X-Message-Number: 19212
From: 
Date: Thu, 6 Jun 2002 07:33:37 EDT
Subject: Re: CryoNet #19196 Advance in physics

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Thomas Donaldson said:

> For those who seem to think that advances in physics have ceased,
> please either answer my comments (and read the articles in SCIENCE)
> or shut up and admit you're wrong.
> 
> 

There is  a lot of small advance in physics, but nothing as dramaticas the 
invention of Relativity, quantum mechanics or gauge theories ( the 
electro-weak unification or color SU(3) hadron force.

May I suggest an small input?
Gauge symetries defines electromagnetism with U(1) nuclear weak force with 
SU(2) and color with SU(3). Why not SU(4) and so on?
There is my guess: U(1) geometry is the Moebius band, you need 2 dimensions 
at least to see it. SU(2) geometry is the projective plane, you need 4 
dimensions to produce it. Similarly, SU(3) needs 6 dimensions and SU(N) would 
need 2N dimensions. Now, from euclidean 3 dimensional space, the largest 
mechanical space you can built is a 6 dimensional phase space using Jacobi's 
mechanics. With this space, you can't see anything beyond SU(3).

Now, in relativistic thermodynamics, you can built infinite dimensional phase 
space and so you would be able to see SU(N) for any large N. Can we see the 
SU(3) boundaries of SU(4) at high energy particle accelerators?  I think it 
would be interesting to do the experiment, it could open the way to the 
discovery of an infinite set of new "fundamental" forces, one for each SU 
symetry.

Yvan Bozzonetti.

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