Arcadian Functor

occasional meanderings in physics' brave new world

My Photo
Location: New Zealand

Marni D. Sheppeard

Thursday, November 09, 2006

TWP Duality

TWP is an excellent popular account of the current status of physics, provided the reader appreciates that the alternative ideas mentioned in later chapters are by no stretch of the imagination adequate to meet the experimental challenges that currently face our field. For example, Category Theory is not even mentioned. This is a serious omission in the present climate of ideas. On the other hand, the personal anecdotes about pivotal events in the development of String Theory are particularly enjoyable. Smolin mentions, for example, his great surprise at the non-discovery of proton decay. I come from a slightly younger generation: the real DWAT (Don't Worry About That) generation. The current form of the Standard Model was well established before I became an undergraduate in the late 1980s.

The most common response to questions that our generation asked was: DWAT. We haven't seen proton decay? DWAT. No Higgs? DWAT. No Gravitational Waves? DWAT. Needless to say, after having thought quite a bit about physics over the years, by the time it came to the observations of type IA supernovae my generation greeted the supposedly obvious explanation with some skepticism.

On page 210 of TWP, Smolin mentions Milgrom's Law, which is the observation that the apparent breakdown of Newton's law in galaxies occurs at a scale whose value of acceleration matches the apparent acceleration of the cosmological constant. Rather than follow the r^(-2) law, outlying bodies appear to obey a r^(-1) law.

Now it was shown by Bertrand [1] in 1873 that central forces for closed orbits can only obey one of two possible laws: either the r^(-2) law or the r law (Hooke's law). The latter is the inverse of the law that we would like to obtain. Is there a simple way to rescue this situation? Yes, of course. When there is a correlation between a cosmological scale and a local scale we should not be afraid to apply T duality and/or S duality to the problem. M theory dictates that this is indeed the way to look at things.

We can then remove ourselves from the empirical world of MOND by viewing the effect as Dark Matter in the form of black holes. This is still a form of modified gravity, so both of the popular views may be seen to be correct, in some weak sense. The black hole picture can explain why we should expect a correspondence of scales, because the cosmic horizon is naturally correlated to Dark Matter in this form.

[1] Goldstein Classical Mechanics


Blogger Mahndisa S. Rigmaiden said...

11 09 06

Well Kea:
The more people don't explore new ideas, the more you can play with them;)

I was thinking about the last post I did and realized that my usage of the term adic linguistics was crouched in a categorical theoretic framework. Then I came across the works of Pierce and saw that category theory is THE tool to use! Everything has something to do with categories, everything is a relation from one set to another.

Particularly in linguistics, this concept is applicable...Take care and keep up the unorthodox ways of thinking.

November 10, 2006 6:22 AM  
Blogger Kea said...

Yes, Mahndisa. Peirce is one of my heros. He founded category theory way back in the 19th century, and only now are we beginning to appreciate it.

November 10, 2006 11:25 AM  

Post a Comment

<< Home