Hot answers tagged big-list
24
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
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 ...
12
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.
11
Actually the golden ratio does show up in at least one interesting physical situation: cobalt niobate is an experimental realization of the 1D Ising model, which -- in a magnetic field transverse to the axis that neighboring spins are coupled along -- has a quantum phase transition. In 1989 Zamoldchikov studied this model and discovered an amazing thing that ...
11
A model that has shown some interest in recent years is the golden chain. In the golden chain you deal with a one-dimensional chain of spin-like particle, similar to the Heisenberg (or Ising) model. But in this model the spin degrees of freedom are replaced by (non-Abelian) anyons (see e.g. this thread). The type of anyon used in this model are the Fibonacci ...
9
I will go with:
P.W. Anderson, More is different, Science 4 August 1972: 393-396.
on the topic of emergence and complexity in systems with a macroscopic number of constituents.
8
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
I like this paper because it's all of four pages long. Electroweak unification. Spontaneously broken symmetry. It's a thrilling paper to read!
Steven Weinberg, A Model of Leptons, Phys. Rev. Lett. 19, 1264–1266 (1967)
7
In addition to the others, there are other famous theoretical predictions that were then seen in the sky:
Neptune!
Asteroids. (from the failure of Bode's law)
Lagrange point objects
Inspiralling neutron star binaries
Supernova neutrinos(Colgate and White 1966).
GZK cutoff
The recent cosmology revolution was a combination of theory and experiment. The ...
6
Anyone starting in physics has probably already purchased this book at their university bookstore, but I recomend it:
Griffiths, David (1987). Introduction to elementary particles (New ed.). New York: Wiley. ISBN 0471603864.
6
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.
6
One that I learned in my first ungergrad year:
You have a Dragon inside a cage $D_0=3m$ long, a Knight wants to kill him, he jumps in his Unicorn, that can canter at $v=0.8 c$, aiming his $L_0=2m$ lance towards the Dragon. From the Dragon's reference frame, the lance should contract:
$
L = L_0 \sqrt{1-\beta^2} = 2\sqrt{1- 0.8^2} = 2\frac{3}{5} = ...
5
Even tough it is not about physics, I suggest the following:
J.A. Gallian, Advice on giving a good powerpoint presentation, Math Horizons, April. 2006:25-27
It is a short and concise list of DOs and DON'Ts when giving a talk or a lecture. And it is a pity that many scientists, despite years of frequent practice, make very simple mistakes on that issue.
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
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 ...
4
Your best bet might be the EPFL or École polytechnique fédérale de Lausanne in Switzerland. Their master courses are in English, while others are in French. They also have strong links with CERN and produce a lot of amazing research in a wide variety of fields. (they even have an on campus tokamak fusion reactor and a good ole fission reactor)
Here's the ...
4
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
How can one not have a desire to read some history:
Planck, Max (1901). "Ueber das Gesetz der Energieverteilung im Normalspectrum [On the Law of Distribution of Energy in the Normal Spectrum]" (in German) (pdf). Annalen der Physik 309 (3): 553–563. (1901). "On the Law of Distribution of Energy in the Normal Spectrum (in English)" (PDF). Annalen der Physik ...
3
India: The Indian Institute of Science is quite good. (A lot better than the IITs, at least in the sciences)
Europe: ETH Zurich, University of Basel, German universities like Technical University Munich, Bonn University, etc., University of Utrecht in Netherlands
Singapore: National University of Singapore and Nanyang Technological University are quite ...
3
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, ...
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 ...
3
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 ...
3
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. ...
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
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
This is the way in which all physical theories get formulated--- you first acquire certainty regarding the behavior of many special cases you have some experimental data or theoretical insight about, then you try to formulate a precise theory which extends these heuristic laws to a precise understanding, and when you succeed in matching the heuristic laws ...
2
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 ...
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