Quantum Wittgenstein: Metaphysical debates in QM don’t get at ‘truth’

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EXCERPTS (Timothy Anderson): I first learnt about Plato’s allegory of the cave when I was in senior high school. [...] this notion that we could experience a shadow-play of a reality that was nonetheless eternal and immutable...

[...] Eventually, I turned to physics, hoping to reground my Platonist aspirations in the eternal laws that governed the physical reality of the cosmos. But quantum theory exposed that, too, as a fantasy: even though we could define rules and equations for physical laws, we could not explain what they meant...

[...] The view that emerged from this haggling came to be known as ‘the Copenhagen interpretation’ – coined by Heisenberg in 1955, and predicated on the presence of a fundamental split between the observer and the system being observed. Meanwhile, the polymath John von Neumann came up with an idealised mathematical description of what happened when you measured a particle’s wavefunction: it collapsed upon interacting with the observer. Where the rest of the wave went, or whether it was ever real in the first place, was anyone’s guess.

[...] By the late 20th century, dozens of other interpretations had appeared under exotic names: the many-worlds theory, superdeterminism, consistent histories, the modal interpretation, superselection, Bohmian mechanics, Lindblad equations. I even invented my own: dynamic histories. While a few, like mine, proposed new theories that could come into conflict with quantum mechanics, most of them don’t. They are metaphysical, not physical.

The big question lurking behind all this is: what does the wavefunction mean? Does it represent something real or not? Most interpretations are ‘realist’ in the sense that they assume the wavefunction is a real entity and then go on to explain what it represents – but a few say it doesn’t exist at all, such as Quantum Bayesianism or QBism, as it is known.

[...] Plenty of physicists have grown tired of this debate and its seemingly endless and unsatisfying arguments between realists and anti-realists. They want us to ‘Shut up and calculate!’ in the words of the physicist David Mermin: to stop trying to interpret quantum mechanics at all and get back to doing it. Philosophers, on the other hand, tend to dismiss this latter group as being philosophically ignorant. There’s a suspicion that, deep down, such physicists simply possess a metaphysics that they don’t want to admit, because they don’t want to come down on the side of an interpretation that has no scientific backing.

Yet those who follow Mermin’s injuction have a friend in one of the great philosophical minds of the 20th century – one who provides not only support for their position, but philosophical reasoning for why it is the only correct one.

[...] What Ludwig Wittgenstein understood is that you can’t use words to explain representation, because words are representations themselves. ... Thus, Wittgenstein, even in his early work, suggests that the realist versus anti-realist debate is meaningless because both sides are trying to say things that are only showable. ... To ask what the wavefunction represents is like asking what Michelangelo’s statue of David or Van Gogh’s painting The Starry Night represents: any explanation beyond the mere facts is insufficient and subjective.

You might find this explanation unsatisfactory. Yet Wittgenstein was serious in that he believed we could not talk about things that are not in the world. While we might talk about quantum mechanics in terms of particles, measurements and calculations, any philosophical attributes that ascribe significance to what we can observe (such as ‘real’ or ‘unreal’) are nonsense. We must be silent on ascribing additional meaning to the wavefunction.

Wittgenstein’s exploration about what we can and cannot talk about in philosophy, however, would evolve over the next several decades, and lead to a rejection of even those philosophical concepts such as the picture theory upon which he built the Tractatus.

[...] In his Philosophical Investigations, Wittgenstein rejects the theory of meaning entirely while making one of his most powerful contributions to it. All language, he says, gains its definitions from how it is used in specific cases. All language is a game like chess or poker – we learn the rules by playing, not theorising or defining. So the very notion of a universal definition is an artifice, a bit of subterfuge. One cannot talk about what words really mean; one can only use them. This applies as much to mathematics as it does to ordinary words.

[...] The late Wittgenstein entirely rejects his own picture theory of reality. Pictures are nice and satisfying, but usage is what actually matters. The wavefunction, on this reading, isn’t like a picture of reality at all. All that matters is that physicists now have the ability to do calculations, which lead to predictions that can be verified by measurements. The point is not the measurements themselves, however – as a logical positivist might claim – but how the physicists behave. Do they calculate in a way that leads to more and better physics? Language and mathematics are a means of controlling and modifying collective human action so that work gets done.

This is language as culture rather than language as picture. And culture includes ritual. Like all ritualistic communities, physics contains its rules, interpretations, specialised vocabulary, a community of adherents who are admitted to the arcane arts, levels of indoctrination, and gatekeepers. While some societies relate ritual to the appeasement of gods and spirits, in science they serve to therapeutically appease our philosophical needs...

[...] Evolutionary cultural anthropology backs up this view, having demonstrated that language is deeply connected to ritual and religion. Likewise, the vocabulary, grammar and procedures of science are themselves ritualistic, with each subdiscipline having its own mores and norms. These are necessary because it is impossible for scientists to evaluate new research purely based on factual merits; it often takes years to validate a new theory or experimental result...

[...] Hence, quantum interpretation is not really an investigation into reality, and it tells us nothing new about the world. Rather, it is a grammatical investigation or, in anthropological terms, a cultural one. It is a competition between differing philosophical therapies, satisfying different emotional-cultural needs.

[...] The conclusion from all of this is that interpretation and representation in language and mathematics are little different than the supernatural explanations of ancient religions. Trying to resolve the debate between Bohr and Einstein is like trying to answer [..a..] Zen kōan...

[...] It’s evidently true that the wavefunction has a multiverse interpretation, but one must assume the multiverse first, since it cannot be measured. So the interpretation is a tautology, not a discovery.

I have humbled myself to the fact that we can’t justify clinging to one interpretation of reality over another. In place of my early enthusiastic Platonism, I have come to think of the world not as one filled with sharply defined truths, but rather as a place containing myriad possibilities – each of which, like the possibilities within the wavefunction itself, can be simultaneously true. Likewise, mathematics and its surrounding language don’t represent reality so much as serve as a trusty tool for helping people to navigate the world. They are of human origin and for human purposes.

To shut up and calculate, then, recognises that there are limits to our pathways for understanding. Our only option as scientists is to look, predict and test. This might not be as glamorous an offering as the interpretations we can construct in our minds, but it is the royal road to real knowledge... (MORE - missing details)

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