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I'm not sure trying to instill an "intuitive" sense of quantum mechanics by appealing to classical principles in this way is such a great idea. The example of e

I'm not sure trying to instill an "intuitive" sense of quantum mechanics by appealing to classical principles in this way is such a great idea. The example of entanglement given here implies that each system was a circle or a square "all along" i.e. from the moment of being entangled. That's not actually how it works, and thinking about it that way will lead to misunderstandings later on, should you try to study QM more deeply. You will have to unlearn the lesson taught here. It also leaves you unequipped to reason about quantum computing, by the way. Also: > 1. A property that is not measured need not exist. > 2. Measurement is an active process that alters the system being measured. These are both misleading enough that they can probably just be called 'wrong' as well. We shouldn't assign mysterious properties to "measurement" as though it's some magical thing that just makes quantum mechanics happen. Just call it what it is: entangling the state of your brain with the results of an experiment. That conveniently also provides for a good jumping off point into Many Worlds / Relative-State Formulation of QM.

millstone 10y ago
Describing measurement as "entangling your brain" is a particular viewpoint that is not widely accepted. Most physicists would agree that the LHC's particle collision data constitute measurements, even though most of those results have never been looked at by a human. Measurement is at its most mysterious in the MW interpretation, because measurements are probabilistic and probabilities are hard to get out of a purely deterministic theory like MW.
- deciplex 10y ago
  It's not clear what point you're trying to argue. Yes, the particle collision data constitutes a measurement in the sense that it is entangled with whatever medium the data is being stored on (and, in practice, a while lot else), even if a human hasn't looked at it yet. Measurement as we usually mean it when talking about this stuff in the context of QM means a human looking at a thing, but sure that need not always be the case. I mean if you want to split hairs we can go back and forth all day, but that doesn't strike me as an interesting or enlightening avenue of discussion.
Xcelerate 10y ago
I upvoted you since I don't know why you're so far down the page. What you say is essentially correct. The error most people make when trying to understand quantum mechanics is assuming that the measuring system is independent of the measured system. But the overall composite system can't be factored like that since it evolves unitarily (and deterministically) into a state that isn't representable as a tensor product.
effie 10y ago
> Just call it what it is: entangling the state of your brain with the results of an experiment. This is a particular viewpoint on the role of the Schroedinger equation in theory, incompatible with the Born interpretation of |\psi|^2 which is the orthodox way to use it. It is a different thought scheme that has no support in experiment. No experiment uses Schr. equation to consider how experimenter's brain gets entangled with their measurement apparatus; the ones that use it at all use it to calculate measurable values and probabilities of measurement results.
- deciplex 10y ago
  The Born rule isn't an interpretation it's a fundamental law derived from observation of how the probabilities work out. If you've got some interpretation of stuff that explains the Born rule I'd really like to hear about it. And, are you saying that your brain isn't entangled with an experimental result after observing it (at the latest)? If so, what is special about brains, that shields them from it?
  - effie 10y ago
    There are actually two Born rules - the first one gives probability of configuration as integral of square of \psi - int |\psi(x)|^2dx, and the second one gives probability of result of measurement as square of integral of psi |int \phi_k^*(x)\psi(x)dx|^2. The first one was introduced to give meaning, i.e. interpret, Schroedinger's psi-function, the second one soon followed to connect the theory with the quantum ideas. Of course, the rule has been successful - but as far as the goal is to understand \psi, it is just an interpretation of \psi. It says nothing about what \psi itself actually is, only how to use it to get probabilities. Regarding the entanglement of brain with experiment, that is totally unfounded extrapolation of applicability of many-particle Schroedinger's equation. It is useful for atoms and molecules, but it is practically intractable for systems of few atoms. For macroscopic objects, like arm indicator of an ammeter, the Born rule assumes that results of measurements are definite, so probabilities can be assigned to them. In the picture where the indicator or brain is just a part of the system that gets entangled, no definite results of measurements are obtained and it makes no sense to talk about their probability in the way all successful applications do.

millstone 10y ago

Describing measurement as "entangling your brain" is a particular viewpoint that is not widely accepted. Most physicists would agree that the LHC's particle collision data constitute measurements, even though most of those results have never been looked at by a human. Measurement is at its most mysterious in the MW interpretation, because measurements are probabilistic and probabilities are hard to get out of a purely deterministic theory like MW.

deciplex 10y ago
It's not clear what point you're trying to argue. Yes, the particle collision data constitutes a measurement in the sense that it is entangled with whatever medium the data is being stored on (and, in practice, a while lot else), even if a human hasn't looked at it yet. Measurement as we usually mean it when talking about this stuff in the context of QM means a human looking at a thing, but sure that need not always be the case. I mean if you want to split hairs we can go back and forth all day, but that doesn't strike me as an interesting or enlightening avenue of discussion.

Xcelerate 10y ago

I upvoted you since I don't know why you're so far down the page. What you say is essentially correct. The error most people make when trying to understand quantum mechanics is assuming that the measuring system is independent of the measured system. But the overall composite system can't be factored like that since it evolves unitarily (and deterministically) into a state that isn't representable as a tensor product.

effie 10y ago

> Just call it what it is: entangling the state of your brain with the results of an experiment. This is a particular viewpoint on the role of the Schroedinger equation in theory, incompatible with the Born interpretation of |\psi|^2 which is the orthodox way to use it. It is a different thought scheme that has no support in experiment. No experiment uses Schr. equation to consider how experimenter's brain gets entangled with their measurement apparatus; the ones that use it at all use it to calculate measurable values and probabilities of measurement results.

deciplex 10y ago
The Born rule isn't an interpretation it's a fundamental law derived from observation of how the probabilities work out. If you've got some interpretation of stuff that explains the Born rule I'd really like to hear about it. And, are you saying that your brain isn't entangled with an experimental result after observing it (at the latest)? If so, what is special about brains, that shields them from it?
- effie 10y ago
  There are actually two Born rules - the first one gives probability of configuration as integral of square of \psi - int |\psi(x)|^2dx, and the second one gives probability of result of measurement as square of integral of psi |int \phi_k^*(x)\psi(x)dx|^2. The first one was introduced to give meaning, i.e. interpret, Schroedinger's psi-function, the second one soon followed to connect the theory with the quantum ideas. Of course, the rule has been successful - but as far as the goal is to understand \psi, it is just an interpretation of \psi. It says nothing about what \psi itself actually is, only how to use it to get probabilities. Regarding the entanglement of brain with experiment, that is totally unfounded extrapolation of applicability of many-particle Schroedinger's equation. It is useful for atoms and molecules, but it is practically intractable for systems of few atoms. For macroscopic objects, like arm indicator of an ammeter, the Born rule assumes that results of measurements are definite, so probabilities can be assigned to them. In the picture where the indicator or brain is just a part of the system that gets entangled, no definite results of measurements are obtained and it makes no sense to talk about their probability in the way all successful applications do.