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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 ...


Books Galileo and Einstein very interesting book, 200 pages, by Michael Fowler , Text for Physics 109, Fall 2009 (from Babylonians and Greeks to Einstein) Physics Made Easy Karura notes Classical and quantum mechanics via Lie algebras by Arnold Neumaier, Dennis Westra , 502 pages, (arxiv) by Hans de Vries: 'Physics Quest' Understanding Relativistic ...


A large portion of the 'big science under developement' is directed towards astrophysics and cosmology. The Square Kilometre Array (SKA) and the European Extremely Large Telescope (E-ELT) are the two flagship facilities for ground-based astronomy in the future. Both are planned to be operational in the twenties of this century. SKA - artist impression ...


Arthur Suvorov gives a nice comment, I am just going to give a list of a few specific physical problems I can think of from the top of my head. Yang Mills existence and mass gap (Millenium Prize) and generally the problematic of rigorous definitions and constructions of quantum field theories Navier Stokes equations and smoothness (also Millenium) - it's ...


I'm really excited about the results of Fermilab and J-PARC on the measurement of $(g-2)_\mu$, that is, the anomalous magnetic moment of the muon. The current value of $g-2$ is \begin{align} a_\mu^\mathrm{exp}&=0.001\;165\;920\;91(63)\\ a_\mu^\mathrm{SM}&=0.001\;165\;917\;64(52) \end{align} where $\mathrm{SM}$ is the full Standard Model prediction, ...


There is a lot of good books in CM, QM, EM... but what every physicist should read, undoubtly, are The Feynman Lectures on Physics.


The Gaia Spacecraft is another hugely anticipated physics experiment. First conceived of in the early 90's it has been operational since 2013. The aim of this ambitious experiment is to create a 3D map of the location and velocity of up to 1% of all objects in the Milky Way. This should enable us to refine our models on galactic dynamics and allow us to ...


One that jumps to mind is Hooke's law (extension of a spring). Hang a spring or thick elastic band and load it with increasing weights. See that extension is proportional to load at least initially. A natural extension of that is to also measure oscillation time/frequency. Another one would be Archimedes principle, and play with floating/sinking different ...


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 ...


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.


A Sizable Mystery Here's a mystery that remains poorly understood, though there have been many attempts to explain it: Why does volume -- the ability of matter to fill up space exclusively -- depend on how particles rotate? By volume I mean for example the fact that you can pound on a desk with your fist, and your fist stops at the desk. The matter in ...


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 ...


The Reference Frame it is the only one that is challenging.


The worst analogy I have seen is that of general relativity where they show a curved sheet and how a ball revolves due to the curvature. (Source: , CC-BY-NC license) As far as I remember, I have seen this at two places: The movie "Einstein and Eddington" where Arthur Eddington explains Einstein's theory to his housemaid Carl Sagan ...


There are plans for a linear collider of electron positron, to study the new physics that is appearing at the LHC, two are in design. The International Linear Collider (ILC) is a proposed linear particle accelerator.1 It is planned to have a collision energy of 500 GeV initially, with the possibility for a later upgrade to 1000 GeV (1 TeV). The host ...


Quantum field theory Fields, by W. Siegel Quantum Field Theory, by Mark Srednicki Superspace, or One thousand and one lessons in supersymmetry by S.J. Gates Jr, M.T. Grisaru, M. Rocek and W. Siegel


You want the book by V.I. Arnold, Mathematical Methods of Classical Mechanics. It takes a very rigorous, axiomatic approach to Lagrangian and Hamiltonian mechanics, and it should be accessible to, and enjoyable by, a broad spectrum of mathematicians. For more details see this review by Ian Sneddon, which also covers Walter Thirring's A course in ...


Mathematical Tools for Physics, James Nearing Also available in paperback from Dover. Undergraduate-level math methods book. Clear writing, many problems and exercises (usually without solution). IMHO better than Boas.


Structure and Interpretation of Classical Mechanics Sussman, Wisdom, Mayer A No-Nonsense Introduction to General Relativity, Sean Carroll


I think everyone needs to read Feynman's QED: The Strange Theory of Light and Matter. While there are many great books on QFT, this one shows you the inner workings of the microscopic world like none other. It also gets bonus points for being accessible to basically everyone.


John Baez's Stuff It is more mathematics, but a lot of physics/mathematical physics related "stuff" also.


One formative book for me was Ed Purcell's Electricity and Magnetism. Purcell was my early education in thinking like a physicist. It introduced me to thought experiments, simple models, and the usefulness of new mathematical tools. It's mathematically very clear, and physically insightful. The problems are extremely rich. It manages a huge deal of ...


The "solar system" analogy of the atomic nucleus and electrons is certainly a very misleading one, in many ways. Unfortunately, this is all too often the model taught until late high school or early undergraduate level. The Bohr model, or more usually the fuller quantum mechanical description, is of course required to do any useful physics. The shell model ...


Cosmic Variance Science, Technology, and The Future NOTE It would be great if someone who knows the blog well would write a few words about it. Just give a little more detail of what it's about. 3 sentences is more than enough. This is community wiki, so most people can edit it freely.


There's a fantastic article on the relationship between the Riemann Hypothesis and "quantum chaos" at (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 ...


The Old Man and the Sea by Ernest Hemingway It is terribly important to recognize that stupendous effort does not always result in substantial gain.


The deflection of light by the sun was first predicted by Einstein's general relativity, then observed in a solar eclipse.


The flow of a fluid, such as air, is something very common place. It is what provides lift and drag on airplanes. You can feel its effects if you stick your hand out the window of a moving car. However, we still do not know everything about the state of fluid flow called turbulence and how a laminar flow transitions to it. Although the governing equations ...


Roger Penrose: The Road to Reality: A Complete Guide to the Laws of the Universe, before they start studying. If that doesn't discourage you you're up to the task.

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