On Tuesday, April 24, 2018 at 1:48:51 PM UTC-5, [email protected] wrote: > > > > On Tuesday, April 24, 2018 at 6:26:59 PM UTC, [email protected] wrote: >> >> >> >> On Tuesday, April 24, 2018 at 6:14:49 PM UTC, Brent wrote: >>> >>> >>> >>> On 4/24/2018 9:24 AM, [email protected] wrote: >>> >>> >>> >>> On Tuesday, April 24, 2018 at 4:10:30 PM UTC, Brent wrote: >>>> >>>> >>>> >>>> On 4/24/2018 12:03 AM, [email protected] wrote: >>>> >>>> >>>> >>>> On Tuesday, April 24, 2018 at 5:14:25 AM UTC, scerir wrote: >>>>> >>>>> According to Kennedy tensor product (in QM) has a very interesting >>>>> story. >>>>> >>>>> https://philpapers.org/rec/KENOTE >>>>> >>>> >>>> >>>> >>>> On the empirical foundations of the quantum no-signalling proofs >>>> <https://philpapers.org/go.pl?id=KENOTE&proxyId=&u=http%3A%2F%2Fdx.doi.org%2F10.1086%2F289885> >>>> >>>> J. B. Kennedy <https://philpapers.org/s/J.%20B.%20Kennedy> >>>> *Philosophy of Science <https://philpapers.org/asearch.pl?pub=827>* 62 >>>> (4):543-560 (1995) >>>> Abstract >>>> I analyze a number of the quantum no-signalling proofs (Ghirardi et al. >>>> 1980, Bussey 1982, Jordan 1983, Shimony 1985, Redhead 1987, Eberhard and >>>> Ross 1989, Sherer and Busch 1993). These purport to show that the EPR >>>> correlations cannot be exploited for transmitting signals, i.e., are not >>>> causal. First, I show that these proofs can be mathematically unified; >>>> they >>>> are disguised versions of a single theorem. Second, I argue that these >>>> proofs are circular.* The essential theorem relies upon the tensor >>>> product representation for combined systems, which has no physical basis >>>> in >>>> the von Neumann axioms.* Historically, the construction of this >>>> representation scheme by von Neumann and Weyl built no-signalling >>>> assumptions into the quantum theory. Signalling between the wings of the >>>> EPR-Bell experiments is unlikely but is not ruled out empirically by the >>>> class of proofs considered >>>> >>>> Wow! Thank you. It costs $10 to get a copy for a non-member, but very >>>> likely well worth it IMO. AG >>>> >>>> >>>> I wouldn't pay $0.01 for a paper written by a guy who says something is >>>> not ruled out *empirically* by some *mathematical proofs*, and says >>>> something has no *physical* basis in *axioms*. He seems very >>>> confused about the difference between mathematics and empiricism. >>>> >>>> Brent >>>> >>> >>> I'll pay the money and see what he has to say. He's saying the tensor >>> product states do not follow from the axioms of QM. Seems pretty clear even >>> if wrong. But you can save me the fee if you can clearly state how the >>> tensor product states follow from First Principles, that is, from the >>> postulates of QM. AG >>> >>> >>> Physics isn't mathematics. It's not required to derive everything from >>> a few axioms. The mathematics is invented to describe the physics, no the >>> other way around. If you want to understand the use of the tensor product >>> in quantum mechanics read this: >>> >>> >>> https://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013/lecture-notes/MIT8_05F13_Chap_08.pdf >>> >>> Equation 1.20 answers your question about singlets. >>> >>> Brent >>> >> >> Thanks. This looks good. AG >> > > *I can't copy and paste some pertinent paragraphs of the pdf scerir sent > me, but from reading some of Kennedy's claims, he seem to be saying that > although he doesn't dispute the validity and usefulness of tensor products > in quantum mechanics, unlike other quantum axioms which ARE empirically > based, tensor products are NOT empirically based. Perhaps your link says > otherwise. AG* >
Tensor products are just ways states in two Hilbert spaces are tied to each other, which is what is meant by entanglement. It is just a sort of exterior product that ties states of one system with those of another system. There is nothing mysterious about this, and if one wanted to this could be done (rather inconveniently IMO) without tensor products. LC -- 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 post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
