On Monday, November 4, 2019 at 6:23:14 PM UTC-6, Lawrence Crowell wrote: > > On Sunday, November 3, 2019 at 4:17:28 PM UTC-6, Brent wrote: >> >> >> >> On 11/3/2019 10:43 AM, Philip Thrift wrote: >> >> In order for this statement to be useful, we need to solve the preferred >> basis problem. For example, consider the mathematical identity >> >> |u a w> + |e d c> = |n+ s+ f+> + |n+ s- f-> + |n- s+ f-> + |n- s- f+> (2) >> >> where >> >> |n+> = |u> + |e>, |n-> = |u> - |e> >> |s+> = |a> + |d>, |s-> = |a> - |d>, >> |f+> = |w> + |c>, |f-> = |w> - |c>. >> >> Unless we introduce a further piece of interpretive apparatus, we are in >> danger of supposing that the system described by |phi> is also described by >> |n+ s+ f+> or each of the other components in (2), which would mean we have >> not solved the original problem. However, this is easily solved, as follows: >> Postulate 1. A quantum system and environment described by the state >> |phi> is also described by one of the states of the basis in which the >> reduced density matrix of |phi> is diagonal after the environment has been >> traced over. >> The `collapse' from |phi> to one of |u a w> and |e d c> is now no >> different from the abrupt change in a classical probability distribution >> when more information becomes available. >> >> >> At this point one is then tempted to ask why not just say the wf >> collapsed? Tracing over the environment is already something the >> experimenter does on paper. It's not part of the Schroedinger equation >> unitary evolution. Sure it makes the off-diagonal terms small...but it >> doesn't make them zero. It's still just FAPP. >> >> >> Brent >> > > In effect at this point it is much the same as with decoherence where a > density matrix is reduced to diagaonals and it is a classical probability > "collapse." > > LC >
Defining "superposition" in terms of a particular mathematical theory solves nothing. There is no consensus of what *the ingredients *at the basis of a mathematical theory of quantum mechanics are in the first place. *Quantum correlations from simple assumptions* Adán Cabello https://arxiv.org/abs/1801.06347 *Deriving Born's rule from an Inference to the Best Explanation* Alexia Auffeves, Philippe Grangier https://arxiv.org/abs/1910.13738 *Mysterious Quantum Rule Reconstructed From Scratch* https://www.quantamagazine.org/the-born-rule-has-been-derived-from-simple-physical-principles-20190213/ The Born rule, which connects the math of quantum theory to the outcomes of experiments, has been derived from simpler physical principles. The new work promises to give researchers a better grip on the core mystery of quantum mechanics. Everyone knows that quantum mechanics is an odd theory, but they don’t necessarily know why. The usual story is that it’s the quantum world itself that’s odd, with its superpositions, uncertainty and entanglement (the mysterious interdependence of observed particle states). All the theory does is reflect that innate peculiarity, right? "the really important task is figuring out which are the physical ingredients common to any universe in which quantum theory holds" (Adán Cabello) Secret ingredients! @philipthrift -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/70590fce-74fa-431e-9ff9-de5fdf9a93f4%40googlegroups.com.
