On Wednesday, November 15, 2017 at 11:33:46 PM UTC-7, Brent wrote: > > > > On 11/15/2017 9:25 PM, [email protected] <javascript:> wrote: > > > > On Wednesday, November 15, 2017 at 9:08:29 PM UTC-7, Brent wrote: >> >> >> >> On 11/15/2017 7:36 PM, [email protected] 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. > > > Didn't I just tell you not to think that!? >
I didn't forget. I just wanted to say something about the constituent particles and their entanglement with the environment, not about excited modes. Thanks for your time. > The particles of an object are all interacting with one another (which is > how they make an 'object') so they are all entangled with one another and > with the environment. But if you think about some mode that might be > excited, then you could represent that mode as a "thing" which was > entangled with a single N2 that had collided with the ball and created that > excitation. > > In some basis, the entangled states are definite states (maybe not the > same basis for each). > > > In theory, any isolated system, not entangled with anything outside the > system, has a definite state. The problem with entanglement is that it > quickly diffuses out of the isolation unless extraordinary circumstances > obtain. > > 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. > > > An entire macro object could be in a definite state if it is sufficiently > isolated, e.g. a Bose-Einstein condensate of a billion H atoms. > http://www.sciencedirect.com/science/article/pii/S0921452699014155 > > > 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.
