Lenny Susskind has a new book out: The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics. At first I was horrified by the title, but upon further reflection it’s grown on me quite a bit.
Some of you may know Susskind as a famous particle theorist, one of the early pioneers of string theory. Others may know his previous book: The Cosmic Landscape: String Theory and the Illusion of Intelligent Design. (Others may never have heard of him, although I’m sure Lenny doesn’t want to hear that.) I had mixed feelings about the first book; for one thing, I thought it was a mistake to put “Intelligent Design” there in the title, even if it were to be dubbed an “Illusion.” So when the Wall Street Journal asked me to review it, I was a little hesitant; I have enormous respect for Susskind as a physicist, but if I ended up not liking the book I would have to be honest about it. Still, I hadn’t ever written anything for the WSJ, and how often does one get the chance to stomp about in the corridors of capitalism like that?
The good news is that I liked the book a great deal, as the review shows. I won’t reprint the thing here, as you are all well-trained when it comes to clicking on links. But let me mention just a few words about information conservation and loss, which is the theme of the book. (See Backreaction for another account.)
It’s all really Isaac Newton’s fault, although people like Galileo and Laplace deserve some of the credit. The idea is straightforward: evolution through time, as described by the laws of physics, is simply a matter of re-arranging a fixed amount of information in different ways. The information itself is neither created nor destroyed. Put another way: to specify the state of the world requires a certain amount of data, for example the positions and velocities of each and every particle. According to classical mechanics, from that data (the “information”) and the laws of physics, we can reliably predict the precise state of the universe at every moment in the future — and retrodict the prior states of the universe at every moment in the past. Put yet another way, here is Thomasina Coverley in Tom Stoppard’s Arcadia:
If you could stop every atom in its position and direction, and if your mind could comprehend all the actions thus suspended, then if you were really, really good at algebra you could write the formula for all the future; and although nobody can be so clever as to do it, the formula must exist just as if one could.
This is the Clockwork Universe, and it is far from an obvious idea. Pre-Newton, in fact, it would have seemed crazy. In Aristotelian mechanics, if a moving object is not subject to a continuous impulse, it will eventually come to rest. So if we find an object at rest, we have no way of knowing whether until recently it was moving, or whether it’s been sitting there for a long time; that information is lost. Many different pasts could lead to precisely the same present; whereas, if information is conserved, each possible past leads to exactly one specific state of affairs at the present. The conservation of information — which also goes by the name of “determinism” — is a profound underpinning of the modern way we think about the universe.
Determinism came under a bit of stress in the early 20th century when quantum mechanics burst upon the scene. In QM, sadly, we can’t predict the future with precision, even if we know the current state to arbitrary accuracy. The process of making a measurement seems to be irreducibly unpredictable; we can predict the probability of getting a particular answer, but there will always be uncertainty if we try to make certain measurements. Nevertheless, when we are not making a measurement, information is perfectly conserved in quantum mechanics: Schrodinger’s Equation allows us to predict the future quantum state from the past with absolute fidelity. This makes many of us suspicious that this whole “collapse of the wave function” that leads to an apparent loss of determinism is really just an illusion, or an approximation to some more complete dynamics — that kind of thinking leads you directly to the Many Worlds Interpretation of quantum mechanics. (For more, tune into my Bloggingheads dialogue with David Albert this upcoming Saturday.)
In any event, aside from the measurement problem, quantum mechanics makes a firm prediction that information is conserved. Which is why it came as a shock when Stephen Hawking said that black holes could destroy information. Hawking, of course, had famously shown that black holes give off radiation, and if you wait long enough they will eventually evaporate away entirely. Few people (who are not trying to make money off of scaremongering about the LHC) doubt this story. But Hawking’s calculation, at first glance (and second), implies that the outgoing radiation into which the black hole evaporates is truly random, within the constraints of being a blackbody spectrum. Information is seemingly lost, in other words — there is no apparent way to determine what went into the black hole from what comes out.
This led to one of those intellectual scuffles between “the general relativists” (who tended to be sympathetic to the idea that information is indeed lost) and “the particle physicists” (who were reluctant to give up on the standard rules of quantum mechanics, and figured that Hawking’s calculation must somehow be incomplete). At the heart of the matter was locality — information can’t be in two places at once, and it has to travel from place to place no faster than the speed of light. A set of reasonable-looking arguments had established that, in order for information to escape in Hawking radiation, it would have to be encoded in the radiation while it was still inside the black hole, which seemed to be cheating. But if you press hard on this idea, you have to admit that the very idea of “locality” presumes that there is something called “location,” or more specifically that there is a classical spacetime on which fields are propagating. Which is a pretty good approximation, but deep down we’re eventually going to have to appeal to some sort of quantum gravity, and it’s likely that locality is just an approximation. The thing is, most everyone figured that this approximation would be extremely good when we were talking about huge astrophysical black holes, enormously larger than the Planck length where quantum gravity was supposed to kick in.
But apparently, no. Quantum gravity is more subtle than you might think, at least where black holes are concerned, and locality breaks down in tricky ways. Susskind himself played a central role in formulating two ideas that were crucial to the story — Black Hole Complementarity and the Holographic Principle. Which maybe I’ll write about some day, but at the moment it’s getting late. For a full account, buy the book.
Right now, the balance has tilted quite strongly in favor of the preservation of information; score one for the particle physicists. The best evidence on their side (keeping in mind that all of the “evidence” is in the form of theoretical arguments, not experimental data) comes from Maldacena’s discovery of duality between (certain kinds of) gravitational and non-gravitational theories, the AdS/CFT correspondence. According to Maldacena, we can have a perfect equivalence between two very different-looking theories, one with gravity and one without. In the theory without gravity, there is no question that information is conserved, and therefore (the argument goes) it must also be conserved when there is gravity. Just take whatever kind of system you care about, whether it’s an evaporating black hole or something else, translate it into the non-gravitational theory, find out what it evolves into, and then translate back, with no loss of information at any step. Long story short, we still don’t really know how the information gets out, but there is a good argument that it definitely does for certain kinds of black holes, so it seems a little perverse to doubt that we’ll eventually figure out how it works for all kinds of black holes. Not an airtight argument, but at least Hawking buys it; his concession speech was reported on an old blog of mine, lo these several years ago.
Well it appears that reeree has assumed the role of Bill O’Reilly here with “Just shut up.”
It might be of interest to note that what I have written with respect to the decoherence of the vacuum state with respect to the radial distance from the event horizon is remarkably similar to what I found at:
arXiv:quant-ph/0302179v1
which discusses a similar issue with respect to Unruh radiation.
It would seem to me that this bog can serve as a way of discussing possibilities or new ideas.
Lawrence B. Crowell
I’m going to step in and agree with ree ree’s angle, even if his tone is rude. This is not the place for discussing “possibilities or new ideas,” when that is a code for stuff that non-mainstream/crackpotty/under-informed. We’ve been very lax about letting it go, but we’re going to start cracking down a lot more, so don’t be surprised if comments start mysteriously disappearing or commenters just start getting banned. We don’t have the time or patience for long back-and-forths with each alternative point of view. Suffice it to say, we are the Voice of the Establishment, working hard to suppress alternative viewpoints, because we are afraid for our cushy jobs and positions in society.
Oh dear! I’m very sorry, Dr. Crowell! Please accept my apologies, sir. I had no idea you had published technical physics books. In fact, I think I will purchase your book “Can Star Systems Be Explored?”, as it sounds very interesting. It’s a topic I’ve always been interested in, actually.
It was certainly a mistake to lump you in with those clowns — Merryman, Qubit, Jeff, and Sam Cox. As for you four, I repeat: go study some physics and shut up. Especially if your “works” have no equations in them. The language of physics is mathematics, not the fantasies of crackpots.
Sean: “Suffice it to say, we are the Voice of the Establishment, working hard to suppress alternative viewpoints, because we are afraid for our cushy jobs and positions in society.”
You forgot to capitalize ‘we’. 😉
Energy and information are related in the first law of thermodynamics plus the Shannon-Khinchin theorem or formula.
L. C.
“ree ree”: All I did was point out a well-known philosophical question about MWI, – i.e. why do you find yourself in a particular branch or world rather than another. If that question makes me a clown, then so be it. And if you can find a mathematical explanation for it, be my guest. Actually, it was probably off-topic, but then the post I was responding to would also be off-topic.
If philosophical implications of physical theories are off-limits on this blog – well, fair enough. However, I do see a fair amount of prose here that is non-mathematical, and sometimes philosophical.
Jeff,
If the MWI is correct, then “we” exist in all possible branches. Why am “I” aware or conscious of only this particular branch? I have absolutely no idea. Thinking about this is like thinking about what happens to me after I die, assuming there is no afterlife. Can you imagine nothingness? Anyway, it is my opinion that the MWI is crap, just like time travel into the past. The best and simplest explanation I can think of as to why I find myself conscious of and existing in this branch rather than the zillions of other branches is that there are no other branches but this one, because MWI is wrong. Quantum mechanics is weird, but I don’t think the “solution” to this weirdness is to posit the existence of an infinity of other universes.
MWI is a quantum interpretation, which is some sort of auxilliary idea meant to “explain” some aspects of quantum strangeness. There are other of these ideas, such as Bohm’s subquantal or inner classical approach. I find the decoherence approach of Hartle, Gel Mann and Zurek and others to be more realistic, for it just discusses entangelement loss in coupling a system to a reservoir of states and in part avoids these inner-quantal ideas.
I think it best to avoid getting too wrapped up into quantum interpretations. I don’t think these things largely buy you much. MWI has achieved a measure of popularity of late, but I wonder if before long that will fade.
MWI implies that we do walk along some path of that is constantly being split off from other paths. One might ponder whether we live these other paths, and whether there is a sort of quantum immortality, where we do in fact consciously experience these paths (eg other lives). Of course again I doubt these ideas don’t really contribute much to any real understanding of physics.
Lawrence B. Crowell
LBC, an interpretation of quantum mechanics is not “some sort of auxilliary idea meant to “explain” some aspects of quantum strangeness”, it is the translation of the mathematical framework of quantum theory into a coherent and consistent picture of the world it describes. As such, it is an integral part of quantum physics, just as the interpretation of Maxwell’s equations is an integral part of electrodynamics. Otherwise it is just maths.
I have it on good authority that the many-worlds interpretation is the current front-runner when it comes to coherence and consistency in interpretations of quantum mechanics. Philosophers of science that I know (Oxford, Cambridge, Maryland) who were not particularly charmed by the MWI are now slowly coming around to it.
As to whether “these things buy you much”, you should be aware that David Deutsch and Peter Shor came to their insights in quantum computing because they adhere the MWI. The “correct” interpretation of a physical theory matters!
Doesn’t MWI imply the QTI? And isn’t that a very BAD thing, almost nightmarish? Not to mention almost impossible to believe?
Isn’t that why David Lewis said something about “you should shake in your boots” if MWI is true?
Thinking about quantum “stuff” already boggles my mind; the MWI just adds to my headache.
Of course, my own personal feelings have nothing to do with whether something is true or not, but still……..
I think that MWI comes from laziness, and taking models too seriously.
How do you consider “information” a scientific or physical quantity in the first place?
Sad, I don’t think that the MWI impies QTI. I think I tried to explain that some time ago on this blog. Basically the idea is that in the MWI you have a static wavefunction, the branches of which contain the sectors in which you live. A time evolved version of you is simply just another branch of that static wavefunction.
The branching you experience as time goes by is just what seems to happen relative to you at some time, it is not the case that the entire wavefunction of the multiverse continues to split. So, all the possible versions of you just exist a priori in the multiverse, each with their subjective notion of time. There are only a finite number of possible versions of you.
So, the whole idea of QTI that at each moment the entire wavefunction splits and if you are old and sick and most branches end in you being death so that you must always end up in that branch were you miraculously survive is simply false. What happens in the MWI is simply that you are always one of the finite number of versions of you that exist with some a priori probability.
collin237, think of it as a degree of freedom.
Quantum interpretations can play a role, so long as you are temperate. Bohm’s approach to QM has a pilot wave with analogues to the Navier-Stokes equation, which might allow one to examine certain types of problems. Also the particle or “beable” might be a good model tool for quantum chaos. Does this mean that I think there really is this inner classical reality to QM? Not on your life! MWI has become popular to a degree, and as pointed out has become a tool in modelling quantum information. As tool it might be fine, but the problem is that anything beyond that seems to become quantum religion.
I might also put the Anthropic prinicple, or the strong AP, in the domain of quantum religion. I am not sure if there is a cosmological principle which requires the existence of conscious observers. It does appear very evident however that in the case of conscious observers here that our biggest function is to tear down this planet’s biological systems and to replace them with garbage and toxic wastes. We appear to be less of some cosmic mindscape and more as some sort of planetary bio-dysfunction or terminator species.
Quantum interpretations do have some utility, but I think they are in a loose sense an aspect of quantum complementarity, or that QM has multiple ways in which it can be examined or modelled. At best quantum interpretations are like cards in your hand — you play those which are needed at the right time.
Lawrence B. Crowell
Anyway… back to the book: I just finished it, and I thought it was great fun to read. His style is very engaging, with lots of interesting anecdotes. I also like it that he does not use the worn-out analogies to explain quantum mechanics, general relativity, etc., but comes up with new ones.
Do you mean a number of degrees of freedom?
If anything, this only affirms our role as “collapsers”. 🙂
MWI appears convenient in information theory because a q-bit of the form
$latex
|psirangle~=~sin(theta)|0rangle~+~e^{iphi}cos(theta)|1rangle
$
will reduce to the 0 state in one world and the 1 state in the other. It is a convenient way of looking at things, in particular with teleporation where a state must be communicated by a classical signal. Yet we could well consider a state reduction as an interaction with an environmet. Say if there is some detector “needle state” which give
$latex
|psirangle~rightarrow~sin(theta)|0rangle|-rangle~+~e^{iphi}cos(theta)|1rangle|+rangle,
$
for the + and – states for a detector. The reduction of the state is when the off diagonal terms in the density matrix are attenuated away. The entanglement phase is lost to the environment — it still exists, but is scrambled up. The outcome is then reduced to a classical “collapse” in one world, rather than single results in two worlds. It is interesting that in both MWI and decoherence we are still left with a dualism — two possible results in this world, or single results in two possible worlds. Take your choice!
MWI can well enough be used for certain applications. Some people appear to regard it with near religious fervor.
One of my crazier questions is whether there is some sort of categorical system or what might be called a quantum “functor,” which can demonstrate an equivalency between quantum interpretations.
Lawrence B. Crowell
collin237: If anything, this only affirms our role as “collapsers”.
Before anything — sorry for not normalizing the above states.
We might almost think of this as a dual principle. Maybe cosmic observers in some Karma sense come to know the universe in it final principles, and then die. Maybe it is a cosmic orgasm, but like a black widow male spider who dies after the process.
Our situation here is frankly very bad, and its is not just global warming. The oceans are in a rapid die off, which in the last decade has raced forward. Imagine if astronauts on a spaceship started to tear up their craft in order to make entertainment systems.
Lawrence B. Crowell
Oops, I apologize for the apology. The states are normalized! The quantum functor calls forth: Bohm, Everett-DeWitt, Zurek, Deutsch, … all have the same quantum muse! But I have no idea how to show this! 🙂
L. C.
Not necessarily. In a quantum computer, one can assume that the states |0> and |1> in whatever device physically stores a q-bit are stable enough that it’s meaningful to speak of the phase e^I phi between them.
However, the states |+> and |-> are not that simple. If there’s any way to define a phase between them, it would require that they both refer to an intact needle. In some interpretations, the unobserved state actually “dissolves”, rather than just “leaving us”. From that standpoint, the phase would actually drop out of the universal information.
Thank you Count Iblis.
I’m no scientist, and much of the time I have no idea what y’all are talking about on this blog, but that QTI stuff (insanely nutty) on top of the MWI (a little bit nutty), had me chewing my fingernails.
To collin237: The complexity of the detector states come in because there may be a whole gemish of states between the system states and some quantum state for the “needle” of the detector. In what you say it amounts to some great trace out of the density matrix to get rid of the complexity. This works FAPP, but there is still a troubling aspect to this. We are effectively destroying a quantum bit in the process. Even if the phase of our system is well specified to start, the stuff we trace out represents reservoir states with lots of various phases, which in the argand plane point everywhere (FAPP) and we are really just saying our nicely prepared phase is being buried away in that noise.
Something similar happens to an infalling observer to a black hole. When the observer approaches the horizon, the notion of a well-defined particle number loses its meaning at the wavelengths of interest in the Hawking radiation; the oberserver is ‘inside’ the particle producing region. As such the observer does not encounter an infinite quantity of particles. On the other hand, energy does have a local significance. In this case, however, although the Hawking flux does diverge as the horizon is approaced, so does the static vacuum polarization, and the latter is negative, or relative to regions removed from the horizon. The infalling observer cannot distinguish operationally between the energy flux due to the oncoming Hawking radiation and that due to the fact that he is sweeping through the cloud of vacuum polarization.
These vacuum polarizations are regions where distinct points near the horizon can hold entangled vacua related approximately by unitary transformations. However, as the distance between two vacua in a polarization increases this breaks down and one has “vacua plus particles,” and there is a randomization of phases. As on coordinates suitable for the outgoing modes approaches I^+, they ultimately get the Hawking temperature at infinity. The radiation is completely decoherent, thermal and indistiguishable from any other black body source observed at a great distance.
Lawrence B. Crowell
colin237, one bit is a single degree of freedom of a system with two possible values. When the system is quantum mechanical the bit is called a qubit.