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.I like the wording in section 9.4, "Applications of the Uncertainty Principle". You will find this: "Now the hand waving begins. — Metaphysician Undercover
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
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
'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
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
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
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
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
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
4. The ket associated with a system evolves over time according to a known differential equation, called Schrodinger's Equation. — andrewk
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
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. — tom
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'.The measuring device is the source of uncertainty in these experiments. — Marchesk
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