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George E. Hrabovsky, President, MAST
Superstring Theory, The DNA of Reality
A few weeks ago Shawn Carlson asked if I would review some material sent by a noted physicist on string theory for the lay public. While a readily assented, I did not hold out much hope for the material, as my experience of string theory for lay people is not very high, with one previous exception.
It was with some joy that I opened the box and saw that the video course was being taught by Professor S. James Gates, Jr. I had browsed some of his papers in the past and had enjoyed his comments as seen on the NOVA series based on Brian Greene's The Elegant Universe. I immediately called Shawn and told him that I knew who this noted physicist was and that he was a big gun in the string theory community.
I sat down and immediately watched the first few lectures. The first lecture lacked focus and would have been confusing to a complete newcomer. (My daughter watched this lecture and told me that she would have been lost had we not talked about cosmology earlier that day for a homework project she did.) Professor Gates' description of Hawking radiation was also a bit muddled.
Hawking radiation is the apparent tunneling of particles out of a black hole by quantum means. It works like this: The vacuum of space has a certain potential energy that constantly causes photons to come into existence and go back out of existence. This happens so quickly that it goes unnoticed. Sometimes when this happens, before the photon goes back into the vacuum potential it produces an electron-positron pair that exists briefly before coming together and annihilating one another, becoming a photon again and then being reabsorbed into the background vacuum . . Were this to occur at the event horizon of a black hole, it is possible that one member of this pair would fall into the black hole, allowing the other to escape. What makes this so weird is not that the black hole seems to be radiating particles (something a black hole should be unable to do), but the fact that an outside observer can't tell that pair production causes particle creation at the event horizon. Instead it seems as though a particle tunneled out of the black hole, thus reducing its mass. This leads to the conclusion that eventually black holes evaporate. Professor Gates did not explain this part, only that black holes seem to give off this radiation of particles.
One aspect of the lectures that struck home very nicely was Professor Gates' analogy of the theorist as a concert musician. While the physicist knows the scores and notes of mathematics, the audience is not required to know them to appreciate a well-composed piece of music. Through the technology of computers it is now possible to create graphical representations of even the most complicated mathematics so that those who wish to may appreciate the score without being able to compose. See more on this theme in the concluding remarks below.
The course comprises twenty four lectures and I found them engaging, entertaining, and inspirational. I found myself stopping the DVD player, jumping up, and rushing to my office to work. I found that Professor Gate's passion and energy impassioned and energized me. While his presentation was at time philosophical and hopeful, he was never preachy (as some string theorists can be). I was refreshed by the realistic and pragmatic views expressed; here is a theorist who has not lost touch with real science.
I highly recommend this course to anyone interested in physics.
Mathematica Version 6
A little more than a month ago I acquired the new version of Mathematica. It is nothing short of revolutionary. Why? The inclusion of a simple idea: interactivity. For those who already know me, my claim to fame is not that I study relativity and tornado physics, but that I am a Mathematica consultant and trainer. The previous version of Mathematica was awesome. What is so great about the new version?
There are some minor changes, and the addition of rudimentary drawing software makes illustration much easier. The expansion of import filters to include just about everything is also extremely useful.
The major innovation is the inclusion of the Manipulate command. This allows you to create a plot or expression with some specified parameter and be able to manipulate that parameter on the fly. With this one inclusion, all of the dreams of computer-based learning come into reach. With this simple addition you can make arbitrarily complicated demonstrations that allow the student (or researcher) to manipulate values on the fly and see what happens immediately.
This, along with the totally free Mathematica Player, available from this web site http://www.wolfram.com/products/player/download.cgi, allows a teacher to build completely interactive modules that anyone with Internet access can view, download, and manipulate for free. The same is true for researchers. You can specify a model with all parameters and then change those parameters and study the results as you change them.
Mathematica and The DNA of Reality
What do these two have in common? Professor Gates, in his course, refers to drawing pictures to represent mathematics without having to teach the mathematics. In some ways this is what the new version of Mathematica allows you to do. Here are two demonstrations. If you do not have Mathematica 6 you can use the link above to download the Viewer and play with them.
The first example is a plot of the solution of the harmonic oscillator equation from t=0 to t= Pi. You can find this demonstration here. In the second example, I will expand a sum of two values in powers up to fifteen. To download this click here.
In this next example, I will expand a sum of two values in powers up to fifteen. To download this click here.
As you will see these simple demonstrations are impressive. What is more impressive is that they took me less than a minute to write both together. Thus we can visualize the mathematical results without having to do all of the mathematics. Even more importantly, the user does not need to own or understand anything about Mathematica!
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