Schwarzschild’s solution

Posted by on Feb 23, 2013 in Blog, Science | 0 comments

Schwarzschild’s solution

Einstein published his general relativity in 1915; and in this, he included an approximate solution for the orbit of Mercury. At that time, Karl Schwarzschild had been deployed by the German army to the Russian front. Schwarzschild wrote Einstein with an exact solution to the field equations on December 22, 1915 (my oldest sister’s birthday, for whatever that’s worth). Schwarzschild used polar coordinates instead of the rectangular Cartesian coordinates that Einstein had originally employed; and this makes much more sense in any system with spherical symmetry, of course. I want...

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Energy and momentum

Posted by on Feb 11, 2013 in Blog, Science | 0 comments

Energy and momentum

When Einstein began to develop the theory that became general relativity, there were a number of elements that were going to be essential to the result. The basic papers on special relativity were published in 1905 and general relativity was not made public until 1915. Special relativity had already dealt with coordinate transformations between inertial frames of reference; general relativity was to incorporate accelerated frames of reference. Einstein would also have had in mind the equivalence principle; namely, that a gravitational field was equivalent to an accelerated frame of...

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Einstein, Hurst, and network congestion policy

Posted by on Sep 23, 2012 in Tutorial | 0 comments

Einstein, Hurst, and network congestion policy

We begin our story with good old Albert Einstein and his considerations of Brownian motion. In 1905, Einstein delivered four papers for publication that, in turn, addressed the photoelectric effect, Brownian motion, special relativity, and energy-mass equivalence. He could have been swept from the earth in 1906 and he’d still have been rightly famous for his work of 1905. Over 100 years later, folks are still struggling with the meaning of his work in that year. You can read what Albert had to say about Brownian motion for yourselves. Let’s turn to the bit on Brownian motion for...

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