## Classical, non-hidden variable solution to the QM measurement problem

• 367
I like your questions. This one touches upon an important issue. When we say there is a unique ket for each physical state, we are saying that the relation between physical states and kets is a 'function', as that word is technically understood in mathematics. That means that any physical state can only have one associated ket. It does not, however mean that two different physical states cannot have the same ket, and that's where your point about complete descriptions comes in. For any two different states to necessarily have different kets would imply that the ket is a complete description of the physical state. The postulates of QM do not claim that the ket is a complete description. Claims of completeness or otherwise of the kets are either interpretations of QM, or part of theories that seek to extend QM. They are not part of core QM.

If the ket is a complete description then the function that maps physical states to kets is one-to-one ('injective' is the technical term). If it is not complete then the function is many-to-one, like for instance the functions f(x)=x^2 and g(x)=sin x.

I didn't completely grasp all of your question, but I answered it as best I could. Let me know if I left anything out.
• 367
But what does the operator operate on?tom
Good question. The rough answer is that it 'operates on' kets. A more mathematically pure answer is that the name 'Hermitian operator' is simply a formal label for an element of a subset of H x H (the Cartesian product of the Hilbert space with itself) that obeys certain properties (functionality, linearity, Hermiticity), so we don't have to think of it as operating on anything.

Except when a measurement is made according to 3.tom
Quite right. I forgot to add that bit.
None of this [postulate 3] is a necessary axiom to do quantum mechanics though. Why not drop it?tom
You're right that there's no need for it in the context of a discussion about the 'measurement problem' (which I'm guessing this thread is somewhat related to, but I'm still very unsure of that), as Decoherence gives us all we need (I think). But in applied QM it is very useful as it removes the need to think about the measuring apparatus.
• 759
There are no particles as such prior to the act of measurement. Literally all there is is the possibility of there being one.

I don't know what that means, though, unless one is an anti-realist, which I'm not.

It is the measurement which reduces the probability to actuality.

But how do you go from probability to actuality? What is the mechanism? Is this just brute?
• 759
ou're right that there's no need for it in the context of a discussion about the 'measurement problem' (which I'm guessing this thread is somewhat related to, but I'm still very unsure of that),

At the beginning of the talk I linked to, Alan Bar introduced the measurement problem for the audience, then Simon Saunders argued for MWI, followed by James Binney discussing HMI, I guess, although he didn't give his interpretation a name. The Youtube title is: "The 1st Ockham Debate - The Problem of Quantum Measurement - 13th May 2013".
• 367
At the beginning of the talk I linked to, Alan Bar introduced the measurement problem for the audience, then Simon Saunders argued for MWI, followed by James Binney discussing HMI, I guess, although he didn't give his interpretation a name. The Youtube title is: "The 1st Ockham Debate - The Problem of Quantum Measurement - 13th May 2013".
Thank you, that clarifies it nicely. Given that it's about the 'measurement problem', the references to uncertainty will have nothing to do with the Heisenberg Uncertainty Relation and instead will refer to the lack of knowledge prior to measurement about which of the eigenvalues of the ket of the observed system will be the result of the measurement.

Discussion of that issue involves interpretation, not just core QM, as is indicated by the letter 'I' at the end of the two abbreviations 'MWI' and 'HMI'. So it would appear that the people involved are debating interpretations and not challenging the postulates of QM, or deductions therefrom like the Heisenberg Uncertainty Relation, which would have been a worry.
• 759
Just to pick up one of the possible meanings, if 'uncertainty' refers to the probabilistic nature of the value obtained from the measurement, as assessed prior to the measurement, and based only on information about the observed system and not the measurement apparatus, then that agrees with the Decoherence theory, which is widely accepted. If that's what was meant then the prof is not saying anything controversial, or new, at all

No, that's not what he was arguing for. Binney stated several times that the probabilistic nature of the value obtained was due to our epistemic uncertainty about the exact quantum state of the measuring device, and not anything fundamental about the state of the particle prior to being measured. A little reading up on HMI reveals that this particular interpretation understands probability to be entirely epistemic (our ignorance or inability to measure everything accurately) and not ontological or fundamental.

My understanding is that decoherence has to do with normal macroscale objects, such as detectors, interacting with isolated quantum systems, which are fundamentally probabilistic, or at least the math describes those systems as being so, causing them to lose their coherence, leaking the quantum information out into the wider environment.

But it doesn't do away with superposition. In the cat thought experiment, although it explains why we don't see both a live and dead cat when opening the box, it doesn't explain what happens to us and the rest of the universe. That still requires an interpretation, and I believe MWI is compatible with decoherence.
• 759
o it would appear that the people involved are debating interpretations and not challenging the postulates of QM, or deductions therefrom like the Heisenberg Uncertainty Relation, which would have been a worry.

Yes and no. I'm pretty sure Binney challenged taking the postulates of QM literally (realistically), when interpreting the results. He said they were very useful tools, but the Schrodinger Equation, for example, has unreal properties (such as leading to a superposition of states). He also mentioned the Heisenberg Uncertainty Relation, and I'm pretty sure his interpretation is at odds with taking that realistically, since he thinks probability is epistemic, and not fundamental. Thus, a measuring device has an exact quantum state (state that all the particles and molecules are in), and not a wavefunction.
• 2.1k
There are no particles as such prior to the act of measurement. Literally all there is is the possibility of there being one.
— Wayfarer

I don't know what that means, though, unless one is an anti-realist, which I'm not.

Well that's the whole measurement problem in a nutshell. All the big arguments are about this very point. Realists want to insist that there is a real particle, something 'mind-independent'; that is just what is being called into question. One of Bohr's quotes is 'that there is no particle prior to the act of measurement'; which is why Einstein asked the rhetorical question 'does the moon still exist when nobody is looking at it?' It is why there are all the arguments in the first place. Many Worlds simply outsources the problem to 'other worlds', but it seems a desperate remedy to me.
• 759
One of Bohr's quotes is 'that there is no particle prior to the act of measurement'; which is why Einstein asked the rhetorical question 'does the moon still exist when nobody is looking at it?'

Let's say Bohr was right. Why the interference pattern, then? Why not some other probability distribution? It's highly suggestive that something is interfering. After all, that's what observable waves do.

And science has a track record of positing what are initially unobservables, and then coming up with instruments to make those observations. At one time, atoms were just theoretical posits. Anti-realists could have (and maybe did) argue that they were useful fictions for making sense of experiments at the time. But now we can observe them, so obviously they are more than useful fictions.
• 759
Einstein asked the rhetorical question 'does the moon still exist when nobody is looking at it?'

It's gravity certainly does. The unobserved particles have properties that are important to atomic structure and fields of force. It's similar to noting that the floor keeps holding you up even when you don't notice it. Somehow the stuff of everyday life is held together despite not observing all the particles making it up.
• 1.1k

The "useful fiction" argument doesn't make sense in the way it's often termed. For physics, the important question is its descriptive power. What makes it "real" is that it accounts for the world, not a particular emprical form-- I mean where is the state of "energy?" Yet, we don't go around saying energy somehow isn't real.

Let's imagine for a moment that atoms weren't a particular state of the world (which is sort of true of the Borh model), would it mean that atomic theory wasn't how the world worked? Not at all. If our objects still behaved in that way, atomic theory would still be expressed by the world; it would be description of how the world really worked, despite the absence of particular atoms which someone could pick-up and hold with atom tweezers.
• 2.1k
Why the interference pattern, then? Why not some other probability distribution? It's highly suggestive that something is interfering.

As I understand it, which may be not very well, the probability wave really is a distribution of probabilities - nothing more than that. So it's not actually 'a wave' at all, it simply behaves like a wave - it is 'wave-like' but there really isn't a wave as such, because it doesn't transmit energy or move in a medium, like light waves or water waves. That is why, I think, it is 'rate independent' - the 'wave pattern' really is embedded in the fabric of reality itself, it is of a different order to the physical. That is why the 'nature of the wave function' is the metaphysical question par excellence.

At one time, atoms were just theoretical posits. Anti-realists could have (and maybe did) argue that they were useful fictions for making sense of experiments at the time. But now we can observe them, so obviously they are more than useful fictions.

But the meaning has been changed in the meantime. 'Atom' used to mean 'indivisible particle'. But if you look up the definition of 'atom' now, it is 'the smallest particle of a chemical element that can exist'. But as soon as the atom was shown to be mainly empty space, then I think it ceased to be an atom in the classical sense, i.e. a truly 'indivisible particle'. The idea of 'atoms and the void' could no longer hold. So the atom is no longer the ultimate explanans that is was considered to be by materialism. That is the sense in which physics has undermined materialism.
• 367
No, that's not what he was arguing for. Binney stated several times that the probabilistic nature of the value obtained was due to our epistemic uncertainty about the exact quantum state of the measuring device, and not anything fundamental about the state of the particle prior to being measured. A little reading up on HMI reveals that this particular interpretation understands probability to be entirely epistemic (our ignorance or inability to measure everything accurately) and not ontological or fundamental.
That's fine. I am sympathetic to everything you report him as saying there, and it's a widely held interpretation. All I was concerned about was whether he was rejecting either the postulates of QM, or results derived from them alone, such as the Heisenberg Uncertainty Relation. It is now clear that he was not. Questions of whether certain things are epistemological or ontological are matters of pure interpretation, since the postulates make no distinction between the two.

In your later post you said Binney said people shouldn't take the QM postulates literally or realistically. I can agree with that too, because it also is about the interpretation, not the calculation. He's not saying we shouldn't believe the predictions they make, which are purely about observations. I do not subscribe to the ontological perspective sometimes known as 'Realism' - but which I think of by the (IMHO) more accurate title 'Materialism'. I lean towards Bohr rather than Einstein.
• 2.1k
I lean towards Bohr rather than Einstein.

(Y)
• 759
That is why, I think, it is 'rate independent' - the 'wave pattern' really is embedded in the fabric of reality itself, it is of a different order to the physical. That is why the 'nature of the wave function' is the metaphysical question par excellence.

This is where I get confused about the Copenhagen interpretation. Is it anti-realist, or is it saying that reality is this non-classical stuff of possibilities that behave like a wave? That seems to be two different interpretations.

The first one leaves questions unanswered. It's the sort of thing Landru of the old forum would have been happy to endorse. Our experiences have a structure. We don't know why, but realism just presents a regress, etc. In terms of the double slit experiment, we don't know why it results in an interference pattern when there isn't a detector on one of the slits. That's just what happens, and physicists developed the math to describe/predict it, because science is merely concerned with prediction (on Landru's account of it).

While the second one, that the world is actually made of probability waves until a measurement (or decoherence) takes place, is puzzling, weird, and almost mystical. The second one is making an ontological claim.
• 759
I am sympathetic to everything you report him as saying there, and it's a widely held interpretation.

I didn't explain what I heard well. It was only after several pages of replies that I figured out how to express it clearly.
• 2.1k
This is where I get confused about the Copenhagen interpretation.

You're not alone.

I would simply make the point that 'the Copenhagen Interpretation' is not a scientific hypothesis. It is only a description of the kinds of things that Bohr, Heisenberg and Pauli used to say in debates and discussions about interpretation; the term itself wasn't even coined until the 1950's.

that the world is actually made of probability waves until a measurement (or decoherence) takes place, is puzzling, weird, and almost mystical.

During the early days of quantum physics, there was quite a bit of mysticism about. (See Quantum Mysticism - Gone but not Forgotten. And have a read of The Mental Universe.)
• 795
Alright point taken, but the question is whether the Schrödinger equation is describing the real state of the particle before it's measured, or it just has predictive power as a useful tool, and the reality is something else. Afterall, what the hell is a probability wave supposed to be?

The wavefunction is NOT a probability wave! It's not even a probability amplitude wave! According to Copenhagen, it does not exist. According to Binney it seems to not exist either.

According to the only known REALIST interpretation that agrees with QM, the wavefunction is an element of reality, but exactly what? The mathematical properties of the wavefunction correspond to features of reality, and the only way to make sense of this is to accept that the wavefunction represents a branching (and occasionally recombining) world-density function.

It turns out that under realist QM - i.e. the sort where the only dynamics is UNITARY evolution of the wavefunction, then probability is not part of the theory, it is not required. That is not to say that probability is not an extremely useful MODEL in most circumstances.

In context of Binney and HMI, if the reality would be our epistemic uncertainty about the complex state of the measuring device having a large influence on the particle it's detecting.

For Binney, quantum mechanics is not a physical theory. If you ask me, everyone else in the discussion section of the video you posted was embarrassed into silence. It was a car-crash. At least he does not believe in objective propability - i.e. his version of QM is a stochastic theory of human ignorance.

If MWI is the case, then probability wave is a description of other worlds. Or it could be pilot waves guiding the particle. But then again, perhaps reality is a jumble of possibilities when we're not looking? Question is why does measurement make it classical? Why is our lived experience mostly classical?

For systems of more than one particle, QM takes place explicitly in Hilbert space - not in the space-time. This should at least indicate that the idea of "probability waves" flying around is wrong. In fact, under the Heisenberg picture, the wavefunction is stationary - it does not change - and all dynamics is contained within the observables! Why does no one talk about observables flying around?

If MWI is the case, then probability wave is a description of other worlds. Or it could be pilot waves guiding the particle. But then again, perhaps reality is a jumble of possibilities when we're not looking? Question is why does measurement make it classical? Why is our lived experience mostly classical?

Decoherence.
• 795
This is where I get confused about the Copenhagen interpretation. Is it anti-realist, or is it saying that reality is this non-classical stuff of possibilities that behave like a wave? That seems to be two different interpretations.

The Copenhagen is anti-realist; it is a purely epistemic theory. The "Standard" interpretation, taught at most (American) universities calls itself Copenhagen, but it's not. It is based on the famous book by von Neumann "The Mathematical Foundations of Quantum Mechanics". That interpretation definitely has a realist feel to it. In British universities, the treatment tends to be closer to Dirac, which again feels realist.

Quantum mechanics is quite hard, and is made more so by obfuscators like Binney. You aren't going to be asked for an essay on ontology or epistemology in your final exam, but you are going to need to shut up and calculate.

In terms of the double slit experiment, we don't know why it results in an interference pattern when there isn't a detector on one of the slits.

Yes we do!
• 759
Yes we dotom

Feynman said that nobody understands, assuming that wasn't taken out of context, but I always understood him to be saying that nobody knows why the double slit and other experiments give the results they do. How many nuances to the various interpretations are there, btw?

For systems of more than one particle, QM takes place explicitly in Hilbert space - not in the space-time.tom

What is Hilbert space, and what makes it any more real than probability waves? And I don't mean what is the math, I mean what does the math represent?
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