Friday, September 27, 2019

Just how conceptually economical is the Many Worlds Interpretation?

An exchange of messages with Sabine Hossenfelder about the Many Worlds Interpretation (MWI) of quantum mechanics has helped me sharpen my view of the arguments around it. (Sabine and I are both sceptics of the MWI.)

The case for Many Worlds is well rehearsed: it relates to the “measurement problem” and the idea that if you take the “traditional Copenhagen” view of quantum mechanics then you need to add to the Schrödinger equation some kind of “collapse postulate” whereby the wavefunction switches discontinuously from allowing multiple possible outcomes (a superposition) to having just one: that which we observe. In the Many Worlds view postulated by Hugh Everett, there is no need for this “add on” of wavefunction collapse, because all outcomes are realized, in worlds that get disentangled from one another as the measurement proceeds via decoherence. All we need is the Schrödinger equation. The attraction of this idea is thus that it demands no unproven additions to quantum theory as conventionally stated, and it preserves unitarity because of the smooth evolution of the wavefunction at all times. This case is argued again in Sean Carroll’s new book Something Deeply Hidden.

One key problem for the MWI, however, is that we observe quantum phenomena to be probabilistic. In the MW view, all outcomes occur with probability 1 – they all occur in one world or another – and we know even before the measurement that this will be so. So where do those probabilities come from?

The standard view now among Everettians is that the probabilities are an illusion caused by the fact that “we” are only ever present on one branch of the quantum multiverse. There are various arguments [here and here, for example] that purport to show that any rational observer would, under these circumstances, need to assign probabilities to outcomes in just the manner quantum mechanics prescribes (that is, according to the Born rule) – even though a committed Everettian knows that these are not real probabilities.

The most obvious problem with this argument is that it destroys the elegance and economy that Everett’s postulate allegedly possesses in the first place. It demands an additional line of reasoning, using postulates about observers and choices, that is not itself derivable (even in principle!) from the Schrödinger equation itself. Plainly speaking, it is an add-on. Moreover, it is one that doesn’t convince everyone: there is no proof that it is correct. It is not even clear that it’s something amenable to proof, imputing as it does various decisions to various “rational observers”.

What’s more, arguments like this force Everettians to confront what many of them seem strongly disinclined to confront, namely the problem of constructing a rational discourse about multiple selves. There is a philosophical literature around this issue that is never really acknowledged in Everettian arguments. The fact is that it becomes more or less impossible to speak coherently about an individual/observer/self in the Many Worlds, as I discuss in my book Beyond Weird. Sure, one can take a naïve view based on a sort of science-fictional “imagine if the Star Trek transporter malfunctioned” scenario, or witter on (as Everett did) about dividing amoebae. But these scenarios do not stand up to scrutiny and are simply not science. The failure to address issues like this in observer-based rationales for apparent quantum probabilities shows that while many Everettians are happy to think hard about the issues at the quantum level, they are terribly cavalier about the issues at the macroscopic and experiential level (“oh, but that’s not physics, it’s psychology” is the common, slightly silly response).

So we’re no better off with the MWI than with “wavefunction collapse” in the Copenhagen view? Actually, even to say this would be disingenuous. While some Everettians are still happy to speak about “wavefunction collapse” (because it sounds like a complicated and mysterious thing), many others working on quantum fundamentals don’t any longer use that term at all. That’s because there is now a convincing and indeed tested (or testable) story about most of what is involved in a measurement, which incorporates our understanding of decoherence (sometimes wrongly portrayed as the process that makes MWI itself uniquely tenable). For example, see here. It’s certainly not the case that all the gaps are filled, but really the only thing that remains substantially unexplained about what used to be called “collapse” is that the outcome of a measurement is unique – that is, a postulate of macroscopic uniqueness. Some (such as Roland Omnès) would be content to see this added to the quantum formalism as a further postulate. It doesn’t, after all, seem a very big deal.

I don’t quite accept that we should too casually assume it. But one can certainly argue that, if anything at all can be said to be empirically established in science, the uniqueness of outcomes of a measurement qualifies. It has never, ever been shown to be wrong! And here is the ultimate irony about Many Worlds: this one thing we might imagine we can say for sure, from all our experience, about our physical world is that it is unique (and that is not, incidentally, thrown into doubt by any of the cosmological/inflationary multiverse ideas). We are not therefore obliged to accept it, but it doesn’t seem unreasonable to do so.

And yet this is exactly what the MWI denies! It says no, uniqueness is an illusion, and you are required to accept that this is so on the basis of an argument that is itself not accessible to testing! And yet we are also asked to believe that the MWI is “the most falsifiable theory ever invented.” What a deeply peculiar aberration it is. (And yet – this is of course no coincidence – what a great sales hook it has!)

Sabine’s objection is slightly different, although we basically agree. She says:

“Many Worlds in and by itself doesn't say anything about whether the parallel worlds "exist" because no theory ever does that. We infer that something exists - in the scientific sense - from observation. It's a trivial consequence of this that the other worlds do not exist in the scientific sense. You can postulate them into existence, but that's an *additional* assumption. As I have pointed out before, saying that they don't exist is likewise an additional assumption that scientists shouldn't make. The bottom line is, you can believe in these worlds the same way that you can believe in God.”

I have some sympathy with this, but I think I can imagine the Everettian response, which is to say that in science we infer all kinds of things that we can’t observe directly, because of their indirect effects that we can observe. The idea then is that the Many Worlds are inescapably implicit in the Schrödinger equation, and so we are compelled to accept them if we observe that the Schrödinger equation works. The only way we’d not be obliged to accept them is if we had some theory that erases them from the equation. There are various arguments to be had about that line of reasoning, but I think perhaps the most compelling is that there are no other worlds explicitly in any wavefunction ever written. They are simply an interpretation laid on top. Another, equally tenable, interpretation is that the wavefunction enumerates possible outcomes of measurement, and is silent about ontology. In this regard, I totally agree with Sabine: nothing compels us to believe in Many Worlds, and it is not clear how anything could ever compel us.

In fact, Chad Orzel suggests that the right way to look at the MWI might be as a mathematical formalism that makes no claims about reality consisting of multiple worlds – a kind of quantum book-keeping exercise, a bit like the path integrals of QED. I’m not quite sure what then is gained by looking at it this way relative to the standard quantum formalism – or indeed how it then differs at all – but I could probably accept that view. Certainly, there are situations where one interpretational model can be more useful than others. However, we have to recognize that many advocates of Many Worlds will have none of that sort of thing; they insist on multiple separate universes, multiple copies of “you” and all the rest of it – because their arguments positively require all that.

Here, then, is the key point: you are not obliged to accept the “other worlds” of the MWI, but I believe you are obliged to reject its claims to economy of postulates. Anything can look simple and elegant if you sweep all the complications under the rug.


Peter Morgan said...

If we can find a different way to eliminate collapse of the wave function, then presumably MWI would be less compelling. One mathematically natural way to do so is to note that when we measure A followed by B, collapse of the state after a measurement A to a mixture of eigenstates of A can also be presented mathematically as a measurement of A followed by a measurement of B-after-A, with no collapse of the state, where B-after-A commutes with A. That is, real, actually joint measurements must be modeled by mutually commutative operators.
I have a longer discussion of this on Facebook, two days ago.
All the above assumes that we do not feel compelled to a many worlds interpretation of ordinary probability just because coins when tossed always come up heads or tails.

Marty Tysanner said...

It’s certainly not the case that all the gaps [in the decoherence picture] are filled, but really the only thing that remains substantially unexplained about what used to be called “collapse” is that the outcome of a measurement is unique – that is, a postulate of macroscopic uniqueness.

This statement confuses me, because in my understanding the crucial content of the idea of wave function collapse is that it obtains a unique outcome in all cases, even though it glosses over (ignores) the interference that presumably plays an important role in a measurement. If decoherence cannot be shown to obtain a unique outcome in all cases then it doesn't remove the mystery; employing a postulate that ensures uniqueness seems to me another way of conveying the notion of collapse, packaged differently.

What am I missing here?

Coel said...

"Another, equally tenable, interpretation is that the wavefunction enumerates possible outcomes of measurement, and is silent about ontology."

It seems to me that MWI makes sense only if one proposes that the wavefunction is not telling us *about* ontology, but that the wavefunction itself *is* ontological (and is the only thing that is ontological). Thus, the one and only thing that actually "exists" is the wavefunction, one wavefunction containing within itself everything.

From there, the "many worlds" trivially exist as the different de-cohered terms of the wavefunction. And that's all there is to it.

Arun said...

By adding the measurement apparatus and the environment to the quantum system of interest, decoherence theory tries to build a completely quantum theory of measurement. Yet it seems to me that the theory yields only classical dice, and the unique outcome we experience requires further explanation.

That is, if I have a spin-up particle and choose to measure spin along the left-right axis, decoherence theory will give me the equivalent of a fair coin toss with heads-left and tails-right but can't tell me how the coin toss will actually fall. Perhaps the only recourse is that while identically prepared quantum systems are arguably, even provably identical and have no hidden variables, identically prepared macroscopic measurement apparatus really form an ensemble of roughly identical quantum systems, and so the uniqueness of any particular outcome arises from which one of this ensemble the particular run of the experiment encounters.

Jayarava said...

"The most obvious problem with this argument is that it destroys the elegance and economy that Everett’s postulate allegedly possesses in the first place.... The most obvious problem with this argument is that it destroys the elegance and economy that Everett’s postulate allegedly possesses in the first place."

I don't get this objection. If each observer ends up on the different branch for each quantum observation one does need a line of reasoning, but one doesn't have to add an expression to the Schrodinger Equation. Evolution of the system over time is still governed by one equation under all circumstances.

It seems pretty basic to *all* of the interpretations of all modern physical theories of the world at scales not immediate visible to our sense, that you have to explain how the universe appears versus how it actually is. It's not special to MWI. We had to do it with relativity too.

"What’s more, arguments like this force Everettians to confront what many of them seem strongly disinclined to confront, namely the problem of constructing a rational discourse about multiple selves. "

I also don't get this objection. There are never multiple selves from the point of view of any given observer. There is only ever one.

But worse, the objection seems to be based on an outdated idea about what constitutes "self". As we now know from extensive experimental evidence the sense of self is generated by the brain, from moment to moment. The target properties of a first person perspective are also part of this same representation. There is no enduring self. Anyone on a branching timeline can look back in time and see what appears to be a continuously evolving history - though in fact it is demonstrably discontinuous at the micro-level. Each instance can't be aware of other branches - which are orthogonal in Hilbert Space.

And yet this is exactly what the MWI denies! It says no, uniqueness is an illusion, and you are required to accept that this is so on the basis of an argument that is itself not accessible to testing!

MWI interpretation does not say that your world is not unique. You can only have one perspective - all the other perspectives are orthogonal to your reality. So your world is absolutely unique. In each possible world, that world has a unique history and will have a unique future. It's just that all possible unique worlds exist in Hilbert Space.

But this is why Sabine's objection is the only one that makes sense. We can never, under any circumstances get any information about those "other worlds". So this world is in every meaningful sense unique (and this vitiates your objection).

However, it is a consequence of taking the Schrodinger equation seriously that we can infer that those "worlds" must exist. If we are not taking the Schrodinger equation seriously, then we'd have to say why, because it is the single best description of reality ever conceived and has passed every test we can think of to date.

If a quantum system does not evolve according to the schrodinger equation under some circumstance, then how does it evolve? Under what circumstances? And what is special about those circumstances? But this is just a restatement of the measurement problem.

I don't understand it when you say that "many worlds" are not in the Schrodinger equation. The Schrodinger equation does say that when you make an observation all possibilities are real. All the other formulations of the measurement problem introduce ways of eliminating the other possibilities, i.e. the real possibilities that you don't see. This is what motivated the idea of the wave function collapse in the first place: it eliminates the possibilities that we do not see. All formulations do this.

Are you not just saying that MWI is wildly counter-intuitive?

Zephir said...

My take on this subject is summarized here:

David Brown said...

"So where do those probabilities come from?" The answer to the preceding question might depend upon understanding Milgrom's MOND.
The failures of the standard model of cosmology require a new paradigm by Kroupa, Pawlowski, and Milgrom, 2013
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