On 4/24/2018 1:33 PM, [email protected] wrote:
On Tuesday, April 24, 2018 at 7:59:32 PM UTC, Brent wrote: On 4/24/2018 11:48 AM, [email protected] <javascript:> 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 <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. AGI 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. AGPhysics 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 <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*Read this and then tell me what "empirically based" means https://pdfs.semanticscholar.org/2fb0/4475228ff385a44a16e3ba42b432d3bf5b17.pdf <https://pdfs.semanticscholar.org/2fb0/4475228ff385a44a16e3ba42b432d3bf5b17.pdf> As far as I know the only empirical basis for a theory is that it always gives the right answer when empirically tested. Kennedy seems to have a strange concept of circular reasoning. He says that adopting an equation that implies no-signaling and then using it to prove quantum theory avoids FTL signaling is circular. He misses the point that the reason for adopting the no-signaling is the empirical success of special relativity, which would be violated by FTL signaling. BrentFor now I will just remark that "empirically based" means that the physical world suggests by its behavior the mathematics we need to describe it. E.g., the discrete spectra of the elements indicates that we need operators with discrete and real eigenvalues to reproduce the spectra. And I'm pretty sure that Schrodinger inferred his equation from real world observations. And so on. The tricky one I've never understood is the need for non commuting operators for position and momentum,. AG
It's not that there's a "need", although it would fall out of the discrete spectra for momenta in a box. It comes naturally from the group generators. There's good discussion/examples here:
https://physics.stackexchange.com/questions/130800/what-is-the-physical-meaning-of-commutators-in-quantum-mechanics?noredirect=1&lq=1 Brent -- 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.
