Thursday, July 14, 2016

GRW-style objective collapse theories are stupid, trivial to disprove

For a few weeks, the mass media pretending to write about science have saved our nerves and avoided the promotion of the anti-quantum jihad. As a reader pointed out, the hiatus is over. Nude Socialist has printed a new article with a revolutionary title announcing that quantum mechanics was overthrown again:
Collapse: Has quantum theory’s greatest mystery been solved?
If the title hasn't made you angry, the subtitle should do the job:
Our best theory of reality says things only become real when we look at them. Understanding how the universe came to be requires a better explanation.
Wow, quite a logic. Our best theory – quantum mechanics – is defined by the fact \(F\) that facts about Nature only appear at the moment when an observer makes an observation. In particular, this theory's being the best one also means that it is better than the previous framework, namely classical physics, which postulated \({\rm non}(F)\) i.e. the existence of lots of facts about Nature that exist independently of observations.

Because \(F\) is known to be better than \({\rm non}(F)\), a theory disagreeing with \(F\) surely cannot be "a better explanation". So what the hell are you talking about? The subtitle contradicts basic logic.

Note that the word "Universe" appears in the subtitle. The anti-quantum zealots love to assign the Universe with some religious powers. The Universe is someone who can team up with them to overthrow the laws of physics and the laws of logic, too. It can also restore a theory that was ruled out a century ago, these zealots apparently believe. Or at least, they want their readers to believe this assumption.

In reality, the Universe is just another physical object. The universal laws of physics apply to all physical objects – a muon, a hydrogen atom, DNA molecule, rat, human, Earth, Milky Way, and the Universe, indeed. You may have noticed that these universal laws and postulates are called universal which is a word that sounds awfully similar to the "Universe". It's no coincidence. The universal laws of physics are meant to primarily apply to the Universe.

Quantum mechanics is a universal law of physics. Its basic rules are known as the universal postulates of quantum mechanics. So how could possibly the Universe get an exception? The momentum of a muon only becomes a fact once it's observed by an observer. The same thing in principle holds for any property of the Universe.

The subtitle only implies one thing: that the writer and those who were helping him is hopelessly prejudiced, no amount of experimental evidence will ever convince him otherwise, and he is willing to use the word "Universe" as the ultimate weapon to bully all opponents and fight against any evidence – much like the Inquisition was using the word "God". But according to the scientific rules, the strength of such weapons is zero so everyone who is talking in this way remains an embarrassingly naked imbecile from any genuine scientist's viewpoint.

When I was a kid, I just couldn't understand why it could have taken more than a century after Copernicus for the apparent intellectual elite to adopt heliocentrism. Heliocentrism is so much obviously natural and more compatible with the observations. The people of that era had to be some semi-monkeys, I thought. However, now I see that they were pretty much the same people as the mankind today. It has been almost one century when quantum mechanics – with its important defining finding that facts only exist once they are observed – was discovered. And so many people pretending to be smart or intellectuals or physicists – the true contemporary counterparts of the Inquisition – are still violently fighting against the very basic lessons.

Most of these people just don't understand quantum mechanics, refuse to accept it, and don't bother proposing any alternatives. Those who propose alternatives may be largely categorized to three pseudoscientific sects: the Bohmian, the Everettian, and the Ghirardian sect. A month ago, the mass media wanted their readers to drown in the Bohmian and Everettian cesspools. So it's probably fair that in their new salvo of anti-quantum jihad, Nude Socialist has decided to defend the Ghirardian sect i.e. the "objective collapse" theories.

The first TRF blog post fully dedicated to the Ghirardi-Rimini-Weber collapse theories was written in 2011. Dozens text mentioning this paradigm were posted afterwards. Two most straightforward ways to show that this whole line of thinking is wrong are: the low heat capacities that disprove any realistic theory with many classical degrees of freedom (and you need many to emulate quantum mechanics); and the silence of the matter.

I insist that the rest of the blog post is a sequence of arguments that an intelligent reader should understand, refine, and rediscover in less than an hour and become sure that these "objective collapse" theories are completely wrong; and never positively touch this garbage in her life again. Everyone who fails to do so and who keeps on working with this stuff is a retarded bigot. That clearly includes Angelo Bassi, an objective collapse inkspiller, a repeated co-author of GianCarlo Ghirardi's, and a main "authority" backing the pseudoscientific article in Nude Socialist.

(You may look at this interview with Bassi. He gets excited and smiles only once, around 1:25 when the troglodyte explains what it means for him not to "believe in quantum mechanics".)

OK, what are the "objective collapse theories"? They're classical theories in which the wave function from quantum mechanics follows the same Schrödinger's equation as it does in quantum mechanics. But its interpretation is completely changed. Like in other realist theories, it's interpreted as "a set of classical degrees of freedom" that describe the reality in the same way as degrees of freedom always did in any classical theory – as some information that exists "out there" independently of any observer(s).

However, Schrödinger's equation "spreads" the wave packets all over the space, into superpositions of macroscopically different states and we never perceive such superpositions. In quantum mechanics, this fact is guaranteed by the postulate that observers only observe eigenvalues of operators linked to observables they want to observe; and the corresponding eigenstate is the post-observation state of the system. That state can be used to make additional (probabilistic) predictions in the future.

In the "objective collapse" theories, they want to achieve a similar collapse but without an observer. So they postulate that the wave function is (sometimes) collapsing objectively. Nature Herself sends Her officials to do a similar "work of collapse" on the wave function (at random moments) that observers do (when they want to observe something). A modification of the Schrödinger's evolution has to be applied to the theory. This modification "protects" the wave functions from becoming too spread or becoming the well-known unintuitive superpositions of macroscopically different states, the Schrödinger cat states that all the anti-quantum zealots by definition hate (although they are equally allowed as any other states by the basic linearity-of-Hilbert-space postulate of quantum mechanics).

How does it work? Every particle (they need an identification and counter of particles, so the setup has similar problems to be reconciled with quantum field theory as the Bohmian pseudoscience) has an extra classical random generator in it. Randomly, in average, once in \(T=10^{15}\,{\rm years}\), the density matrix "objectively collapses" in an effort to prevent the given particle from "quantum spreading" too much. The matrix elements of the density matrix get transformed by\[

\bra{q}\rho_{\rm new}\ket{Q}= \bra{q}\rho_{\rm old}\ket{Q}\cdot e^{-(q-Q)^2/ 4R^2}

\] in this collapse. So the off-diagonal elements in which \(q,Q\) are too far from each other (those that know about the relative phase of the wave function for two different positions), namely further than some distance scale \(R=\sqrt{1/\alpha}\approx 10^{-7}\,{\rm m}\), are suddenly suppressed.

(This prescription still allows the probabilities to be large for very different values of the position after the collapse, so the action on the density matrix is just a form of an artificially induced decoherence that doesn't require any environment. Alternative versions of the "objective collapse" theories also localize the position itself.)

Note that the Gaussian profile of the "filter defining the collapse" is arbitrary (there's obviously no evidence that such a function should be preferred) and so are the parameters \(R,T\). Proper quantum mechanics doesn't allow any "objective collapse" – which may be described as the \(R\to \infty\) or \(T\to \infty\) (or a compromise) limit of the "objective collapse" prescription above. (These processes disappear if the frequency goes to zero; and they also disappear when the degree of localization allows complete delocalization, i.e. when the exponential factor reduces to one).

Because the "objective collapse" people don't like the superpositions, they need to pick a finite value of both \(R\) and \(T\). However, at the same moment, this implies deviations from proper quantum mechanics when \(R\) and \(T\) are finite. And if \(R\) and \(T\) are small enough, and they need to be in order to ban the superpositions that the anti-quantum zealots hate, the deviations may be easily seen to rule out the "objective collapse" theories in all forms.

Why? They really want the "objective collapse" to be a reason why a small piece of dust that you may barely see with your eyes has a seemingly well-defined position. Maybe you may use a great magnifying glass or a microscope. With that tool, you can resolve some \(0.1\) microns. So the "objective collapse" priest should believe \(R\lt 0.1\,{\rm microns}\), otherwise he would still need some observation-dependent way to explain why small things we see seemingly have well-defined positions.

Also, the collapse should be taking place sufficiently frequently so that the dust doesn't have enough time to quantum evolve into some spread packets. So the frequency of a collapse per particle is once per at most \(T\lt 10^{15}\,{\rm years}\). The number of collapses per unit time that a piece of dust makes is proportional to the number of elementary particles it contains. And with the numbers I mentioned, you can explain why this small object objectively has a position that is sharp with the same accuracy with which you can observe it with a microscope or something like that. If it's not enough, lower either \(R\) or \(T\) or both.

However, a basic fact is that in this way, we have changed the theory. Doesn't it lead to some phenomena that could be observed and decide whether Nature follows quantum mechanics or its "objective collapse" deformation? You bet. We said that the objective collapse multiplies the wave function (or density matrix) by some Gaussian whose width is \(R\), some \(0.1\,{\rm microns}\). What is the interpretation of this multiplication in the momentum basis? Well, the multiplication in the \(x\)-basis gets mapped to a convolution in the \(p\)-basis. So the collapse is replacing the wave function by its convolution with the "dual Gaussian packet" whose width is some \(\Delta p\sim \hbar / R\).

Because the \(R\) we mentioned to be "appropriate" according to the "objective collapse" bigots is comparable to the wavelength of the light emitted by the hydrogen atom, you won't be surprised that the corresponding \(\Delta p\) is comparable to the momentum of the photon emitted by the hydrogen atom, some \(1\eV/c\). So when it comes to the motion of the particles, the "objective collapse" is nothing else than a kick that adds some uncertainty to the particle's momentum and the uncertainty is comparable to \(\Delta p\sim 1\eV/c\).

One electronvolt is small relatively to \(13\TeV\), the center-of-mass energy at the LHC, so it could be invisible at the LHC. However, one electronvolt is very high relatively to energies that are important in condensed matter physics. For example, the binding energy that holds a Cooper pair together is some \(0.001\eV\). The "objective collapse" must apply to every electron and once it hits an electron in a Cooper pair, the Cooper pair is violently broken to pieces because it's hit by an energy that exceeds the binding energy by orders of magnitude.

That's too bad because the "objective collapse" theory unavoidably predicts that superconductors are noisy and immediately start to produce friction. They're predicted to lose the superconductivity very soon. Obviously, none of these things is taking place. Superconductivity works. So quantum mechanics is confirmed while the "objective collapse" theories are hopelessly killed. I discussed these things in the blog post on the silence of matter.

Let me refine the discussion a little bit. If the momentum of an electron changes by \(1\eV/c\), it doesn't mean that the energy changes by \(1\eV\) because the electron is basically non-relativistic. So the impact of the "objective collapse" on the motion of an electron is smaller than I indicated. In fact, we don't need to talk about the momentum at all. The discussion in the position basis is OK.

The size of a Cooper pair is some 1000Å, the coherence length in this discussion, which happens to be exactly \(0.1\,{\rm microns}\). So the size of the Cooper pair is exactly of the same order as the proposed \(R\) describing the "objective collapse". A Cooper pair has a wave function that is analogous to that of a hydrogen atom except that there are two electrons inside; they are held together by the exchange of virtual phonons, not photons; and the size is 1,000 times greater. But you can see that the multiplication of the wave function by the Gaussian excites the Cooper pair where the electron belongs at a probability of order 50% and breaks it apart with a similar probability.

If you wanted to avoid the falsification, you would need to choose an "objective collapse" with \(R\gg 0.1\,{\rm microns}\), much longer \(R\) than the size of Cooper pairs. The rate of the breaking of the Cooper pairs could become small in that case. But Cooper pairs aren't the only things with electronvolt-like energies you can encounter in condensed matter physics. There are lots of binding energies in chemistry that are much smaller than an electronvolt. The "objective collapse" theory would still predict that all these chemical compounds must decay rather quickly.

Moreover, even \(R\sim 0.1\,{\rm microns}\) is already too long to represent the "desired" explanation that "objects seem to have classical positions because they do have classical positions". Why? Because the electrons running through Intel chips effectively obey the law of classical logic – Intel microprocessors are classical, not quantum, computers. And you know that the size of the Intel transistors is currently at 14 nm which is \(0.014\,{\rm microns}\), seven times shorter than \(0.1\,{\rm microns}\).

So the electrons in Intel microprocessors behave "classically" and they know into which transistor they belong even though this "classicalization" cannot be explained by the "objective collapse"! The objective collapse only localizes the electrons within \(0.1\,{\rm microns}\) while we would need \(0.014\,{\rm microns}\) to make their positions "classical" with the accuracy of the Intel architecture.

This is just a very particular example of a general fact that is totally misunderstood by all the anti-quantum zealots: Quantum mechanics doesn't have to be made "more classical". It is similar to a classical theory exactly to the degree it should be similar to a classical theory. When an experiment shows that some phenomenon behaves according to the classical theory, it behaves according to the quantum theory, too! Quantum mechanics allows superpositions of an electron at two different transistors. But that does not mean that this superposition is routinely created (with a high probability) in the quantum evolution of an Intel chip. The fact that quantum mechanics allows superpositions does not imply that every Intel chip behaves as a quantum computer.

It just doesn't. You shouldn't look for any "cure" of the superpositions because there is no disease. All the superpositions are allowed and must be allowed because it is one of the most universal laws of Nature – and these superpositions are indeed vital to understand a huge spectrum of quantum mechanical experiments. But this law of Nature isn't "bad" in any sense. It is not producing any wrong predictions by itself. It agrees with everything we have ever observed.

All these Everettian, Bohmian, and Ghirardian sects are based on the religious dogma that there is a disease of quantum mechanics that you shall cure. But there's no disease. As Ronald Reagan said about the government:
The observer-free mental frameworks are not a solution to our problem; the observer-free mental frameworks are the problem.
Whenever you try to deviate from the laws of quantum mechanics, you clearly make things worse – less natural, less universal, or incompatible with the observations. Whenever you try to describe what is the "alleged problem" quantitatively, you will unavoidably see that the "cure" either doesn't solve it, or only solves it for the price of predicting contradictions with the experiment.

Similarly, the "objective collapse" theories predict huge heat capacities of atoms, sharply contradicing the experimental fact that the heat capacity of every atom is comparable to \(k_B\). The wave functions of atoms are reinterpreted by Ghirardi et al. as collections of very many classical degrees of freedom. Even if you modify the wave function slightly, you get a state that is in principle mutually exclusive. (That's not how it works in quantum mechanics; only orthogonal states are mutually exclusive.)

If you have many atoms, you must assign some probabilistic distribution to the possible profiles of the atoms' wave functions that you get in an equilibrium. Even if the atoms' wave functions are supposed to be near the ground state wave function, oscillations around that state are possible. Because the Ghirardian theory is conceptually classical, the amplitudes of the oscillation of the "objectified wave function" around the ground state may be arbitrarily small. So it doesn't matter that the frequency is high.

Whether you like it or not, you basically restore the ultraviolet catastrophe of classical physics. Every degree of freedom that may oscillate will oscillate and bring the average countribution to the energy of \(k_BT\) or \(k_BT/2\) – and to the entropy of order \(k_B\). Because there are infinitely many degrees of freedom in the "objectified wave function", e.g. all the complex amplitudes \(c_n\) in front of all the excited energy eigenstates (and these complex amplitudes behave as 2D classical harmonic oscillators in every realist theory that borrows the mathematics of evolution but not the correct interpretation of the state vector from quantum mechanics), the heat capacity of the atom will unavoidably be infinitely many times \(k_B\). At most, you may truncate the highly excited states of the atom in some way and turn it into a "large multiple" of \(k_B\). It is experimentally excluded, anyway.

While the anti-quantum zealots believe that objects such as the quantum mechanical wave function "should" be interpreted as some classical degrees of freedom, the observation of low heat capacities etc. are pretty much direct experimental observations of the fact that they are not. Experiments really observe pretty much directly that Heisenberg, Born, Jordan, Bohr, Dirac, Pauli etc. are right while all those who disagree are wrong. Once you accept that there have to be objects in a viable theory that carry at least as much information in the mathematical sense as the wave function, the experiments are enough to directly and instantly prove that these objects cannot be interpreted as something that "objectively exists out there".

It's terrible that now, 90 years after the birth of quantum mechanics, there still exists a whole community of crackpots pretending to be scientists who are trying to return us before 1925 – much like the geocentrists wanted to "undo" the insights of Copernicus 90 years after those were made. And it's terrible that magazines that pretend to write about science – such as Nude Socialist – are openly helping to promote this unscientific or really anti-scientific rubbish.

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