some non-inertial coordinate system (in GR or SR), the the speed of light can vary (and the way it varies would depend entirely on the choice of coordinate system, nowhere in Einstein’s theory will you find any mathematics that gives you an objective coordinate-independent answer to the ratio of light’s speed at different distances from a black hole); I’m equally sure both would agree that if you define it in terms of local measurements in an infinitesimally small freefalling inertial system, they would both agree the speed of light doesn’t vary from one location to another.
It’s not a non-response, Jesse. It’s an attempt to make you distinguish artefact from objective reality. Your gedanken scenario features an accelerating observer, but there is nothing following behind him. He merely can’t see some things behind him. This is very different to the black hole. It’s there, it’s massive, it pulls the observer in. And the inertial observer is not analogous to the observer in freefall, because the former is subject to constant SR time dilation while the latter is subject to decreasing gravitational potential and increasing GR time dilation. The objective fact is that optical clocks go slower when they’re lower. No observer sees them going faster. And defining the speed of light to be constant in a gravitational field is not something Einstein would agree with. He said on repeated occasions that the SR postulate did not apply to GR:
1911: If we call the velocity of light at the origin of co-ordinates cₒ, then the velocity of light c at a place with the gravitation potential Φ will be given by the relation c = cₒ(1 + Φ/c²)
1912 : On the other hand I am of the view that the principle of the constancy of the velocity of light can be maintained only insofar as one restricts oneself to spatio-temporal regions of constant gravitational potential.
1913: I arrived at the result that the velocity of light is not to be regarded as independent of the gravitational potential. Thus the principle of the constancy of the velocity of light is incompatible with the equivalence hypothesis.
1915: the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned.
1916: In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position.
Unfortunately the English translations feature the word “velocity”, and many assume this to be a vector-quantity velocity rather than the common usage, as per “high velocity bullet”. The German word Einstein used was geschwindigkeit. That’s speed. It’s clear he was referring to speed because the SR postulate concerns speed, not vector-quantity velocity. And because he if was referring to velocity, he would have been saying “A curvature of rays of light can only take place when light curves”. That’s a tautology that simply doesn’t make sense. I’m sorry Jesse, but there’s no other way for me to say this: the GR you’ve been taught is not in line with Einstein, and in some important respects, it is wrong.
Your gedanken scenario features an accelerating observer, but there is nothing following behind him. He merely can’t see some things behind him. This is very different to the black hole. It’s there, it’s massive, it pulls the observer in.
The event horizon isn’t massive though, it’s just a boundary he can’t see past because light from beyond it won’t ever make it to him, just like light beyond the Rindler horizon won’t ever make it to the accelerating observer (or any observer who accelerates in any way that prevents them from crossing the Rindler horizon). Sure, the horizon in the event horizon is related to a massive object and the Rindler horizon isn’t, but it’s a complete non-sequitur to say “therefore, time really stops at the event horizon but doesn’t really stop at the Rindler horizon”–you haven’t presented any argument as to why the presence of mass should be relevant to our conclusions about whether time “really stops”, this is just vague handwaving.
And the inertial observer is not analogous to the observer in freefall, because the former is subject to constant SR time dilation while the latter is subject to decreasing gravitational potential and increasing GR time dilation.
“Time dilation” entirely depends on your coordinate system–it’s always measured in terms of a ratio of clock time to coordinate time. The inertial observer experiences constant time dilation in an inertial frame in SR, but not in a non-inertial one like Rindler coordinates (which are constructed in such a way to ensure that different accelerating Rindler observers all have fixed position coordinates that don’t change with coordinate time). In GR all large-scale coordinate systems are non-inertial, and all are equally valid–you could construct a coordinate system where the falling observer’s time dilation was constant, or was decreasing as she fell in, if you wished. Again, the only objective claims you can make about times in either theory are ones based on local events, like a signal from the first clock reaching the location of the second clock, or the two clocks being brought together to compare their readings at the same location (as in the “twin paradox”).
The German word Einstein used was geschwindigkeit. That’s speed. It’s clear he was referring to speed because the SR postulate concerns speed, not vector-quantity velocity.
How is this supposed to be relevant to my comment about Ellis and Einstein being in agreement about all physical questions? Speed is just as much a coordinate-dependent quantity as velocity (it’s just the magnitude of the velocity vector, ignoring the direction), and I even used the word “speed” rather than “velocity” in my comment. Again, when Einstein talked about the speed of light varying he was talking about speed in global non-inertial coordinate systems in GR, it’s obvious he would agree that A) there is no objective coordinate-independent way to define the ratio of light speeds at different locations in a gravitational field, it depends entirely on what coordinate system you choose, and B) if you choose to restrict your attention to local inertial frames as opposed to global non-inertial ones, then relative to these specific coordinate systems, the speed of a light ray will be the same at any point on its path (if you think Einstein would disagree on either of these points, please writings of his where he specifically addresses either the issue of coordinate-invariance for A, or the issue of speed in local inertial frames for B). Likewise, it’s obvious Ellis would agree that the coordinate speed of light does vary in non-inertial coordinate systems (if you think Ellis would disagree, please provide a quote where he specifically discusses coordinate speed in non-inertial coordinate systems). So again, there would be no disagreement between them about any real physical question involving the speed of light, it’s just a matter of different possible ways of defining what you mean by that phrase.