Re: Time and context

["Tim Gwinn" <***>]

Continuing my thoughts on time....

I've been pondering how else one might encode our dynamical universe other
than by a 3+1 dimension system of space+time. At the moment, I can't come up
with an alternative.

I keep coming back to : what is our basis for "time"? And it seems to be
that it rests on having some natural system (call it C) to act as a clock
with one or more observables {c1,...,cn}, and it is the measurements of such
an observable(s) which (when they generate distinct values) serve as labels
of time. We have no way of considering "time" other than by choosing some
system to act as C and choosing certain of its observables to act as the
{ci}, and choosing certain of the equivalence classes of those measurements
of the selected observables to serve as the "ticks" of time, and the
relations between those ticks to serve as the "units" of time.

(This is essentially also how Rosen describes it. As an aside, it also
appears that Aristotle had a roughly similar view of time [Physics IV.11] ,
where he states that "For that is what time is: number of change in respect
of the before and after. So time is not change but is that in respect of
which change has a number."  Except that for Aristotle, what he calls
"numbering", rather than being merely labels, becomes identified with points
on a line, and rather than this numbering scheme and the associated line
being merely abstractions, seems to have for Aristotle some real meaning:
"It is manifest then that time is a number of change in respect of the
before and after, and it is continuous, for it is a number of what is
continuous". This notion of the infinite continuous also leads him in the
next section to his proposal for an "unmoved mover" - a first cause.)

In this way, time is a rather arbitrary concept: it consists of a
subjectively chosen relationship between two or more natural system, one
being C, the clock system, and S (or {Si}), the system(s) under study.

It then occurred to me that our penchant for "equal units" of time is,
accordingly, also quite arbitrary since our choice of the clock system C is
arbitrary. Rather than choose one second as "the period equal to
9,192,631,770 cycles of the radiation which corresponds to the transition
between two energy levels of the ground state of the Cesium-133 atom" as the
NIST does, we could just as well have left it to be some fraction of a solar
day. Because of variations in the solar day, the latter would mean that the
meaning of one second would then vary as well.

There is nothing erroneous about the latter choice, it simply seems to us
cumbersome. Our preference for mechanistic systems leads us to find some
system C like the NIST definition which is 1) context independent, and 2)
has its basis in the microscopic. The latter is, I think, also part of a
reductionist viewpoint as well: the idea being that if we could just find
the most fundamental unit of time on the most fundamental microscopic level
of physical reality then we will find that all other more macroscopic
measures of time will be some multiple of this "primitive" unit of time. In
this way, perhaps a reductionist hopes to not only reduce matter to some
proposed fundamental entities, but also achieve a similar reduction of
dynamics on the basis of a proposed universal fundamental unit of time.
(This leads me to wonder if measuring/modelling the dynamics of biological
systems, or complex systems in general, would benefit from the use of
non-mechanistic clocks, which may have unusually varying and unequal "units"
of time.)

But if reductionism is false, then we cannot give any particular system C a
preferred status. There is no truly objective character to time. In this
way, we ought not make statements such as "the 'now' is always emerging",
because such a statement presumes a god-like objective perspective of
reality where time is endowed with metaphysical meaning beyond our reference
to some subjectively chosen physical local system C. "Now" only has meaning
with reference to some observer with some clock system C (which may be a
system internal to the observer).

Mach similarly says in "The Science of Mechanics":
"Nay, we may, in attending to the motion of a pendulum, neglect entirely
other external things, and find that for every position of it our thoughts
and sensations are different. Time, accordingly, appears to be some
particular and independent thing, on the progress of which the position of
the pendulum depends, while the things that we resort to for comparison and
choose at random appear to play a wholly collateral part. But we must not
forget that all things in the world are connected with one another and
depend on one another, and that we ourselves and all our thoughts are also a
part of nature. It is utterly beyond our power to _measure_ the change of
things by _time_. Quite the contrary, time is an abstraction, at which we
arrive by means of the changes of things; made because we are not restricted
to any one _definite_ measure, all being interconnected. A motion is termed
uniform in which equal increments of space described correspond to equal
increments of space described by some motion with which we form a
comparison, as the rotation of the earth. A motion may, with respect to
another motion, be uniform. But the question whether a motion is _in itself_
uniform, is senseless. With just as little justice, also, may we speak of an
"absolute time" - _of a time independent of_ change. This absolute time can
be measured by comparison with no motion; it has therefore neither a
practical nor a scientific value; and no one is justified in saying that he
knows aught about it. It is an idle metaphysical conception." [ch. II.VI.2]

Regards,
Tim