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.
When 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
I'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 :(
Without 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.
Ah, 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.
We had was a Brazil-born British citizen who won a Nobel in medicine. He could have been a brazilian citizen, but he renounced his citizenship to avoid Brazil's mandatory military service, which to this day is still mandatory.
But still happens, happened to me when I turned 18 in 2004. Even though I was in college and already working as an intern, I only managed to get out because I have an uncle who is a navy official.
> Through the math competitions, Avila discovered IMPA, where Brazil held its Olympiad award ceremonies each year. There, he met prominent mathematicians like Carlos Gustavo Moreira and Nicolau Corção Saldanha, and while still technically in high school, he began studying graduate-level mathematics.
>In Brazil, Avila could relish mathematics without the career pressures he might have faced in the United States. “It was better for me to study at IMPA than if I were at Princeton or Harvard,” he said. “Growing up and being educated in Brazil was very positive for me."
Come on, let's not be too hard on ourselves. He went to a Brazilian federal university and then to IMPA, which is arguably a world class institution.
Sure, he probably couldn't get where he got without moving abroad, but then most of the Brazilian top football players play for foreign clubs, and yet nobody will claim that we don't encourage kids to play football. You have to take into account the sheer economic disparity between Brazil and the developed West.
A lot of his work was developed at IMPA (Brazils Institute for Pure and Applied Mathematics), which has historically been somewhat connected to french mathematics universities. But, yeah, our best minds still go abroad to become fully developed.
The big problem in Brazil is that our basic education is crap. We do have good higher institutions, but a lot of the people who end up there never had a good base.
>our best minds still go abroad to become fully developed
and this is what made me angry, our best researchers needs to leave the country to work because here they don't have a proper support, and when they finally succeed in something the people remember that he is brazilian like it was a determinant factor.
How is the media reacting in Brazil? If only they showcased him alongside the famous footballers...
I come from India which is fanatic about Cricket. You would think media will understand the need to give India's chess grandmasters the same exposure as cricketers, but in reality it is mostly run as a business :(
Unfortunately little to no reaction at all, and I don't think there will be more coverage, specially after a plane crashed today carrying a presidential candidate.
I agree. He was in every news TV show, including the biggest of them "Jornal Nacional". Also very good coverage of IMPA, the math institute behind his education.
But sure, now with the sad news about Eduardo Campos he will be nowhere to be seen. I hope in the next months and years he is remembered and popularized (is that a word?).
Congrats to him! It was also just announced that in 2018 the International Congress of Mathematicians will occur in Rio de Janeiro (being called the "Math World Cup" in Portuguese).
From the video interview, I understand he has been living in Paris for a while but his English accent is surprisingly non-Brazilian (sounds Russian with his Rs and closed vowels).
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.