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Jan 20, 2017 at 6:08 history edited DanielSank CC BY-SA 3.0
added 222 characters in body
Jan 19, 2017 at 21:29 comment added Emilio Pisanty Of course, this is all just in-theory, but then so is the third law of thermodynamics ('can never reach absolute zero in a finite number of steps', but it doesn't say anything about procedures that take $10↑↑↑↑↑↑↑↑10$ steps, which I think you'll be equally uncomfortable with). The question is at heart a theoretical question about the third law, so I don't see how those arguments are irrelevant.
Jan 19, 2017 at 21:19 comment added DanielSank @EmilioPisanty I think everything you're saying would be correct if the map between theory and real life were arbitrarily accurate. See my comments on your answer.
Jan 19, 2017 at 21:17 comment added Emilio Pisanty @DanielSank The way I see it, saying $T=0$ means that the phase-space volume occupied by the state has collapsed to a single, mathematical point: no matter how precise my measurement instrument, I will never observe the system away from that point. Saying $T=\delta T>0$ means that there exists (in principle) an instrument that will be able to resolve that phase-space cloud (/not-quite-pure quantum state). If $\delta T$ is tiny then I will need to work correspondingly hard to detect it, but if it's zero then I will never resolve it.
Jan 19, 2017 at 21:16 comment added DanielSank @EmilioPisanty I guess I don't understand why $T=10^{-10^{10000}} $K is different from $T=0$. Are there real, not just in-theory phase transitions that only happen at $T=0$? My experience has been that this sort of thing never actually happens because e.g. phase transitions are always rounded off by finite size effects and coupling to the environment, etc.
Jan 19, 2017 at 20:53 comment added Emilio Pisanty @DanielSank uh... one of them is consistent with the third law of thermodynamics and the other one isn't? $T=0$ and $T>0$ look very different to me, no matter how small a positive temperature you've got.
Jan 19, 2017 at 20:07 comment added DanielSank @EricTressler Yes I understand that distinction, and for mathematics it's an important one. For a physical system, I think this distinction is unimportant.
Jan 19, 2017 at 20:03 comment added Eric Tressler @DanielSank They're logically different. Saying "I can get arbitrarily close to 0" means "for any epsilon > 0, I can reach a temperature below epsilon". That does not imply that I can reach 0.
Jan 19, 2017 at 18:41 comment added DanielSank @EmilioPisanty please explain how those are very different.
Jan 19, 2017 at 9:37 comment added Emilio Pisanty Also, it's important to note that "arbitrarily close to absolute zero" is very different to actually reaching absolute zero.
Jan 19, 2017 at 9:35 comment added Emilio Pisanty Just to mesh with other standard terminology, I imagine this 'quantum backaction limit' is not the Doppler limit (i.e. $\hbar \Gamma$ in energy) but rather the Sisyphus cooling limit (i.e. $\hbar k$ in momentum)?
S Jan 19, 2017 at 9:15 history edited DanielSank CC BY-SA 3.0
homophone correction
S Jan 19, 2017 at 9:15 history suggested Neil_UK CC BY-SA 3.0
homophone correction, and gratuitous zero-effect formatting to get to the character count
Jan 19, 2017 at 9:04 review Suggested edits
S Jan 19, 2017 at 9:15
Jan 19, 2017 at 8:00 comment added zeldredge And note that conventional laser cooling (Doppler, Sisyphus, etc) does have such a hard limit set by the atomic transition in question, so having a cooling technique which is not fundamentally limited is a significant advance.
Jan 18, 2017 at 23:26 comment added user140606 +1 I learnt an (embarrassing large) amount from your answer, ta for posting it.
Jan 18, 2017 at 23:20 vote accept Sasha
Jan 18, 2017 at 23:16 history answered DanielSank CC BY-SA 3.0