More physics as philosophy.

So re the Schrodinger equation, do you disagree with this statement: "The associated wavefunction gives the probability of finding the particle at a certain position"?

From ~25mins for the purely QM stuff. — tom

I agree that the ontology of probability is interesting. This 'from 25 mins on' wasn't 'purely QM stuff' at all, though, it was a prolonged lecture about metaphysics. My view of philosophy is that you imagine all the best arguments people can put up against you, and you rebut them. In this lecture Deutsch seems instead to be imagining a series of feeble opponents who haven't considered the slightest subtlety in their position. Even an actuary has a defence to the notion of probability, let alone proponents of statistical mechanics and so on. I don't see how this sort of stuff furthers the debate. Plenty of people who disagree with Deutsch's interpretations of MWI will agree that probability is epistemic, especially scientific realists, for they don't want 'the world' at heart to be indeterministic. And, it must be something you're not seeing because you admire Deutsch, but to the uncommitted outsider the lecture seems to show a pompous man over-reaching himself. Why isn't all this in a peer-reviewed paper where his intellectual equals like Wallace and Timpson could respond and critique it?

If you take the pilot wave route, determinism is preserved, but it posits hidden variables which, as you may guess from the name, there is no evidence for. — Andrew M

It's redundant to say there is no evidence for hidden variables. If there was evidence, they wouldn't be hidden. But "evidence" is a property of the mind which seeks relationships, it is not a property of the physical world. So evidence may be right in front of one's eyes, or even right on one's list of observations, but if that individual does not establish the appropriate relationships, it is not seen as evidence, and so it is claimed, "there is no evidence".

Evidence is a funny thing. If we are looking for evidence, we must create logical relationships in advance, to know what we are looking for. Without this, nothing is evidence, because there is nothing which we are looking for evidence of. So let's say that we are looking for evidence of "hidden variables". Well, the variables are hidden, we know not what they are, so we have no idea of what we are looking for evidence of. Until the possible variables are brought out into the open, and exposed as possible variables, we cannot even begin to look for evidence.

I submit to you, that there is an immense quantity of evidence of hidden variables. The variables are hidden in the mathematics. That is the way in modern physics, and it's become epidemic since the practises of general relativity. Whenever a variable pops up, mathematics is created to work it into the theory, and it becomes lost into the theory, hidden by the mathematics. Let's consider general relativity as the prime example. Special relativity is a particular theory, gravity is a variable in relation to this theory. The mathematics of general relativity allow this variable to become hidden within the theory, so that it doesn't appear to be a variable any more. It is a hidden variable, hidden by the mathematics. That is the practise in modern physics, create mathematics to deal with the variables, this obscures their presence, such that they become hidden variables, hidden by the mathematics.

But a consequence of that is that the world 'splits' at the point of measurement, and/or that there are countless 'parallel worlds'. Once again - doesn't that seem intuitively strange to you? — Wayfarer

Yes it's counterintuitive. That's not a valid argument against it. If that's the way the world is, then we should change our intuitions.

What does it say about other 'fundamental laws' like the conservation of energy? — Wayfarer

Energy is conserved. I recommend Ask a Physicist's excellent answer on this.

Why do you think the probabilistic nature of the wave-function is sufficiently troublesome to consider such an alternative? — Wayfarer

I think for much the same reasons that Einstein found Copenhagen troublesome. Lack of causality, non-locality and anti-realism. Contra Bohr, I think the task of physics is to find out how nature is.

Thanks Tom, I'll take a look.

So re the Schrodinger equation, do you disagree with this statement: "The associated wavefunction gives the probability of finding the particle at a certain position"? — Terrapin Station

No I don't disagree. That's the self-locating uncertainty that I mentioned. The wave function assigns a complex number (called an "amplitude") for each measurement outcome. Per the Born Rule, the probability of seeing a particular measurement outcome is the square of the amplitude.

Okay, but that's the probability I'm talking about there being a desire to remove. There's still a probability of what one will observe in one's world, but it's no longer a probability that only one outcome will obtain (via measurement) while others do not obtain.

I agree that the ontology of probability is interesting. This 'from 25 mins on' wasn't 'purely QM stuff' at all, though, it was a prolonged lecture about metaphysics. My view of philosophy is that you imagine all the best arguments people can put up against you, and you rebut them. In this lecture Deutsch seems instead to be imagining a series of feeble opponents who haven't considered the slightest subtlety in their position. Even an actuary has a defence to the notion of probability, let alone proponents of statistical mechanics and so on. — mcdoodle

But you haven't addressed a single one of his arguments.

Why isn't all this in a peer-reviewed paper where his intellectual equals like Wallace and Timpson could respond and critique it? — mcdoodle

Try this paper by Marletto.

https://arxiv.org/abs/1507.03287

or this paper where Deutsch invented the idea.

http://xxx.lanl.gov/abs/quant-ph/9906015

or this paper where Wallace defends Deutsch

https://arxiv.org/pdf/quant-ph/0303050.pdf

or this paper where Wallace improves Deutsch's argument

https://arxiv.org/pdf/quant-ph/0312157.pdf

or this paper where Wallace establishes the formal proof of Deutsch's idea

https://arxiv.org/pdf/0906.2718.pdf

Or chapters 5 and 6 of this book by Wallace:

https://www.amazon.co.uk/Emergent-Multiverse-Quantum-According-Interpretation/dp/0198707541

If you take the pilot wave route, determinism is preserved, but it posits hidden variables which, as you may guess from the name, there is no evidence for. — Andrew M

So, the point Andrew M, I am a metaphysician, not even a physicist, and I can identify numerous possible hidden variables, such as gravity, expansion of space, dark matter, dark energy, so I don't know how many possible hidden variables there really is. Very many I would say. From my perspective there is massive evidence for hidden variables.

It's redundant to say there is no evidence for hidden variables. If there was evidence, they wouldn't be hidden. But "evidence" is a property of the mind which seeks relationships, it is not a property of the physical world. So evidence may be right in front of one's eyes, or even right on one's list of observations, but if that individual does not establish the appropriate relationships, it is not seen as evidence, and so it is claimed, "there is no evidence". — Metaphysician Undercover

Hidden variable theories are ruled out by the many no-go theorems: Bell, Leggett, Kochen-Specker, Free Will Theorem, PBR.

There is no existing hidden variable theory that is able to replicate the results of Quantum Mechanics up to electrodynamics and field theory. They don't work or don't exist.

All hidden variable theories disagree with quantum mechanics, so they are wrong.

So, the point Andrew M, I am a metaphysician, not even a physicist, and I can identify numerous possible hidden variables, such as gravity, expansion of space, dark matter, dark energy, so I don't know how many possible hidden variables there really is. Very many I would say. From my perspective there is massive evidence for hidden variables. — Metaphysician Undercover

What you have demonstrated is that you haven't the first clue what is meant by the term "hidden variable". Look it up!

Yes it's counterintuitive. That's not a valid argument against it. If that's the way the world is, then we should change our intuitions. — Andrew M

There doesn't need to be a valid argument against it. I already quoted the passage where Everett, 'after a slosh or two of sherry', sat around with a couple of mates thinking of 'ridiculous things you could say about quantum'.

@Metaphysician Undercover - here's a good video on hidden variables/pilot waves:

Okay, but that's the probability I'm talking about there being a desire to remove. There's still a probability of what one will observe in one's world, but it's no longer a probability that only one outcome will obtain (via measurement) while others do not obtain. — Terrapin Station

So there isn't a desire to remove that probability in Everettian QM, which would amount to an ad hoc change to QM.

As an example, consider a particle in a superposition of spin-up and spin-down. The wave function includes the particle in superposition, and also the external environment which includes Alice. Now Alice measures the particle spin. The wave function evolves to a superposition of (Alice measures spin-up) and (Alice measures spin-down). Each of these superposition states are assigned an amplitude which, per the Born Rule, are convertible into equal probabilities that Alice measures spin-up and spin-down. Both measurement outcomes are present in the wave function.

Dynamical collapse theories add an ad hoc postulate to remove one of those measurement outcomes. Copenhagen goes further and denies the reality of the wave function. Whereas Everettian QM leaves the wave function intact and explains Alice's reported measurement as the natural consequence of self-locating uncertainty.

So, the point Andrew M, I am a metaphysician, not even a physicist, and I can identify numerous possible hidden variables, such as gravity, expansion of space, dark matter, dark energy, so I don't know how many possible hidden variables there really is. Very many I would say. From my perspective there is massive evidence for hidden variables. — Metaphysician Undercover

As Tom mentions, hidden variables have a particular history in a quantum context. In particular, Bell's Theorem shows why no physical theory of local hidden variables can reproduce all of the predictions of quantum mechanics.

What you have demonstrated is that you haven't the first clue what is meant by the term "hidden variable". Look it up! — tom

I have looked it up. And I've watched the clip Wayfarer provided above, thank you Wayfarer. Furthermore, I know very well what a variable is, and I know very well what it means for a variable to be hidden. And as I explained, I see many variables hidden behind mathematics, the mathematics making them appear as constants.

All hidden variable theories disagree with quantum mechanics, so they are wrong. — tom

You seem to be in some sort of state of denial, afraid to face the possible reality of non-locality. You deny that hidden variable theories are even applicable just so that you can claim that MWI is the only realist interpretation. Do you really think that Many Worlds is a more plausible interpretation than non-locality? Are you afraid to face the fact that special and general relativity may be wrong? Clearly they do not provide us with an adequate representation of time.

As Tom mentions, hidden variables have a particular history in a quantum context. In particular, Bell's Theorem shows why no physical theory of local hidden variables can reproduce all of the predictions of quantum mechanics. — Andrew M

The fact remains that the best theory which physics has, for dealing with gravity is general relativity, and this is far from adequate from a metaphysical stand point.

Each of these superposition states are assigned an amplitude which, per the Born Rule, are convertible into equal probabilities that Alice measures spin-up and spin-down. Both measurement outcomes are present in the wave function. — Andrew M

But in MWI, the probability that both are measured is 100%, no? One is measured in one world. The other is measured in another world.

But in MWI, the probability that both are measured is 100%, no? One is measured in one world. The other is measured in another world. — Terrapin Station

Yes. The point is that there is no ad hoc modification to QM to preserve determinism. Everettian QM is just the natural interpretation of the wave function evolution.

The ad hoc part is that we posit the ontological ridiculouslessness of parallel worlds.

The parallel worlds can't be removed from QM without also changing its predictions. Which is why Everettian QM is used in practice even if people don't want to believe it.

I have looked it up. And I've watched the clip Wayfarer provided above, thank you Wayfarer. Furthermore, I know very well what a variable is, and I know very well what it means for a variable to be hidden. And as I explained, I see many variables hidden behind mathematics, the mathematics making them appear as constants. — Metaphysician Undercover

So in a double-slit experiment with a particle, name the hidden variable.

You seem to be in some sort of state of denial, afraid to face the possible reality of non-locality. — Metaphysician Undercover

Name a non-local hidden variable theory that agrees with the results of quantum mechanics up to at least quantum field theory.

The predictions are supplied by the mathematics, correct?

So in a double-slit experiment with a particle, name the hidden variable. — tom

The hidden variable is the concept of activity itself. Notice how you say, "in a double slit experiment with a particle". You are misrepresenting the experiment, because what is there in that experiment is activity. That activity may be expressed as energy or it may be expressed as a wave, and that is a variable.

There are two distinct types of activity. One is called change, and it is internal to an object. The other is called motion and it is objects changing in relative position. Relativity theories cannot be applied to change unless that change is represented as motion. Relativity theories represent change as objects moving relative to each other. The modern concept of energy is intrinsically tied to relativity theories, and therefore relative motions. In understanding activity as energy, that activity is represented as motion, and relativity theory is applied. If internal change is an activity, that activity must be understood, or represented as motion, in order that it can be expressed as energy. Therefore in order to understand any activity as "energy", that activity must be represented as motion.

A wave is an internal activity of a substance. It is a change, not a motion. If one desires to represent this internal wave activity as energy, then it must be rendered conceptually as a motion. Relativity theory does not do this, it only allows that energy is the property of moving objects, there is no wave energy. The method by which wave activity (which is an internal change to an object) is transformed to energy (relative motion of objects) is the hidden variable here.

Or chapters 5 and 6 of this book by Wallace: — tom

Thanks for the list, Tom. I don't have access to the book, but David Wallace has lots of papers on his Academia page so it's easy enough to read his arguments. What I'm not clear about is what the up to date arguments are. I'm looking at 'Many worlds', a 2010 collection of essays by people of all sorts of opinion, including Wallace, though some of the essays seems to have had online updates later.

Both Wallace and Deutsch along the way have offered 'proofs' relating to their approach, which you have tended to gloss as 'They have proved...' I don't have the maths to spot the problems in the proofs, or not, but it seems clear once you read around the literature that the key issue is what assumptions one brings to the party before proposing a so-called 'proof'. It's all, for the moment, metaphysical debate of one kind or another. Some ideas lack empirical support and have fallen by the wayside, but there are many that are alive and kicking.

The strongest critic of Wallace in the book above is Adrian Kent, a Reader in quantum physics at Oxford. Here is how he summarises his criticism:

Wallace's strategy of axiomatizing a mathematically precise decision theory within a fuzzy Everettian quasiclassical ontology is incoherent. Moreover, Wallace's axioms are not constitutive of rationality either in Everettian quantum theory or in theories in which branchings and branch weights are precisely defined. In both cases, there exist coherent rational strategies that violate some of the axioms. — Adrian Kent

I've got to say, because I didn't know much about this field before being stimulated by the frequent forum debates to have a closer look, I'm amazed the Deutsch-Wallace approach hinges on decision theory and assumptions about rationality. Decision theory is quite a hotly-debated topic in its own right so I wouldn't build a mountain on it. Well, maybe a rough algorithm for how people act, but no 100% right view.

They (D-W) end up arguing, as I understand it, that we can by fiat state what rational agents should do (and therefore by implication do do) in certain situations, including the knock-on situations - the first 'sub-branch' in one language beyond the initial branching. And if certain probabilistic arguments are empirically sound, then the 'weights' of the supposed branches in the Everettian world(s) are, as Kent says, going to have known values, and there are rational-for-agents decisions that don't fit Wallace's axioms.

I'm not clear that they do then answer the question that opened this particular thread? I don't see how an idealization dissolves the question of echoing footfalls - where do the other branches go? It seems in some of them our laws of nature won't apply? - most elegantly put by T S Eliot:

What might have been and what has been
Point to one end, which is always present.
Footfalls echo in the memory
Down the passage which we did not take
Towards the door we never opened
Into the rose-garden. — T S Eliot

The predictions are supplied by the mathematics, correct? — Terrapin Station

Yes. Consider, for example, an emitted particle in the double-slit experiment.

The Schrodinger wave equation describes the evolution of the particle and its surrounding environment, including the apparatus and the observer. Particle paths through both slits must be included in order to predict the observed interference pattern on the back screen.

If only one of the paths through one of the slits is included then the prediction changes.

don't have the maths to spot the problems in the proofs, or not, but it seems clear once you read around the literature that the key issue is what assumptions one brings to the party before proposing a so-called 'proof' — mcdoodle

They're very strong assumptions about what must be considered real. It's the ambiguity of the interpretation which realism can't stand - something has to be either real (1) or not (0). It can't cope with the idea that there are 'degrees of reality'. So the move is to export the uncertainty to a whole set of putative 'worlds', in each of which the outcome is certain or definite.

The predictions are supplied by the mathematics, correct?
— Terrapin Station

Yes — Andrew M

Right. And how are you seeing any mathematics as amounting to any sort of ontological commitment whatsoever?

Name a non-local hidden variable theory that agrees with the results of quantum mechanics up to at least quantum field theory. — tom

What about this and this?

The strongest critic of Wallace in the book above is Adrian Kent, a Reader in quantum physics at Oxford. Here is how he summarises his criticism:

Wallace's strategy of axiomatizing a mathematically precise decision theory within a fuzzy Everettian quasiclassical ontology is incoherent. Moreover, Wallace's axioms are not constitutive of rationality either in Everettian quantum theory or in theories in which branchings and branch weights are precisely defined. In both cases, there exist coherent rational strategies that violate some of the axioms. — Adrian Kent — mcdoodle

It's difficult to address a criticism which is just a slur.

Anyway, Kent doesn't like MW. His solution is to append some extra mathematical structure to QM in order to make it a single-world theory. He is thus an advocate of hidden variables. The trouble with this is that no hidden variable theory that does not contradict QM exists.

So, Kent advocates changing the physics, because he does not like the implication of currently known physics.

I'm amazed the Deutsch-Wallace approach hinges on decision theory and assumptions about rationality. Decision theory is quite a hotly-debated topic in its own right so I wouldn't build a mountain on it. Well, maybe a rough algorithm for how people act, but no 100% right view. — mcdoodle

Maybe you should watch the video I linked to. Stochastic theories are normative! Very weird.

What about this and this? — Michael

Maybe you could briefly describe those theories and indicate to what extent they are capable of dealing with particle interactions etc.

Maybe you could briefly describe those theories and indicate to what extent they are capable of dealing with particle interactions etc. — tom

I don't understand them. I only know (from what's been said of them) that they add to the de Broglie–Bohm theory the one thing that it doesn't normally explain; particle creation and annihilation. If that is indeed what they do then they are non-local hidden variable theories that agree with the results of quantum mechanics up to at least quantum field theory.