Explain the Symmetries
Ed Fredkin
>* If you believe that Nature is based on purely discrete degrees of
>freedom, how do you explain the following - apparently continuous -
>symmetries of the observed world?
In physics, every apparently continuous symmetry is associated, via
Noether's Theorem, with a conserved quantity. Examples include
translation and rotation symmetries which are associated with
conservation of momentum and of angular momentum. Noether's Theorem
itself is symmetrical in that for every conserved quantitiy there
should be a corresponding apparent continuous symmetry. In a totally
discrete system (discrete space, time and state) such as a Cellular
Automata, it is possible to have fundamental rules such that the
representations of physical quantities are conserved exactly. While
it is obvious that the CA lacks continuous translation and rotation
symmetries, it is possible for the informational process taking place
in the CA to have what we call "asymptotic translation and rotation
symmetries." Both symmetries would appear at some scale above that of
the lattice.
The answer to "discrete nature vs. continuous nature" must be based on
experiment. A prediction of Digital Mechanics is that every
apparently continuous symmetry of nature will someday be shown to be
violated by some experiment. As we have seen in looking at B and B
bar, not every such experiment will fit on a table top.
Ed F