That is an interesting paragraph as it encapsulates to me the philosophy-of-science debate going back and forth here. Mathematically states in a quantum superposition are probabilistic. 'Merely' is a matter of taste. A measurement occurs, the outcomes are mathematically understood. — mcdoodle

Mathematically, the states in a quantum superposition are represented as probability amplitudes (complex numbers), not probabilities (real numbers between 0 and 1).

You quote Duhem in arguing that putting things merely mathematically like that is not 'an explanation', but Duhem is long dead and there are new sorts of empiricists about who might happily use the word 'explain' about mathematical models. I think here it's realists who are also being rigid about what an explanation must involve; it can be a circular demand, in that if one isn't some sort of realist then what is one explaining? I do think that's a fruitless side-alley. — mcdoodle

I don't think it's unreasonable to ask why quantum interference effects occur or what nature is really like. I don't see the point in calling interpretations like Copenhagen "explanatory" if they deny that there can be answers to such questions.

The realist in turn only feels ok if like you they can point to what is 'real' (albeit hypothetical in that it's unobservable) in order to apply something like ordinary language to what happens in the maths. It *is* hard to talk about. — mcdoodle

Sure, it is hard to talk about. We don't knowingly encounter superpositions in everyday life, so QM is counterintuitive. But that doesn't mean that we should abandon ordinary language and realism. That's the crucial philosophical issue. Mathematical models help us to correct our intuitions and find the language we need to better reflect the world we find ourselves in.

Even the Wikipedia article you referred me to clearly discusses probability amplitudes in terms of probabilities. It says in the first line of the article: "The modulus squared of this quantity represents a probability or probability density." — Metaphysician Undercover

You're misunderstanding that sentence. The modulus squared is the probability that that particular quantity (the amplitude) will be measured.

The amplitude is a complex number associated with a quantum system. It's about the ontology. Whereas the probability (a real number between 0 and 1) is the predicted likelihood that that quantum system will be observed if a measurement were made. It's about the epistemology.

I don't see the premises whereby you make this conclusion. If we have a coin toss of 50/50 probability, and add another coin to the toss with a 50/50 probability, the fact that the two coins could interfere with each other in the air does not produce the conclusion that our description of the toss is not probabilistic. — Metaphysician Undercover

I'm referring to a coin that has already been flipped, where there is a single state that is unknown (e.g., it's hidden under my hand). Whereas a coin held in a superposition of heads and tails has two superposed states.

In both cases, the 0.5 heads/0.5 tails probabilities are predictions about what state will be observed, not about what states actually exist prior to observation.

Probabilities are not fundamental to QM, they are simply useful. — tom

Agreed. Probabilities relate to observer predictions, not the world itself.

Probability is inherent within the Hamiltonian and therefore inherent within the Schrodinger. — Metaphysician Undercover

The Hamiltonian tells you how a quantum state will (deterministically) evolve. When it is applied in the Schrodinger equation, it produces a superposition of states which are expressed as probability amplitudes (complex numbers), not probabilities.

This matters. If states in a quantum superposition were merely probabilistic, with only one state being real as with a coin flip, then they could not constructively or destructively interfere with each other to produce interference patterns. That is why all of those states must be real.

It is only the Born rule, which is not part of the Schrodinger equation, that enables us to extract the probabilities for observing those states when a measurement is made.

According to Wikipedia: "Its spectrum is the set of possible outcomes when one measures the total energy of a system." — Metaphysician Undercover

Note the word "measures".

Probabilistic language relates to the measurement of the system, not its ontology, which is what the Schrodinger equation describes. Here's Wikipedia:

The Schrödinger equation describes the (deterministic) evolution of the wave function of a particle. However, even if the wave function is known exactly, the result of a specific measurement on the wave function is uncertain.

Therefore the equation does represent possibilities — Metaphysician Undercover

The Schrodinger Equation describes the deterministic evolution of the wave function of a quantum system. In the double-slit experiment, the system evolves from the initial state when the particle is emitted, to states at both slits and finally to states at the back screen.

This process is fully deterministic. There are no probabilities in the system, only amplitudes for each quantum state which are represented as complex numbers.

That is the ontology of the system. Probabilities only arise when making predictions about measurements within the system and this is governed by the Born rule.

The interference effects are phenomenal. The phenomenon is described as possibilities. — Metaphysician Undercover

Quantum interference effects are real and are predicted by Schrodinger's equation. You won't find any mention of possibilities or probabilities in the Schrodinger equation.

It's a contradictory notion that all possible worlds are actual. In my understanding of possibilities, any possibility must be actualized before it can become an actuality. If all possible worlds are assumed to have actual existence, without a cause (source of actualization), then this is contradictory to my understanding of "possible". — Metaphysician Undercover

MW is a causal theory - the wave function evolves deterministically with the parallel branching and merging built in. I've been making just your argument that possibilities - an epistemic term - cannot be invoked to explain interference effects. Only real superposition states can cause real interference effects.

Now, it's when the model which is necessitated by the successful math, does not make sense, as is the case with MW, that we have to turn back to the principles whereby the mathematics is applied, to see where the mistakes are. — Metaphysician Undercover

So what about MW does not make sense, or is mistaken, on your view?

It's just a matter of what people consider an explanation or not. And a large percentage of relevant academics consider mathematical equations read instrumentally to be explanations. — Terrapin Station

Explanation is an account of why something happens. I've just quoted Duhem, probably the main proponent of instrumentalism in the 20thC, who rejects that physical theories are explanatory. Do you have any cites to back up your contrary claim?

I don't buy that we can observe a multiplicative relation or that mathematics is observational. — Terrapin Station

Multiplication is a scaling transformation. An example of observing this is when we see a car moving towards us from 200 meters to 100 meters away and consequently appears twice the size.

Mathematical models on their own, sans ontological commitments, are taken to be sufficient for explanatory scientific theories. — Terrapin Station

If a scientific theory, per instrumentalism, makes no ontological commitments (i.e., is neither true nor false), then neither can it be offering an explanation. In Duhem's words, "A physical theory is not an explanation; it is a system of mathematical propositions whose aim is to represent as simply, as completely, and as exactly as possible a whole group of experimental laws."

This is essentially taking an instrumentalist approach to mathematical models, but it's neither an alternative nor a rejection of realism--it's rather noncommittal on the question because it's avoiding any ontological commitments. — Terrapin Station

OK, but...

Reading the Schrodinger equation as implying real, parallel worlds, rather than simply being a mathematical model that allows accurate predictions, is making ad hoc assumptions that are not implied by the mathematical model. — Terrapin Station

This is akin to saying that the heliocentric model makes accurate predictions but it's an ad hoc assumption to suppose the model implies that the earth orbits the sun.

What you're calling an ad hoc assumption just is the implication of the model, whether or not you choose to be agnostic or instrumentalist about it.

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

That's what it means to regard QM as an explanatory scientific theory. The alternatives are to either change the theory (e.g., dynamical collapse or Bohmian mechanics) or to abandon realism (Copenhagen, instrumentalism).

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.

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.

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.

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.

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.

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.

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.

The second edition of Everett's thesis was published as “Wave Mechanics Without Probability'. Why do you think it was called that? — Wayfarer

Because Everett considered the wave function to be real and the world as not inherently probabilistic.

Bell - local realism falsified
Leggett - non-local realism falsified

It has been shown by experiment that both local and non-local realist theories disagree with Reality. Quantum Mechanics has never been shown to disagree with Reality. — tom

Just to clarify this, Everettian QM is a local realist theory. What Bell's theorem falsifies are realist theories that depend on local hidden variables.

Meanwhile my impression of MWI is that it's ad hoc to preserve determinism. — Terrapin Station

The determinism is built-in to QM - the wave function evolves deterministically according to the Schrodinger Equation. And self-locating uncertainty is a prediction of QM.

Copenhagen has to deny the reality of the wave function to avoid that determinism and it cannot explain measurement uncertainty. 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.

But it's not. It is the result of a simple conjecture: 'hey, what if the wave collapse DOESN"T OCCUR?' That's all it is — Wayfarer

There is a lot more to the issue than that. There is nothing at all in QM that implies or predicts wave function collapse. Copenhagen doesn't postulate wave function collapse, it wholesale denies that the wave function is real. That is, the philosophy of the Copenhagen Interpretation is anti-realism. It's worth repeating the quote by Bohr which makes it very clear what anti-realism entails:

There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature. — Bohr

The Ptolemaic epicycles were ad hoc additions to preserve geocentric intuitions.

The branching is intrinsic to QM. So it's dynamical collapse and hidden variables that are ad hoc, in order to preserve classical single-world intuitions.

"....local realism doesn’t work. For example, say you are experimenting with entangled photons. As soon as you measure one of the entangled photons in a detector and find that its polarization—that is, the orientation of its waves—is horizontal, the other one in the pair is instantly projected into a horizontal state. And this happens not because the photons were both horizontally polarized from the beginning. That is contradicted by the experiments. It doesn’t matter whether you look at the two particles at the same time, separated over large distances, or one after the other; the results are the same. So it seems as if quantum mechanics doesn’t care about space and time."
— Anton Zelliger — Wayfarer

As you probably know by now (even if you don't like it!), local realism works just fine under Everettian QM. If you measure one of the photons and its polarization is horizontal, you can then deduce that the polarization of the other photon is also horizontal. That's because the initial measurement entangles you on the same branch as that pair of photons (and not the vertically-polarized photon pair). So QM respects space and time - no superluminal effects required.

There is no such thing as the convergence of particle world lines, each is an individual. You could create an average, or a gravitational centre, but this requires another completely different assumption. — Metaphysician Undercover

You can approximate the apple as a point, or treat it as an extended volume (which would be a world tube) or aggregate the segments of the individual particle world lines that converge.

But don't you agree that the true philosophical approach, and consequently the scientific approach, would be to attempt to determine and understand the activities of this cause? — Metaphysician Undercover

Sure, we should try to figure out what the cause is. My only point is that we don't need to doubt the existence of the apple just because we don't know what that specific cause is. We know there is a cause (because it's not random coincidence), but it may be that no-one can explain exactly what it is or perhaps our current best explanation will end up being overturned tomorrow. Regardless, we can continue to intelligibly identify apples as existents in everyday life just as we always have.

Potential is real, and therefore must have some type of existence, though it is distinct from actual existence. We can assign "actual existence" to what has occurred, and this is the basis for observation. Anything observed, has occurred. The existence of an actual object is something observed. The object is in the past, as it has been observed. There are no objects in the future, yet the potential is there. What type of existence could this potential have? Clearly it is non-temporal existence, because time only occurs at the present, as time passing. Only things in the past have experienced time passing, so only things in the past have temporal existence — Metaphysician Undercover

Your explanation needs to account for the double-slit experiment. What goes through the slits, if anything, such that an interference pattern is observed on the back screen?

I just did a quick read on Wikipedia and found that a world line applies to a point. Yet you referred to a "distribution of particles". So it appears impossible that a distribution of particles could follow a single world line. — Metaphysician Undercover

World lines apply to objects, whether particles or apples. The world line for an apple is the convergence of particle world lines.

That's a causal explanation. But in everyday life, it is intelligible to talk about an apple as persisting because we know its continued appearance is not random coincidence, whether or not a causal explanation is readily available. Which is sufficient justification for the claim that the apple exists.

So on what grounds are you denying that apples exist? There is a distribution of particles following a world line that we can identify as the apple.

I understand the distinction. So how do you explain double-slit interference patterns in terms of potentially-existing objects?

No, that is not what is at issue here, you don't seem to get it. We know what is meant by "apple", or "object", temporal continuity is implied, but the question is whether or not this is a misconception. We know that the word "apple": is being used to refer to the appearance of a persistent similitude on the table. We know that the idea of temporal continuity is implicit with the concept of "apple", but the question is, is this temporal continuity real, or is it just an appearance. If it is just an appearance, then this is a misconception. — Metaphysician Undercover

So help me out here. Do you think there is a causal basis for the apple on the table appearing as it does from moment to moment? Or do you think that, for all we know, it's just random coincidence?

But you know that is an understatement by a very long way! — tom

Indeed. But I'm leaving open the possibility of extra postulates. For example, QM would be incomplete if there were demonstrated to be disappearing worlds, per Copenhagen.

What you're not allowing for is the possibility of 'real abstractions'. In your view 'abstractions' are simply 'mental phenomena', which must be consequent to the physical, right? Mental phenomena are the products of the brain, which is the product of evolution, which is ultimately governed by physical laws, right? So there is no way to understand how 'abstractiions' can be real in any objective sense. — Wayfarer

I think of abstractions in an Aristotelian sense, not Platonic sense. That is, universals exist when they are instantiated in things. In this sense, abstractions existed prior to people being around to talk about them. They are something we discover, not create.

Underline added. Heisenberg is suggesting that sub-atomic particles can't be said to exist in the way stones or flowers exist. In what way do they exist? Elsewhere, he says they are:

"something standing in the middle between the idea of an event and the actual event, a strange kind of physical reality just in the middle between possibility and reality."

Heisenberg called this "potentia," a concept found in Aristotle. So in this framework, the observation made by the physicist 'actualises' the potentially-existing 'object' into a particle, which doesn't really exist prior to that observation. — Wayfarer

It's a creative theory. But what does it mean? Do potentially-existing objects interfere in the double-slit experiment?

Notice that in David Wallace's podcasts on MW, it states upfront the fact that among the problems that are solved is that of the requirement for there to be an observer - the crux of the measurement problem. MWI disposes of that by saying that there is 'no collapse', i.e. all the observations are equally real in some parallel world. Doesn't that just strike you as being a monumentally bizarre idea - that there are endless replicas of the universe? If you can't see how bizarre it seems, then I'm afraid we do live in different worlds after all. — Wayfarer

Yes, it sounded bizarre when I first encountered it. But having worked through the math, there's really no way around it. The other interpretations are just creative attempts to avoid the straightforward implications of QM.

Everettian QM is unitary, local, causal, realist, parsimonious, explanatory and testable - just the sorts of things one would expect of a robust scientific theory. On the other side is Copenhagen QM, which just shrugs and says the math is meaningless and the world is intrinsically unknowable.

So that is the context for judging these two interpretations. Everettian QM violates our natural intuitions, but has all the hallmarks of a correct theory.

on the grounds of the inherent implausibility there being parallel universes. Given the assumption there are, there are mathematical 'solutions' to various paradoxes and conundrums. But if their grounding assumption is unreal, then what kinds of 'solution' are they really? — Wayfarer

They would be no solution at all. But this would imply the QM formalism being either wrong or incomplete. And QM is a very well tested theory.

QM is counterintuitive to humans because we don't knowingly encounter things in superposition in everyday life. People intuitively think we live in an classical world where particles have precise positions and momenta at the same time. But we don't - we live in a quantum world and so it's really our intuitions that need to change.

Once we stop thinking of superposition states as possible states that the particle can be in (the classical intuition) and instead as actual states that interfere with each other (the quantum intuition), then the idea of parallel worlds (or branches or paths) naturally follows.

The philosophical issue is whether mathematical equations provide insight into the world we live in, or whether they are mere Platonic abstractions that nonetheless may have instrumental value.

No, it's really a matter of justification. You can sit and watch the apple all day, and even see it change, without taking your eyes off it, so you know that no one has switched it. You know that it has changed, so you know that it is not the same apple. Yet we say that it is the same apple. — Metaphysician Undercover

Yes we do. That's because object persistence is part of the ordinary concept of an apple.

Saying that it is the same apple does not cause it to be the same apple. — Metaphysician Undercover

That's correct, but the issue here is what is meant by the term "apple".

You're taking a particular time slice as constitutive of what it is to be an apple, like an individual frame in a film. But, in ordinary usage, the entire time line (or world line) is understood to constitute the apple.

To use the film analogy, it is the same film despite the fact that its frames are different. But there would be a legitimate issue if the second half of the film were replaced by frames from another film. This latter issue is where justification is relevant.

but when the initial decision is made to entertain the notion of many worlds, then a whole series of consequences flow on from that. But I'm sceptical of the very first assumption. Actually, I'm not just sceptical - I'm dismissive of it. I think it is a fantasy. Everett himself says he had been drinking when the idea came to him. 'Hey, what if all the outcomes are real?' — Wayfarer

I think the issue is that if Everettian QM both explains our observations and solves a bunch of problems, as Tom points out, then on what grounds are you dismissing it?

In terms of consequences, we can continue to hold the same kinds of views around personal identity and decision-making as we always have. It's just that the world would be larger than previously thought.

(Sorry for the delay MU - life interrupting philosophy...)

I hope you understand, that to say the apple consists of matter and form, in the Aristotelian sense, is to invoke a type of dualism. — Metaphysician Undercover

Aristotle doesn't claim that two kinds of substance exist or that two kinds of properties exist, which is the usual sense of dualism. Instead substance (i.e., a thing that exists such as an apple) is an integration of matter and form.

If we cannot validate the existence of matter, then we cannot justify that the apple continues to be the same apple despite changing, because we know that even the molecules and atoms are changing. — Metaphysician Undercover

The simple explanation is that the apple's identity doesn't depend on its molecules and atoms being the same. Instead object persistence is implied when we talk about particular apples. What would be relevant is if someone secretly took the apple from the table and replaced it with a different apple.

So the issue is really about meaning and use, not justification.

But don't you agree that if you eat the apple, at some point it will no longer exist? And, don't you think that the apple came into existence at some time? Unless you can describe what marks the difference between the existence and the non-existence of the apple, why do you feel so confident that the apple exists? I mean, to me, it appears like you just take it for granted that the apple exists, without even knowing what it means to exist. If you knew what it means to exist you could probably tell me what constituted the apple coming into existence, and what constitutes the apple going out of existence. — Metaphysician Undercover

At some point the apple grew on a tree and before that the tree grew from a seed. And in the other direction, at some point the apple will be eaten or decompose and perhaps its seeds will grow into into new trees. This is just matter changing form such that we can identify substances like apples. So the boundaries at the coming-into-existence and going-out-of-existence of an apple can be vague or ill-defined. But the apple is clearly identifiable when it is fully formed. And so we can develop language to talk about it.

OK, if we agree here, then let's go back and take a look at the Aristotelian principle, to see the difference. Instead of defining the existence of the object through its relations with other objects (relativity theory), or as I discussed with apokrisis, defining the object as being in a context, Aristotle defined a principle of existence (matter) which is inherent within the object. — Metaphysician Undercover

Right. The logical form of the apple is not sufficient for existence. Matter is also required.

Do you agree that these are two very distinct ways of defining existence? The way of modern physics is to define the object's existence through its relations to other objects. The way of Aristotelian physics is to assume that there is existence inherent within any object, regardless of its relationships with other objects, it has substance. Now let's consider the apple on the table. Which do you think is the truth concerning the existence of the apple? Do you think that the apple only has existence because it has relationships with other objects, the table etc., or do you think that there is something inherent within the apple itself, which constitutes its existence? — Metaphysician Undercover

The latter. The way I would put this is to say that if the apple has form and matter then it is substantial. That is, it exists.

To relate this back to QM. The formalism is the Schrodinger equation. The primary dispute is whether the equation is substantial. That is, is the wave function real? If it is, then that explains why we see interference effects.