On 11/15/2017 9:25 PM, [email protected] wrote:
On Wednesday, November 15, 2017 at 9:08:29 PM UTC-7, Brent wrote: On 11/15/2017 7:36 PM, [email protected] <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. BrentGenerally 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!? 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
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