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32

I'm not sure i'll be able to post all the links i'd like to (not enough 'reputation points' yet), but i'll try to point to the major refs i know. Matilde Marcolli has a nice paper entitled "Number Theory in Physics" explaining the several places in Physics where Number Theory shows up. [Tangentially, there's a paper by Christopher Deninger entitled "Some ...


13

Neutron stars were predicted in 1934 by Baade and Zwicky, one year after the discovery of the neutron. They were not observationally confirmed until 1965 by Hewish and Okoye. It's hard to beat a prediction that sat around for 30 years before being confirmed.


13

Off the top of my head, the Cosmic Microwave Background radiation was hypothesized as a consequence of Big Bang Theory before it was observed by accident by Penzias and Wilson. Also the light element abundances, also a consequence of BBT, was theoretical and is still being refined today through observations that supported the initial theory. I don't know ...


9

A semi-silly idea that I've read about is the Primon gas, a model where the Riemann zeta function arises as the partition function of a quantum statistical mechanical system. More seriously, take a look at the papers of Yuri Manin and Matilde Marcolli on the hep-th arxiv, which attempt to connect the holographic principle to arithmetic geometry. I think ...


8

I really like The Princeton Guide to Mathematics (Amazon, Google) Even though I believe it was meant more as a sort of Encyclopedia rather than an actual Textbook, I really like to read it as a "normal" book. Basically, whenever I understand some new mathematical concept I look it up in the Guide and see how it branches out and often find new interesting ...


7

A perfect example for what I think you are looking for is J.S. Bell's Speakable and unspeakable in quantum mechanics (Amazon, Google). Although it is a collection of papers, this is a very readable account of some aspects of quantum foundations.


5

There's a fantastic article on the relationship between the Riemann Hypothesis and "quantum chaos" at www.msri.org/ext/Emissary/EmissarySpring02.pdf (starts on page 1, continues on page 12). Here's an excerpt (recall that Montgomery's Conjecture is a conjecture about the expected number of zeros of the Riemann zeta function that follow a zero in an ...


4

I recall being stunned (they can do that?) by the mere mention of the technique called "Zeta Function Regularization", see http://en.wikipedia.org/wiki/Renormalization, http://en.wikipedia.org/wiki/Zeta_function_regularization , to sum divergent series like zeta(-n) to get finite results. I thought that was the limit. Then I heard about p-adic strings, ...


4

If you're into general relativity, you could try General Relativity for Mathematicians, by Sachs and Wu. I only know general relativity for physicists, so I can't comment on whether this book is any good, but it might be worth a try. Sachs is the one known to relativists and cosmologists for the Sachs-Wolfe effect. He taught my E&M class when I was a ...


4

For quantum field theory I like Folland's book "Quantum Field Theory. A Tourist Guide for Mathematicians", because it is written by a mathematician with mathematicians as readers in mind. It is full of comments and explanations that a mathematician needs and are usually not in the physics books. Also he clearly says which parts a rigorous, from a mathematics ...


4

For mechanics at the next level (or perhaps skipping a level), you could try Jerrold E. Marsden & Tudor S. Ratiu, "Introduction to Mechanics and Symmetry", Springer, 1994. For quantum field theory, a recent attempt at a moderately elementary level is http://www.amazon.com/Quantum-Theory-Mathematical-Surveys-Monographs/dp/0821847058, by Gerald B. ...


4

What comes to my mind are black holes. Their existence was postulated by Karl Schwarzschild in 1916, the theory was refined during the 1960s, but as to their existence, we still rely only on indirect evidence. There was a program to find flashes related to the final stages of the evaporation of a black hole started in 2008, but no hard evidence has been ...


3

A brief list of miscellaneous "technical" (not popular science) books I read on the bus, and I enjoyed every page: Everything from R.P. Feynman, from his "Lectures on physics" to "Statistical mechanics", the "Lectures on computation" or "Gravitation". "QED: the strange theory of light and matter" may be considered as (extremely good) popular science, but it ...


3

I find the book Geometry of quantum states: An Introduction to Quantum Entanglement by Ingemar Bengtsson and Karol Życzkowski both readable and useful. I already referred to it in three different occasions on this site. It focuses on the geometrical description of the spaces of quantum states and maps of finite level quantum systems. This subject is rapidly ...


3

I personally don't know of particular books dedicated to the subject covering all areas of physics (maybe "Mathematical Methods for Physics and Engineering" by Riley, Hobson and Bence isn't quite what you're looking for), but if you happen to come across the subject of Quantum Field Theory then I suggest you have a look at "Quantum Field Theory for ...


3

Lots of properties that were found to hold locally (in space and time) turned out to be only local approximations. Flat earth hypothesis - long journey. Galilean transformations - breaks at large velocities. Global curvature of spacetime, locally it is flat - large distances. Spacetime is not expanding - breaks at large distances (Hubble's law) Classical ...


2

You might try, now in paperback, Th. Frankel: The Geometry of Physics, An Introduction, Cambridge U.P. (Cambridge), 1997. It's a course in differential geometry, actually, but one oriented towards physics, with succinct but comprehensive enough developments of physical theories (mechanics, electromagnetism, thermodynamics, Yang-Mills ...). It's a bit ...


2

One particularly fun book that I really enjoy is "Road to Reality" by Roger Penrose. However it is most certainly not as self contained as it describes itself, and should be supplemented by other sources (both math and physics) if you want to have a good understanding of the material. But still, I personally love his writing style and he still keeps the ...


1

You might also try working through the math-physics relationship from the other end: start with a math book. Larson and Stewart's Calculus textbooks are some pretty general books that cover basic calculus--starting from algebraic/geometric principles--to elementary multi-variable calculus and differential equations, with some other cool stuff thrown in ...


1

One great place to start (assuming a knowledge of calculus) is a college upperclassman level E&M book like Griffiths. While Electrodymamics is an interesting field in its own right, and gives a whole lot of motivation for later topics, its place in a physics curriculum is also the first place that students are introduced to the machinery of solving ...


1

Basic areas of mathematical physics are: analysis linear algebra Depending on specific physics area like QM or ART u have to enhance ur knowledge with functional analysis or differential geometry. But without basic areas knowledge u will not see any light at the end of the tunnel ;) Sites like hyperphysics try to keep the math as simple as possible. ...


1

I would start with any good high school or introductory college text on physics. The textbook will not only show you conceptually what is going on, but will, out of neccessity of fulfilling the purpose for which it was written, give you the math along with it. One caveat to that is that physics will not teach you calculus, and a college-level text will ...


1

The main difference between mathematicians and physicists is that the former define their terms, and the latter do not. I.e., mathematicians are logical, physicists, even theoretical physicists, except for Dirac, are willing to be illogical. A novel about Oxford life had in it the line «Of course, you began by defining your terms...» so this distinction is ...


1

E. Zeidler, Quantum Field theory I Basics in Mathematics and Physics, Springer 2006. http://www.mis.mpg.de/zeidler/qft.html is a book I highly recommend. It is the first volume of a sequence, of which not all volumes have been published yet. This volume gives an overview over the main mathematical techniques used in quantum physics, in a way that you cannot ...


1

Mathematics is a language in which physicist express their ideas. It is mathematics which helps to reach and imagine results which are far beyond reach of direct imagination of a physicist mind, at times. Mathematics really helps to imagine complex ideas. A mathematician has all the tools ready in his hand to learn physics, as physics utilizes power of ...


1

The equivalent in Physics of a counterexample in Mathematics would be a failed experiment. For example: the Michelson Morley experiment is a counterexample to the ether conjecture. But was it big? Can any experiment be "big" in the same sense as Mathematics? Possibly not. I make a conjecture: "any physical conjecture can be disproved with a fairly ...



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