Stephen P. King (stephenk1@home.com)
Mon, 04 Oct 1999 21:32:39 -0400
Dear Lance and Friends,
I have been thinking hard about the meaning of clocking and am always
arriving at the notion that clocking is the invertible mapping of a set
of objects to a set of representations. This seems to follow from the
naive definition in conventional physics of a clocking as the mapping of
the set of space-time events to the set of numbers R^1.
If we are to consider the possibility that each LS is an observer and
that the observations of LSs are of particles as external centers of
mass of other LSs, then would there not be a space-time like
relationship between the particles that are the objects of observation
of any given LS? Could we define "events" in terms of LSs such that a
conventional clocking, as defined above, can be recovered under specific
circumstances?
The key difference I see in local system theory is that it denies the
possibility of unique a priori and absolute transitivity orderings of
events for all possible observers. This would be problematic unless we
can redefine causality, e.g. the transitivity operation, such that it
would be a constructive process.
I am advocating the idea that the behavior of information that is
implicit in the configurations of particles that are observed by an LS
is just as important as the behavior of the particles themselves. I say
configuration A of particles causes (->) configuration B iff (if and
only if) the information implicit in B (B*) logically entails (<-) the
information implicit in A (A*). We then define transitivity in this
context as:
A -> B & B -> C == A -> C iff A* <- B* & C* <- B* == C* <- A*. (1)
The mapping discussed above shows up when we set up (1) as a
commutation diagram:
A -> B B -> C A -> C
| | & | | == | |
A* <- B* B* <- C* A* <- C*
The horizontal lines represent the mappings...
I hope my abuse of notation is forgivable. ;^) Does this idea make
sense and, even more importantly, is it helpful?
Another related idea is that when we consider all physical processes as
generating entropy and the idea that "in a closed system the total
entropy plus information remains fixed" implies that the selection of
the "next" event is a computation of the logical precedence of the
information content of the event's "prior". This amounts to saying that
the evolution of matter (towards complete thermodynamic equilibrium) is
dual to the evolution of information (towards a complete
equidistribution of information).
Kindest regards,
Stephen
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