On Tuesday, April 24, 2018 at 12:14:06 AM UTC, agrays...@gmail.com wrote: > > > > On Monday, April 23, 2018 at 11:54:15 PM UTC, Bruce wrote: >> >> From: <agrays...@gmail.com> >> >> On Monday, April 23, 2018 at 7:38:30 PM UTC, agrays...@gmail.com wrote: >> >>> On Monday, April 23, 2018 at 1:20:05 PM UTC, agrays...@gmail.com wrote: >>>> >>>> >>>> >>>> On Monday, April 23, 2018 at 8:58:53 AM UTC, Bruce wrote: >>>>> >>>>> From: <agrays...@gmail.com> >>>>> >>>>> >>>>> On Monday, April 23, 2018 at 5:53:59 AM UTC, Bruce wrote: >>>>>> >>>>>> From: <agrays...@gmail.com> >>>>>> >>>>>> >>>>>> Let's agree that electrons A and B form a singlet entangled system. >>>>>> Let's further agree that they are non separable. What do you do with the >>>>>> fact that when their spins are measured, they ARE in different spatial >>>>>> locations, not even space separated in Bell experiments. How do we deal >>>>>> with this FACT? AG >>>>>> >>>>>> >>>>>> What do you want me to do with the fact? I learn to live with facts >>>>>> that I can't do anything about. The fact that the system is non-local is >>>>>> a >>>>>> fact that you just have to come to terms with. >>>>>> >>>>>> Bruce >>>>>> >>>>> >>>>> *ISTM that when you have a theory that seems correct and in some sense >>>>> is well tested, but there are facts which contradict it, in this case a >>>>> key >>>>> fact right in front of your nose which contradicts it -- the fact that we >>>>> see as plain as daylight that the subsystems as spatially separated -- >>>>> invariably the theory must be wrong. AG* >>>>> >>>>> >>>>> I wish you luck with your project to prove quantum mechanics wrong. >>>>> >>>>> Bruce >>>>> >>>> >>>> *Right now I have a more modest goal. Starting from the postulates of >>>> QM, how do you justify writing the wf of the singlet state as a >>>> superposition of tensor product states? TIA AG * >>>> >>> >>> *What it's not. It's not the SWE. It's not Born's Rule. It's not the >>> operator correspondence with observables. AG * >>> >> >> *I suppose it could be traced to the superposition principle; that the >> state vector of the singlet state is a linear combination of the states >> which are members of the corresponding Hilbert space of the system. But why >> are these states tensor product states? AG* >> >> >> Why try worrying these things out for yourself? The easiest thing is to >> go and look up a text book. >> >> Bruce >> > > *Recall when I asked whether entanglement necessarily implies non > locality. You replied "not necessarily" and gave the classical example of > elastic scattering of billiard balls where the momentum of its constituents > and the whole system is known exactly. No uncertainty. In the wf for the > singlet system you assume a definite net spin angular momentum, zero. How > can you treat the singlet system quantum mechanically and at the same time > assume you know its spin momentum exactly? Do you think this question could > be answered in a text book? How could I even pose it to an inert, non > responsive medium? AG * >
*I just took a quick look at chapter 15, section 4 of Merzbacher, Quantum Mechanics (Third Edition). The tensor equation can't be copied. It appears in the blank lines below. Immediately you can see the problem with this kind of treatment. It doesn't explain WHY, from First Principles, the tensor product can be used to describe the composite system. It's virtually impossible to find an explanation from First Principles. AG* 4. Quantum Dynamics in Direct Product Spaces and Multiparticle Systems. Often the state vector space of a system can be regarded as the direct, outer, or tensor product of vector spaces for simpler subsystems. The direct product space is formed from two independent unrelated vector spaces that are respectively spanned by the basis vectors /A;) and I B;) by constructing the basis vectors Although the symbol @ is the accepted mathematical notation for the direct product of state vectors, it is usually dispensed with in the physics literature, and we adopt this practice when it is unlikely to lead to misunderstandings. If n1 and n2 are the dimensions of the two factor spaces, the product space has dimension nl X n2. This idea is easily extended to the construction of direct product spaces from three or more simple spaces. > > -- 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
