# conservation of information

August 18, 2013 11:11 AM Subscribe

A Black Hole Mystery Wrapped in a Firewall Paradox - "A paradox around matter leaking from black holes puts into question various scientific axioms: Either information can be lost; Einstein's principle of equivalence is wrong; or quantum field theory needs fixing."

-The Storytelling of Science: Lawrence Krauss, Tracy Day, Brian Greene, Ira Flatow, Neil deGrasse Tyson, Richard Dawkins, Bill Nye & Neal Stephenson (Part 2/2)

-Leonard Susskind: Why is Time a One-Way Street?

-How the Speed of Light was First Measured

- If you dropped an encyclopedia into a black hole, where would the information go?
- When you dump information into a black hole, which then evaporates away via Hawking radiation, where does the information go?
- It's hard to explain the firewall problem in black hole physics.

-The Storytelling of Science: Lawrence Krauss, Tracy Day, Brian Greene, Ira Flatow, Neil deGrasse Tyson, Richard Dawkins, Bill Nye & Neal Stephenson (Part 2/2)

-Leonard Susskind: Why is Time a One-Way Street?

-How the Speed of Light was First Measured

Pretty obvious that when information gets dropped into a black hole it doesn't disappear, it is sent into the past. That is how it got there to begin with.

posted by Ad hominem at 11:48 AM on August 18, 2013 [5 favorites]

posted by Ad hominem at 11:48 AM on August 18, 2013 [5 favorites]

I wish I had the background to properly understand this, but:

Anyone who has lost a huge amount of typing to the ether in a web form POST glitch can tell you this is true. This probably has no bearing on the subject.

philip-random: "

Me too.

posted by double block and bleed at 11:49 AM on August 18, 2013 [1 favorite]

*...information can be lost...*Anyone who has lost a huge amount of typing to the ether in a web form POST glitch can tell you this is true. This probably has no bearing on the subject.

philip-random: "

*I can say this with absolute certainty because I...never took a physics course past Grade 10.*"Me too.

posted by double block and bleed at 11:49 AM on August 18, 2013 [1 favorite]

paging physicsmatt.

amazing how people decry ignorance in a fricking

posted by lalochezia at 11:51 AM on August 18, 2013 [21 favorites]

amazing how people decry ignorance in a fricking

*hip-hop*thread, but are positively proud of it when it comes to physics.posted by lalochezia at 11:51 AM on August 18, 2013 [21 favorites]

*If you dropped an encyclopedia into a black hole, where would the information go?*

This seems to be an odd way of putting it...all that's lost is the paper, cardboard, and ink that make up the physical object, surely? It's not like any inherent "knowledge" is imbued in the book itself, that suddenly disappears along with the physical matter. Am I misunderstanding something?

posted by Greg_Ace at 12:05 PM on August 18, 2013 [1 favorite]

Mod note: Please don't open with jokey snark. Thanks.

posted by restless_nomad (staff) at 12:08 PM on August 18, 2013 [2 favorites]

posted by restless_nomad (staff) at 12:08 PM on August 18, 2013 [2 favorites]

There is nothing mathematicians hate more than some good old enthalpy. This is the scientific equivalent of angels dancing on a pin, an extreme edge case of the universe.

posted by nickggully at 12:08 PM on August 18, 2013

posted by nickggully at 12:08 PM on August 18, 2013

Or does "information" in this context mean any sort of organizing principle that purposely forms a thing called - for instance - a "book", with a cover, pages, and ink deposited in a coherent language, out of random molecules? Or am I thinking of (the opposite of) entropy?

posted by Greg_Ace at 12:16 PM on August 18, 2013

posted by Greg_Ace at 12:16 PM on August 18, 2013

Except those extreme edge cases are the interesting ones, and the ones most likely to show us the seams in our universe, the places where our ordinary physical laws give way for more profound, underlying ones. Also, angels don't exist.

posted by JHarris at 12:17 PM on August 18, 2013

posted by JHarris at 12:17 PM on August 18, 2013

*...or does some research assistant need to re-calibrate an instrument or just make sure the wiring connections are not loose.*

This one isn't about conflicts of experimental evidence with theory; it's about the consequences of different theories appearing to be mutually incompatible.

More specifically, when you combine quantum theory - the theory of the very, very small - and the theory of general relativity - the theory of the very, very big - you end up with a bit of a mismatch at what happens at the boundary of black holes - a paradox. There are various competing explanations about how to resolve this, but they involve us having to revise one of these major theories somewhat, which scientists are loathe to do unless they're absolutely sure they have to. Professor Hawking, who is a leading expert on quantum theory decided he was wrong a few years ago about this issue, but further work on his information paradox shows that he may have given up too easily (after 30 years!). Einstein himself hated quantum theory, and didn't believe it could be correct.

Note, this is not a conflict in a liberal arts sense, but the result of fiercely complicated mathematics where you cannot have two things valid at the same time. It's the same sort of mathematics that proves* that you cannot know both a particle's momentum and position absolutely - the more you know of one, the less you know of the other, aka Heisenberg's uncertainty principle.

* I did used to be able to do this proof, but it's been a while.

The problem is that both theories have been heavily confirmed through experiment and observation - and quite a bit of modern tech relies on one or both - and both seem to be valid as is. If this was an earlier time, they'd be called Laws, not theories, but pretty much since Einstein proved that Newton's laws are basically approximations and not actually correct at the really big scale, we're a lot more wary about using that term any more.

Which is a bit of a head scratcher, and it's not like we can just go and have a look inside the event horizon of a black hole to find out.

Personally, I like the wormhole shared identity hypothesis, which allows for both theories remaining true as is, but it's very early days and there's a lot more work that needs to be done on that.

In any event, it's cutting edge theoretical physics where we're trying to understand how the universe fundamentally works, and involves, amongst other things, trying to figure out where space-time and gravity actually come from.

posted by ArkhanJG at 12:26 PM on August 18, 2013 [8 favorites]

I wasn't joking. I was blowing your mind, man.

posted by Ad hominem at 12:28 PM on August 18, 2013

posted by Ad hominem at 12:28 PM on August 18, 2013

IANAPhysicist (and I invite any physicists to correct me), but my understanding of a physicist's information isn't

The information described is like the

posted by JHarris at 12:29 PM on August 18, 2013 [3 favorites]

*that*divorced from our concept of it. Although an encyclopedia is a bad example because to the universe it really contains not much less or more information than an equivalent amount of random matter. What makes some of the information in an encyclopedia visible*to us*is*our interpretation*of that matter, we've arranged the atoms so that it encodes information in a language we understand and can readily read it. But information is there whether we can interpret it or not.The information described is like the

*history*of the atoms and particles included. If an atom is moving in a certain way, how did it come to do so? How did those particles come together to form it? Each is vibrating (remember: heat is jiggling) in a way that is the sum of all the interactions it has had throughout its history. A theoretical observer with perfect measuring equipment could deduce its history by examining it and those other particles it's interacted with, their motions, positions and vibrations. But not if it falls into a black hole; the formulas that describe a black hole's behavior are simpler. In fact, since we now know that mass has a way of escaping from a black hole, through Hawking radiation, it really looks like a kind of a hole for information.posted by JHarris at 12:29 PM on August 18, 2013 [3 favorites]

Information in the physics sense isn't so much about information (i.e. 1+1 = 2) but rather how things are configured. Greg_Ace, your second statement is closer. Entropy is a way to measure information (as posited by Claude Shannon).

Wikipedia says it like this on the "Information Theory" page:

In this particular notion, the concept, IIRC, is can you restore something once it has been put into a black hole. The laws of physics as generally posited outside of extreme conditions like a black hole state that it is possible (theoretically) to reconstruct the original state of an item. That is - if you set a book on fire and it all turned to ash, there is, in theory a way to convert that back into the regular book. (Sean Carroll in From Eternity to Here discusses this (the link points directly to the page it's on in google books.)

The question is, whether there is a way to do that after it has been put into a black hole. This is the source of a famous argument between Steven Hawking and Leonard Susskind (who is mentioned in the OP), and which Susskind talks about in his book, The Black Hole War. (Hawking originally thought that information was irrevocably lost, but it is my understanding that he has come around to the view that it is not, but my memory might serve wrong... best to do your own research on anything I say here.)

posted by symbioid at 12:32 PM on August 18, 2013 [5 favorites]

Wikipedia says it like this on the "Information Theory" page:

These are very very very abstract notions when we get into the physics of black holes (at least very abstract for us non-physicists), but they deal with the fundamentals of how the universe works (in particular with regards to the laws of thermodynamics, and ultimately, the flow of time itself).A key measure of information is entropy, which is usually expressed by the average number of bits needed to store or communicate one symbol in a message. Entropy quantifies the uncertainty involved in predicting the value of a random variable. For example, specifying the outcome of a fair coin flip (two equally likely outcomes) provides less information (lower entropy) than specifying the outcome from a roll of a die (six equally likely outcomes).

In this particular notion, the concept, IIRC, is can you restore something once it has been put into a black hole. The laws of physics as generally posited outside of extreme conditions like a black hole state that it is possible (theoretically) to reconstruct the original state of an item. That is - if you set a book on fire and it all turned to ash, there is, in theory a way to convert that back into the regular book. (Sean Carroll in From Eternity to Here discusses this (the link points directly to the page it's on in google books.)

The question is, whether there is a way to do that after it has been put into a black hole. This is the source of a famous argument between Steven Hawking and Leonard Susskind (who is mentioned in the OP), and which Susskind talks about in his book, The Black Hole War. (Hawking originally thought that information was irrevocably lost, but it is my understanding that he has come around to the view that it is not, but my memory might serve wrong... best to do your own research on anything I say here.)

posted by symbioid at 12:32 PM on August 18, 2013 [5 favorites]

(I love these discussions!)

posted by JHarris at 12:34 PM on August 18, 2013 [2 favorites]

posted by JHarris at 12:34 PM on August 18, 2013 [2 favorites]

I take it, as a not-too-bright layman, when talking about "information cannot be lost" in a physics sense, we're talking not about losing learning or discoveries--for example, if a brilliant scientist with an unpublished theory was squished by a bus--but actually losing the ability to ever know about the item in question? As a very bad analogy, if the "knowledge" of the color red was lost in a black hole in this way, red would disappear from the universe, so to speak?

posted by maxwelton at 12:44 PM on August 18, 2013

posted by maxwelton at 12:44 PM on August 18, 2013

I always go to Peter Woit's blog for a skeptical opinion-

I take this to mean that if you don't think string theory explains anything, the firewall paradox isn't that interesting.

posted by bhnyc at 12:48 PM on August 18, 2013

*The black hole information paradox has been around for nearly forty years, with the story 10 years ago that it supposedly had been resolved by AdS/CFT and string theory. For the past year or so arguments have been raging about “firewalls” and a version 2.0 of the paradox, which evidently now is not resolved by AdS/CFT and string theory.... As usual though, my interest in quantum gravity questions that have nothing to say about unification is limited.*I take this to mean that if you don't think string theory explains anything, the firewall paradox isn't that interesting.

posted by bhnyc at 12:48 PM on August 18, 2013

*The question is, whether there is a way to do that after it has been put into a black hole. This is the source of a famous argument between Steven Hawking and Leonard Susskind...*

This ties into to holographic theory, of which Susskind has had a big hand in. Basically, if you were to look at the universe from the outside of it (which is kinda hard, because there isn't any 'there' outside) you could see all the information that makes it up as a 2D surface - it only looks 3D from the inside, at low energies. Rather like a hologram is a 2D surface that looks like a 3D object as you move around it.

As far as we know, information cannot be destroyed, in the same sense that energy (entropy) cannot be destroyed, only converted. If you have all the information describing a thing, then no matter how you add new information, you can (theoretically) reconstruct its original state. With black holes, when you add entropy, it emits entropy to remain in balance, i.e. Hawking radiation. The problem is, Hawking sumised that there was no link between the information going in and the information coming out, which violates the rule that you can't destroy information, thus the information paradox.

Susskind worked out that if you treated the horizon of a black hole as a 2D surface, you can use the fluctuations of the surface to describe all the information that has been absorbed - and these fluctuations affect the entropy coming out, so by combining the two, the original information can be recovered. Thus the analogy that information is 'smeared' on the surface of a black hole, rather than absorbed or destroyed, which is the view Hawking came round to.

This leads to the holographic principle - if you can do it for the gravitational boundry of a black hole, you should be able to do it for a larger body on any light boundry, such as the edge of the cosmos - i.e. represent the whole 3D shebang as a 2D surface of information, and I understand is one of the leading theories at the moment.

At a higher level, that means that energy and matter (and gravity and spacetime) as we perceive them are not fundamental, but just different forms of information.

String theory is the combination of quantum physics and relativity, and effectively becomes the theory of everything. The confirmation of the Higgs Boson is a definite boost to string theory, and the theory of quantum gravity. The current 11-dimensional version of string theory, M-theory, has a lot of support as being a stepping stone to the theory of everything.

Trying to combine string theory and the holographic principle then becomes an interesting challenge.

However, it's still not settled at all; Marolf has a new paper saying that holographic theory doesn't need strings at all.

A defining feature of holographic dualities is that, along with the bulk equations of motion, boundary correlators at any given time t determine those of observables deep in the bulk. We argue that this property emerges from the bulk gravitational Gauss law together with bulk quantum entanglement as embodied in the Reeh-Schlieder theorem. Stringy bulk degrees of freedom are not required and play little role even when they exist. As an example we study a toy model whose matter sector is a free scalar field. The energy density (\rho) sources what we call a pseudo-Newtonian potential (\Phi) through Poisson's equation on each constant time surface, but there is no back-reaction on the matter. We show the Hamiltonian to be essentially self-adjoint on the domain generated from the vacuum by acting with boundary observables localized in an arbitrarily small neighborhood of the chosen time t. Since the Gauss law represents the Hamiltonian as a boundary term, the model is holographic in the sense stated above.Simples! *sob*

posted by ArkhanJG at 1:48 PM on August 18, 2013 [3 favorites]

Physicist here, although I don't specialize in treating black holes theoretically...

The laws of quantum mechanics are said to be Unitary. To evolve a quantum state some time interval t, you multiply it by U=exp(-i H t), where H is a special operator that encodes the specifics of the laws of physics. Called the Hamiltonian, H must also be Hermitian: taking its complex conjugate is the same as taking its transpose. Here i is the sqrt of -1. Similarly, U is Unitary, which means that the complex conjugate (replacing i by -i) is the same as the inverse, as you can easily check: exp(i H t) x exp(-i H t) = I, the identity operator.

Basically, this allows you to run a state forward in time, but mathematically, given the end state and the laws of physics as encoded in H, you could also run the state back in time (just operate on by exp(i H t)). You'll never be in a situation where there are two possible earlier states that gave rise to the current one. You can always recover the past from the present, given the state and H.

So it seems to be this very basic feature of quantum mechanics is in trouble if information could be lost down the black hole. Drop an encyclopedia, and given that a black hole "has no hair" (only presents mass, charge, and spin to the outside world) and radiates blackbody radiation (which should be random), how are you supposed to work backwards to recreate the encyclopedia from the black hole state?

posted by Schmucko at 1:55 PM on August 18, 2013 [7 favorites]

The laws of quantum mechanics are said to be Unitary. To evolve a quantum state some time interval t, you multiply it by U=exp(-i H t), where H is a special operator that encodes the specifics of the laws of physics. Called the Hamiltonian, H must also be Hermitian: taking its complex conjugate is the same as taking its transpose. Here i is the sqrt of -1. Similarly, U is Unitary, which means that the complex conjugate (replacing i by -i) is the same as the inverse, as you can easily check: exp(i H t) x exp(-i H t) = I, the identity operator.

Basically, this allows you to run a state forward in time, but mathematically, given the end state and the laws of physics as encoded in H, you could also run the state back in time (just operate on by exp(i H t)). You'll never be in a situation where there are two possible earlier states that gave rise to the current one. You can always recover the past from the present, given the state and H.

So it seems to be this very basic feature of quantum mechanics is in trouble if information could be lost down the black hole. Drop an encyclopedia, and given that a black hole "has no hair" (only presents mass, charge, and spin to the outside world) and radiates blackbody radiation (which should be random), how are you supposed to work backwards to recreate the encyclopedia from the black hole state?

posted by Schmucko at 1:55 PM on August 18, 2013 [7 favorites]

String theory is the combination of quantum physics and relativity, and effectively becomes the theory of everything. The confirmation of the Higgs Boson is a definite boost to string theory, and the theory of quantum gravity. The current 11-dimensional version of string theory, M-theory, has a lot of support as being a stepping stone to the theory of everything.--ArkhanJG

I think it's a little more controversial than that (at least in some quarters). The Higgs boson was expected even without string theory, and many string theorists hoped that the LHC might show evidence of supersymmetric partners for known particles, which has not happened. M theory is promising in some theoretical ways (it can find black hole entropy) but many balk at the "Landscape" of different theories it seems to be compatible with.

posted by Schmucko at 2:00 PM on August 18, 2013 [1 favorite]

*(I love these discussions!)*

If you haven't, read "The Information" by James Gleick.

Amazon Link

You'll have brain spasms, both good and bad all through at least the first half.

posted by DigDoug at 2:58 PM on August 18, 2013 [2 favorites]

Great post, though I think you buried the lede. GUYS, WE'RE TALKING ABOUT WORMHOLES!

This is my favorite quote from the main article:

This is my favorite quote from the main article:

Instead of a tunnel snaking through hyperspace and opening at the maw of another black hole, the wormhole would split into a zillion spaghetti-like strands ending on each of the pieces of Hawking radiation. That would mean that Bob, the Hawking particle in the cartoon version of the theory mentioned above, might be light years away from the event horizon, but he would still be connected to the interior of the black hole, as if there were a doorway in New Jersey that opened up into a basement in Manhattan.posted by funkiwan at 4:16 PM on August 18, 2013 [1 favorite]

*"I take it, as a not-too-bright layman, when talking about "information cannot be lost" in a physics sense, we're talking not about losing learning or discoveries--for example, if a brilliant scientist with an unpublished theory was squished by a bus--but actually losing the ability to ever know about the item in question?"*

Information loss is the inability to reconstruct a previous state. It is strongly related to entropy (changes that cannot be undone). Information theory was devised as a way of formalizing the properties of a transmitted signal, applied directly to things like radio, telephony, computer science, and encryption. It turns out that the mathematical foundation of information theory is useful for talking about any situation where an observer would try to recover evidence of an original or past state.

Depending on the system you define, what you talk about could be an information loss. The textbook examples are frequencies of voltages on a wire being converted into a message, but with a huge amount of work we could formally describe the "system" of human ideas and discovery as propagated in a culture, and the scientist being hit by a bus would be an information loss event.

This is only very weakly related to the black hole information loss problem - kind of like how a binary star system and the number of pennies in my pocket are both examples of the number "2".

posted by idiopath at 5:18 PM on August 18, 2013

Since I'm not sure if the NYT article links to it, but since many of you are technical folk, this is the article which started this controversy.

Otherwise, I think there is one point that I'm not sure the NYT article makes clear. Since Schmucko above has a good description of the original conflict between classical black holes/quantum mechanics, I'm just going to jump off the end of that.

After Hawking radiation was discovered (black holes look as if they have a (small) temperature; so just like any hot object, they radiate), it seemed like something could come back out of the black hole. However as Schmucko mentioned, what comes back out is (classically) supposed to be perfectly random-- no information. Of course, if we could really do quantum gravity, we expect that classical gravity would just be an approximation; so maybe the information is really coming out, just all mixed up and hard to see. Unfortunately even if the info does come back out in the (corrected) Hawking radiation, there's still a bit of a paradox.

One of the other rules of quantum mechanics is that you can't quantum copy; that is, if you have a quantum state, you can't xerox it and end up with two copies of the original state.

So, imagine you start with Bob and Alice, outside of a black hole. They throw some quantum system into the black hole, and then they throw Alice into the black hole.

Inside the black hole, Alice measures the system and figure out what state it's in. Outside the black hole, Bob waits, collects the Hawking radiation, does some hard quantum gravity calculation to figure out what it must have come from-- and then hey, he knows what state that system is in too!

The problem here is that we have "quantum copied"-- Alice has the state, and Bob has the state.

The idea of black hole complementarity was that it didn't really matter; Alice was inside the black hole, and couldn't even theoretically tell Bob about what she knew. So they could never compare notes, and so the "paradox" wasn't a problem.*

Now what's new about the AMPS paradox is that it shows that complementarity alone won't resolve the original paradox. It's a more precise version of the old paradox**. Now Bob and Alice end up in the same place and can compare their notes-- and there's a problem. So something's gotta give-- either we're wrong about quantum mechanics, we're wrong about how quantum mechanics and gravity interact, or something terrible must happen to Alice so she and Bob can't compare notes.

A "firewall" is the name for whatever terrible thing happened to Alice. Poor Alice, when she jumps into a black hole...

*This idea of black hole complementarity actually has nothing to do with string theory in particular, except that is mostly where the inspiration came from. It's an idea about the way quantum gravity might behave, and you could test whether *any* theory of quantum gravity behaves that way. So I (of course, duh, I'm a string theorist) don't agree with Peter Woit-- I think anyone studying any sort of quantum gravity should care.

**Not going to try to describe this in detail. Some of the links in the OP do, but honestly, it's pretty tough to get it straight even with another physicist working in this field. There's a reason most people thought complementarity solved the original paradox; the updated version of the paradox has to be pretty particular to get around it.

posted by nat at 6:08 PM on August 18, 2013 [3 favorites]

Otherwise, I think there is one point that I'm not sure the NYT article makes clear. Since Schmucko above has a good description of the original conflict between classical black holes/quantum mechanics, I'm just going to jump off the end of that.

After Hawking radiation was discovered (black holes look as if they have a (small) temperature; so just like any hot object, they radiate), it seemed like something could come back out of the black hole. However as Schmucko mentioned, what comes back out is (classically) supposed to be perfectly random-- no information. Of course, if we could really do quantum gravity, we expect that classical gravity would just be an approximation; so maybe the information is really coming out, just all mixed up and hard to see. Unfortunately even if the info does come back out in the (corrected) Hawking radiation, there's still a bit of a paradox.

One of the other rules of quantum mechanics is that you can't quantum copy; that is, if you have a quantum state, you can't xerox it and end up with two copies of the original state.

So, imagine you start with Bob and Alice, outside of a black hole. They throw some quantum system into the black hole, and then they throw Alice into the black hole.

Inside the black hole, Alice measures the system and figure out what state it's in. Outside the black hole, Bob waits, collects the Hawking radiation, does some hard quantum gravity calculation to figure out what it must have come from-- and then hey, he knows what state that system is in too!

The problem here is that we have "quantum copied"-- Alice has the state, and Bob has the state.

The idea of black hole complementarity was that it didn't really matter; Alice was inside the black hole, and couldn't even theoretically tell Bob about what she knew. So they could never compare notes, and so the "paradox" wasn't a problem.*

Now what's new about the AMPS paradox is that it shows that complementarity alone won't resolve the original paradox. It's a more precise version of the old paradox**. Now Bob and Alice end up in the same place and can compare their notes-- and there's a problem. So something's gotta give-- either we're wrong about quantum mechanics, we're wrong about how quantum mechanics and gravity interact, or something terrible must happen to Alice so she and Bob can't compare notes.

A "firewall" is the name for whatever terrible thing happened to Alice. Poor Alice, when she jumps into a black hole...

*This idea of black hole complementarity actually has nothing to do with string theory in particular, except that is mostly where the inspiration came from. It's an idea about the way quantum gravity might behave, and you could test whether *any* theory of quantum gravity behaves that way. So I (of course, duh, I'm a string theorist) don't agree with Peter Woit-- I think anyone studying any sort of quantum gravity should care.

**Not going to try to describe this in detail. Some of the links in the OP do, but honestly, it's pretty tough to get it straight even with another physicist working in this field. There's a reason most people thought complementarity solved the original paradox; the updated version of the paradox has to be pretty particular to get around it.

posted by nat at 6:08 PM on August 18, 2013 [3 favorites]

Also idiopath-- there is actually one proposal for resolving the new AMPS paradox via quantum information ideas, like how long it takes to do the quantum calculation once you get Bob and Alice back together. Can they ever figure out there's a problem?

And I forgot to mention that in the new paradox, the place Bob and Alice end up together-- is inside the black hole. So I guess now it's not so great to be Bob either. And yeah, they might run out of calculation time-- if they hit the black hole singularity before they finish their calculation, then they never know there's an issue either.

On a silly note with respect to information theory, a lot of times you have Alice sending a message to Bob, which Eve* is trying to corrupt or intercept in some way. So I was talking to my boyfriend (info theory guy) and he asked, in this paradox, who's Eve? We decided Eve's got to be the black hole.

*I've got no idea why anyone picked Eve as the name here. Well I have an idea but it doesn't make me happy. Does anyone know the real story?

posted by nat at 6:15 PM on August 18, 2013 [2 favorites]

And I forgot to mention that in the new paradox, the place Bob and Alice end up together-- is inside the black hole. So I guess now it's not so great to be Bob either. And yeah, they might run out of calculation time-- if they hit the black hole singularity before they finish their calculation, then they never know there's an issue either.

On a silly note with respect to information theory, a lot of times you have Alice sending a message to Bob, which Eve* is trying to corrupt or intercept in some way. So I was talking to my boyfriend (info theory guy) and he asked, in this paradox, who's Eve? We decided Eve's got to be the black hole.

*I've got no idea why anyone picked Eve as the name here. Well I have an idea but it doesn't make me happy. Does anyone know the real story?

posted by nat at 6:15 PM on August 18, 2013 [2 favorites]

Thanks, nat (who I can verify is a string theorist!) These new versions of the paradox are fascinating. (I don't think your link to the original paper came through?)

posted by Schmucko at 6:40 PM on August 18, 2013

posted by Schmucko at 6:40 PM on August 18, 2013

Looks like it is just convention that built up over time.

Similar to the taxonomy of standard metasyntactic variables.

posted by idiopath at 6:42 PM on August 18, 2013

Similar to the taxonomy of standard metasyntactic variables.

posted by idiopath at 6:42 PM on August 18, 2013

I think what seems strange about Eve in this problem is that they skipped a bunch of letters after Alice and Bob... And Eve's kind of loaded symbolically in Genesis. idiopath's link suggests Eve might also refer to "eavesdropping".

posted by Schmucko at 6:49 PM on August 18, 2013

posted by Schmucko at 6:49 PM on August 18, 2013

If the information content of a black hole depends on its surface area then what happens if you merge black holes?

Say I have 729 ordinary spheres of a unit radius (and hence surface area = 4 * pi, and volume = 4/3 * pi). If I squashed them together the volume would be 729 * 4/3 * pi units, implying that the radius is 9 units. But if they were 729 black holes of unit radius then the surface area must be 729 * 4 * pi which implies that the radius must be 27 units! So black holes that merge must grow in radius at least according to the square root of their mass, not according to the cube root.

But I looked black holes' radius up on Wikipedia and found that the radius actually varies according to the mass - not the square or cube root! So our 729 little black holes squashed together would form one with a radius of 729 units! Huge! And its surface area would be 531,441 times greater than little black hole, meaning that the more mass (information) you pump into it, the more sparsely that mass (information) must be reflected in the surface. And the less its density, too: that varies as the

Eventually I suppose you would end up with a universe-sized black hole that is a nearly perfect vacuum and with an almost perfectly uniform surface. Everything would be inside it, but it would basically be negligible. It would be everything and nothing at the same time. Does this sound right?

posted by Joe in Australia at 9:08 PM on August 18, 2013

Say I have 729 ordinary spheres of a unit radius (and hence surface area = 4 * pi, and volume = 4/3 * pi). If I squashed them together the volume would be 729 * 4/3 * pi units, implying that the radius is 9 units. But if they were 729 black holes of unit radius then the surface area must be 729 * 4 * pi which implies that the radius must be 27 units! So black holes that merge must grow in radius at least according to the square root of their mass, not according to the cube root.

But I looked black holes' radius up on Wikipedia and found that the radius actually varies according to the mass - not the square or cube root! So our 729 little black holes squashed together would form one with a radius of 729 units! Huge! And its surface area would be 531,441 times greater than little black hole, meaning that the more mass (information) you pump into it, the more sparsely that mass (information) must be reflected in the surface. And the less its density, too: that varies as the

*cube*root of the mass.Eventually I suppose you would end up with a universe-sized black hole that is a nearly perfect vacuum and with an almost perfectly uniform surface. Everything would be inside it, but it would basically be negligible. It would be everything and nothing at the same time. Does this sound right?

posted by Joe in Australia at 9:08 PM on August 18, 2013

Right, Joe in Australia--except what we figured historically went in the opposite direction. The radius of a black hole (the Schwartzschild radius for a black hole with 0 spin) depends on its mass. The fact that the surface area of merged black holes always equals or exceeds the surface area of the separate black holes is what motivated (Bekenstein?) to identify surface area with entropy (information content).

posted by Schmucko at 10:03 PM on August 18, 2013 [1 favorite]

posted by Schmucko at 10:03 PM on August 18, 2013 [1 favorite]

My mind is being blown. Hey, what happens to the particles that are just within the radius of a black hole when a massive object passes by them just outside the radius? Shouldn't its gravity make the black hole's boundary recede and therefore allow information to leak between the particles and the massive object?

posted by Joe in Australia at 11:39 PM on August 18, 2013

posted by Joe in Australia at 11:39 PM on August 18, 2013

-Black hole firewalls and all that

also btw...

also btw...

- Freeman Dyson reviews the new biography of Oppenheimer by Ray Monk - "In 1939 Oppenheimer published with his student Hartland Snyder a paper, 'On Continued Gravitational Contraction', only four pages long, which is in my opinion Oppenheimer's one and only revolutionary contribution to science. In that paper, Oppenheimer and Snyder invented the concept of black holes..."
- Here's an Edward R. Murrow interview with Oppenheimer mentioned in the book

Wormholes May Save Physics From Black Hole Infernos - "physicists gathered this week at the Kavli Institute for Theoretical Physics at UCSB to talk over the options. (They've been doing a great job uploading videos of all the talks, so if you're interested in watching smart folks try to hash out knotty thought experiments in near-real time, you can follow along at home.)"

posted by kliuless at 3:03 PM on August 25, 2013

posted by kliuless at 3:03 PM on August 25, 2013

Hmm, my linking skills have atrophied (and I got busy writing a paper, oops). Let me try again:

This should be the original AMPS paper.

posted by nat at 11:49 PM on August 25, 2013

This should be the original AMPS paper.

posted by nat at 11:49 PM on August 25, 2013

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posted by sammyo at 11:36 AM on August 18, 2013