[time 713] Re: [time 707] Symmetry => Dynamics

stephen p. king (stephenk1@home.com)
Wed, 08 Sep 1999 13:17:08 -0400

Dear Matti,

Matti Pitkanen wrote:
> > Matti, are you saying that the dynamical law is a priori to time? How?
> [MP] Dynamical laws in sense of standard physics by definition assume
> geometric time as an additional dimension. In QM Hamiltonian
> is Lie-algebra generator of time translation symmetry and Lie symmetries
> require manifold structure and metric.

        So, are you saying that we have to have an a priori defined manifold
with a metric on it for Lie group symmetries to exist? Could we just say
that they are "co-existent"; this is a "chicken or egg" problem to me!
> One can also consider formulations in which one has just a sequence of
> events governed by some rule. The proposal of Smolin for spin network
> dynamics is good example. The concept of energy becomes however
> problematic since energy is symmetry related concept and symmetry assumes
> geometric time plus time translation symmetry.

        Is your "geometric time" the parameter of variation of the
differentiable manifold and the "symmetry" is given by the invertibility
of this parameter?

> The nondeterministic dynamics of quantum jumps partially dictated by NMP
> is second example.

        Again, I must protest since I do not understand what "NMP" is!
> What supports the concept of geometric time is the success of
> quantum field theories: Hamiltonian is derived
> from action principle as generator of time translation symmetry
> and yields S-matrix which describes this world excellently!
> Note the beauty and economy of all this: symmetry determines dynamics!

        I fail to see how the particular symmetry that is observed was selected
in the first place!

> > I see the "dynamical law" as defining a pattern of behavior of a system
> > as it evolves in its time. When we say that we localize it in time, we
> > are refering, to be consistent, to the time of the localizing agent, not
> > the system in question's time. There is no "time" for all unless we are
> > merely considering the trivial case when all systems are synchronized...

        Does this mean anything to you?



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