Timeline for Dispensing with the "a priori equal probability" postulate
Current License: CC BY-SA 3.0
6 events
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| Apr 29, 2015 at 3:05 | comment | added | tom | I never thought of QM that way :) Also, this paper: sbfisica.org.br/rbef/pdf/060601.pdf is a good read if you're familiar with the basics of Measure theory, and even if you're not. It shows how ergodicity would indeed settle most disputes (it even implies the microcanonical distribution is the unique (sensible) equilibrium distribution). I was particularly surprised to find that the ergodic hypothesis & mixing has been proven for the general hard-ball model (i.e. n-dimensional billiards) which gives me a lot of confidence in it's validity or near-validity. | |
| Apr 28, 2015 at 6:42 | comment | added | Selene Routley | @tom This is the sum total of all I feel that I truly understand about classical statistics: (1) bare measure-theoretic models and mathematical proofs of their properties from axiomatic definitions of Borel algebras and measure (2) a practical notion of statistical hypothesis testing: if something comes out 6 sigma from your model's predictions, you know you're in strife (3) my intellectual capacity craps out somewhere not too far beyond (1) and (2) and I find classical probability utterly bewildering. | |
| Apr 28, 2015 at 6:33 | comment | added | Selene Routley | ... can always ask Nature for the answer in a QM problem by doing an experiment: classical probability seems mind bendingly harder to me in comparison. | |
| Apr 28, 2015 at 6:31 | comment | added | Selene Routley | @tom "'hard mathematics' category is much simpler than the 'hard philosophy' one! " I heartily agree. Probability theory is MUCH harder than most people believe and very much a work in progress: have you seen the discussions of e.g. "Chance versus Randomness" at the Stanford Encylopoedia of Philosophy? One of the questions people often ask on this site that amuses me is "Why can't QM be modelled by classical statistics", with the clear undertext that they think classical probability would be easier than complex amplitudes. My reaction to this is that QM is "easy" in the sense that one ... | |
| Apr 28, 2015 at 6:26 | comment | added | tom | Thanks, I've read a number of Jaynes papers, including the one you reference, but I must admit I'm not sure what to make of them :) Instinctively, I want more of a 'mechanical' justification! I'm feeling now that the ergodic hypothesis really does capture the heart of the issue, except that it is too weak (we need ergodicity over reasonable time lengths, not in the limit) and too strong (we don't really need complete ergodicity, just good enough.) But I feel more comfortable, as the 'hard mathematics' category is much simpler than the 'hard philosophy' one! | |
| Apr 28, 2015 at 5:15 | history | answered | Selene Routley | CC BY-SA 3.0 |