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He is doing an investigation into the underlying foundations of statistical mechanics. Statistical Mechanics and thermodynamics are the basis for a huge amount
by ealloc 12y ago
He is doing an investigation into the underlying foundations of statistical mechanics.
Statistical Mechanics and thermodynamics are the basis for a huge amount of technology and scientific models of the world, yet they rely on a fundamental assumption which is in some sense unjustified, known as the 'Ergodic hypothesis': Even though (classically) we know that the current position of gas particles in a box can be determined from their positions in the past, in thermodynamics we make the (unjustified) assumption that their positions are actually random and independent of their previous positions. In other words, these models for the world are probabilistic, which contradicts our more fundamental models of the world which say it is deterministic (and even QM is deterministic, with the single exception of the born rule). What he's doing here helps justify the probabilistic treatment, and understand when it does or does not apply.
I have always though this to be one of the great 'foundations' questions in physics (The others being QM foundations/origin of the born rule, and foundations of Field Theory). These are 'hard' and borderline philosophical questions, which most scientists (with good reason) simply assume to be true, to the point they often find them uninteresting. Lately though there seems to be renewed interest in them.
- chunky1994 12y agoWhen you say QM is deterministic except for the Born rule, I would add that a lot (almost all) of QM is based off of the Born rule [1], so as to avoid potentially misinforming the unfamiliar reader. [1] The Born rule in QM is the rule that allows us to calculate the probabilities that a particular experiment would have a given outcome. http://en.wikipedia.org/wiki/Born_Rule http://en.wikipedia.org/wiki/Born_Rule
- pizza 12y agoIs there any way that, with some effort, a slightly-more-than-layperson could understand his work? Like blog posts and stuff.
- auxbuss 12y agoWithout maths, I don't think there is. QM starts with the Schrödinger equation -- which allows you to find a wave function -- followed by Born's Rule, which is a statistical interpretation of the wave function. There are questions of interpretation even at this point. Schrödinger himself was skeptical of his own equation[0]! The classic intro text is Griffiths', Introduction to Quantum Mechanics. But it's a mathematical treatment -- as it has to be -- although it might be readable by accepting the key equations as axioms and reading the text. A smart, determined person would get something out of that, but I don't know how much. After all, QM is notoriously difficult to understand even by the super-smart, mathematically adept folk. I'm not sure that a pop-sci book could convey sufficient detail to allow someone to follow many QM debates, even the philosophical debates; there is just too much background required -- which I am not claiming I possess; still learning. Personally, I think QM is in the process of building an ever increasing body of information. The distillation of knowledge is yet to come. It's a hell of a trip, though. [0] Bloch, Physics Today, December 1976
- pizza 12y agoAh, well I meant math included but for someone at the level of learning what the heck a differential form is, that kinda level. Thanks for the pointers. Since I've got your attention here, I might as well ask if you know any good resources for learning about this "negative" probabilities business w. quantum? Something to do with 2D probability? Was reading some lecture notes [0] that mentioned something about using matrix transformations to describe state transitions (reminded me of Markov chains), maybe you'd know where I could learn about that. [0] http://www.scottaaronson.com/democritus/lec9.html http://www.scottaaronson.com/democritus/lec9.html
- murbard2 12y agoI've always found E.T. Jayne's treatment of the topic to be good. Randomness is in the mind of the experimenter, it does not represent an intrinsic characteristic of the system but the ignorance of the experimenter. This is, in my mind, the most satisfactory answer to Gibbs paradox. Born rule on the other hand, I can't wrap my mind around. Absent wave function collapse (for which there is zero evidence), what exactly are Borne probabilities probability off :(
- jjoonathan 12y agoahem Do you have a moment to speak about accepting Many Worlds Theory as your savior?
- murbard2 12y agoI do accept Many Worlds, that's why Borne probabilities make no sense :-/