From: <[email protected] <mailto:[email protected]>>
On Tuesday, June 5, 2018 at 7:02:11 PM UTC, Brent wrote: On 6/5/2018 2:48 AM, [email protected] wrote:*One objective was to convince myself whether the wf you have written for decoherence makes any sense. Originally I thought one needed mutual interference of all components for it to be viable. I doubted whether each component interferes with the others in your proposed wf because the |e> wave functions have no well defined deBroglie wave lengths (which I thought were necessary for a valid quantum superposition).*de Broglie wave lengths are useful when thinking about a particle, but a complex system with many degrees of freedom has many different energy levels available to it and each one evolves with a different frequency. So the de Broglie wavelength is not very useful. Brent*Agree. That's what Bruce wrote, in effect, when he noted that the macro states in the superposition for decoherence are just symbols for the multitude of entanglements, each presumably with its own deBroglie wave length**. But now I don't see the problem -- the weird implications --with these superpositions involving macro systems as dependent on interference. If the S Cat's wf can be written as a sum of two states, each entangled with the radioactive source, the implication is that the Cat is simultaneously alive and dead. It's like a simple vector in the plane -- those pointy things -- which can be written as the sum of a horizontal and vertical vectors (or a non orthogonal basis). If it can be written as a sum, it can be interpreted as manifesting both vectors in the sum simultaneously. So, if you want to write state vectors to include entanglements with macro systems, you will get cats that are alive and dead simultaneously, and in the decoherence case, you'll ger copies of this universe, inclusive of copies of observers, etc. That was Schrodinger's point; the fallacy of entangling quantum and macro states in one wf. AG*
Yes, Schrödinger's original intention with the cat scenario was to provide a /reductio ad absurdum/: the conclusion of cats being simultaneously alive and dead was patently absurd. In later life Schrödinger regretted introducing his wave equation. His idea had been to formulate quantum phenomena in terms of something easily visulizable in a classical way, such as wave motion. This was as an antidote to what many saw as the increasing obscurantism of Bohr and the Copenhagen school. However, he was disappointed by the results, and by the fact that his wave equation became the standard way of thinking about quantum processes. Schrödinger was undoubtedly aware that there were other ways of doing quantum calculations than in terms of his wave equation; Heisenberg matrix mechanics was already available, then there is Schwinger's mathematical approach, path integral approaches, and so on. None of which need mention a wave or a wave equation. They all give the same results for quantum probabilities so since they were equivalent in this sense, they were, according to the metaphysics of the time, all considered to be the same theory.
But it is doubtful if they are all actually the same theory, since they seem to imply different ontologies. Schrödinger's wave mechanics has led to the reification of the wave function itself, and the result is many worlds theory. But if you don't have a wave equation and work only with matrices, there is no reason to postulate any multiplicity of worlds. The model that you use for calculations in the theory implies an ontology, and not all implied ontologies are the same, or even equally useful. People are all to ready to believe that the simplest ontology of their model is what is "really real". But they are generally mistaken, as the negative induction of scientific realism points out.
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