On Wednesday, November 15, 2017 at 9:08:29 PM UTC-7, Brent wrote: > > > > On 11/15/2017 7:36 PM, agrays...@gmail.com <javascript:> wrote: > > > > On Wednesday, November 15, 2017 at 7:54:27 PM UTC-7, Brent wrote: >> >> Interesting questions. Whenever we talk about a system being in a >> quantum state, we're thinking of the "system" as some degrees of freedom >> that are isolated, so they are not interacting with and becoming entangled >> with other things. An SG experiment typically uses silver atoms and refers >> to their state as UP or DOWN or LEFT or RIGHT. But that's not a complete >> description of the silver atom. It has other degrees of freedom, which we >> ignore as irrelevant to the SG measurement. So a "system" which we >> describe as having a state, isn't necessarily the same as an object, like a >> baseball or even an atom. A classical object like a baseball has lots of >> degrees of freedom and they are interacting with the environment, so they >> are entangled with states of the environment. Only certain collective >> variables, e.g. the conserved ones like momentum, are stable in the stat >> mech sense. These ones that are stable against interaction with the >> environment are the einselected values we can measure classically. So we >> could write a wave-function for the baseball as if it were an isolated >> particle, like the silver atom, and ignore all the internal dof which are >> not in any definite state because they're entangled with atmospheric >> molecules and IR photons, etc. >> >> Whether something is in a superposition of states isn't an interesting >> question because the answer is always "Yes...relative to some basis." The >> interesting point is that since constituents in the baseball have >> interacted with and are now entangled with air molecules, those >> constituents of the baseball are not in any definite state. Only the >> constituent PLUS the molecules it is entangled with has a definite state. >> In any basis we can imagine measuring, they will be in a superposition >> relative to that basis. But in theory there would some basis in which the >> isolated baseball plus molecules would be an eigenstate; it's just so >> complicated we could never measure in that basis. But if were to consider >> a very simple system, like a few electrons then we might be able to measure >> in the eigenbasis. >> >> Brent >> > > TY. That was very informative. Let's go on. How does a micro constituent > of a macro object get entangled with, say, an air molecule? When I think of > entanglement, I think of some special process to it.create it. How does it > happen spontaneously? Is it stable or does it decay rapidly, and if so into > what? TIA. > > > Don't think of the constituents as objects, think of them as degrees of or > modes of excitations. So an N2 molecule collides with the baseball and it > excites a certain vibration mode of the ball. Now that mode and the motion > of the N2 molecule are entangled. If you're just interested in the ball > you can just average over, trace out, the N2 molecule modes and then you're > left with a mixed density matrix for the modes of the baseball. Of course > all this changes very quickly, spreading the entanglement to more modes of > the baseball, radiating some away as IR photons, more collisions of N2 and > O2 molecules. That's decoherence that washes out all the coherent > interference that we can observe with carefully isolated systems. It isn't > decaying, it's diffusing the information about the microscopic dof into the > environment. > > Brent >
Generally speaking, some particles of the macro object are entangled with the environment, and some not. In some basis, the entangled states are definite states (maybe not the same basis for each). Can we say the same about unentangled particles (understood as modes of excitations)? Do they have definite states? Is there any sense in which the entire macro object is "in a definite state" (albeit fluctuating)? TIA. -- 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.
