By Logsdon M.I.

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The Hilbert space associated with a multi-component system is the tensor product space H = H1 ⊗ . . ⊗ HN , where the Hilbert spaces associated with the individual systems are H1 , . . , HN . The properties of the tensor-product space H1 ⊗ . . ⊗ HN are very different from those of the Cartesian-product space H1 × . . × HN . For example, the dimension of the tensor-product space H equals the product of the dimensions of the individual Hilbert spaces H1 , . . , HN , whereas the dimension of the Cartesian-product space H1 × .

As I shall argue, however, in Chapter 10, there is no genuine ‘non-locality’ (worth the name) involved in quantum theory, which means that we should perhaps not welcome the explicit non-locality pilot wave theory introduces. Objections and challenges Pilot wave theory has been criticised in many respects, often unfairly, based on spurious grounds and misunderstandings. Sometimes it is rejected on purely aesthetic grounds, for example by Rudolf Peierls, declaring that ‘I must confess that the scheme, with both hidden variables and probability rules seems to me exceedingly ugly’ (Peierls [1991], p.

The probability density for collapse at a space-time point q is chosen identical to the Born Rule probability density |ψ(q)|2 . This allows one to recover the original quantum theoretical predictions in the presence of spontaneous localisation processes. Interpretations as Solutions to the Measurement Problem 41 A crucial element of the GRW model, which allows it to be compatible with the manifest empirical facts, is that for multi-component systems the collapse probability per second is dramatically increased as a consequence of the entanglement relation between the states of the individual component systems.

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A Mathematician Explains by Logsdon M.I.


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