Redundant synonyms of decoherence

 Luboš Motl, October 03, 2014

Wojciech H. Zurek – the father of decoherence, if we use a somewhat pompous language – wrote an article for Physics Today,

Quantum Darwinism, classical reality, and the randomness of quantum jumps,

which you will probably be unable to access because the server will probably demand $30 from you and you will probably think that it’s too much to pay, especially because you may get older, almost identical texts by the author, as well as a newer 2009 free article in Nature.

You know, decoherence is a genuine process. The insights about it are right and probably needed to explain some aspects of quantum mechanics to those who believe that there is something wrong about quantum mechanics because of what they call the «measurement problem».

But I have increasingly felt that the fans of the word «decoherence» and related words, including Zurek himself, have contributed to the proliferation of quantum flapdoodle – redundant talk about non-existent problems.

What is decoherence? It’s a simple process to explain. When you study the wave function in a basis, it is described by complex amplitudes \(c_i\) multiplying the states of the observed system \(\ket{\psi_i}\). All absolute values and phases (except for one overall normalization and one overall phase of the wave function) have physical consequences.

When this system of interest interacts with some environmental degrees of freedom, \(\ket{\psi_i}\) evolves to \(\ket{\psi_i}\otimes \ket{\text{envir}_i}\) and the phase of the complex amplitude \(c_i\) in front of this basis vector is chaotically evolving and therefore becomes ambiguous or ill-defined. It’s the first indication that you are losing the information about the relative phases and only \(|c_i|^2\) in this basis remains accessible.

More clearly, when you admit that you can’t keep track of the detailed environment at all, you have to trace over the tensor factor of the Hilbert space involving the basis vectors \(\ket{\text{envir}_i}\) and if these states that just reflect the state of the object of interest become orthogonal to each other, and be sure that they quickly do, then the reduced density matrix of interest acquires a diagonal form with \(|c_i|^2\) on the diagonal.

The eigenvalues of the density matrix are probabilities and we have isolated a basis in which the reduced density matrix is diagonal – so purely orthodox quantum dynamics does imply that some basis for the object of interest is «preferred». The information about all the phases is lost.

Because the off-diagonal elements quickly decrease to zero (often expo-exponentially, like \(\exp(-\exp(t))\), schematically speaking) and because the off-diagonal elements had known about the relative phases of the amplitudes, we see that the information about the relative phases is getting lost. If the relative phases remain the same or at least controllable, we talk about «coherence» (think about the light from a LASER). So the opposite, the loss of the information about the relative phase i.e. the disappearance of the off-diagonal matrix elements, is decoherence.

That’s it. Similar considerations – direct application of completely standard, 1920s-style rules of quantum mechanics to composite system involving a nucleus and a cat, or something else – imply that the basis vectors «alive cat» and «dead cat» are indeed preferred. But they are preferred not because of some a priori choice; they are preferred because of a dynamical, Hamiltonian-dependent process. In a different basis of «more general linear superpositions», the reduced density matrix wouldn’t be diagonal which means that the probabilities wouldn’t really be «well-defined» (in the sense of eigenvalues) for those basis vectors.

So decoherence is an explanation why «alive cat» and «dead cat» are indeed preferred as a possible basis, as a possible list of outcomes we may observe, and this conclusion – and all similar conclusions about our observations – do follow from completely unmodified rules of quantum mechanics, the theory introduced in the mid 1920s.

All of this is nice and one could spend another hour by discussing these things pedagogically. We could add a few examples, and so on. But note that the tiny space in between the two ads was really enough to explain what decoherence is conceptually. Nothing else is really needed. Nevertheless, just like any clear insight of quantum mechanics, even decoherence – which isn’t really needed as an addition to quantum mechanics in any sense because it modifies nothing about what the founders used to say – is viewed as an invitation to write hundreds of convoluted papers opening new controversies, and so on. Decoherence has been around for over 30 years but the obsession with the idea that «something needs to be clarified» hasn’t gone away – even though the literature has grown more muddy than it was 30+ years ago.

Even Zurek himself would coin not just one but at least four different words related to decoherence:

• pointer states
• decoherence
• einselection
• quantum Darwinism

In reality, the actual idea behind all these things is always the same – it’s pretty much my summary written in between the two ads. The pointer states are meant to represent the «preferred» basis of the apparatus, decoherence is the initial process in which the density matrix is becoming diagonal, while einselection is supposed to be the «final conclusion» resulting from decoherence.

Quantum Darwinism is a term meant to suggest that Zurek has discovered something almost as important as Darwin – the «classical» information (the diagonal probability values) is the information that is able to increasingly imprint itself into the environment, and therefore reproduce itself much like viable animals (or animal species). The analogy is of course vague and everyone who understood the decoherence at the beginning could have come up with this poetic interpretation. It changes nothing, there is no new physics beef in it. But it’s being sold as physics.

Also, the einselection (which is short for «environmentally induced superselection») is really just another redundant word. There is no «real process» happening after decoherence. Superselection in quantum mechanics always means that we want to treat subspaces of the Hilbert space separately – so we never want to give much importance to the relative phase of two wave functions from different superselection sectors because we really never want to imagine general non-trivial superpositions as the initial (and therefore final) state. We don’t want to mix them at all. Because decoherence also makes these relative phases physically undetectable or meaningless (even though this «ban» occurs in the final state only), decoherence may be viewed as a «kind of superselection». And yes, it is induced by the environment.

Again, all the papers written with the assumption that there is something «else», on top of decoherence, that is needed to explain something or solve some «problems» in quantum mechanics are pure nonsense. Decoherence itself isn’t really any modification of quantum mechanics or an addition to quantum mechanics. It’s just a template for a completely standard quantum mechanical derivation of the evolution of a composite system whose subset of degrees of freedom (the environment) is or is considered unmeasurable or uninteresting – so this subset is treated differently.

If you feel (or have felt) that things make more sense when you learn about decoherence, you should view it as a proof or at least evidence that quantum mechanics does work and has always worked. You may go home and politely inform those who are still struggling that they are just too stupid. If you draw the opposite lesson, namely that you should double your efforts with the «interpretations of quantum mechanics», then it is just too bad! There isn’t any problem with quantum mechanics and you have just seen some proof that a particular problem doesn’t exist so if this episode strengthens your belief that there is a problem, it suggests that your whole brain is defective or unable to think rationally.

At the end, all these debates about «interpretations of quantum mechanics» are just physically vacuous streams of consciousness, verbal exercises that are evaluated according to the criteria of the humanities, not according to the criteria of natural science. I am not saying that people may understand more deeply or less deeply how quantum mechanics actually works. Some people may have learned the equations mindlessly – and they just parrot something without understanding it deeply, at the individual basis. But the number of physicists who really understand quantum mechanics well – who know or knew that it works, is free of inconsistencies, and may be applied to small as well as large systems – still is and always has been very high. Some of them were better speakers than others but this shouldn’t be what decides about the validity of theories in physics.

By repeated comments about «new solutions to puzzles in quantum mechanics», one isn’t actually collecting credit for discovering something really new in science. Nothing new has been discovered about the general foundations of quantum mechanics since the 1920s. One is getting credit at most for pedagogic achievements – for having explained to some people what they were completely confused about (although many others haven’t been confused for decades). Sadly, most of the credit goes to the people who are spreading more confusion than clarity which isn’t surprising given the fact that most of the people who currently work in the «interpretation of quantum mechanics» community are incompetent morons.

Much of this undesirable evolution is made unavoidable by the misleading, tendentious, loaded language. Even Zurek whose substance is mostly right is guilty. This may be said about pretty much every sentence but just for fun, let’s look at the subtitle of Zurek’s new article:

The core principles that underlie quantum weirdness also explain why only selected quantum states survive monitoring by the environment and, as a result, why we experience our world as classical.

Relatively to the fuzzy standards of the discipline, this sentence is OK and I know what he means. However, if you viewed it as a path towards some precision understanding of quantum mechanics, the sentence above would have to be classified as an atrocious one.

First, there is no «quantum weirdness». The adjectives such as «weird» are spread in order to lick the rectums of the misguided people who think that it’s quantum mechanics, and not themselves, who is responsible for their tense relationship with quantum mechanics. I have discussed this point before.

Second, we are told that only «selected quantum states survive something». This is really misleading. By unitarity that holds for the whole system including the environmental degrees of freedom, all states survive. They survive any process that may happen. Any evolution will always respect unitarity. So this «Darwinian» language about someone who survives and someone who doesn’t survive is deeply misleading.

What can be correctly said is that due to the «undecodable» or «chaotic» character of the environment, certain properties of the system cannot be extracted after a sufficiently long interaction of the system of interest with the environment. Decoherence implies that the properties that may still be extracted in practice are the probabilities of the «preferred states» – the squared absolute values of the corresponding amplitudes. The relative phases become unpredictable and unmeasurable. But that doesn’t mean that they have «died». Fundamentally speaking, they’re still there; the «death» of some states is a subjective feeling.

Finally, third, and this is arguably new, I would like to point out that even the seemingly innocent statement that «we experience the world as classical» is deeply misleading. What is it supposed to mean? What do we do when «we experience the world as classical»?

Let’s think for a while. For example, we observe that a cat is dead. Do we experience the world as classical when we see a dead cat? Yes, perhaps, because classical physics used to claim or imagine that it implied the existence of dead and alive cats, too (even though it couldn’t really explain even the stability of atoms in the cat, discreteness of its DNA code, and tons of other things).

But when we see a dead cat, «we experience the world as quantum mechanical», too! There is really nothing exclusively classical about a dead cat or any other observation! We are only tempted to use this «classical» language because for centuries, people would imagine that classical physics was behind dead cats and all other objects and processes, so they were also imagining that the two things («dead cat» and «classical physics») are linked. But they are not linked, at least not exclusively.

Quantum mechanics is a theory that says that what we may observe are eigenvalues of observables, and it gives us a machinery to calculate the probability of these observations. The death status of a cat is such an observable. Quantum mechanics offers a radically new framework to calculate the probabilities of such observations and no classical theory (with the desired symmetries and/or locality properties) could emulate the correct quantum mechanical theories – but at the end, the observations are the same as those that were assumed in classical physics. It doesn’t mean that there is something intrinsically classical about our observations. It just means that when it comes to «the existence of our experience», classical physics and quantum mechanics agree. Yes, we may have experiences, both frameworks say. Classical physics was also failing in explaining (and honestly, was never required to explain) some metaphysical or nearly religious aspects of consciousness, so there is no fair justification why something like that should be «demanded» from quantum mechanics. Their position is really the same. They admit the existence of «subjective perceptions» and give us tools to calculate (deterministically or probabilistically) what the perceptions are going to be.

For the same reasons, there is also nothing exclusively «classical» or «quantum mechanical» about probabilities. The term «probability» is something that exists independently of the classical vs quantum framework of physics – because it really exists independently of physics. Probabilities can’t be exclusively linked to classical physics or quantum mechanics because the difference between classical physics and quantum mechanics isn’t in the question whether it’s OK to think in terms of probabilities (it always is) and what the probabilities mean (it’s always the same thing) but how the probabilities are being calculated for physical processes.

The text above was composed of «just words», too. One must understand that human words are very inaccurate and open to interpretations, misinterpretations, evolution, generalizations, overgeneralizations, and so on. The quantitative, high-precision, repeatable, nearly universal predictions of the actual formalism of quantum mechanical theories is what may decide whether someone is right or wrong. One may show that all the realist theories (attempting to «model» quantum mechanics as a new type of a classical physics theory) are wrong, to mention an important example. Experiments show that the laws of physics are local and Lorentz-invariant but local realist theories imply Bell’s inequalities that are experimentally excluded.

However, when someone already knows that physics has switched to a fundamentally new, intrinsically probabilistic, non-realistic, non-classical, quantum mechanical framework, the question whether he would «exactly agree» with a monologue such as the blog post above or Zurek’s article is a question from the humanities. The words are so vague and the meaning of sentences involving such words so strongly depends on what a particular speaker wants to emphasize or de-emphasize that the question whether we say that «someone is right» depends on the personal psychology and not a genuine agreement between two theories or hypotheses how the world works.

In other words, «shut up and calculate». As I tried to argue, it’s a good message not only for those who are intrigued by various wrong, realist «theories» of what is behind quantum mechanics. It is a wise recommendation for those who understand that and how quantum mechanics works, too.

And that’s the memo