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

• 369
I like the wording in section 9.4, "Applications of the Uncertainty Principle". You will find this: "Now the hand waving begins.
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.
• 810
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.

Sure, if there was no such thing as the measurement problem, there would be no need to solve it.
• 1.3k
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.
• 791
The ket associated with a system evolves over time according to a known differential equation, called Schrodinger's Equation.

Problem being that when a measurement takes place, Schrodinger's equation fails to predict the outcome, unless of course MWI is endorsed.
• 791
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.

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.

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.
• 369
That's entirely dismissive and not a good counter argument.
I'd go further: it's not a counter-argument at all, because no argument has been presented to counter.
• 791
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.
• 1.1k

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).
• 791
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.

No, it's about accounting for the measuring device, not removing it.
• 791
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.
• 323

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.
• 791
However, for science the math is what countsRich

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.
• 791
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.
• 1.1k
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.
• 810
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]

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'

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'.

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.

Except when a measurement is made according to 3.
• 1.3k
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]

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.
• 810
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.

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!
• 791
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?
• 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. It is the measurement which reduces the probability to actuality.
• 369
The measuring device is the source of uncertainty in these experiments.
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.
bold
italic
underline
strike
code
quote
ulist
image
url
mention
reveal