Timeline for Ignorance in statistical mechanics
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
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| Mar 11, 2012 at 8:56 | history | edited | Arnold Neumaier | CC BY-SA 3.0 |
added my interpretation of the density matrix
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| Mar 11, 2012 at 8:45 | vote | accept | Arnold Neumaier | ||
| Mar 6, 2012 at 21:55 | comment | added | BebopButUnsteady | I'm not sure why the fact that "no macroscopic object can be assigned a pure state" is an issue for the ignorance interpretation. One is merely ignorant about the reduced density matrix instead of the state. (Also I think the quotation is sensitive to one's interpretation of QM). As to my point, perhaps I should say the question is whether the penny is coupled at all to the environment. If it is not, it's energy is conserved and well defined, and so the canonical ensemble is not appropriate. If it is coupled, than we do not expect it to be in a pure state. | |
| Mar 6, 2012 at 20:23 | history | edited | Arnold Neumaier | CC BY-SA 3.0 |
added link at the end
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| Mar 6, 2012 at 19:36 | comment | added | Arnold Neumaier | @BebopButUnsteady: The penny is by assumption in thermal equilibrium, but need not be in equilibrium with the environment (e.g, if I just opened the window, thereby changing the environment.) - But any macroscopic body (not only a penny, and not only in a canonical ensemble, and even if far from equilibrium) is always entangled with its environment. The consequence is that no macroscopic object can be assigned a pure state, not even in principle. But this flatly contradicts the ignorance interpretation of statistical mechanics. Thus more things to defend for the upholders of orthodoxy! | |
| Mar 6, 2012 at 19:19 | comment | added | BebopButUnsteady | Arnold, perhaps this a minor point, but use of the canonical ensemble implies to me the penny is in thermal equilibrium with an environment. This would mean that the penny is entangled with the environment and therefore it would not be described by a pure state. Your questions do not seem to be as sharp if they are posed to the microcanonical ensemble. | |
| Mar 6, 2012 at 18:49 | history | edited | Arnold Neumaier | CC BY-SA 3.0 |
added further clarification on the temperature of my penny
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| Mar 6, 2012 at 18:27 | comment | added | N. Virgo | @ArnoldNeumaier yes, but "everything that makes a difference to the system [as measured by macroscopic instruments]" != everything. MaxEnt is founded precisely on ignoring the microscopic details that do not make any difference to the macroscopic state, while not ignoring anything that does. Ignoring things that don't make any difference is good, because it means you don't have to calculate them! | |
| Mar 6, 2012 at 18:09 | history | edited | Arnold Neumaier | CC BY-SA 3.0 |
added 1567 characters in body
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| Mar 6, 2012 at 16:00 | answer | added | Kostya | timeline score: 3 | |
| Mar 6, 2012 at 16:00 | history | edited | Frédéric Grosshans |
change tags
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| Mar 6, 2012 at 15:59 | answer | added | Frédéric Grosshans | timeline score: 11 | |
| Mar 6, 2012 at 15:40 | answer | added | N. Virgo | timeline score: 26 | |
| Mar 6, 2012 at 15:24 | comment | added | Arnold Neumaier | Science must be objective, observer independent, hence it should not depend on choices of an observer. So whatever choices there ar, there should be an objective way of assessing them. - I analyzed Max Entropy in Section 10.7 of my book lanl.arxiv.org/abs/0810.1019 Classical and Quantum Mechanics via Lie algebras, and found it wanting:If you choose to ignore things that you shouldn't (such as the energy content) you get completely wrong results in clear contradiciton to experiment. To get a correct theory you must choose to know at least everything that makes a difference to the system! | |
| Mar 6, 2012 at 15:15 | comment | added | genneth | Is this not the same problem as the MaxEnt school "runs into" (scare quotes because they don't really) that physics seems to change depending on how much one chooses to ignore? The resolution there is that ultimately one is doing science, so one needs a condition like "this set of control variables is empirically sufficient to control the outputs". | |
| Mar 6, 2012 at 15:15 | history | edited | Arnold Neumaier | CC BY-SA 3.0 |
improved again the final argument.
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| Mar 6, 2012 at 14:50 | history | tweeted | twitter.com/#!/StackPhysics/status/177043438951350272 | ||
| Mar 6, 2012 at 11:56 | history | edited | Arnold Neumaier | CC BY-SA 3.0 |
corrected final statement
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| Mar 6, 2012 at 11:39 | history | asked | Arnold Neumaier | CC BY-SA 3.0 |