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More precisely (Quantum Mechanics, McIntyre): "Postulate 5 (projection postulate): After a measurement of A that yields the result a_n, the quantum system is i

by kgwgk 8y ago

More precisely (Quantum Mechanics, McIntyre): "Postulate 5 (projection postulate): After a measurement of A that yields the result a_n, the quantum system is in a new state that is the normalized projection of the original system ket onto the ket (or kets) corresponding to the result of the measurement: ∣ψ′⟩ = P_n ∣ψ⟩ / sqrt( ⟨ψ∣ P_n ∣ψ⟩ )" I agree that there are reasons to prefer waves to idealized point-like particles as the more fundamental description (singularities are always difficult to handle). But that's essentially unrelated to the single-world / many-worlds debate, I think.

scotty79 8y ago
This sounds much more like something I imagine. Before collapse you have a system which evolution is governed by some equations, then interaction happens, then you get new system that is a transformation of old system into something dependent on result of interaction (measurement) but what we get in the end is still of the same nature and still evolves according to same equations as initial system.
- kgwgk 8y ago
  That's QM in a nutshell. Of course, it's not completely clear why two different regimes are needed and when should one or the other be used. But as John Bell wrote in his "Against 'measurement'" article (https://www.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf https://www.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf): "ORDINARY QUANTUM MECHANICS (as far as I know) IS JUST FINE FOR ALL PRACTICAL PURPOSES". Quoting Everett's dissertation (http://www.weylmann.com/relative_state.pdf http://www.weylmann.com/relative_state.pdf): We take the conventional or "external observation" formulation of quantum mechanics to be essentially the following [1]: A physical system is completely described by a state function ψ, which is an element of a Hilbert space, and which furthermore gives information only to the extent of specifying the probabilities of the results of various observations which can be made on the system by external observers. There are two fundamentally different ways in which the state function can change: Process 1: The discontinuous change brought about by the observation of a quantity with eigenstates φ_1, φ_2, ... , in which the state ψ will be changed to the state φ_j, with probability |(ψ,φ_j)|^2. Process 2: The continuous, deterministic change of state of an isolated system with time according to a wave equation dψ/dt = Aψ, where A is a linear operator. This formulation describes a wealth of experience. No experimental evidence is known which contradicts it. [1] We use the terminology and notation of J. von Neumann, Mathematical Foundations of Quantum Mechanics, translated by R.T.Beyer (Princeton University Press, Princeton, I955).

by kgwgk 8y ago

scotty79 8y ago

This sounds much more like something I imagine. Before collapse you have a system which evolution is governed by some equations, then interaction happens, then you get new system that is a transformation of old system into something dependent on result of interaction (measurement) but what we get in the end is still of the same nature and still evolves according to same equations as initial system.

kgwgk 8y ago
That's QM in a nutshell. Of course, it's not completely clear why two different regimes are needed and when should one or the other be used. But as John Bell wrote in his "Against 'measurement'" article (https://www.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf https://www.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf): "ORDINARY QUANTUM MECHANICS (as far as I know) IS JUST FINE FOR ALL PRACTICAL PURPOSES". Quoting Everett's dissertation (http://www.weylmann.com/relative_state.pdf http://www.weylmann.com/relative_state.pdf): We take the conventional or "external observation" formulation of quantum mechanics to be essentially the following [1]: A physical system is completely described by a state function ψ, which is an element of a Hilbert space, and which furthermore gives information only to the extent of specifying the probabilities of the results of various observations which can be made on the system by external observers. There are two fundamentally different ways in which the state function can change: Process 1: The discontinuous change brought about by the observation of a quantity with eigenstates φ_1, φ_2, ... , in which the state ψ will be changed to the state φ_j, with probability |(ψ,φ_j)|^2. Process 2: The continuous, deterministic change of state of an isolated system with time according to a wave equation dψ/dt = Aψ, where A is a linear operator. This formulation describes a wealth of experience. No experimental evidence is known which contradicts it. [1] We use the terminology and notation of J. von Neumann, Mathematical Foundations of Quantum Mechanics, translated by R.T.Beyer (Princeton University Press, Princeton, I955).