I like the wording in section 9.4, "Applications of the Uncertainty Principle". You will find this: "Now the hand waving begins. — Metaphysician Undercover

Brilliant pick-up MU! I love it. I'd never noticed it before, as I only skimmed the rest of the chapter once I'd worked through the derivation of the uncertainty relation (item 9.2.14 in the Second Edition). It perfectly exemplifies what I'm saying. Section 9.2, in which the uncertainty relation is derived, is two pages of pure maths. As the chapter goes on, he starts to discuss interpretations and consequences of the relation that rely on more assumptions and approximations than are justified by the bare postulates. That's where that quote you found comes in.

As for the postulates, here's a rough attempt to give them in prose:

1. To any possible state of a system (collection of particles) there corresponds a unique set of information about it, called a 'quantum state', which is uniquely represented by a mathematical object called a 'ket' which is part of a collection of such objects, called a 'Hilbert Space'. [Later on, this is generalised so that kets are replaced by operators, in order to allow for non-pure states, but we won't worry about that here]

2. To every aspect of the system that can be measured as a number - called an 'observable' - there corresponds a unique mathematical object called a 'Hermitian operator'

3. If a system is in state s, to which corresponds ket S, and a measurement is made of observable m, which corresponds to Hermitian operator M then, immediately after the measurement is made, the particle will be in a state s' whose associated ket has the mathematical property of 'being an eigenket of the Hermitian operator M', and the value observed from the measurement will be a number that is 'the eigenvalue of that eigenket'. Further, as assessed prior to the measurement, the probability of the state after the measurement having ket S' is proportional to the square of the 'inner product' (another maths term) of S with S'.

4. The ket associated with a system evolves over time according to a known differential equation, called Schrodinger's Equation.

The MWI proponent conceded to Binney that MWI would be totally unnecessary if the measuring device is the culprit, but doubted that having more exact knowledge of its quantum state would make the uncertainty disappear. — Marchesk

Sure, if there was no such thing as the measurement problem, there would be no need to solve it.

Thanks Andrewk for the clear explanation. I'm going to dwell on that for a bit, but I think we speak two different languages, you mathematics, me English. I don't think one is completely translatable into the other, there are roadblocks, things that just don't translate.

The ket associated with a system evolves over time according to a known differential equation, called Schrodinger's Equation. — andrewk

Problem being that when a measurement takes place, Schrodinger's equation fails to predict the outcome, unless of course MWI is endorsed.

Yes, I have no idea what he is saying, let alone what he meant to say. I am suspicious of all prose presentations of QM. QM is mathematics and needs to be presented as such. — andrewk

But the interpretations stem from the measurement problem, which is not accounted for by the mathematics. That's one thing.

The second thing is to recall history when Newton proposed the law of gravity, and his critics wanted to know how an invisible force acted at a distance on objects. This troubled Newton as well, but he didn't have a good answer at the time.

Now imagine Newton and allies telling everyone to shut up and calculate, the math was all that mattered. And maybe they did back then. But we know now that Newton's formulation of gravity was incomplete. And how did Einstein come up with a better formulation?

It certainly wasn't from math, it was from asking deep questions about gravity and related phenomena, and then doing (or finding) the required math to make it work for GR.

'm not going to criticise Prof Binney though because I haven't watched his video, just as I don't read designs for perpetual motion machines or proofs that one can trisect an angle. I don't need to because I know it either doesn't say what people think it does, or it is wrong. — andrewk

That's entirely dismissive and not a good counter argument. You need to be able to show how Binney and advocates of Hidden Measurement are wrong about the measuring device introducing the uncertainty.

That's entirely dismissive and not a good counter argument. — Marchesk

I'd go further: it's not a counter-argument at all, because no argument has been presented to counter.

The argument:

The measuring device is the source of uncertainty in these experiments. You don't agree, fine. You don't want to watch the video or research his position, fine. You don't wish to counter the argument, fine.

But calling it not an argument? That's bollocks. In fact, I would say your response is irrational.

I don't know that his or the HMI interpretation is right. It could be entirely wrong. I just wanted to hear legitimate feedback. My suspicion is that taking into account the measuring device won't make the uncertainty of the particle disappear. Too many experiments suggesting otherwise. But it's worth considering, just in case our understanding of QM resides on not taking something into account.

The problem is it doesn't work. Take out the measuring device and one is talking about a different interaction in the world. It is no longer a state we are measuring with a device. A measurement without a measuring device is nothing more than an incohrent fantasy.

Practicing a measurement is inseperable from the measuring device. It makes no sense to speak as if our measurement (or description) is spoiling our knowledge. There is no measurement or description without it.

Binny is therefore stuck (or rather simply irrelevant in the first instance). The hidden effect of the measuring device cannot be used to predict with certainity. Even if we knew it all it would do is describe the interactions of a measuring device as they occured. All those interactions not involving the measuring device, or those which behaved otherwise to what we expected, would not be covered--uncertainty remains.

Is the cat in the box alive or dead? It won't be defined with certainity until it is measured(effect of the measuring device inclusive).

The problem is it doesn't work. Take out the measuring device and one is talking about a different interaction in the world. It is no longer a state we are measuring with a device. A measurement without a measuring device is nothing more than an incohrent fantasy. — TheWillowOfDarkness

No, it's about accounting for the measuring device, not removing it.

One other thing about the math in QM.

The experiments are primary, not the math. Math is used to model and predict experimental results. Schrodinger's equation exists because of the double slit experiment and others like it.

So a natural question to ask is whether the math fully takes everything relevant into account. In this interpretation, the unknown quantum state of the measuring device is a potential source of something important not being taking into account.

I agree that the math is just to tool and lots of written and spoken words as well as experiments preceded and followed. However, for science the math is what counts. For philosophers, everything else is most relevant.

In so far as as the"measuring device" is concerned, and I'm quite surprised that Binney does not recognize it, exactly what are the boundaries to the "measurement device" and how do you ever establish its state if it is constantly changing?

This topic was well discussed and Bohr addresses it in the paper I referenced above.

To put a sharp point on the problem, light (or photon) limits certainty. So, the next question for a philosopher is what exactly is light? - and I am referring to something more than the scientific definition.

However, for science the math is what counts — Rich

Science isn't math though. It's an empirical investigation of the various phenomena in the world. As such, the world has the final say, not math. Experiments and observation are what ultimately drive the math.

so far as as the"measuring device" is concerned, and I'm quite surprised that Binney does not recognize it, exactly what are the boundaries to the "measurement device" and how do you ever establish its state if it is constantly changing? — Rich

That is a big problem. Perhaps as big as not being able to detect other worlds or pilot waves.

But that's the problem. The only way to account for the measurement ( including the device) is through describing it. This preculdes certain prediction because the measurement is not defined prior to itself-- we can't tell what happens for certain until the event is present. Binny's speculation leaves us in the same place as other accounts of QM: unable to predict with certainity because we can't derive a measurement from outside itself. Rather than solve the "measurement problem," he's just pointing out uncertainy collapses with measurement, much like many other accounts of QM, from CI to MWI.

1. To any possible state of a system (collection of particles) there corresponds a unique set of information about it, called a 'quantum state', which is uniquely represented by a mathematical object called a 'ket' which is part of a collection of such objects, called a 'Hilbert Space'. [Later on, this is generalised so that kets are replaced by operators, in order to allow for non-pure states, but we won't worry about that here] — andrewk

So, the laws of physics operate the "unique set of information" and not on the actual physical system?

2. To every aspect of the system that can be measured as a number - called an 'observable' - there corresponds a unique mathematical object called a 'Hermitian operator' — andrewk

But what does the operator operate on?

3. If a system is in state s, to which corresponds ket S, and a measurement is made of observable m, which corresponds to Hermitian operator M then, immediately after the measurement is made, the particle will be in a state s' whose associated ket has the mathematical property of 'being an eigenket of the Hermitian operator M', and the value observed from the measurement will be a number that is 'the eigenvalue of that eigenket'. Further, as assessed prior to the measurement, the probability of the state after the measurement having ket S' is proportional to the square of the 'inner product' (another maths term) of S with S'. — andrewk

None if this is a necessary axiom to do quantum mechanics though. Why not drop it?

4. The ket associated with a system evolves over time according to a known differential equation, called Schrodinger's Equation. — andrewk

Except when a measurement is made according to 3.

1. To any possible state of a system (collection of particles) there corresponds a unique set of information about it, called a 'quantum state', which is uniquely represented by a mathematical object called a 'ket' which is part of a collection of such objects, called a 'Hilbert Space'. [Later on, this is generalised so that kets are replaced by operators, in order to allow for non-pure states, but we won't worry about that here] — andrewk

Here's a question concerning this postulate, perhaps you can find an answer for me. Refer to the time-energy uncertainty which I mentioned at the end of my other post, and is described at the end of Shankar's ch. 9. If this uncertainty is excluded from the ket which represents the quantum state (as I believe it is, if I understand correctly), how is the ket said to be the "unique" representation? And how is the set of information which is said to be the quantum state, "unique"? I ask this because some at tpf claim that this unique set of information, and unique representation constitutes a complete description of the state.

But since this time-energy uncertainty is excluded, and time is made to be a parameter rather than a dynamical variable, as Shankar says, then it follows that there is some uncertainty with respect to the quantity of energy within the system. Accordingly, I would conclude that the ket which represents the quantum state, and even the conceived "quantum state" itself, is not a complete representation of the system, and probably not even an accurate representation of the system.

The experiments are primary, not the math. Math is used to model and predict experimental results. Schrodinger's equation exists because of the double slit experiment and others like it.

So a natural question to ask is whether the math fully takes everything relevant into account. In this interpretation, the unknown quantum state of the measuring device is a potential source of something important not being taking into account. — Marchesk

That is not historically accurate, and you really need to stop pretending quantum mechanics is a "model", it's not, it's a theory i.e. a statement about what exists in reality, how it behaves and why.

The Schrödinger equation dates from ~1925. The first double-slit experiment with particles (ignoing photons) was not performed until 1965! Entanglement wasn't observed until ~1984, "macroscopic" superpositions ~1990s, and decoherence was discovered in 1970s, but I don't think it has been observed. Then of course is the yet-to-be-realised quantum computer.

All of these phenomena, and many more besides, are deductions from the theory!

That is not historically accurate, and you really need to stop pretending quantum mechanics is a "model", it's not, it's a theory i.e. a statement about what exists in reality, how it behaves and why. — tom

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?

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.

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?

There are no particles as such prior to the act of measurement. Literally all there is is the possibility of there being one. It is the measurement which reduces the probability to actuality.

The measuring device is the source of uncertainty in these experiments. — Marchesk

The sentence is way too vague to be considered a claim. 'Uncertainty' could mean any of several very different things, each of which involves a completely different discussion. The statement reminds me of some of the debating topics we used to have, when there was a (mercifully temporary) fashion to set deliberately vague topics in order to make the debates less predictable. A favourite was 'The end is nigh'.

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.

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.

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.

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.

It is the measurement which reduces the probability to actuality. — Wayfarer

But how do you go from probability to actuality? What is the mechanism? Is this just brute?

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), — andrewk

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".

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". — Marchesk

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.

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 — andrewk

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.

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. — andrewk

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.

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. — Marchesk

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.

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?' — Wayfarer

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.

Einstein asked the rhetorical question 'does the moon still exist when nobody is looking at it?' — Wayfarer

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.