Geometry and Topology for Physicists Thursday, Oct 26 2006 

Previous post reminded me of one link I wanted to post earlier but somehow forgot:

Geometry and Topology for Physicists

I think these are quite a gem.
As the webpage says: “No particular mathematics background is required beyond that usually expected of graduate students in physics (linear algebra, complex analysis, etc), but it will help if you have some familiarity with mathematical notation and ways of thinking”.


Books by Sternberg Wednesday, Oct 25 2006 

Prereq. : Varies. But, I guess some amount of “math-maturity” and interest can take one far. 😉

Link :

Some good mathematical books written by sternberg. The books available are

* Theory of Functions of real variable (2 Meg PDF)
* Advanced Calculus (58 Meg PDF)
* Dynamical systems (1 Meg PDF)
* Lie Algebras (900 K PDF)
* Geometric Asymptotics (AMS Books online)
* Semiriemannian Geometry (1 Meg PDF)

And over here, you can see a list with names of many math books.

COBE gets the Nobel Tuesday, Oct 3 2006 

The history of science is filled with many a dead theory – theories which couldn’t stand up to the onslaught of experiments. But, once in a while, there comes a theory/a model which is so suceessful, so successful that it is just fun to watch graph after graph, observation after observation fit with what the model predicts.

Our present model of the universe had such a moment when COBE went onto measure anisotropies in cosmic microwave background.And it is this that the Nobel Committee has chosen to immortalise through the 2006 Nobel Physics prize. To quote them

This year the Physics Prize is awarded for work that looks back into the infancy of the Universe and attempts to gain some understanding of the origin of galaxies and stars. It is based on measurements made with the help of the COBE satellite launched by NASA in 1989.

The COBE results provided increased support for the Big Bang scenario for the origin of the Universe, as this is the only scenario that predicts the kind of cosmic microwave background radiation measured by COBE. These measurements also marked the inception of cosmology as a precise science. It was not long before it was followed up, for instance by the WMAP satellite, which yielded even clearer images of the background radiation. Very soon the European Planck satellite will be launched in order to study the radiation in even greater detail.

According to the Big Bang scenario, the cosmic microwave background radiation is a relic of the earliest phase of the Universe. Immediately after the big bang itself, the Universe can be compared to a glowing “body emitting radiation in which the distribution across different wavelengths depends solely on its temperature. The shape of the spectrum of this kind of radiation has a special form known as blackbody radiation. When it was emitted the temperature of the Universe was almost 3,000 degrees Centigrade. Since then, according to the Big Bang scenario, the radiation has gradually cooled as the Universe has expanded. The background radiation we can measure today corresponds to a temperature that is barely 2.7 degrees above absolute zero. The Laureates were able to calculate this temperature thanks to the blackbody spectrum revealed by the COBE measurements.

COBE also had the task of seeking small variations of temperature in different directions (which is what the term ‘anisotropy’ refers to). Extremely small differences of this kind in the temperature of the cosmic background radiation – in the range of a hundred-thousandth of a degree – offer an important clue to how the galaxies came into being. The variations in temperature show us how the matter in the Universe began to “aggregate”. This was necessary if the galaxies, stars and ultimately life like us were to be able to develop. Without this mechanism matter would have taken a completely different form, spread evenly throughout the Universe.

COBE was launched using its own rocket on 18 November 1989. The first results were received after nine minutes of observations: COBE had registered a perfect blackbody spectrum. When the curve was later shown at an astronomy conference the results received a standing ovation.

The success of COBE was the outcome of prodigious team work involving more than 1,000 researchers, engineers and other participants. John Mather coordinated the entire process and also had primary responsibility for the experiment that revealed the blackbody form of the microwave background radiation measured by COBE. George Smoot had main responsibility for measuring the small variations in the temperature of the radiation.
Read more about this year’s prize
Information for the Public(pdf)
Advanced Information (pdf)

You can find the telephone interviews of the winners here and here.Here is the link to the official wesite of the COBE and here are the links to various posts in physics blogsphere and around the web .

(Click to magnify)
From NASA site

Cosmic Microwave Background (CMB) spectrum plotted in waves per centimeter vs. intensity. The solid curve shows the expected intensity from a single temperature blackbody spectrum, as predicted by the hot Big Bang theory. A blackbody is a hypothetical body that absorbs all electromagnetic radiation falling on it and reflects none whatsoever. The FIRAS data were taken at 34 positions equally spaced along this curve. The FIRAS data match the curve so exactly, with error uncertainties less than the width of the blackbody curve, that it is impossible to distinguish the data from the theoretical curve. These precise CMB measurements show that 99.97% of the radiant energy of the Universe was released within the first year after the Big Bang itself. All theories that attempt to explain the origin of large scale structure seen in the Universe today must now conform to the constraints imposed by these measurements. The results show that the radiation matches the predictions of the hot Big Bang theory to an extraordinary degree….