ABSTRACT
Time, of itself, is dynamic and relational
in yielding globally synchronous time from locally asynchronous
ones, while both Newtonian absolute time and relativized time
in special and general relativity have taken the occurrence of
globally synchronous time to be an irreducible fundamental. Although
globally synchronous time has to be observed in the record of
finished events in any case, the occurrence of locally asynchronous
time constantly precedes the establishment of globally synchronous
one. Time in the making of the record differs from time in the
record. It is time in the making of the record that makes time
dynamic of itself.
KEYWORDS
Absolute time; asynchronous time; clocks; dynamic time; global; local; relativized time; synchronization; synchronous time
INTRODUCTION
Time is taken to be a fundamental attribute of any dynamics. Nonetheless, it remains as a perpetual enigma. A major difficulty with the notion of time rests upon the ambivalence in whether time is of itself dynamic or something else is dynamic in time. In this regard, contemporary physics serves as a witness to the impasse surrounding the issue of time. Many practitioners share with Davies (1974) the view:
"Present day physics makes no provision whatever for a flowing time, or for a moving present moment. ... Eddington has written that the acquisition of information about time occurs at two levels: through our sense organs in a fashion consistent with laboratory physics, and in addition through the back door of our minds. It is from the latter source that we derive the customary notion that time moves."
This view on time is in fact traced back to Kantian notion of time as an a priori category for our consistent perception of the outside world as paraphrased in Newton's words (Newton, 1687):
"Absolute, true and mathematical
time, of itself, and from its own nature, flows equably without
relation to anything external."
Newtonian absolute time that is declared
to flow uniformly in space in a globally synchronous manner has
already incorporated into itself a very specific form of dynamics
on how time could move. Any dynamics in Newtonian absolute time
is nested and grounded upon the one-level deeper dynamics of time
facilitating its uniform flow in a globally synchronous manner.
Curiously enough, however, Newtonian absolute time prohibits us
from asking how it could attain the uniform global synchronism
in the first place, while taking it for granted. This prohibition
of asking the likelihood of globally synchronous time is even
more reinforced in special and general relativity, despite admitting
the absence of any means for a simultaneous communication over
a distance, by imposing the articulated scheme of global synchronism;
the Lorentz transformation for special and the covariance for
general relativity. Globally synchronous time remains intact even
in relativity.
Globally synchronous time is thus
absolute and non-relational as dispensing with any material means
for accomplishing the global synchronism. Nonetheless, when it
is conferred upon empirical phenomena of material origin, globally
synchronous time is seen unidirectional and irreversible in its
flow. Empirical unidirectionality of the flow of time is associated
with those temporal asymmetries in the decay of the neutral K
meson, measurement in quantum mechanics, irreversible thermodynamics
or the second law, expanding radiation and no contraction, development
and evolution in biology, learning and memory in psychology, cosmic
evolution in the Big-Bang cosmology, and domination of black holes
over white holes (e.g., Davies, 1974). The apparent unidirectionality
of time in the empirical domain is unquestionably relational in
that globally synchronous time is related to material phenomena
in one way or another. In particular, we humans who have been
evolutionary latecomers in the empirical domain on the planet
earth are responsible for coining globally synchronous time. This
anthropic aspect of coming to terms with globally synchronous
time now invokes a convoluted reflection upon whether the time
itself might be intrinsically relational instead of being absolute
contrary to Newton's original
claim, because the Kantian justification of absolute time as an
a priori category for us humans is anthropocentric. Anthropocentric
time is fundamentally relational to what we humans are.
Relational aspect latent in what
one calls globally synchronous time is already implicit in general
relativity. The presence of closed timelike curves in the realm
of general relativity discovered by Gödel (1949) suggests
that unless globally synchronous time is constrained internally,
the forward causation along a closed timelike curve would come
to destroy the causation itself when it returned to the younger
stage while rounding the closed curve in the forward direction.
That is the grandfather paradox, referring to the scenario that,
for instance, a boy travels into the past and shoots his grandfather
at a time before he became father, ending up with no such boy
traveling into the past in the first place (Earman, 1995). Although
this paradox may look almost nothing but a science fiction, it
is quite pedagogical in pointing out the possibility that globally
synchronous time conceived in general relativity as a self-contained
theoretical framework could not remain internally consistent in
itself. General relativity may require some additional constraints
in order to remain consistent even in its theory alone. Globally
synchronous time in general relativity can be relational in observing
the global self-consistency at the same time.The likelihood of
globally synchronous time being relational is thus both empirical
and theoretical. We shall first examine a relational underpinning
of globally synchronous time in the empirical domain, because
an empirical discourse can minimize intrusion of theoretical artifacts.
CONSISTENCY IN RECORDS
At issue is whether the global synchronism
could remain irreducible in itself. In order to examine this problem
further, one cannot take a global perspective for granted any
more. Global stance makes the Cartesian split between subject
and object inevitable, and lets the descriptive object remain
globally immutable. Such an immutability of the global object
is, however, strictly of methodological origin thanks to the convention
that the descriptive subject may be entitled to make an access
to the descriptive object from its outside without disturbing
it even to the slightest degree. Needless to say, unless global
consistency of a descriptive object is guaranteed, no descriptive
enterprise could be sanctioned (even including the present article).
This observation comes to urge us to explore a possibility of
grounding the global stance and the accompanying Cartesian split
on a much deeper level, if any.
A likely candidate for facilitating
a global consistency and description is the presence of a record
of finished events as a time capsule (Matsuno, 1989, 1996; Barbour,
1994). For instance, a fossilized rock to a paleontologist looks
like a record of finished events frozen in a time capsule. The
fossilized rock remains immutable as it is. What concerns the
paleontologist is to figure out a consistent description of what
those fossilized rocks combined together are all about. The split
between the paleontologist and the fossilized rocks is guaranteed
because the latter are there in their own right irrespective of
whether the former is present on the scene. The split between
an onlooker and a time capsule does not require the Cartesian
split, though both may look similar. The similarity is, however,
superficial. The time-capsule split from the onlooker is not methodological,
but intrinsic to the notion of the time capsule itself in that
nobody who found time capsules is allowed to forge them. Although
the Cartesian split forces the subject to separate itself from
the object for the sake of its own sustenance whatever the object
may be, the time-capsule split from the onlooker begs the time
capsule to allow the onlooker to move around. The time-capsule
split makes the presence of an object a principal cause for the
participation of a descriptive subject, while the Cartesian split
lets the subject be the sole cause for establishing the presence
of an invariant object.
At this point, it should be emphasized
that the time-capsule split from the onlooker does not necessarily
imply that the onlooker could satisfactorily describe what the
time capsule is all about. Only the competent paleontologist can
do that. The descriptive burden within the time-capsule split
is on the descriptive subject, in sharp contrast to the Cartesian
case in which a complete immunization of the descriptive subject
to whatever object is methodologically guaranteed. Even if the
description completed in the scheme of the time-capsule split
may look similar to that obtained in the descriptive scheme of
the Cartesian split, the difference will be substantial. Those
descriptive subjects who failed in coming up with a consistent
description over a whole array of time capsules are not allowed
to participate in the completed description. In contrast, no such
failure is approved of by any of Cartesian subjects.
The situation is totally upside down.
If one starts from the Cartesian split, the global descriptive
consistency of the object will have to be respected at all cost.
No one is allowed to question how such a global descriptive consistency
could be guaranteed. Otherwise, the Cartesian split would fail.
If how the global descriptive consistency could come into being
becomes a matter of concern, on the other hand, the Cartesian
split is methodologically incompetent for the task. An alternative
can be the time-capsule split from the onlooker, because the presence
of an object suggests only a possibility of attaining its globally
consistent description. What is required is how to read out the
available time capsules in a mutually consistent manner, and no
more. Extrapolation of the fossil record into the future is strictly
prohibited. Nonetheless, one can cope with how the globally consistent
description could come into being while admitting successive alternation
of the participating descriptive stances and subjects. This viewpoint
may provide us with a likelihood for reading out any relational
aspect latent in globally synchronous time, because the latter
is unquestionably embodied in any time capsules available at the
present moment insofar as they can eventually be deciphered in
a mutually consistent manner.
LOCALLY ASYNCHRONOUS TIME
Globally synchronous time latent
in a globally consistent description resides in the contrast between
the presence of an invariant object to be described and the act
of describing the object in terms of linear linguistic strings.
The activity of forming, tracing, and processing a sequence of
linear strings in globally synchronous time is destined to preserve
the invariant nature of the object. Uniform progression of processing
linear strings while maintaining the descriptive object invariant
is certainly consistent with the linear progression of globally
synchronous time whose global synchronism comes to guarantee the
presence of the global object completely separated from the descriptive
subject. However, those descriptive activities yielding a globally
consistent description in the effect without presupposing any
privileged global perspective in the beginning cannot proceed
in globally synchronous time. When there is no privileged global
perspective to begin with, the resulting description would be
at most a consequence of the interplay among the participating
local perspectives. Time associated with each local perspective
is also local. Each local time is asynchronous, and there is no
a priori mechanism for their synchronization. Only those
local times that could succeed in synchronizing among themselves
would come to survive in the consequent global description that
is also accompanied with its a posteriori globally synchronous
time. Unless it is forcibly taken to be irreducible in itself,
globally synchronous time can be seen as a consequence of the
interplay among locally asynchronous times that are equated with
possible local perspectives of description internal to the object
to be described globally only in the effect.
Locally asynchronous time internal
to each local perspective of description is both transitory and
contingent, but still goes ahead of globally synchronous one.
Internal descriptions unique to local perspectives precede external
description of an invariant object in a global perspective. Each
internal description provides the context which others of the
similar nature would consult, and at the same time constantly
keeps modifying its own context so as to be incorporated into
a globally consistent description in the effect. Those internal
descriptions that would eventually fail in participating in the
finished global description are constantly wiped out. Locally
asynchronous times are thus seen as relational components upholding
globally synchronous time via intermediaries of internal description
of a local character.
The relational characteristic latent
in the globally synchronous time deciphered in terms of locally
asynchronous ones is, however, more than just the matter of description.
It is also dynamic in itself as an object of description. The
activity of internal description unique to each local perspective
manifests the capacity of awareness in that perspective. Awareness
as a fundamental attribute of measurement suggests that measurement
internal to material bodies of whatever kind may also be associated
with their locally asynchronous times (Matsuno, 1989, 1996). That
measurement internal to material bodies, or internal measurement
in short, is rendered to be an object of description again makes
both internal measurement and internal description indistinguishable.
Locally asynchronous time is intrinsic to internal measurement
as much as to any internal description in a local perspective.
This is consonant at least methodologically with globally synchronous
time in global dynamics, in which a globally consistent description
of the dynamics yields time no other than that of being globally
synchronized. The difference in the descriptive stance is, however,
significant.
In particular, the local-to-global
transformation in any dynamics described in globally synchronous
time is just a matter of integration. Any local dynamic laws parameterized
in globally synchronous time such as those expressed in differential
equations of local field variables are taken to yield a global
description through their integration. This likelihood of integration
rests in the premise of taking a globally synchronous time for
granted from the very beginning. Time in the global dynamics is
not dynamic, but simply a parameter in the dynamics. In contrast,
the local-to-global transformation in locally asynchronous time
is dynamic in letting time itself be involved in the dynamic motion
for generating a globally synchronous time. Time in internal measurement
is dynamic in locally moving and being moved by others. Such capacity
is primary to locally asynchronous time, whereas no agency in
globally synchronous time.
CONCLUDING REMARKS
Asking absoluteness of globally synchronous
time could be metaphysical at the best. Unless such metaphysical
stipulations are imposed forcibly, time remains relational and
accordingly locally asynchronous. Relational capacity latent in
globally synchronous time can be envisaged only if one views it
from the perspective of locally asynchronous time. This points
to a practical problem of how to synchronize two separate clocks,
a time-honored enigma first perceived by Gottfried Wilhelm von
Leibniz (Leydesdorff, 1994). He proposed only three alternatives
for the solution; through a material means, through an intervention
of immaterial agency, or due to the internal precision of each
clock. Although Leibniz was in favor of the third alternative,
the actual solution remains far from its completion. A major difficulty
with the notion of a clock is in its proclaimed global synchronization
without being equipped with the actual material underpinning.
Any clock presumes its global synchronization. A remedy for the
present malaise is appraisal of locally asynchronous time by letting
both globally synchronous time and clocks conceived there be a
consequence of the dynamic time that is local.
Describing any dynamics is an activity relating time to something else. Recognition of locally asynchronous time makes time itself relationally nested. Time capsules frozen in fossilized rocks when read out in a mutually consistent manner, are certainly the carrier of globally synchronous time, and the nested remnant of locally asynchronous time will be wiped out after the successful deciphering. However, there are also living fossils as evidenced in living organisms. What makes living fossils distinct from fossils in rocks is in the activity of making time capsules. In addition to time frozen in time capsules, there is also time making time capsules. It is time in the time capsule in the making that makes time intrinsically dynamic.
REFERENCES