# Time as a Lattice of Partially-Ordered Causal Events or Moments

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On Saturday, August 31, 2002, at 11:31  PM, Brent Meeker wrote:```
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> Time is a construct we invented to describe things.  Most
> basically we use it to describe our sequence of experiences
> and memories.  We feel hot and cold, but we needed to
> quantify hot and cold and give them operational definitions
> in order make definite predictions about them. So we
> invented temperature and thermometers.  For mechanics we
> needed a quantified, operational definition of duration -
> so we invented time and clocks.
>
> Besides psychological time,there are at least three
> different possible definitions of time used in physics  What
> they all have in common is that they assign numbers to
> different physical states, i.e. they index different states
> into some order so that this sequence of states can be
> compared to that sequence of states.

I don't have a comprehensive theory of time, but I am very fond of
"causal time."

Picture events as a series of points in a lattice (a graph, but with
the properties I talked about a while back in a post on
partially-ordered sets). Basically, a lattice of events where there is
at most one edge connecting two points. (There are formal properties of
lattices, which the Web will produce many good definitions and pictures
of.)

Lattices capture some important properties of time:

* Invariance under Lorentzian transformations...any events A and B
where B is in the future light cone of A and A is in the past light
cone of B, will be invariantly ordered to all observers.

* The modal logic nature of time. Multiple "futures" are possible, but
once they have happened, honest observers will agree about what
happened. (Echoing the transformation of a Heyting algebra of
possibilities into the Boolean algebra of actuals...this sounds like it
parallels quantum theory, and Chris Isham and others think so.)

* Personally, I believe the arrow of time comes from more than
statistical mechanics. (I believe it comes from the nature of subobject
classifiers and the transformation Heyting --> Boolean.)

* I am indebted to the books and papers of Lee Smolin, Fotini
Markopoulou, Louis Crane, Chris Isham, and several others (Rovelli,
Baez, etc.) for this interpretation.

None of us knows at this time if time is actually a lattice at Planck-
or shorter-time-scale intervals. But discretized at even the normal
scales of events (roughly the order of seconds for human-scale events,
picoseconds or less for particle physics-scale events), the
lattice-algebraic model has much to offer.

* I don't see any conflict with Huw Price, Julian Barbour, and others
(haven't read Zeh yet), though I don't subscribe to all of their
idiosyncratic views.

--Tim May

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