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Interpretation #3: Hidden Variable / pilot-wave / DeBroglie Bohm is by far the simplest and also easiest to understand. It's a shame that it's not the default that's taught.

As a very lose analogy, the world is "normal" ( no collapsing or multiple universes or anything). It's simply that every particle leaves a "wake" just like a boat on a lake. That's it.

Classical interaction is two boats interacting with each other (crashing into each other, or one pushing the other, or pulling the other like a tugboat). And the only way two boats can affect each other is directly.

Quantum interactions are "wakes"/"waves" in the water interacting with boats. One boat can be far enough away, but if it's big enough it's wake can move your boat. This as you'd imagine happens more to smaller lighter boats. And as waves push small boats around they affect where a boat will be when you look to measure them. (Measurements also create a wake)

Finally a boat's wake can interfere with another boat's wake. And that can be constructive or destructive interference just like two waves in the water can cancel each other out. Finally a boat on the other side of the lake can affect your boat via it's wake, meaning interactions aren't strictly "local".

It's that simple (more or less), it explains all the predictions of QM and yet it's taking forever for Copenhagen to die off and all the absurd questions of collapse and the rest...

DeBroglie-Bohm is the only item that makes sense, people are just slow to accept that locality isn't always the case.

I can't quite see how it's easier or more plausible than e.g. many worlds? That one is as easy conceptually and is not without elegance.

Physics has a history of elegant theories that eventually turned out to be wrong. Phlogiston theory looked great at the time, and things like one-electron universe strike as beautiful when you first read about them.

Pilot wave theory might be easy to visualise if you don't consider entanglement, but it suffers from the conceptual problem that it's just many worlds with extra undetectable structure.

The pilot wave is the entire uncollapsed wave-function, exactly like in many worlds. There is also a particle and instant, universe-wide collapse, neither of which are detectable even in theory. Nothing except the wave function affects the dynamics at all.

All three interpretations are 'just the wave function'. What separates them is the metaphysical interpretation of what is 'behind' the wave function.

> Physicists tend to like the many worlds interpretations.

According to Sean Carroll, this is because if you 'buy' the mathematics of the wavefunction, even before collapse you already have to accept "many worlds" at the quantum level. "many worlds" for them simply means superposition/linear combinations. After all, if you already accept "superposition" at the level of quantum states, you don't have to invoke anything new to deal with so-called "collapse", if everything simply stays as superpositions i.e. linear combinations.

Or, in other words, if you assume classical behavior first, and you need to get that out of superpositions at the quantum level, you need wavefunction collapse.

but if you start with superpositions at the quantum level, you already have superpositions, and then classical behavior can simply be derived from locating yourself in one of those superpositions.

Explained this way, "many worlds" doesn't seem so shocking, if you have already resigned yourself to quantum level superpositions.

I think of many worlds as kind of a literal interpretation that quantum superpositions are fundamentally real, as opposed to quantum superpositions merely being a very accurate mathematical model. (Most scientists think QM represents something real instead of some lucky equations.)

This sounds a lot like someone has fallen for a subtle confusion of map and territory...

well you might want disagree with the most senior research prof at Caltech, but I woudln't.

That's what they really think of many worlds. And, really, is it any worse than any of the alternatives?

I'm just responding to this:

> I think of many worlds as kind of a literal interpretation that quantum superpositions are fundamentally real, as opposed to quantum superpositions merely being a very accurate mathematical model.

If the stance is predicated on that assumption, as you suggest (and I'm inclined to agree, having read other of Carroll's writings), then I have to continue disagreeing. If the rest of the world of physicist luminaries were unanimously aligned with Carroll it would be more difficult (but still tempting...)—but luckily that's not the case.

At some level, if we take scientific theories seriously as descriptions of the world out there, and not merely tools for prediction, then we have to assume some sort of isomorphism between the map (our theory) and the territory (the world), even if they're not the same thing. This isn't only for quantum theory.

Isomorphism, yes, exactly—that's the basic principle of a map: it's a description that enables us to make predictions about the territory, because it's possible to put the two into systematic correspondence. However once you start considering the 'representational' features of the map, which aren't an essential part of the isomorphism, as equally real (because you've made the simplification: dealing with the map is the same as dealing with the territory—our minds are predisposed to do this in many cases)—then you're in trouble.

> we have to assume some sort of isomorphism between the map (our theory) and the territory (the world)

But a mathematical model != a theoretical model. The very same mathematical model will be compatible with uncountably many theoretical models. (By 'theoretical model' I mean something like 'an interpretation of what the math is representing'.)So you can't read off theoretical structure from mathematical structure. And so you can't read off the structure of the world from mathematical structure.

> (By 'theoretical model' I mean something like 'an interpretation of what the math is representing'.)So you can't read off theoretical structure from mathematical structure. And so you can't read off the structure of the world from mathematical structure.

Occam's razor favours a theoretical model that corresponds more closely to the mathematics, rather than one that adds a bunch of epicycles to arrive at a different interpretation. If you follow your logic then you can never reject geocentrism, because it's possible to create a geocentric model that generates the same predictions as a heliocentric one; nevertheless we would generally say that heliocentrism is "more true" and "more physically real" than geocentrism.

What Occam's razor favours is irrelvant. It has no predictive power [1]. The more complex answer is just as likely to be the correct one.

[1] http://scienceblogs.com/developingintelligence/2007/05/14/wh...

Physics tends to be simpler than we originally thought, and Occam's razor correctly predicts this: electricity, magnetism, and light turn out to be facets of the same phenomenon, electricity and the nuclear forces turn out to conform to the same theory, electromagnetism, gravity, and spacetime turn out to behave in the same way. Your link's lazy "11 dimensions! OMG!!!1one" non-argument is in no way an adequate refutation of that history.

You're cherry picking. You pick the places where Occam's razor picks the correct answer and ignoring all the places it doesn't. For any new situation we can't predict which of those possibilities the answer will fall. Hence my statement that Occam's razor has no predictive powers.

I just linked to the first article I found that talked about the subject. And it's interesting that you look for something lazy instead of addressing more serious issues like Newton's model vs Einstien's. Very clearly the (much!) more complex answer is more correct than the simple one. Here's [1] another link discussing the issue and gives 2 examples.

[1] http://neuralnetworksanddeeplearning.com/chap3.html Search for "Occam"

> I just linked to the first article I found that talked about the subject. And it's interesting that you look for something lazy instead of addressing more serious issues like Newton's model vs Einstien's.

You should give links you're willing to stand by. I didn't go looking for something lazy, I went looking for talk about fundamental physics (where Occam's Razor is appropriate, and what we're talking about) and found only the barely even wrong throwaway line about M-theory.

> Very clearly the (much!) more complex answer is more correct than the simple one.

Newton and Einstein don't make the same predictions. When you include the amount that you'd have to add on to Newton's theory to generate the predictions Einstein gives you about the behaviour of light, Einstein ends up simpler.

> Here's [1] another link discussing the issue and gives 2 examples.

The "new particle" example shows the opposite of what's claimed. Bethe's only reason to dismiss a new particle as an explanation was Occam's razor. The part about Newton/Einstein is just wrong about the history; relativity wasn't developed as an effort to explain the orbit of Mercury, it was developed out of Maxwell and Lorentz's work on electromagnetism. A universe in which the only reason to believe relativity was those deviations in the orbit of Mercury probably would be a universe in which the true theory was Newtonian gravity with small correction terms, not a universe in which relativity was true.

>Bethe's only reason to dismiss a new particle as an explanation was Occam's razor.

Thank you for pointing out the other fault of Occam's razor: both sides of most arguments tend to assume the razor is on their side. This aspect was addressed in the second article I linked.

It's possible to make a mistake in the application of any principle, particularly when the mistake suggests you've made an important discovery. I think there would have been a clear consensus among third-party physicists that the razor favoured Bethe in that case.

But what does 'corresponds more closely to the mathematics' mean? The relevant point is just that the mathematics, alone, doesn't settle the theoretical question.

In general, it's hard to use Occam's razor in a non-question-begging way.

Well, the mathematics describes reality. If humans can't agree about whether one way of interpreting the mathematics in human terms is more or less complex than another way of doing so, then that's a human problem and potentially insoluble. But I don't think things are actually that bad: people are generally capable of reaching consensus about what a given piece of mathematics "means", and the relevant cases here are pretty clear-cut: either we interpret the wavefunction as being physical reality, or we interpret some derived structure as being physical reality, and the latter gets us further away from the wavefunction.

In physics the map IS the territory. Or, if you prefer, we're not merely constructing a map, but a model, that is, we try to feel out and understand the territory, what it's made of, and how it works.

So you think an electron IS a mathematical expression, not that a mathematical expression describes its behavior?

> ...we're not merely constructing a map, but a model, that is, we try to feel out and understand the territory, what it's made of, and how it works.

'map' is a metaphor there. You're description of what physics is doing still fits within the metaphor. It doesn't change the fact that there is something 'out there' and then there's our description of it, via physics, and our description is not the thing that's out there.

Suppose we develop a unified theory in physics which supersedes current formulations of quantum theory. Then would the old quantum theory still BE the territory at that point? Or would it be just a less accurate description than the new one we came up with?

>So you think an electron IS a mathematical expression, not that a mathematical expression describes its behavior?

No, I think that a mathematical expression describes the behavior of something real as close as possible to our knowledge -- it's not just a picture of how it looks.

In other words, in contrast with the map analogy, the equations for electrons etc can be used for a simulation.

>Suppose we develop a unified theory in physics which supersedes current formulations of quantum theory. Then would the old quantum theory still BE the territory at that point? Or would it be just a less accurate description than the new one we came up with?

Why assume one can describe the territory in just a single (perfect) level of representation? For some things not even the full precision we can muster today is even needed (e.g. I don't need Relativity to know where a baseball will land).

Are you saying that after a certain level of accuracy, it is impossible to be sure, but you CAN say for certain within an error radius?

> So you think an electron IS a mathematical expression, not that a mathematical expression describes its behavior?

To the extent that "is" means anything, yes.

> Suppose we develop a unified theory in physics which supersedes current formulations of quantum theory. Then would the old quantum theory still BE the territory at that point? Or would it be just a less accurate description than the new one we came up with?

I think it's useful to treat "isness" as something analogue rather than binary here. The old theory sort-of-is the territory. The new theory a-bit-more-is the territory. But there's no Platonic ideal of the territory as a separate thing from the mathematical model that reality implements. There is no there there.

There is lots of mathematical evidence that every quantum state maps 1-to-1 on a physical state¹, or at least be uniquely determined by the physical state². The main assumption both make is that there is some physical state.

So it doesn't really matter if it's a map or not - it tells you something about the territory.

[1] The completeness of quantum theory for predicting measurement outcomes, https://arxiv.org/abs/1208.4123

[2] On the reality of the quantum state, https://arxiv.org/abs/1111.3328v3

> The main assumption both make is that there is some physical state.

I'd phrase this as: the main assumption is that reality is literally encoded by some sort of objective hidden variables theory.

I'm not sure what your point is, but it doesn't have to be hidden and in this case, objective just means two parties agree on the outcomes of experiments.

> if you already accept "superposition" at the level of quantum states, you don't have to invoke anything new to deal with so-called "collapse"

All three interpretations of QM 'accept' superposition, construed as a mathematical construct. What's at issue is how this mathematical construct maps onto reality.

If you mean something more by 'accepting superposition', you have to spell out what that is. And doing that just leads you right back to the three different interpretations.

Well you may as well just accept nonlocality. After all, the other interpretations do nothing to rule it out!

There are lots of signs that locality is not tenable

I want to keep locality. Being able to derive it would be a happy bonus, but I'm perfectly willing to adopt it as its own axiom.

>> Many Worlds - Quantum phenomena cause the world the branch into multiple worlds. The probabilities of quantum mechanics represent the 'share' of reality that branches in each direction.

I seem to have access to only one of these universes. How does nature decide which determinate state would my universe take? It still requires the magical collapse. (Or is it that I am branching off too and loosing access to myself in other branches?)

>> So long as you're willing to abandon locality, hidden variables can work.

(Asking, not questioning) Why is this so? I have read a bit or two about Bell's Inequalities, but do not understand why locality needs to be abandoned. With particles having random but entangled spins showing correlations even when separated out, how do we know there were no random hidden state associated with these particles when they separated. That is, how do we know that the decision on which particle has which spin did not happen during separation itself (getting stored as a hidden variable)?

> Or is it that I am branching off too and loosing access to myself in other branches?

Yes, you also split into branches. Of course the whole branches thing is a rough approximation - for example quantum computers work because they aren't branching.

> Why is this so? I have read a bit or two about Bell's Inequalities, but do not understand why locality needs to be abandoned.

I would recommend looking up the explanation from Dr. Chinese. Briefly it's because you measure each half of an entangled pair randomly on 1 of 3 angles, and you see that measurements of equal angles always disagree, yet measurements on different angles agree over 50% of the time. That's impossible to do with pre-determined values.

> quantum computers work because they aren't branching.

Or rather, the branch universes diverge and do their computing in parallel, and then finish by matching perfectly, with all universes having the same answer. Any interference from the environment outside of the qubits results in the universes not being perfectly similar at the end and you don’t get an answer back.

Question: where does the hidden variable/pilot wave interpretation say that the computation in a quantum computer takes place? Many-worlds says that it takes place in parallel universes.

> how do we know that the decision on which particle has which spin did not happen during separation itself

It's difficult to explain concisely, but John Stewart Bell wrote a nice albeit lengthy essay on this exact question:

https://cds.cern.ch/record/142461/files/198009299.pdf

> How does nature decide which determinate state would my universe take? It still requires the magical collapse. (Or is it that I am branching off too and loosing access to myself in other branches?)

You're branching too. It remains to be explained why your subjective probabilities of which branch you find yourself in follow the Born probabilities, but that's the only known way of assigning subjective probabilities that behave as probabilities should (in terms of things like "probability of A or B <= probability of A + probability of B").

> That is, how do we know that the decision on which particle has which spin did not happen during separation itself (getting stored as a hidden variable)?

Conway's "Free Will Theorem" offers a simplified proof that this can't happen: if you measure the particle along three orthogonal axes then you will always get two of one result and one of another, but there's no way to preassign values to all possible axes such that this remains true. So the result you get from measuring in a given direction cannot be fixed if you have a free choice about which set of directions you're measuring in.

>So long as you're willing to abandon locality, hidden variables can work. Given that the other two interpretations posit equally weird things, abandoning locality won't seem so weird.

Abandoning causality (that goes along with locality) wont seem so weird?

Precisely how to understand causation is controversial.

But I'll just say that most philosophers don't find anything incoherent in the idea of nonlocal causation. (Hume's classic attack on local causation might be worth a look.) See BoiledCabbages comment for a nice explanation of a model that involves nonlocal causation.