Sunday, June 12, 2011

Ghirardi, Rimini, Weber: a collapsed pseudoscience

Many people are incapable of understanding that the experimental as well as theoretical evidence shows that quantum mechanics is right.

They can't see or don't want to see that the world is described by state vectors that inevitably have a probabilistic interpretation, that evolve according to linear equations and satisfy the superposition principle, that all measurable properties of the physical systems are described by linear Hermitian operators, and that probabilities are the only predictable things that always arise from squared magnitudes of some complex probability amplitudes.

Various people who dream about the resuscitation of classical physics and a reversal of the last 85 years of physics have done pretty much all the conceivable mistakes and have proposed lots of diverse, deluded, and fundamentally flawed schemes whose only purpose is to hide the most important insight of the 20th century science, the framework of quantum mechanics, from the authors' eyesight.

Bohmian pseudoscience

I have spent lots of time with explaining why various major frameworks designed to deny quantum mechanics are deeply flawed. The de Broglie-Bohm pilot wave theory claims that there exist both particles and waves. The waves are guiding the motion of particles in a manifestly non-local, non-relativistic way (when there are at least two particles). There are other aspects that make it incompatible with relativity and quantum field theory - e.g. its impossible coherent description of the spin and quantum fields.

But much more generally, what is flawed about the approach is that it is imagining that there are some "preferred" observables - usually positions - that have well-defined values at a given moment (a particle is really there) while other observables such as the spin with respect to an axis are "not real" because there's no way how to describe them consistently in the Bohmian framework - and moreover, the authors of the scheme must kind of understand that different observables don't commute with each other in the proper physics, so it is fundamentally misguided to try to define all of them at a given moment.

This separation of observables to the real "primitive" observables or beables and the "contextual" or unreal ones that still have to obey quantum mechanics in some sense is completely spurious and artificial. As a result, the approach totally disagrees with the insights about decoherence. Decoherence shows that the physical quantities that "behave approximately classically" after some time in a given environment are fully determined by the Hamiltonian, by the dynamical laws of the theory. There's absolutely no freedom for you to pre-decide which quantities should behave classically (or be "primitive") and which observables shouldn't (and remain "contextual") because the Hamiltonian has the responsibility for this decision: see TRF.

Decoherence really kills the very basic pillars of the de Broglie-Bohm paradigm and I am amazed that some people still haven't noticed.

Everetian pseudoscience

Recently, I have also discussed the many worlds pseudoscience initiated by Hugh Everett III. In that picture, one is imagining that the other alternative outcomes of the experiments are "real worlds somewhere". Except that this picture, while it depends on the real existence of "other worlds", can't provide us with any mechanism how and when the worlds really split so that the possibility of a later interference is not destroyed. (And 0.1 microns is already too long a distance for a good "classical description" - because even distances 10^{-15} meters are known to behave perfectly classically, so GRW really don't solve what they wanted solve.)

Also, this picture can't really give any interpretation to the main set of numbers that every quantum mechanical theory is all about - the probability amplitudes - because the different alternatives are "equally real worlds". Again, it is strikingly obvious that the whole paradigm is incorrect because there is never any exact "splitting of the worlds". Different histories or different outcomes of a measurement only become "mutually exclusive" in the classical sense because of decoherence which is never quite complete. Classical physics only emerges in a limit and always stays approximate - and this is also true for the strict classical logic and classical probability theory that emerge from another approximate description of a phenomenon in terms of decoherence. The world fundamentally remains quantum mechanical.

In principle, there's always some possibility for different terms in the state vector to interfere with each other at some later moment. This possibility is just becoming very unlikely because the off-diagonal elements of the density matrix for observable degrees of freedom expo-exponentially rapidly converge to zero. But it's fundamentally flawed to imagine that there is any moment in which the different outcomes have been objectively and "strictly split".

Ghirardi, Rimini, Weber: a real collapse

But I want to discuss another approach that hasn't been described on this blog yet: the GRW approach. The basic 1986 paper in PRD has 1217 citations as of today which is just gigantic if you realize that the paper is complete crackpottery:
Unified dynamics for microscopic and macroscopic systems (PDF full)
Much like in the other anti-quantum approaches, this approach is trying to make some "classical reality". Unlike the Bohmian pseudoscience, it doesn't add any sharp positions of the particles. Instead, it keeps Schrödinger's equation only and adds some nonlinear "flashes" into the evolution that are meant to squeeze the state vector in the mantinels that the authors consider "appropriate".

It's very easy to describe what their proposal is - even though you may have a hard time to extract this basic point from the dozens of useless pages of the paper above. Imagine Schrödinger's equation for N non-relativistic particles - like the Bohmian pseudoscience, the formalism is linked to particles of the non-relativistic type, so all attempts to apply it to fields are inevitably awkward.

It is evolving according to Schrödinger's equation but GRW don't like that it's spreading because they want to imagine that the wave function is a "real object" and "real macroscopic objects" are not spreading - a classical misinterpretation of the wave function by all the anti-quantum "thinkers". Well, it obviously is spreading and there are many outcomes that have various probabilities - which doesn't hurt - but GRW just don't like it. So they decide that the wave function shouldn't freely spread! How do they ban the spreading? Well, that's easy for GRW.

They say that every 10^{15} seconds, which is a randomly chosen new bureaucratic constant of Nature (whose value is of course completely fabricated and has nothing to do with any justifiable laws of physics or any observations) each particle is obliged to prove to the census officials that it has a rather well-defined location. So there is a Poisson process running for each particle that once per 10^{15} seconds in average, it says "flash" to each particle. The more particles you have, the more flashes you obtain.

Each flash is associated with a particle label "J" - pretend that the particles are distinguishable. The flash is also characterized by a position in the real space, R = (x,y,z). What does the flash do? It changes the wave function discontinuously. How? The wave function Psi(r1,r2, ... rn,t-epsilon) before the flash is changed to a new
# Psi(r1,r2, ... rn) exp(-(rJ - R)2/2a2)
The factor # is chosen to preserve the normalization of the wave function - you surely know how to calculate it as the square root of an integral to guarantee that the new wave function is normalized if the old one is. The whole Gaussian profile is randomly invented. Different functions would produce different theories. Clearly, there's not a glimpse of a justification for a particular function.

The flash is associated with the point in space, R. You see that the wave function for the J-th particle is modified so that the J-th particle will suddenly be more concentrated around the point R (while its finer patterns remain unchanged - it just eliminates the portions of the wave function that is too far from R). You don't want the particles to jump to random locations, so R is chosen randomly from the distribution that coincides with the probability distribution for the J-th particle before the flash - the integral of Psi*Psi over all the other particles' positions.

So it's more likely for the position of the J-th particle to collapse to the place where its wave function is concentrated. Needless to say, the distance parameter "a" is another awkward unjustified bureaucratic dumb parameter that the GRW theory needs to add.

So you see that these particular "physicists" are obsessed with the idea that quantum mechanics, including the superposition principle and the freedom of wave functions to spread freely, has to be bureaucratically suppressed, so they invent a random time scale 10^{15} seconds and a random new width of a wave function for a particle, 0.1 microns, that force individual particles to keep a rather well-defined citizenship. Every 10^{15} seconds, each particle has to undergo a census in which it has to fill its position with the accuracy of 0.1 microns. Because the relative positions between particles are kind of constrained in the bound states, a flash acting on a single particle affects other particles that share a macroscopic object with the flashed particle - so all of them become "localized".

Now, this doubly artificial prescription - depending on two new and totally unphysical bogus parameters (the only genuinely universal parameter that decides about the validity of the classical approximation to quantum mechanics is hbar!) - may seemingly have the "right impact" that makes the world "look like" it does in the proper quantum mechanics. Morever, we've added some perturbation to the system. Does it hurt?

Of course, the bureaucratic values of the timing and the width of the the collapsed packet are chosen to express the feelings of the authors about "what is microscopic" and "what is macroscopic". The collapse is meant to make large objects behave classically. Only if you have 10^{15} particles or more - a macroscopic object - you get a collapse every second. But doesn't it hurt the quantum properties of the objects?

You bet. While the "accuracy of the citizenship" is chosen to be 0.1 microns - which is very high relatively to the size of the atom - it is still vastly smaller than the distance scales at which real particles in the real world may be delocalized according to the wave functions. The latter is, of course, infinite. There is no limit. Particles may have delocalized wave functions. It's a basic point of quantum mechanics.

Consider a large crystal or metal, e.g. a cube whose side is 10 meters. You can buy those. It's 1,000 cubic meters and the weight could be almost 10^7 kilograms or 10,000 tons. Now, does the squeezing of the wave functions of the electrons affect them in a measurable way? You bet.

The linear size is 10 meters which is 10^{11} times the atomic radius. So there are about 10^{33} atoms in it so that 10^{33-15} = 10^{18} flashes appear each second. Obviously, the census officials will keep the position of the crystal "classical". But will they also preserve the internal integrity of this bound state of many nuclei and electrons?

If an electron has a wavelength that is longer than those GRW 10^{-7} meters, then the flash will substantially change its energy. It means that the electron's wave number "k" should be smaller than 10^{7} inverse meters. The spacing of "k" in each direction is 0.1 inverse meters (the inverse size of the crystal), so there are 10^{8} possible values of "kx" as well as "ky" and "kz" for which the electron has a lower energy before the flash. Consequently, there are 10^{24} electrons in our crystal that satisfy the condition. Each 10^{24-15} = 10^{-9} seconds (one nanosecond), the GRW flash will substantially kick an electron so that it has a very different energy.

Similar "flashes" will also destroy the coherence of laser beams (which may have much more than 10^{15} photons that are coherent at distances much longer than 0.1 microns) and do many other nasty things. Every time you have a flash, you really shift the position of the whole system by 0.1 microns. Do you think it couldn't be seen? Don't be silly. Interferometers may measure positions of their arms with the accuracy of 10^{-15} meters or so.

Now, you may try to observe those "predictions" and be sure, you will never see any of these pathological GRW effects because they're just completely unsubstantiated violations of basic principles of quantum physics such as the superposition principle. You may try to slow down the frequency of the flashes or make the post-flash packets wider, so that the predicted pathological effects of the GRW flashes are diminished. And indeed, when you do so, you will restore quantum mechanics in the ultimate limit because the GRW additions will become inconsequential.

If you go to the limit, i.e. if you send the GRW time scale to infinity and/or you send the GRW distance scale to infinity, will you get a valid theory that agrees with the observations of microscopic as well as macroscopic objects in the real world? You bet. In the limit I described, you obtain proper quantum mechanics and you can be damn sure that the predictions of unmutated untwisted unmessed-up-with quantum mechanics agree with the observed behavior of all systems in the world, despite the attempts of anti-quantum zealots to claim otherwise. They surely agree with the behavior of the microscopic objects - that's what GRW agreed with which is why they chose quantum mechanics as their starting point. But quantum mechanics also agrees with the behavior of the large objects: in particular, it predicts that one will never observe a large object "at two points simultaneously". The sign "+" in the wave function or density matrix doesn't mean "AND": it means "OR". If you want a symbol for "AND", you need "x", multiplication.

Quantum mechanics works perfectly well for any kind of objects which is the first thing that people should try to understand before they start to spend years with completely unjustifiable and thoroughly idiotic attempts to mess up with quantum mechanics.

Don't mess up with quantum mechanics.

And that's the memo.

By the way, I had to write this rant because I had to go through the end notes of The Hidden Reality supplementing the chapter on quantum mechanics. I am pretty much sure that all other popular books on quantum mechanics look similar if not worse but it just drives me up the wall! Pretty much every sentence is fundamentally wrong, usually upside down. Ten years ago, I wouldn't believe that I could say anything like that about the author's text on quantum mechanics.


  1. "...quantum mechanics is right."

    It may be right, but it isn't physics, since the only reality it allows is "complex probability amplitudes", that are somehow capable of interfering with one another, but only formally (and I would add, but not really, and you would adamantly disagree -- neither one of us knows the answer, the only difference is you think you do, and I refuse to "believe"). It's all just beautiful Hamiltonian mathematics+transform theory (between space and phase space, r and p, so really TWO realities, or one Reality with two faces, "dual" to one another -- Good Lord), and the 19 year-old me who first encountered them enthusiastically agrees it is beautiful, at first blush; but hard reality has never relinquished its hold upon me, and frankly, there's nothing there in your summary of quantum mechanics. No one has ever done anything with it, despite the claims for lasers and semi-conductor electronics. It's like looking at some beautiful celebrity: She's amazing, thrilling, perfect -- but you can't have her, you can't touch her. No one has ever touched quantum mechanics, in my 45 years of scientific adulthood. It is a fantasy, that enervates true insight.

  2. Hi, quantum mechanics not only is physics. Quantum mechanics is *all* of physics.

  3. It's hard to disagree with Lubos on this one. It may be difficult to ontologically define what "is really happening" in quantum mechanics but some of the proposed interpretations to get rid of the strangeness of the theory are more akin to scientific flavoured fantasy than actual demonstrable science.

    In fact, most misunderstandings about interpretations of quantum theory seem to stem from misunderstandings in the interpretation of probability theory, particularly of its frequentist flavour. Baez has written some very interesting remarks on that point.

    I say we stop telling god whether or not he should throw dice.

    And on a related note, your comment on the block of metal makes this particular approach terribly easy to disprove: all you need to do is measure its thermal and electrical conductivities, which are effected directly by electron delocalization. The values calculated from quantum mechanics agree withe experiment. Is this also true of the values calculated with GRW?

  4. HDH,

    You suffer from the same delusion as all the others who just can't get QM. It is the classical view, which assumes that "reality" exists independently of any observer. We all experience reality every waking moment and it is a real leap to dismiss all that experience but reality is not well defined mathematically and, thus, cannot be a scientific concept. Until you get over the very idea of reality you will be unable to grasp QM. Reality has nothing to do with physics!
    By the way, I have almost a decade on you as a professional scientist.

  5. And all of physics is just a mathematical model of some parts of the sensory experience. Models are just that - models.

    Also, I have a feeling models can be expressed in a wide range of formalisms, how can one be sure QM can't be equally well expressed using tools other than Hilbert space theory, wave functions and the like?

    Sorry if my comments sound silly, I'm not a physicist.

  6. Lubos, I'm gratified to see you criticize the IMHO deeply flawed MWI. MWI as such should indeed simply yield an effective probability of 50/50 frequentist ratio (since if the WFs continue to evolve, their amplitudes in effect "go to waste" and we just count up relative branches.) From what I can make of attempts to derive the Born rule instead, they are ultimately circular reasoning where the BR is somehow put in by hand instead of a genuine consequence in no need of additional assumptions.

    However, you still seem sympathetic to the decoherence approach to "explaining collapse" despite giving it some appropriate knocks here. Note that hard core supporters of the DI imagine that decoherence separates the alternative states, which effectively leads to MWI anyway. Also, they are trying to indeed resuscitate classical type physics by saying, there is *ultimately* no real statistics, since the WF continues to evolve deterministically.

    I don't think it's a matter of how complete the decoherence is. The exact distribution of the superpositions only affects statistics of many measurements, it shouldn't determine the logical exclusivity per se of a single case versus "seeing the superpositions." A less coherent wave is just that, still spread out, still superposed, and not something logically different in principle. Note that if decoherence was really vital to not seeing superpositions anymore, then how would we find coherent quantum statistics too? We'd never have statistical proof of the coherent double slit interference!

    I proposed an experiment at to test whether decoherence can turn a superposition into a mixture (even just "effectively" so), readers might find it interesting.

  7. Right, the probability is never derived from anything in MWI - even though *all* quantitative knowledge about the quantum phenomena is a function of these probabilities. From this viewpoint, MWI has exactly *zero* to do with physics.

    I don't understand why you think that decoherence "leads" to MWI. Decoherence is just a provable process in quantum mechanics - in Copenhagen or any similar quantum mechanics.

    The wave function *does* evolve deterministically but the interpretation of the wave function is that it predicts probabilities of phenomena in the real world. There is no contradiction and I assure you that any opinion that there is a contradiction is a result of a sloppy thinking.

    Much like others, you seem to invent non-existent problems of quantum mechanics. I have answered all the questions you have asked about 50 times already. Why the hell people are still asking these elementary questions?

  8. Lubos - I should have been more careful in my wording to keep a characterization seeming to be my own opinion. First, of course the process of decoherence exists. However, advocates of a concept sometimes called "the decoherence interpretation" think that:
    1.Decoherence causes the various elements of a superposition (like, oversimplified, alive cat + dead cat) to be unable to "interact" in any way. They say, incredibly to me, that decoherence "turns a superposition into a mixture." (Well no, they are both still there unless something other than mere muddying of amplitude relations takes one of them away.)
    2. These states all continue to evolve, and are never removed by a collapse event.
    3. Since the allegedly separated states don't interact ("can't interfere anymore"), they are equivalent to MWI - but that depends on buying their claim that the states exist but don't interact! My experiment is designed to disprove their claim, and hence cast doubt on MWI.

    I don't agree with them, I'm just putting forth how they try to combine the two ideas. I myself agree that the universe is literally probabilistic: one outcome happens, the other doesn't - period. The reason many people say that is problematical, is if the wave function extends out into space how does collapse localize that and "get rid of" the other alternatives? It's the issue of unitary evolution punctuated by a reordering of the situation.

    Just consider, the photon out of the beamsplitter: the components of the superposition both continue toward detectors, and when one clicks - no determinism about which one, only the statistics - the other WF has to vanish (if we imagine it as realists.) I don't worry a lot since, like some commenters above, I am not a "realist" but a contextualist. I don't think there's a clear cut "actual independent nature" of a WF etc.

  9. Apologies, Neil, I think that what you write makes no sense.

    For example, it's the very point of decoherence that it brings a superposition of states "psi1 + psi2" to a mixture of density matrices, "rho1 + rho2", which is achieved by evolving "psi1 + psi2" to "psi1.psi1(env) + psi2.psi2(env)" and by tracing over the environmental degrees of freedom - a tensor factor of the Hilbert space.

    The resulting mixture behaves equivalently to probabilities in classical physics. If you have any problem with the statement above, it simply means that you don't understand what the concept of decoherence means. It doesn't mean that you have some original great opinions. It just means that you're deluded about those points.

  10. Lubos, I do understand the density matrix concept. I just say it doesn't do the extra work that many people think it does. Remember that it combines the probabilities of different states with the statistics derived from the squared amplitudes. But that doesn't remove the issue of when the wave function turns from superpositions into statistics. Sure, when something converts the superposition *into* statistical results, those statistics are like those of a mixture - but you need some intervention to make that conversion. Otherwise, you just have the disordered superposition.

    The DM simply includes the statistical reduction into itself as a whole, it doesn't explain it or deal with issues of timing and discontinuous evolution. It would be a form of circular argument to think it led to specific results, instead of just representing them as fait accompli with no derivation.

    BTW the experiment I propose would show whether the output from an MZI subject to confuser (Chad Orzels' example) was a mixture as he supposes (and I do not), which is better than any amount of mere debate.

    Even though you are critical of me (I think, due to unnecessary misunderstandings), I applaud you for posting my comments, something for example very hard to do at Woit's blog.

  11. Hi Lubos - any thoughts on Tumulka's work on making GRWflash compatible with relativity?

  12. Science is a process of constant curiosity, and constant revisions to make theories more factual and less mythical. You seem to be saying that quantum mechanics has become a perfect theory at its most unrealistic stage, and that all later developments are heresy -- that's antithetical to science.

    You seem to be saying it's been established beyond a doubt that everything is probabilistic. Don't you realize such a pronouncement is self-contradictory? If quantum mechanics is correct, then it's really correct, and it can't consistently deny the reality that verifies it. On the other hand, if there's no reality, then the results of experiments would be different depending on what the experimenters believe.

  13. Hi Collin, "heresy" isn't really a concept used by scientists. I am not saying that attempts to describe quantum phenomena non-probabilistically are heresy. Instead, they are demonstrably wrong, they are junk science, and people like you who defend them are cranks.

    There is no contradiction in the fact that modern science - which has been fundamentally probabilistic - can establish insights as safely (or more so) as the classical physics. Evidence in science has been of probabilistic character from the beginning, long before the fundamental laws of Nature were shown to be probabilistic, and it still worked. It works in quantum mechanics, too - in many ways, quantum mechanics allows one to make sharper claims than classical physics, e.g. because of the discrete spectrum of many observables.

    The evidence proving that quantum mechanics is fundamentally subjective - it's the perceptions by individual observers - whether you like this fact or not.