Re: Could the 'missing dimensions' be quarks?

Posted by DickT on September 16, 2003 at 16:39:53:

In Reply to: Re: Could the 'missing dimensions' be quarks? posted by rtharbaugh on September 16, 2003 at 15:09:17:

Richard,

Anyway, then the three quarks in a proton would need nine dimensional graphing for complete description

That would plot their positions, but you have also their momenta to consider. That would require 9 more dimensions for the three vector components of each quark's momentum.

The space spanned by the coordinates and the momentum composnents is called Phase Space. A particular state of the quarks would be plotted (mentally) as a point in this 18 dimensional space.

It was invented, I think by Hamilton, the discoverer of quaternions and the Hamiltonian operator. As the system (quarks in a proton) evolves to new coordinates and new momenta, the corresponding point in phase space traces a curve, and much has been drawn from this fact.

Poncare asked does the state of any physical system always return, so that the curve in phase space is closed. Well no, but he proved that the curve of the entire history could eventually be contained in an arbitrarily small volume of the phase space. Nietsche picked up on this - the latest thing from science in his day - and developed his tragic doctrine of the eternal return.

Years later the chaos theorists came upon Poincare's result and saw that if the curve in all its looping length lay in a small volume then the returning branches of the curve, although not intersecting, would get arbitrarily close to each other. So close that no human wile could distinguish them.. Enter the butterfly effect.

There is much more to say about this; the phase space has been one of the work horses of classical physics.

Regards,
Dick


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