Monday, February 13, 2012

Superstring Theory: So You Wanna Be the Hero?

Whatever the result, I’ve finished reading The Elegant Universe by Brian Greene, on January 28th, 2012. It was a difficult book to follow, primarily because the theory itself is difficult, but also because the book is poorly written. Quite often the author says something he want to communicate is easily demonstrated mathematically, but hard to show in any other way. Of course, that is a valid statement because string theory has so much math in it: it almost started with mathematics. However, I would like to ask Mr. Greene, what are you doing here? Wasn’t this a science book for laymen?

I just encountered so many additional question marks while I was reading this book. So I googled about this and that - for example, Calabi-Yau spaces, and even watched the TBC documentaries starring Brian Greene. We learn better by teaching - communicating what we understand. I will attempt that in the following paragraphs.

1. Theory of Everything

Superstring theory is one of the contenders to become the Theories of Everything (TOE), which tries to fill the gap between quantum physics and general relativity. Three out of four basic forces in nature - strong and weak interactions and electromagnetic forces - are unified under the standard model of elementary particle physics. However, gravity could not be unified in the standard model. TOE is expected to do this task, and the Superstring theory is one candidate for the job. I like the Superstring theory explanation on the zero mass of graviton. Strings can perfectly eradicate mass when two (or more, in a collective manner) strings cancel each other out to become zero wave magnitude. As per Fineman’s theory, wave patterns spread to all directions at the same time. Hence, zero wave amplitude (i.e. zero mass) for the particle that mediates gravity.

2. Dimensions

There are 10 or 11 dimensions in the universe according to the Superstring theory. To be more exact, 10 according to vanilla String theory, and 11 for the M-Theory. Since 1 dimension is for time, there are still 9 or 10 spatial dimensions in the universe. Why six more? Greene says it’s math. Anyway, only three dimensions expanded in the inflation phase of the Big Bang, and the remnant remained curled in the tiny tiny space of the pre-Big Bang universe.

3. Black Holes

Brian Greene allocates a whole chapter to the black holes. Black holes are indeed the testing ground for a Theory of Everything, since the black holes are where the theory of general relativity and that of quantum physics must meet. In general, general relativity deals with the vast universe - the macro level of the universe, while the quantum physics deals with the microworld of Planck scale. They do not cross each other. However, in a black hole, which has super massive mass-energy in a ultra tiny dimension, the two theories must come up with a coherent explanation that does not counter each other. The standard model could not do this, so there are several contenders for the Theory of Everything - including the Superstring theory. According to the Superstring theory, a possible wreck of the space-time dimension - i.e. a singularity point - can be described as being looped by a single string. This can explain the stability of a singularity point existing in the universe. What if the singularity point is too large to be covered by a single string? Here comes the (to my thought) the most thrilling part of the theory.

4. T-Duality

A very surprising revelation by the Superstring theory is that there is no measurable difference between a really small universe and an extremely large one. More exactly, the theory states that a string that loops around a dimension smaller than itself and a string that move along larger dimensions do not have measurable differences. In technical terms, a string with a wavelength of x and momentum y in a universe with radius R, will be basically identical to a string with a wavelength of y, a momentum of x in a universe with a radius of 1/R. See the picture below.

(Picture courtesy of

In other words once more, things happening in a dimension of R does not differ from things happening in a dimension of 1/R. To illustrate this in an interesting way, we might actually be living in a tiny universe with a infinitesimally small size. This micro universe does not show any detectable difference from a immensely vast universe.

5. Criticism

Superstring theory has many shortfalls as well. Most notably, the formulas for Superstring theory yields infinite numbers of solutions. Another problem is this theory is almost impossible to test via experiments. The energy level required to test the theory is said to require a particle accelerator with the size of our Solar system!

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