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May 25, 2013
This raises some interesting questions. I read Brukner's "Quantum State Preparation with Universal Gate Decompositions," which seems related to this matter. I am also curious as to whether this has some relationship to the cellular automata idea of 't Hooft. This is not so much to support the idea of hidden variables, but more in the way in which a continuum description of configuration variables is related to the quantum states they represent.
Cheers LC
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Cheers LC
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LC
re: your last sentence and later statement below...
"Quantum mechanics involves non-contextual observables, but the act of performing a measurement imposes a context"
Isn't the context you speak of in the measurement about putting the squeeze on degrees of freedom leading to a temporary quantization of a normally continuous variable? Like between energy levels of a free electron and those of an electron in an atom?
Marcel,
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re: your last sentence and later statement below...
"Quantum mechanics involves non-contextual observables, but the act of performing a measurement imposes a context"
Isn't the context you speak of in the measurement about putting the squeeze on degrees of freedom leading to a temporary quantization of a normally continuous variable? Like between energy levels of a free electron and those of an electron in an atom?
Marcel,
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You seem to be saying something almost right. The context in the case of a spin 1/2 particle is the orientation of the Stern-Gerlach apparatus. The observer chooses the orientation of the instrument and the basis upon which the measurement is made.
Cheers LC
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Cheers LC
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LC
Or, maybe you understood it almost right. Be it Stern-Gerlach or Zeeman or any other measurement, measurement applies an additional constraint which comes to be one more and last quantum number. The measurement is making it quantized. Same as a particle in a box; constraint is forcing the temporary quantization.
Marcel,
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Or, maybe you understood it almost right. Be it Stern-Gerlach or Zeeman or any other measurement, measurement applies an additional constraint which comes to be one more and last quantum number. The measurement is making it quantized. Same as a particle in a box; constraint is forcing the temporary quantization.
Marcel,
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Phrases as «According to standard interpretations, quantum objects do not have well-defined properties, until those properties are measured by an observer.» are repeated too often in the literature but do not agree with what quantum mechanics really says.
Moreover, contrary to claims in this article, there exist chemical and physical processes that cannot be explained by quantum mechanics. Several extensions are known and used in the lab. For instance, "The Liouville Space Extension of Quantum Mechanics". T. Petrosky and I. Prigogine. Adv. Chem. Phys. 99, 1-120.
Of course that extension emphasize still more inherent randomness of nature and this is a very important point, explains how randomness survives at the classical level under certain conditions: Poincaré Resonance and the Extension of Classical Dynamics 1996: Chaos, Solitons and Fractals 7(4), 441-498
I.e. randomness is not restricted to quantum systems.
And generalizations of their theory are already at our hand. Finally, information theory has not provided any new result that were not known previously.
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Moreover, contrary to claims in this article, there exist chemical and physical processes that cannot be explained by quantum mechanics. Several extensions are known and used in the lab. For instance, "The Liouville Space Extension of Quantum Mechanics". T. Petrosky and I. Prigogine. Adv. Chem. Phys. 99, 1-120.
Of course that extension emphasize still more inherent randomness of nature and this is a very important point, explains how randomness survives at the classical level under certain conditions: Poincaré Resonance and the Extension of Classical Dynamics 1996: Chaos, Solitons and Fractals 7(4), 441-498
I.e. randomness is not restricted to quantum systems.
And generalizations of their theory are already at our hand. Finally, information theory has not provided any new result that were not known previously.
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Quantum mechanics is perfectly deterministic. The wave equations are not stochastic. However, the Fourier components of a wave are amplitudes which define probabilities as the modulus squared. Stochasticity enters into the picture with measurements or outcomes. Quantum mechanics involves non-contextual observables, but the act of performing a measurement imposes a context. This means measurements, or the contextual basis for quantum observation is not something which is predicted by quantum mechanics. The outcomes satisfy a Kolmogoroff entropy, and define the maximal randomness for a set of outcomes. This is not computable by the Chaitan-Kolmogoroff theorem, which suggests there is some form of incomputable aspect to quantum measurement. In other word context is not computable by QM, but contextuality still exists with respect to observations.
Cheers LC
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Cheers LC
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Quantum mechanics is a non-deterministic theory, as has been known for more than a century. The Schrödinger equation is not stochastic and thus cannot explain measurement processes (nor other processes) as any basic textbook emphasize.
The measurement process in quantum mechanics is covered by the measurement postulate (again check any textbook), but this postulate does not describe the details of the measurement. The details are described in the generalizations of quantum mechanics, as the one cited above.
At the more simple level of theory, one obtains a stochastic generalization of the Schrödinger equation (sometimes named Ito-Schrödinger). This stochastic generalization allows for a dynamical description of the transition from amplitudes to probabilities (a transition "from potentialities to actualities" in Born's words).
The Kolmogoroff entropy is not the thermodynamic entropy of the physical system, and it is rather unuseful unless complemented by a non-unitary dynamical law describing the interaction between the system under observation and the measurement system. In my own FQXi forum I gave more details about stochastic generalizations of the Schrödinger equation and the several approximations involved in quantum mechanics.
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The measurement process in quantum mechanics is covered by the measurement postulate (again check any textbook), but this postulate does not describe the details of the measurement. The details are described in the generalizations of quantum mechanics, as the one cited above.
At the more simple level of theory, one obtains a stochastic generalization of the Schrödinger equation (sometimes named Ito-Schrödinger). This stochastic generalization allows for a dynamical description of the transition from amplitudes to probabilities (a transition "from potentialities to actualities" in Born's words).
The Kolmogoroff entropy is not the thermodynamic entropy of the physical system, and it is rather unuseful unless complemented by a non-unitary dynamical law describing the interaction between the system under observation and the measurement system. In my own FQXi forum I gave more details about stochastic generalizations of the Schrödinger equation and the several approximations involved in quantum mechanics.
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I am saying that QM is deterministic in the sense that that a wave function, perfectly prepared in a lab, evolves as ψ(t) = U(t – t_0)ψ(t_0) in a completely predictable manner. However, to back this data out one must perform measurements on identically prepared systems. The stochastic nature of QM enters in with measurement itself.
Cheers LC
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Cheers LC
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Measurements in quantum mechanics are a problem because of the fact the scale of the instrument the instruments are not only giving data but also at the same time influencing the object, and so it can even become impossible, like trying to measure a living fly with a centimeter, once you pin down the fly he is dead, you can measure it, but is is no longer a fly, the essence has gone. It is not very scientific but it is how I explain the uncertainty principle.
keep on thinking free
Wilhelmus
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keep on thinking free
Wilhelmus
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The "final theory" will be a specific informational interpretation of quantum mechanics that can be tested and counter-falsified. That's what we need to look for.
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