Correct me if I am wrong, but it seems to me that the "decoherence" line of research presumes that the Many-Worlds interpretation of quantum mechanics is correct and that the Copenhagen interpretation is wrong, no? In the Copenhagen interpretation, a "measurement" sees the collapse of the wave function: the electron is suddenly found to be either | spin up> or | spin down> rather than (1/root(2))| spin up> + (i/root(2))| spin down>. In the Many-Worlds interpretation the electron's wave function retains its | spin up> and its | spin down> components, but they become entangled with the rest of the universe's wave function in such a way that the two branches no longer have any influence on each other.
Posted by DeLong at April 3, 2004 04:45 PM | TrackBack | | Other weblogs commenting on this postEconomist.com | Quantum computing: ...There are currently several different approaches to quantum computing, all of which rely on fundamentally different technologies, including ultra-cold ions that are cooled by lasers, pulses of laser light, nuclear-magnetic resonance and solid-state devices such as superconducting junctions or quantum dots (which are confined clouds of electrons). What all these technologies have in common is that they can be used to invoke and exploit the bizarre phenomenon of superposition.
Superposition is not simple. Though a qubit may, for a while, be in a state of superposition between 0 and 1, it must eventually choose between the two. And in even the best quantum computers, that choice, or “decoherence”, happens in a fraction of a millisecond. Just how the choice is made, and how to prolong the preceding period of “coherence” that allows quantum computations to be made, constitute a long-unexplained gap at the heart of modern physics. For nearly 80 years, since the inception of quantum theory in the 1920s, most physicists were content to gloss over the process. What is perhaps surprising is that the technological challenge of quantum computing is now a driving force behind efforts to understand the most abstract and philosophical underpinnings of quantum mechanics.
Until a qubit interacts with the macroscopic world, which follows the classical laws of physics, it behaves according to the laws of quantum mechanics, which are well understood, at least by physicists. However, the interaction with the classical world—decoherence—and hence exactly where the divide between the quantum and classical worlds lies, are not well understood. When decoherence is deliberately provoked, the process is known as measurement. Before a qubit is measured, for example, it could have a 90% chance of being 1, and a 10% chance of being 0. After the measurement, it takes on one of these two values. But the details of how it chooses between the two are something that, until the advent of quantum computing, most physicists chose to remain agnostic about. Some even quipped that the answer to that question was beyond the realm of physics. Measurement was thought to occur instantaneously, and its effects were added to the theory ad hoc.
But decoherence, though it occurs on a short time scale, happens gradually, unlike the instantaneous idea of measurement. It can thus be investigated. Wojciech Zurek, of America's Los Alamos National Laboratory in New Mexico, discussed his research group's efforts to investigate decoherence. They recently proved that the rate at which decoherence occurs can be measured by something called the Loschmidt echo. The Loschmidt echo, named after a 19th-century German physicist, is an observable experimental measure of the sensitivity of a quantum system to changes in the energy of the system. (The exact form it takes depends on what sort of physical system is being considered.) Dr Zurek expects that the link between decoherence and the Loschmidt echo should aid theoretical understanding of decoherence.
In a less abstract tack, several papers presented at the conference showed how decoherence could actually be combated. Although the naive expectation is that any interaction between the qubits of a quantum system and the outside world will provoke decoherence, it turns out that the right kind of external signals can in fact prolong the period of coherence.
Chikako Uchiyama of Yamanashi University, in Japan, discussed how, in the general case, the application of very short pulses, poetically known as bang-bang pulses, at regular intervals can serve not only to suppress decoherence, but also to maintain entanglement—the quantum coupling between several qubits which allows computations to get done. It turns out that, in the absence of such pulses, disentanglement happens even faster than decoherence, so there is even more of a need to suppress it. The specific form of the pulses, Dr Uchiyama says, depends on the quantum-computing technology in question—in nuclear magnetic resonance, the pulses could be of the magnetic field, while for quantum dots, it would be the electric field that is pulsed.
Kaveh Khodjasteh of the University of Toronto looked at a related question, focusing on decoherence rather than disentanglement. He showed how a quantum error-correcting code which introduced only one extra qubit for error correction would create a robust system for quantum computation which had tolerance for faults caused by spontaneous emission, another bizarre quantum effect. (Error-correcting codes are used to ensure the integrity of quantum calculations.) Many quantum error-correcting codes have been proposed before, but most require a large overhead of qubits—some need up to eight times as many qubits as those necessary for a computation, while Mr Khodjasteh's code needs only one extra qubit, no matter how many are being used for the computation.
Several other speakers at the conference focused on detailed descriptions of how decoherence occurs in specific systems, such as superconducting junctions, or quantum dots. The promise of quantum computation, spurred on by the insights of Dr Shor and Dr Grover, is inciting physicists to probe, experimentally and theoretically, the junction between the quantum and the classical. They seem to be finding that the process of decoherence is more gradual, quantifiable and open to investigation than was previously suspected. Though a useful quantum computer is probably still many years away, the field of quantum computing is well on its way to solving its first problem.
From what I've read, that seems to be the case. The power of superpositions and entanglement seem to derive from the fact that computation occurs simultaneously in all possible worlds, and we use the entanglement to tease an answer into our own world.
"Minds, Machines, and the Multiverse", by Julian Brown, is a good (non-technical) intro to the whole subject of quantum computing. Also, Mr. Brown is very sympathetic to David Deutsch, who is both a pioneer in quantum computing, as well as a many-worlds zealot. He's quite convincing on the topic.
Posted by: Dan Levine on April 3, 2004 05:21 PMI believe decoherence is an attempt to better describe the joint evolution of an initially prescribed single particle wavefunction and a complicated many-body one. The evolution is governed by a "straightforward" PDE, and neither the collapse postulate nor the many worlds interpretation enters into consideration.
Ah, finally something upon I can comment with some nonzero amount of expertise (I'm a PhD student in Physics at MIT who works Prof. Seth Lloyd on quantum computation. Heck, I've even coauthored two papers on bang-bang control of decoherence, a topic I'm surprised to see explictly mentioned on the pages of the Economist.)
As I have to imminently go out to dinner, I must be brief at the moment:
You're quite right that correlations between a "measurement apparatus" and the quantum system it measures are quantifiable as entanglement between the systems (i.e., technically, time evolution following the Schroedinger equation yielding a joint state of measurement apparatus & measured system that cannot be factored into a tensor product of (measurement-apparatus-alone) and (measured-system-alone) states. You're quite right to think this buildup of correlations defines what the *possible measurement outcomes* are for your apparatus. However, decoherence does *not* explain why you'll record only *one* of these possibilities upon performing a measurement. That's where interpretations of quantum mechanics come in and where it seems we pass from physics to metaphysics, and in particular the debate between realism and postivism.
The essential message of "Many Worlds" is that a funky type of realism quite naturally emerges from positing there is a wavefunction for the entire universe which simply follows Schroedinger's equation whose many components contain all possible outcomes for all that has ever been done, and decoherence explains why these many components don't influence one another and so you needn't notice them.
The essential message of the "Copenhagen" (or perhaps neo-Copenhagen) interpretation is that physicists should be positivists and stick to what they can actually observe or infer as directly as possible. "Reduction" or "collapse" of all the possibilities to a single measurement outcome happens. Don't ask why until you can figure out some way to answer the question objectively. Realize that such a task is going to be especially difficult because:
As presently constituted, wavefunctions seem to mix together in some still unclear amalgam an observer's a priori knowledge of a system's history with the system's own "elements of reality". This is especially so with the "spooky-action-at-a-distance" possible with entangled systems. The manifestly non-classical correlations such systems possess imply measurement of one part of the system instantly cause the wavefunction of the other parts of the system to change, no matter their spatial separation. However, such correlations are unclear until the people observing said parts compare notes on what their measurement outcomes were... that is, the changes in the wavefunction that instantaneously occur when one part of the entangled system is measured will never skew the proababilities for the measurement outcomes for the other parts. Indeed, putting "spooky-action-at-a-distance" entanglement aside, the limits on measurement precision that quantum mechanics imposes seem to make it impossible in many instances to ascribe reality in any conclusive, logically coherent fashion to a measured parameter in the instant before it was measured.
Shoot, that wasn't concise (and possibly not clear either). As Pascal once said (and I paraphrase) "I must apologize since I didn't have time to make this letter short."
Posted by: Bill on April 3, 2004 05:54 PMBill,
When you get back from dinner, perhaps you can explain, briefly, why decoherence folks are so fond of density matrices. I never understood what it adds to the basic theory. (And feel free to make it technical.)
Since a fair amount of Bush bashing goes on at this site (much to my approval), perhaps this will be relevant to our discussion:
http://www.lns.cornell.edu/~neubert/bush_finds_error.html
It's good to know we have a Renaissance man in charge.
Posted by: Warren on April 3, 2004 06:59 PMI'm delighted to stumble upon this thread! (Background: I'm a Caltech physics grad student on leave to work on political projects.)
To respond to the first sentence of Brad's post: I agree that the decoherence picture of measuremment is quite different from the standard Copenhagen interpretation, but disagree with the claim that decoherence and the "many worlds" interpretation are such a good fit for one another (at least as I usually see the many worlds interpretation explained--some may disagree with my below characterization of it).
To explain where I see the distinction between many worlds and decoherence, I'll piggy-back off one of Bill's comments. He wrote: "there is a wavefunction for the entire universe which simply follows Schroedinger's equation whose many components contain all possible outcomes for all that has ever been done, and decoherence explains why these many components don't influence one another and so you needn't notice them."
I would instead say that decoherence explains why these components are _extraordinarily unlikely_ to influence one another.
In the many worlds interpretation (at least as I've seen it commonly explained) a measurement with N possible outcomes causes the universe to split into N universes (one with each outcome) that will never again interact.
By contrast, in the decoherence picture there's still one universe, and one wave function (albeit a really complicated one). Given any two states of the universe, it is possible to mathematically construct a system in which, following Schrodinger's equation one state evolves to the other. So, in the case we care about here, it is possible to construct a system in which the ugly post-measurement wavefunction evolves back to the pristene pre-measurement wavefunction.
However, it's important to note that I said "mathematically" construct. To do this in practice is, in all but the most contrived of circumstances, practically impossible. (Note that labs studying decoherence are expensive to maintain!)
Posted by: brahn on April 3, 2004 07:14 PMDecoherence has nothing to do with interpretation, I'd say, except to make it more difficult. It is an honest to goodness physical effect that can be measured. It has been measured.
(I should mention, by the way, to not believe anything you read in popularizations about the interpretation of quantum mechanics. They're almost uniformly disastrously misleading or wrong.)
To Matt, you need density matrices to describe a portion of a system. For example, if you have two electrons in the state
|up>|up> + |down>|down>
what is the state of the first electron? It's not a pure state, so you describe it as a mixed state using a density matrix.
Posted by: Aaron on April 3, 2004 07:45 PM"Politics, on the other hand, is a sort of sub-atomic or non-Euclidan world where it is quite easy for the part to be greater than the whole or for two objects to be in the same place simultaneously"
22 March 1946
"In the many worlds interpretation (at least as I've seen it commonly explained) a measurement with N possible outcomes causes the universe to split into N universes (one with each outcome)"
right so far ...
"that will never again interact."
Wrong. That would make many-worlds incompatible with the classic double-slit experiment, which it is not. Everett and Wheeler were physicists, not idiots; the point they made was that their view and the Copenhagen interpretation are just two different interpretations of the same mathematics, producing the same answers for any experiment that they knew about. As Deutsch puts it, sufficiently similar "worlds" do interfere. The difference is that many-worlds is an attempt to explain the mathematics, while the Copenhagen interpretation is a kind of a positivist way to avoid explanation, and begs further questions (there is nothing in the mathematics corresponding to wavefunction collapse).
Deutsch wants to claim that many-worlds is needed to understand quantum computation; I don't necessarily think he's right. But he may be right that it is needed to develop an intuition for what is going on, and that intuition may be necessary if people ever expect to effectively design quantum computers and algorithms.
Posted by: Joe Buck on April 3, 2004 11:02 PMTo make my comments clearer (though alas not more concise), here's two key points...
But before getting to these two points, I feel Aaron is quite right to warn laypeople that virtually all popularizations imply ideas contrary to the ideas presented in the undergrad/grad textbooks and specialist monographs. In my humble opinion, one rather successful exception to this sad trend is John Polkinghorne's stunningly concise entry _Quantum Mechanics_ in Oxford's "Very Short Introduction" series, which is full-text viewable at Amazon
http://www.amazon.com/gp/reader/0192802526/ref=sib_dp_pt/104-5807035-8535102#reader-link
Another worthwhile place for the layperson to browse, though it's significantly less friendly to the layperson (even though it's trying), is the website
http://www.decoherence.de
maintained by Erich Joos who did some of the seminal work in explaining how far decoherence can go in explaining the emergence of a classical world from quantum theory.
Now getting to my two points, also by way of agreeing with something Aaron said, namely...
---------
"Decoherence has nothing to do with interpretation, I'd say, except to make it more difficult. It is an honest to goodness physical effect that can be measured."
---------
Many physicists get squeamish when it seems they're about to walk over the boundary from physics to metaphysics. Thus, they often express the hope that somehow the phenomena will suggest their own interpretation. In this vein...
******************************************
Key point #1 (which is in regard to "Many Worlds"):
******************************************
One can argue that once one imagines that the whole universe has a wavefunction and that it follows Schroedinger's equation, then the "many-worlds" interpretation suggests itself in the following way. One can make a (semi)-rigorous argument that the interpretation allows one to *derive instead of posit* "Born's rule" that the probability of an outcome |i> for a system in state |Psi> is equal to |(i,Psi)|^2, the magnitude squared of the inner product of |i> and |Psi> on the system's Hilbert space. In other words, the laws of quantum mechanics applied to the entire universe imply that an observer within the universe cannot register the "split" between different relative relations between subsystems of the universe (i.e., "measurement outcomes" or "worlds") *beyond noting the very same statistical nature to observation that quantum mechanics has always associated with microscopic measurements.
[For both a presentation and a critique of this (semi)-rigorous proof, see Chapter 23 "The Relativity of States" in _Conceptual Foundations of Quantum Mechanics_ by Bernard D'Espagnat, which is full-text viewable for free in its natty 1999 "Advanced Books Classics" reprint edition thanks to Amazon's "Search Within the Book" feature at:
http://www.amazon.com/gp/reader/0738201049/ref=sib_rdr_fc/104-5807035-8535102?%5Fencoding=UTF8&p=S001#reader-page
There's still 3 big questions, though:
(1) How are the possible measurement outcomes are defined? (Notably, why do the possible outcomes eventually look like the world we consider "classical"? In particular, how are certain outcomes robust in that they leave records which survive the continued Schroedinger evolution of the universe allowing its inhabitants to have memories of the past?)
(2) Is it really true that observers can't register the split between measurment outcomes, at least not with any practical resources.
[(3) [For cognoscenti] Schroedinger's equation posits a *classical time parameter* There are numerous major problems in defining time by "internal clocks", i.e., the relative orientations of subsystems of a quantum universe, without having funky things happen like having a nonzero chance of them running backward for arbitrary lengths of "time". Note that the absence of having Schroedinger's equation define quantum dynamics, quantum-ness is still defineable kinematically by having coordinates corresponding to noncommuting operators. This is what quantum cosmologists and quantum gravity types spend their days worrying about.]
This is the problem decoherence ostensibly solves, and this modern version of many worlds (which admittedly is rather popular among certain quantum computational types and quantum gravity types) is called "decoherent histories".
[Reference: See the webpages "Quantum Theory Without Observers" maintained by Sheldon Goldstein of Rutgers at:
http://www.math.rutgers.edu/~oldstein/papers/qts/qts.html
which also covers other interpretations.]
******************************************************
Key Point #2 (which is in regard to the Copenhagen interpretation):
******************************************************
But before you get all excited about "many worlds" note that quantum mechanics perhaps even more strongly suggests that a positivist viewpoint is necessary. Say you're a reasonable chap whose conditions for ascribing objective reality to the wavefunction are as follows:
"I'll ascribe objective reality to a system's wavefunction with respect to a given observable only if when...
1) ... I have a *single* copy of the system, and...
2) ... I don't have full a priori knowledge of the system's preparation, yet...
3) ... I can still somehow determine what the wavefunction is *without changing it in the process* (I impose this since if it's inevitably changed, how could I know I really had it and my measurement wasn't a fluke. I want to be able repeat my measurements to my heart's content until my inner neurotic Bayesian conscience is satisfied.)"
If so, then it strongly appears that quantum mechanics cannot satisfy your criteria for objective reality. One can prove that quantum mechanics as it's currently known will not allow you to obtain *any* information about a system's wavefunction without changing the wavefunction *unless* you have full a priori knowledge of a system's preparation. (For example, say you're told that a system has been prepared in an definite energy eigenstate, but you don't know the full Hamiltonian of the system. There's no way you can determine what the eigenstate from a single copy of the system without changing the state, no matter how slowly---adiabatically--you perform your manipulations. Or, say you're given a spin and told it has a definite orientation, but you're not told what it is. There's no way to determine the orientation of a single spin without changing it unless you already know what axis it lies on.)
[Reference: _Quantum Measurement of a Single System_ by Orly Alter and Yoshihsa Yamamoto, which is also full-text viewable at Amazon
http://www.amazon.com/gp/reader/0471283088/ref=sib_dp_pt/104-5807035-8535102#reader-link
NB: Don't be scared by the mischieviously childish illustrations. Yamamoto is a truly world-class optical and semiconductor experimentalist at Stanford. However, feel free to be put off slightly by the utter sureness Alter and Yamamoto---or at least their publisher and cover blurb writer---have that their conclusions are the last word on the topic of how well you can measure a single system.]
Finally, don't believe anyone who says that "If quantum computers can break a 1,024 bit RSA cryptosystem then you *must* believe the many worlds interpretation (e.g., because the computer *must* have performed more computations in parallel than there are atoms in the entire observable universe... of which your computer is only a teensy-weensy part)" Quantum computation is readily understandable in terms of the Copenhagen interpretation. A introduction to this notion which can be read by someone who knows computer science but no quantum mechanics is the punnily entitled "Copenhagen Computation: How I Learned to Stop Worrying and Love Bohr" by the witty and wise N. David Mermin of Cornell (yes, the Mermin of the canonical Solid State Physics textbook), which is available at:
http://arxiv.org/abs/quant-ph/0305088
Gosh, I should go to bed. Especially now that Daylight Savings Time is over. (Remember to "spring forward" your clocks by 1 hour.)
Posted by: Bill on April 3, 2004 11:18 PMThe real question with the MWI is whether the universes (and observers!) are real who see measurement outcomes different from our own. I think this is where decoherence work supports the MWI. As has been pointed out, in principle you can undo a universe split and rejoin the two universes. David Deutsch came up with a thought experiment for this that might become practical in a century or so.
As decoherence work proceeds, they are taking small steps in this direction, providing theoretical support for the continued reality of the multiple branches of the universe as they begin to decohere. The Copenhagen Interpretation holds that eventually the other branches cease to exist, that they "pop" like soap bubbles. But where and when? How much decoherence do we need before those other branches change from being theoretically detectable (but really really hard to do so) to being theoretically impossible to detect? Well, the answer is always that it happens somewhere beyond where we can detect it now, but before we gete all the way to conscious observation.
The farther we go in terms of gaining theoretical and experimental understanding of decoherence as a continuous quantum phenomenon, the harder it becomes to justify the CI's attempt to "pop" the other universes at some point. The CI makes no attempt to explain this "popping"! It just assumes that it happens, because it seems counter-intuitive that other universes could exist. Physicists have to balance their discomfort with parallel universes against their discomfort at assuming the existence of a phenomenon that has never been observed and for which no evidence exists. I predict that as decoherence work pushes forward, and assuming that no actual evidence of objective state reduction ("popping") appears, eventually the weight of opinion will shift towards the MWI.
Posted by: Hal F. on April 3, 2004 11:29 PMThanks Aaron but your answer brings up the question I always have. Namely, what does the density matrix actually add to the theory? In your case, you say the density matrix "describes" the state of the first electron, but doesn't the original wavefunction also do just that, in the sense that it contains all the information for computing expectations? And in fact, doesn't the original state contain more information than the density matrix?
The mathematical setting for multiparticle systems, i.e. a tensor product Hilbert space, doesn't contain an object describing the state of a single particle, and it seems to me that you are missing that point if you attempt to create such an object.
Of course, if we are talking approximations, then I can understand, because we can't carry around the wavefunction of the universe whenever we want to make a simple calculation. I can understand the density matrix as a practical construction, but I'm not convinced it helps people think more clearly about fundamental issues.
Posted by: Matt on April 3, 2004 11:54 PMMatt,
One cannot always describe a system by a wavefunction alone (the so called pure state vs mixed state). This is because writing down a wavefunction would be unrealistic. An example of this is to consider a gas of particles at a temperature T. In addition to knowing the set of energy levels that the gas particles could occupy, one also needs to know the average number of particles occupying each state at this temperature. If too many occupy any one state, thermal fluctuations would drive more particles out of this state than in, and if there are too few, the opposite happens, so at thermal equilibriun each state has an average occupation that is decided by its energy and the temperature of the gas. Since temperature is external to the quantum description of the gas, a wavefunction would not be sufficient to describe the state of the gas. Strictly speaking, in principle one could incorporate this information as well into a wavefunction description by treating all the collisional and other interactions in the gas and incorporating each of these into the schrodinger equation, but this is not realistic for similar reasons as the ones that form the basis of a statistical mechanical description of a large set of particles.
Matt writes:
Thanks Aaron but your answer brings up the question I always have. Namely, what does the density matrix actually add to the theory? In your case, you say the density matrix "describes" the state of the first electron, but doesn't the original wavefunction also do just that, in the sense that it contains all the information for computing expectations? And in fact, doesn't the original state contain more information than the density matrix?
The purpose of the density matrix is, as other people have said, to distinguish between "pure" and "mixed" states. This just adds more jargon to the problem, though, so I'll try to rephrase.
The example that let me "get it" back when I first learned this stuff is to consider a lot of particles, each having two states, A and B. Now, if these were classical particles, there'd be only two possibilities for each particle, but quantum mechanically, there are three: the particle can be in state A, state B, or a combination of states A and B simultaneously. This is a quantum superposition, and is a fragile thing-- if you try to measure it, you'll find either A or B, but you can see consequences of the superposition in interference effects and the like.
Now, imagine you've got a hundred of these particles, and you measure the state of the system, and find fifty A's and fifty B's. Classically, you'd have the complete description of the system: you put in fifty A's and fifty B's, and that's it.
Quantum mechanically, though, there's another way to get this result: You could put in one hundred particles that are each in a superposition of both A and B states. When you make the measurement, you'll get the same result (fifty A's, and fifty B's, plus or minus a bit), but it's a very different state. You can make a quantum computer out of a hundred particles in a superposition of two states-- you can't do that with particles that are only in one state.
The density matrix is a mathematical tool that allows you to easily distinguish between these two cases. Loosely speaking, if the system is a mix of particles in two different states, you'll get a density matrix that has two terms (a|A><A| + b|B>< B|), while the superposition state will give you a density matrix with four terms (a|A><A| + b|B>< B|+c|A><B| + d|B><A|). The extra terms tell you about the coherence between the states in the superposition. (This isn't a rigorous statement, by the way, as you can always choose a different basis that will make the superposition state diagonal, but for a hand-waving illustration in a weblog comment, it'll do.)
Interesting for a layman to eavesdrop.
My Windows just crashed and deleted quite a long comment of mine. One point was to be that a lot of pop science seems to zero in on the most dramatic examples in order to get buzz. For example, my understanding is that the "Schrodinger's cat" thought-experiment would make the same physics point if it were called the "Schrodinger's photographic film" thought-experiment, since any macro effect of quantum events counts as an observation. And you could also do without the idea that the observer's mind is in some way an essential part of the event. But no buzz that way.
Likewise the term "chaos". As I understand, we know now that certain specific areas of physical reality are neither exactly predictable from observations, nor even can be approximated within a margin of error. This is big, but not quite "chaos", since only part of reality is like that, and while results are erratic, they are distributed erratically over a knowable pattern.
In quantum physics, as far as I know the fact that a particle can "move backward in time" does not in any sense mean that a person or even a speck of dust can move backward in time. Likwise, the multiple-worlds interpretation does not mean that there are an infinite numbers of Zizkas out there. Aren't these phenomena all restricted to the quantum level?
Even relativity -- much of the world we see is still Newtonian. We now have radioactivity, a new history and geometry of the universe, and we also now know where the heat of the sun come from. But most of our world is still governed by the 3 laws of motion and the conservation of matter and energy. (In a contrary sense you could argue that Newtonian physicists saw the sun every day but did not understand it at all.)
A lot of these examples seem to involving fuzzing over the quantum-macro threshold or some other threshold, and letting it seem that effects limited to defined areas are found in other areas too.
My understanding of this kind of thing comes mostly from Prigogine's "Order out of Chaos". I've been told that when Prigogine tried to extend his work into quantum physics his results were poor, but at the macro level I (complete layman) find his stuff convincing and interesting.
Posted by: Zizka on April 4, 2004 11:50 AMRe: "I'm a PhD student in Physics at MIT who works Prof. Seth Lloyd on quantum computation."
That must be a blast. I remember Seth as being brilliant, exceptionally knowledgeable, and witty when he was 21...
Posted by: Brad DeLong on April 4, 2004 01:31 PMThe advice my first quantum mechanics lecturer gave was "don't get caught up in the philosophy, learn how to do some calculations". It was good advice.
So while I guess it is always possible that ways of exploiting entanglement and so on may come out of quantum computing, I am a sceptic/cynic. If something does depend (and I'm typing this in a hurry, and have not read the complete comment thread) on the distinction between many worlds and copenhagen interpretations, then chances are it ain't going to happen. People have been thinking about it for over 70 years now, and it (entanglement paradoxes, not quantum mechanics) hasn't turned anything useful out yet.
So I'll take my stand and predict that quantum computing will be a bust.
Posted by: Tom Slee the Jaded on April 4, 2004 01:52 PMI personally prefer Feynman's take: nobody understands quantum mechanics, and never will. Which is not to say we don't know how to calculate the odds.
Anyway, I wouldn't mind economists being interested in physics, as long as they were doing honest economics. Unfortunately, that is impossible in the academy nowadays, so all evidence to the contrary notwithstanding, I'll have to chalk this one up as just one more case of "physics envy" in the economics profession. Sorry. Maybe it won't always have to be like this.
Posted by: Luke Lea on April 4, 2004 02:59 PMDear Brad,
Oh yes, working with Seth is a blast. You knew him at Harvard? As Seth has only regaled me with what I'd estimate is no more than 20% of the better anecdotes about the wilder side of his youth, if you have anything amusing, salacious, incriminating, etc., I'd certainly be curious. :)
Regards,
Bill
Posted by: Bill on April 4, 2004 03:56 PMTom Slee: Quantum computing is not really interpretation-dependent-- it just depends on the linear state-evolution rules of QM actually holding for the system involved. Now, the many-worlds interpretation has a more expansive view than Copenhagen (or, I should really say, the caricature of it that is today called "Copenhagen") of where the rules do hold, so in that sense there is an interpretation dependence here.
But "Copenhagen" is slippery enough that the collapse can always be pushed back to something more irreversible or complicated. You could easily concoct crude versions of collapse interpretations that would have predicted that quantum-eraser experiments would not work. But they have worked, whenever anyone has tried them, so these versions of collapse are false. It's just that this pushes back the realm in which the collapse must happen. A successful quantum computer would do the same thing.
In other words, it's the success of quantum computing that would retain the indifference between interpretations, not its failure. If a quantum computer failed because of wavefunction collapse, that would knock out the many-worlds interpretation for good.
Now, there are other things that might doom a quantum computer: I've heard speculations to the effect that you could never control sources of error well enough to do much with one. But I don't know whether this is still considered a major objection.
Zizka, the many-worlds interpretation says pretty explicitly that if you were to construct a quantum coin-flipper that used radioactive decay to print out "heads" or "tails" at random (this or the equivalent would not be hard to do using college-laboratory equipment), and you examined the result, the whole wavefunction of the world including you would end up in a superposition of states in which you saw heads and in which you saw tails. Since there are lots of things that presumably magnify quantum noise up to the macroscopic level, we can probably safely say that there are macroscopically different yous out there, if the universal wavefunction is taken literally.
But actually measuring any effect of this would take godlike powers. These paradoxical thought experiments are usually resolved handily by figuring out what it would practically take for them to matter.
I once heard a lecture in which the speaker complained that if Schrödinger's cat could be macroscopically superposed, you could resurrect a certainly dead cat with 50% probability just by measuring an operator whose eigenstates were 50% dead-cat and 50% live-cat. How ridiculous! But I started thinking about what it would actually, practically take to measure such an operator, and realized that if you were capable of doing so, it would actually be easier for you to just take the dead cat apart into its constituent atoms and reassemble them into a live cat.
Matt M,
So there are multiple worlds only for quantum events which happen to be magnified macroscopically. How often does this happen naturally? It would seem that if it happens at all often, we get exponentially many worlds. EG, if there are 5 events in my life I would have the ttttt world, the ttttf world, etc., totalling 3125 Zizkas. but if I shared the world with a different guy with 5 different quantum events, that would be 3125-squared worlds. And of course if one of these events happened to be really significant, e.g. if I was using the flipper as to decide whether to get married, these worlds would diverge significantly (i.e. it wouldn't just be that I had differently marked slips of paper in a desk drawer in the various worlds.)
Sounds like fun science-fiction or an OK strophe for the Diamond sutra ("for every grain if sand in the Ganges there is another Ganges, and for every grain of sand in all these Ganges rivers together there is a universe full of diamonds and jewels") but it doesn't appeal to my reality sense.
What it means "in practice" is what I'm actually trying to get at, which seems to mean that I'm spoiling everyone's fun. A lot of theoretical physicists seem to take pride in the degree to which they violate common sense. While many great scientists did violate the common sense of their time, I don't think that that is a necessary, much less a sufficient condition for scientific advance.
Likewise for the cat -- you can leave out the cat and just use film, right?
My own inclination is to just guess that it will all come out in the wash and that many-worlds gets cancalled out by something or another. More fun would be to specify conditions in which it is of practical significance, just as relativity does have real practical significance in certain important ways even though much of our reality was adequately described by Newton.
Posted by: Zizka on April 4, 2004 09:15 PMMultiple quantum worlds being magnified macroscopically is not a good way to think about relative states (I won't use the term many worlds interpretation because it leads to really poor intuition.)
What happens is that when you measure something, it gets tied into a really big system. This system has tons of degrees of freedom. All these degrees of freedom tangle things up so badly that you can't see interference in the wavefunction any more (the famous two slit experiment is an example of this sort of interference.) The wavefunction can be thought of splitting into two 'decoherent' branches which cannot to a very high degree of certainty affect each other any more.
Some people (Bryce DeWitt in particular, I think) called these decoherent branches of the wavefunction worlds, but that's really not true. There's just one world and just one wavefunction. It's just all about how you look at it.
Just for fun, I'll mention why you cannot think of microscopic worlds. Let's say we have an electron and we've measured it's sping state. It's in the superposition
|up> + |down>
Now, maybe you'd like to interpret this as two different worlds, one in which the electron has spin up and the other in which the electron has spin down. But, there's a problem. The same state as above can be written as
|left> (essentially)
So, should we now interpret this as an electron in only one world with leftwards pointing spin? This is called the basis problem. What we say in quantum mechanics is that the operators for vertical spin and horizontal spin do not commute. This means that one cannot assign a definite value of these spins to a particle at the same time. (The fact that the position and momentum operators do not commute leads to the Heisenberg uncertainty principle.) When operators do not commute, there is no nice basis such that they all have a given value. In other words, in quantum mechanics, there is no well-defined set of 'worlds' one can use. That's why 'many worlds' is a bad way to think of this stuff IMO.
Posted by: Aaron on April 4, 2004 09:56 PMThe interperetation of QM is a notorious intellectual death trap for physicsts.
The smart ones get over it by the time they get to grad school.
Here is my question. What happens to conservation of matter/energy in the many worlds interpretation. If there are so many Zizkas'(and mes' and yous') being generated where is the matter/energy coming from?
Posted by: Vivek on April 4, 2004 11:46 PMhack,
And yet many great physicists return to the fundamental problems in later years. I recently saw Gutzwiller do a calculation in quantum field theory without using the notoriously suspect "in" and "out" states. Gell-Mann is another notable example, and there are many others.
For most of the 20th century, the rate of progress in theoretical physics was so rapid that greater rewards awaited those who didn't stop to smell the flowers. The culture was pragmatic, encouraging young physicists to calculate first and understand later. Now, except perhaps in string theory, the pace is much slower, and I'm not sure the old culture still serves us well.
Posted by: Matt on April 5, 2004 12:24 AMOne of the casualties of QM seems to be the idea that physics studies the basic realities and that it can provide a foundation for an understanding of less basic realities such as biology or human history. The attempts to make it do so are not rare, but usually doubtful: Bohm and "hidden variables", Capra (the Tao of Physics) and bootstrap theory, etc. Many-worlds seems to end up with nothing but weird science fiction (or maybe a more sophisticated Diamond Sutra). There are dozens of books out explaining that "Fundamentally, Time is not real" because physics processes are all reversible, but this doesn't really apply to the biological world, much less the human world.
Posted by: Zizka on April 5, 2004 07:05 AMAaron writes:
---------
Just for fun, I'll mention why you cannot think of microscopic worlds. Let's say we have an electron and we've measured it's sping state. It's in the superposition
|up> + |down>
Now, maybe you'd like to interpret this as two different worlds, one in which the electron has spin up and the other in which the electron has spin down.
------------
I don't like what you're doing, here.
If you've measured the state in the up-down basis, it's not in a superposition any more, and your two "world" are the world where you measured "up" and the world where you measured "down." If it's in a superpositon of "up" and "down," that's because you measured "left" or "right," and you've still got two "worlds," one for each outcome.
You're creating a conflict by abusing the measurement process.
I think you're also confusing where the "worlds" are-- there aren't multiple "worlds" for each of the multiple states in a superposition. The "worlds" appear only after measurement, and you get one for each possible outcome of that measurement.
Posted by: Chad Orzel on April 5, 2004 11:59 AMEditing mistake there. I meant to say 'prepared in the following state' (which is easy to do). The point I'm trying to make is exactly what you say. The popularizations often say that
|up> + |down>
represents two different microscopic worlds. This is wrong.
Posted by: Aaron on April 5, 2004 12:53 PMLook, I'm a teacher of physics at a midsized midwestern university and what I will say is what should be apparent from all the battling monologues already preceding me.
(i) decoherence is a separate topic from many world's interpretation vs. copenhagen interpretation
(ii) the reason why we physicists call them interpretations is that no one has thought up a good empirical way to test if one idea is the correct or not (see Popper, Karl & falsibility, scientific theory criterion)
(iii) All speculation aside, even experts can differ on the *definition* of the interpretations.
The matter of the fact is that Schrodinger's formulation of QM is very ugly. The whole "wave function collapse" idea comes from the way that one puts in "by hand" a measurement by Operating on the Psi with an Operator. The Operator as a mathematical event is very crude, and very traumatic. It works because the time-evolved Psi in practice "collapses" or has its symmetry broken "very quickly". However very quickly is not "instantaneous".
It has been long known that light pulses can prevent Psi collapse - indeed coherent light pulses can indefinitely delay radioactive decay - by exploiting heisenberg uncertainty. It's so well known it's taught in the back of Griffith's QM popular book.
The fact is spin is not spatially oriented in the normal sense until measured. What that means is is it "slides around" in a superposition of possible spatial orientations, and only chooses "one or the other" if one breaks the symmetry of the surrounding space-time with something like a magnetic field (as for the infamous case of the silver ions passing through a magnetic field splitting into two different discrete points on the screen).
However the coupling of the field that breaks the spatial symmetry and the spin of the ion is not instaneous, and is governed by QED. The finite time of relaxation, evolution, and coupling can more or less be modeled now in gross features, leading again to the conclusion that the catastrophic "collapse" of the wavefunction Psi when under the mathematical operation of an Operator is somewhat artificial.
QFT, QED, and QCD as well as even advanced WM while not perfect answer the question of breaking symmetry and coupling fairly well.
What is not well understood is the EPR paradox, quantum entanglement, non-localism, and the Young's Double slit interference pattern happening even when you pass one photon or electron through the slits one at a time. So the particle-waves interfere with each other (exist in a joined superposition of states) not just over space but time. They can be far away from each other or exist only one at a time, but they can still affect one another in a measurable way.
Now that is spooky.
Actually, if you want to do serious physics you try to model particles with the Klein-Gordon or Dirac equations since Schrodingers Psi function is as it turns out a rather poor descriptor with the spin put in by hand which always confuses countless undergraduates. It doesn't make much sense, because it was always a fairly ad hoc insertion unlike Heisenberg's approach.
From there you usually work your way into path integrals and the QED langrangian, and QFT which are much better descriptors, and the questions that Brad raised themselves become kind of moot.
Posted by: Oldman on April 5, 2004 12:53 PMNow that Oldman has implied that those of us with professional physics experience should not only participate in the fray, but inject also some appropriate cautionary words of wisdom...
First, let me second his trio of points:
---------------------
(i) decoherence is a separate topic from many world's interpretation vs. copenhagen interpretation [Bill's Note: Indeed, as others in this comment thread have noted, and as I should have noted in my very first comment, decoherence is measurable phenomenon quantifiable with standard quantum mechanical and quantum field theoretical techniques regardless of whatever your interpretation is, which is a nice segue to...]
(ii) the reason why we physicists call them *interpretations* is that no one has thought up a good empirical way to test if one idea is the correct or not (see Popper, Karl & falsibility, scientific theory criterion)
(iii) All speculation aside, even experts can differ on the *definition* of the interpretations.
------------------------
Second, let me elaborate on the third of his points...
Contrary to what some might believe, interpretation of quantum theory is not solely a topic of metaphysics in the standard (or maybe I should say stereotypical) philosophical sense. Much in the same way it's possible to use rigorous mathematical proof techniques to do metamathematics and illuminate the limits of mathematical proof (e.g., Godel, Turing, Chaitin), it is possible use rigorous physics and mathematics to do metaphysics and illuminate the "meaning" of quantum mechanics.
On that note, if you want a taste of what contemporary professional research is on the interpretation of quantum mechanics (as opposed to professionals popularizing what historically has been said about it), I'd highly recommend the following two references. ("A taste" is the operative phrase since the following are at the level of the professional, peer reviewed physics research literature.]
1) Jeffrey Bub, _Interpreting the Quantum World_ (Cambridge Univ. Press, corrected edition 1999), which is full-text viewable at Amazon.com at:
http://www.amazon.com/gp/reader/0521560829/ref=sib_dp_pt/104-5807035-8535102#reader-link
Bub, who boasts the stunning academic lineage of being a student of physicist David Bohm and philosophers Karl Popper and Imre Lakatos, uses non-Boolean logic to develop a characterization of *all possible* no-collapse interpretations of quantum mechanics, ("all possible" being subject to certain ostensibly innocuous constraints).
[By the way, Boolean logic is the representation of the classical logic one knows and loves, e.g., from high school geometry, in terms of binary (0-1, YES-NO, TRUE-FALSE) variables manipulated by ANDs, ORs, and NOTs. Non-Boolean logics imagine more general values for variables beyond the standard two and also can imagine more general operations on them than the standard ANDs, ORs, NOTs and their concatenations.]
Bub's motivating thesis is:
*********************
"... quantum mechanics is not about physical systems that exhibit a peculiar and elusive ontology, but rather about physical systems with a non-Boolean property structure. The problem is then how to make sense of a quantum world in which the properties of systems 'fit together' in a non-Boolean way." [pp. 232-3]
*********************
[Bill's Perhaps Unhelpful Translation Of The Above Quote: Quantum mechanics shouldn't be taken to imply philosophical realism is logically untenable, but rather that Boolean logic doesn't govern reality]
---------------------------
2) Christopher Fuchs, "Quantum Mechanics as Quantum Information (and only a little more)", available at:
http://arxiv.org/abs/quant-ph/0205039
Fuchs, who works at Bell Labs (Lucent Technologies) on quantum computation and information, has an admirable skepticism of the the blather (and I mean the expert blather!) that has been done on interpreting quantum theory. His motivating thesis can be seen in the following brilliant analogy to what Einstein really contributed to physics in his theory of Special Relativity:
*********************
"The Lorentz transformations [Bill's note: the key equations of special relativity] have the name they do, rather than, say, the Einstein transformations, for good reason: Lorentz had published some of them as early as 1895. [Bill's note: Einstein's epiphany was in 1905.] Indeed one could say that most of the empirical predictions of special relativity were in place well before Einstein came onto the scene. But that was of little consolation to the pre-Einsteinian physics community striving so hard to make sense of electromagnetic phenomena and the luminiferous ether. Precisely because the only justification for the Lorentz transformations appeared to be their empirical adequacy, they remained a mystery to be conquered. More particularly, this was a mystery that heaping further ad hoc (mathematical) structure onto could not possibly solve.
What was being begged for in the years between 1895 and 1905 was an understanding of the origin of that abstract, mathematical structure some simple, crisp physical statements with respect to which the necessity of the mathematics would be indisputable. Einstein supplied that and became one of the greatest physicists of all time. He reduced the mysterious structure of the Lorentz transformations to two simple statements expressible in common language:
1) the speed of light in empty space is independent of the speed of its source,
2) physics should appear the same in all inertial reference frames.
The deep significance of this for the quantum problem should stand up and speak overpoweringly
to anyone who admires these principles." [pp. 3-4]
*********************
In the remainder of the paper, Fuchs makes a compelling argument that the only hope for similarly expressing in straightforward English the fundamental content of the well-known and well-tested mathematical formalism of quantum mechanics is to methodically distill away those aspects of the formalism that have to do with subjective knowledge by use preparers/observers of systems until we get down to whatever distillate of objective system properties actually exists.
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