Is quantum reality «personal»?

Luboš Motl, June 08, 2015

QBism is a strategy to steal credit flavored by tons of redundant babbling

When it comes to the nonsense about quantum mechanics that is written all over the media, I have mostly resigned. But I still do detect new salvos that appear at many places. The newest article at the Quanta Magazine is

A Private View of Quantum Reality by Amanda Gefter

It promotes QBism (formerly Quantum Bayesianism) and Christopher Fuchs, a man associated with it. The main content of this picture is correct within the error margin defined by all the vague nonsense that is being added even in the similarly correct papers about the foundations of quantum mechanics.

But it is not new at all and the amount of sociological and historical nonsense that is being added on top of the correct core is rather amazing.

The title says that the view of quantum reality is «private». The subtitle tells us that physics gets «personal» and it is a price we have to pay (reinforcing the anti-quantum zealots’ thesis that quantum mechanics is a liability if not an embarrassment, to mention a word by a particular anti-quantum zealot at Caltech). And the most characteristic adjective of this philosophy of quantum mechanics is «Bayesian». So we have at least three new cool buzzwords here, «personal», «private», and «Bayesian». Mr Fuchs must have made many deep discoveries – at least these three! 😉

The problem is that in physics – or in any serious science – discoveries are not about the invention of catchy new buzzwords or their promotion in unusual contexts. Discoveries in physics have to have some beef, some ability to predict things that were impossible to predict before; or a proof that some previously arbitrarily looking assumptions and objects are not arbitrary and independent, after all, but they may be derived from more fundamental assumptions.

From this scientific viewpoint, the added value that QBism has brought us is zero. The words «personal», «private», and «Bayesian» are surely impressive but in this context, they are completely synonymous and they are also completely synonymous to the adjectives that were used for the character of the wave function and its description of Nature since the very birth of quantum mechanics: «observer-dependent», «intrinsically probabilistic», or «subjective».

The main question posed by the critics of quantum mechanics has always been the same: Is the probabilistic description unavoidable or is it the sign of some incompleteness of the description of Nature in terms of quantum mechanics? The fathers of quantum mechanics had never had any doubt that the answer was that the description must be intrinsically probabilistic and this form of the laws of physics was unavoidable and complete. The critics kept on dreaming about the opposite answer, despite all the evidence.

If you admit that the probabilistic description is complete, it unavoidably implies that the probabilities are subjective in character; they are personal; they are private; they are Bayesian. All these extra adjectives that you may connect with probabilities mean exactly the same thing, at least in the context of this debate about the foundations of quantum mechanics.

Probabilities may be «frequentist» and «Bayesian».

These are the only two possible – and closely related – meanings of the term «probability» that people could have meant at any moment. If we ask which type of the probabilities are the probabilities predicted by quantum mechanics, it is not hard to figure out what the answer has to be. The probabilities in quantum mechanics may obviously be of both types. It depends when and how you determine them.

The frequentist probability that the event \(x\) occurred is

\[ P(x)\approx {\frac {n_{x}}{n_{t}}}. \] i.e. the ratio of the number of events when \(x\) occurred, \(n_x\), and the number of all events \(n_t\). The obvious implication of this definition is that this value of the probability may only be determined experimentally and after you observe a sufficiently large number \(n_t\to\infty\) of the events. Before you observe them, you just don’t know how much \(n_x\) should be.

This comment that the frequentist probability is only known after many measurements doesn’t depend on special features of quantum mechanics in any way. It is a known fact about frequentist probabilities that was true even before quantum mechanics.

But quantum mechanics was proposed as a physical theory which is a set of ideas and equations that may also predict things. So the value of the probability is known – calculated from quantum mechanics – before you verify this prediction by many measurements! But if that value of the probability exists before the observations, it is clear that this probability must be the probability of the other, non-frequentist type, i.e. the Bayesian probability. There is simply no other type!

When you know something that looks like a frequentist probability but you know it in advance, it must be the Bayesian probability!

So whether some physicists who claimed that quantum mechanics was intrinsically probabilistic or complete said so explicitly or not, they always meant that the probabilities should be understood as Bayesian probabilities. They may have avoided this specific adjective because it wasn’t fashionable but what they said about the need to formulate laws probabilistically and the need to have observers to formulate the laws was exactly equivalent to the comments that the probabilities need to be «personal», «private», or «Bayesian». The improvement in the knowledge of quantum mechanics is exactly zero.

Under Fuchs’ photograph, we read the following:

Christopher Fuchs is the developer and main proponent of QBism, an alternative interpretation of quantum mechanics that treats the quantum wave function as a reflection of ignorance.

Wow. And what about Heisenberg, Bohr, Born, Jordan, Pauli, Dirac, plus others around them (and the following generation) including Wigner, Pauling, von Neumann, Oppenheimer, and many other giants and important figures of physics?

Mr Fuchs is not the «main proponent» of any new ideas in physics – the main proponents of that idea were enumerated in the previous paragraph. And the idea isn’t an «alternative interpretation». The insight that the wave function is a reflection of ignorance is the orthodox, original, and the only known meaningful interpretation of quantum mechanics that was discovered by the fathers of quantum mechanics!

There has been lots of confusions because generations of anti-quantum zealots have completely distorted what the fathers of quantum mechanics were actually saying. So you can see complete rubbish almost everywhere. Some people redefined the term Copenhagen interpretation to denote a theory in which the wave function is a classical wave that objectively collapses by a classical process – a process that could perhaps be decomposed to some more elementary events (like the implosion of a helium balloon) – at the moment of the measurement.

But Heisenberg and pals have never believed and never claimed such a thing. They always emphasized that the wave function was a template to compute probabilities and the collapse was nothing else than the quantum mechanical description of the change of knowledge of the observer caused by the measurement, a change that the observer has to interpret as the change of the world around him as well – the measurement «creates» the outcomes – because the world around him is what he knows – in other words, the change of the probabilities you get in one step of Bayesian inference.

If someone at the University of Copenhagen had believed that the wave function should have been thought of as an objective classical wave, he had to be a janitor! It was the flawed view – for a while, it was defended e.g. by Erwin Schrödinger. But that guy’s views about the foundations of quantum mechanics weren’t right – in other words, using Heisenberg’s technical jargon, they were crap – and Schrödinger has never worked in Copenhagen for a minute of his life.

The buzzwords are not important – and the modern ones are not particularly helpful, anyway. It’s the substance that matters.

Everyone who knows at least some history of physics must be aware of the Bohr-Einstein debates. Bohr has explained his views to his colleagues very well and they understood that everything he had said made perfect sense and was very deep and important. He did help to show that all the valid ideas that were promoted during the quantum revolution did fit together. He wasn’t a terribly comprehensible public speakers and many of his quotes look confusing to many people.

But it is spectacularly obvious that the essence of his interpretation of quantum mechanics and its objects was always the quantum Bayesian one. It’s particularly clear from the quotes of the main opponent in these debates about foundations of quantum mechanics, Albert Einstein. You must have heard that Einstein asked:

Is the Moon there if no one looks?

Einstein wanted to believe that the answer had to be «Yes». In practice, you may say that the answer is «Yes» even if you work with quantum mechanics all the time. But in principle, the answer is «No». Observables – including the projection operator \(P^2=P\) answering the question whether the Moon is there – only acquire well-defined classical values once they are observed by an observer. So if there is no observer, the operator \(P\) simply cannot have a classical value.

Why did Einstein ask the question about the Moon? It was because Bohr had just explained the previous three sentences to Einstein! And Einstein understood that this is what the «real gurus» of quantum mechanics were actually saying. Physics really depends on the observers in this way. An observer is needed for answers to questions to have well-defined sharp values! Without an observer, it just an operator, a \(q\)-number. All \(q\)-numbers may «effectively» become \(c\)-numbers but that only occurs if the state vector is the operator’s eigenstate and the state vector is only well-defined if and when an observer makes a complete set of measurements. There are just no «sharp» \(c\)-number values of physical quantities without observers!

I said that in practice, the answer to the question about the Moon’s existence is well-defined, anyway, because there have been lots of observations done by you or your ancestors – whose reports about the Moon you have observed – and you can’t undo these observations. They are a part of your knowledge. The observables \(L\) you may measure in practice basically commute with \(P\), the operator answering the question about the Moon’s existence, i.e. \(LP=PL\), and that’s why your new feasible measurements don’t change the answer to the question whether the Moon exists. You know that the Moon is out there and it is still there – well, it keeps on revolving. But if there were a region behind some walls where a moon could have been created, or not, and you wouldn’t have made any relevant observations of it, the answer to the question about the moon’s existence would be as undetermined as the usual superpositions in quantum mechanics dictate. You would have to work with this full wave function because there is a potential for this wave function to create interference effects. And only when you make some relevant observation, the answer may «collapse» to «Yes» or «No».

(I talked about walls. You may consider a fancier variation of this situation if you consider moons that may be created inside a black hole. If you are outside the black hole, you can’t know whether an event occurred inside a black hole and indeed, in this case, it seems essential to admit that the value of \(P\) – the answer whether a moon was created inside the black hole – doesn’t have a sharp \(c\)-value. You have to admit that it doesn’t have this value because you are actually routinely measuring other operators \(L\), outside the black hole, and those do not commute with \(P\) thanks to the black hole complementarity.)

The distortion of quantum mechanics by its critics and the popular books they wrote has been taking place for such a long time that many people considering themselves «informed about the debates» in 2015 don’t really have a clue what the founders of quantum mechanics were actually saying – even though they know tons of irrelevant details about what the clueless critics have said.

OK, so Mr Fuchs wants to utilize this omnipresent distortion of the physics and its history and take credit for the discoveries made by Heisenberg et al., discoveries for which Werner Heisenberg and Max Born and partly others got their Nobel prizes. He wants to take credit as the «main proponent» of the very same ideas that are clearly described in Heisenberg’s and Born’s Nobel lectures. Is he serious?

What is the contribution? That together with journalists, he coins the adjectives «private», «personal», or «Bayesian» for the very same ideas that were first clearly described in the mid 1920s, including the right theory?

In reality, the redundant words that add zero to physics go well beyond these three unnecessary adjectives. A huge portion of the article is dedicated to the question why Mr Fuchs prefers «QBism» over «Quantum Bayesianism» now. Well, because the latter was too long. What a shock – or perhaps Schack. Do you really think that a serious physicist would waste two long paragraphs with this irrelevant and arbitrary terminological detail justified by an obvious explanation but ultimately determined by the mood of one guy at one moment?

While the core idea about the Bayesian character of the quantum probabilities is correct, almost all the extra baggage added on top of that is rubbish that has nothing to do with physics, science, or rational reasoning. Or at least nothing to do with their hard and new aspects. For example, a major part of this «QBism paradigm» are references to Bruno de Finetti (1906-1985). And the amount of attention that this not too relevant statistician gets in the «QBism paradigm» is insane, indeed. Fuchs even wanted to use the name «Brunoism» instead of «QBism».

Has Mr de Finetti made some insights that are relevant for quantum mechanics? Not at all. When it comes to «interpretations», he just wrote lots of superficial texts claiming that «probability doesn’t exist» and «the only thing that matters is to win games and lotteries». In other words, he stressed the «operational subjective» character of probabilities. The word «subjective» is the same as «Bayesian» and by «operational», he really meant «profit-driven». We don’t know for sure what will be the outcome but if we know the probabilities (that don’t exist), we may improve our planning that allows us to win games or earn money. So his texts are full of bookmakers and the «Dutch book».

Needless to say, de Finetti’s (20th century) «philosophically far-reaching» insights were not new even as insights about the ordinary probability calculus, let alone quantum mechanics. Was the concept of probabilities (and Bayesian and frequentist ones) and the concept of odds and bookmaking older? You bet [pun intended]. Thomas Bayes lived in 1701-1761. But the rules governing odds – ratios of probabilities – are older still. They were really a part of general knowledge in Shakespeare’s times, too.

Knew that we ventured on such dangerous seas
That if we wrought out life ’twas ten to one

William Shakespeare, Henry IV, Part II, Act I, Scene 1 lines 181–2.And Shakespeare (1564-1616) wasn’t a great mathematician. The 16th century polymath Cardano (the guy who solved the cubic equation) played with odds and was able to determine how quickly the accuracy of the probability improves when you are increasing the number of measurements or elements of the sample.

Literally millions of people have been using the ideas and rules of bookmaking and odds – probabilities as a useful, operational quantification of ignorance – for centuries before Mr de Finetti was even born.

Now, are we supposed to celebrate an «interpretation» of quantum mechanics because it promotes the adjectives «personal», «private», «Bayesian», and especially a random guy who loved bookmaking but his main contribution to the probability calculus is a basically obvious theorem stating that probabilities tend to be calculable as weighted averages of others? (I say it’s obvious because probabilities of different things and identities relating them always result from different ways to clump the terms \(n_x\) from the frequentist definition of the probability into sums and ways to divide them – which makes it clear that almost all the formulae of certain kinds have to be linear i.e. weighted averages.) Just to be sure, this is true for all probabilities – and quantum mechanical probabilities are probabilities in the strict sense, not just some «generalizations» of them. (It is not right to say that the probabilities resulting from quantum mechanics are classical. They are probabilities without adjectives. It is only the dynamical theory that predicts things that may be classical.) The theorem doesn’t really allow you to determine anything you didn’t know before and it has no relevance for specific quantum mechanical questions.

You could perhaps argue that de Finetti did make contributions to the probability calculus although their power and importance is debatable. But to pick this random statistician and put him at the center of something that is said to solve some «problems» in the foundations of quantum mechanics is silly. Also, it is silly to put bookmaking at the center of quantum mechanics. Quantum mechanics is the right theory to predict events everywhere – even in casinos – but casinos don’t play a special role among the other contexts and there is no good reason to formulate quantum mechanics in terms of casinos. Quantum mechanics can predict and explain things outside casinos, too! All this talk is a typical example of the victory of random philosophical musings and a chaotic mixing of eclectic ideas over the substance.

Do we want hundreds of physicists to be paid for inventing things like the Totto Lotto (TM) interpretation of quantum mechanics, the Murphy-law-Kafkaesque-von-Neumann interpretation, and so on? If you pay me the same, I can write totally analogous papers with the same (or larger) amount of internal consistency and the same number of truly new contributions to physics (zero) as Fuchs’ texts.

Mr Fuchs, can we please agree that aside from these original lists of names and adjectives that clueless laymen may find refreshing or original while parroting but that don’t add anything to the knowledge of physics, you have made no contributions to quantum physics? And could you please make this self-evidently true point explicit in the next interview even if you are not asked? Thank you very much.