Abstract
In the following post I propose a definition of the concept of Time as related to causality. The definition that I propose in the first section disregards the effects of relativistic and quantum theories. Otherwise I believe it is clear and very sensible. The second section deals with the discrepancies in this definition due to those effects. The third section attempts to resolve these problems and suggests a modification of the definition in general terms (in the belief that in essence it is still correct), not very successfully - however it invites all readers to contribute their ideas to this discussion in the hope that a more convincing answer would be found.
A Definition of Time Disregarding Relativistic and Quantum Physics
In the following discussion I use the term Time (uppercase
T) for what is known as the time axis, and time (lowercase t) for time
periods (durations) and for specific moments, dates, etc.
Disregarding the non-deterministic approach of quantum physics and
the relativistic dilation of time (I shall deal with them in the next section),
I propose the following definition of Time:
Definition:
Time is the course of universal causality.
I expect that this statement raises the following questions:
1.
What
is the basis for this definition?
2.
Is
this definition of Time comprehensive, i.e. does it cover all aspects of Time?
I shall try to answer these questions.
First, let me discuss what I call the principle of universal causality, which
is the basis for my proposal.
In essence, causality is a generalization of Newton's first law[1]. In
other words, Newton's first law is a private case of causality.
The principle of universal causality as I define it states that at
any moment, the overall state of the universe is the inevitable result of the
immediately prior overall state of the universe. This principle is the basis
for what we perceive as the continuous sequence of states through which all
events proceed. If there were no causality, it would be impossible for events
of any kind, including our existence or the existence of anything at all, to persist
along any interval of time, no matter how short except for zero. Causality, the
principle of cause and effect, determines the temporal order of sequential
events or states of the same event. Hence, causality determines what we
perceive as the "direction of Time". (Actually, Time doesn't move or
change and has no direction. What changes is the totality of events in the
universe, along what is known as the "time axis"). Since it is
logically impossible for cause-effect relations between events or states of the
same event to be interchanged, the so-called "direction of Time"
cannot be reversed.
We cannot imagine the universe without causality. Even the
imaginary concept of a completely static universe, in which absolutely nothing
occurs, is ruled by causality. That is because we cannot imagine the
nonexistence of time and therefore our imaginary static universe persists along
time. At any moment, it cannot be but in the same state as it was in the
immediately prior moment and therefore its state is inevitably the result of
that prior state. Without causality, the totality of momentary states of the
universe (if such could be imagined) would be a random, unordered set of unrelated
states without consecutive order. Hence, Time would have absolutely no meaning.
Therefore I conclude that causality is the factor that makes up Time, which in
turn serves as the course along which causality proceeds.
Since we cannot imagine the universe without causality, we take the
existence of causality for granted. It seems to be so self-evident that we
don't generally pause to wonder what has brought about causality. Was it created by the will of God? Is it the
result of sheer luck? Or perhaps it exists by elimination, since without it the
existence of all things would be impossible (somewhat equivalently to Darwin's principle
of natural selection that eliminates all but the fittest).
Now for the second question – "is my statement a comprehensive
definition of Time?". I believe it is
(disregarding relativistic and quantum effects), since causality not only
determines the sequential order of all events but also the rate at which each
event proceeds. The totality of universal events include among others the
procedure of every device that measures time (be it a clock, a timer, a
stopwatch, whatever) and since causality governs the rate of these instruments
it is the effector of what we perceive in our imagination as the rate at which
Time proceeds (As stated above, Time doesn't proceed but we imagine that it
does).
Effects of Relativistic and Quantum Theories
The discussion so far was based on assumptions that disregard the
approach of modern science with regard to causality. According to the theory of
relativity, an event occurring at a certain point in space can affect the
conditions at another point only after the time required for light to travel
the distance between the two points, no matter how short this distance is. This
period of time must be greater than zero unless the two points in space exactly
coincide (e.g. if they are one angstrom apart – the diameter conventionally
attributed to a hydrogen atom – it would take light approximately 3.336x10-19
seconds to travel the distance – not a big thing yet not zero). Thus, the principle of universal causality mentioned above (that states
that at any moment, the overall state of the universe is the inevitable result
of the immediately prior overall state of the universe) is imprecise. In fact, the term "overall state of the
universe" assumes absolute universal simultaneity whereas the theory of
special relativity implies that simultaneity of
events in space is relative, not absolute, and depends upon the frame of
reference of the observer (i.e. events that appear simultaneous to a
"stationary" observer appear to a "moving" observer to
occur at different times).
That was one blow to my definition. To make things worse, quantum
theory delivers another blow. Heisenberg's uncertainty principle states that
the locality and momentum (velocity x mass) of any subatomic particle are
inherently uncertain. Specifically, the principle states that the product of
the two uncertainties is equal to Planck's constant divided
by 2π, an extremely tiny number but not zero.
Are these apparently minuscule effects slight enough to be regarded
insignificant? The answer, unfortunately for my argument, is "No".
Take for example a toss of a die
(nothing mortal, just a numbered cube). Is the result of the toss absolutely determined
by its precise position in the hand of the player, by the precise movement of
his (or her) hand, by all the environmental conditions that the die underwent from
the moment it left the player's hand until it came to rest and by all other
thinkable parameters? Assume that the die, just before it came to rest, was very
nearly balanced on an edge with almost equal chances to land on either one side
or the other. Suppose that though highly
improbably, the difference between the two chances happened to fall within the
limits of the uncertainty principle (indirectly, meaning that somewhere along
the process the uncertainty in the position and/or momentum of the die lead to
the uncertainty of the final result). That means, unfortunately for my case,
that the result is indeterminate until it happens - practically, not just
theoretically. According to the rules of statistics, such indeterminate instances
occur very often because of the practically infinite amount of events that
occur around us all the time.
So, my definition of time seems to be severely crippled. But it's
not dead yet, all it needs is to be modified adequately to overcome the
quandary. Can I do it? Well, sort of.
My Attempt to Resolve the Predicament
I assume that in the microcosm of elementary particles indeterminism
prevails (I dare not claim otherwise). This means that causality is not
perfect. It may diverge minutely from its course (Time by my definition). But
Time by my definition is not an independent entity. It is an attribute of
causality and would be inexistent without it. So, the imperfections of
causality are manifested in an apparently slight lack of smoothness of its course,
Time. More specifically, wherever (or rather whenever) causality reaches a
point of uncertainty, something happens to the smoothness of Time. Some highly
esteemed scientists today believe that whenever two or more results are
possible, Time and the Universe with it split into multiple universes. My
humble opinion, assuming that the multiple-universe conjecture is wrong, is
that since one unique continuation of the cause-effect process occurs in all cases,
the worst thing that can happen to my definition is that sometimes processes
are not absolutely reproducible. Whatever happens to the smoothness of time is
insignificantly small.
Until I or anyone else finds a better resolution, let's leave it at
that.
As for the relativistic effect, the dilation of time causes our classical
concept of time (the letter t that appears in physical formulas) to be
approximate, with growing inaccuracy as speed increases. Using the correct
(relativistic) formulas we still obtain the proper cause-effect relationships,
but the time periods between cause and effect are relative, not absolute. This
means that Time, being the course of causality, is affected by the relative velocity
between the two frames of reference, that of the cause and that of the effect. The
definition of Time as the course of causality thus needs to be modified to take
into account the possible distortion due to the relativistic time dilation.
Finally, I need to resolve the inconsistency between the notion of universal
causality and special relativity. Universal causality assumes absolute simultaneity
in the overall state of the universe at each instance of time whereas special relativity
claims that simultaneity at different locations is relative. Cause-effect
relations are only possible between events that occur at times that differ more
than the period of time at which light can travel between their locations.This inconsistency requires a replacement of the term "universal causality" in my proposed definition to a more flexible term, which at present I fail to find.
Despite the discrepancies mentioned above, I believe that in
essence my definition of Time is correct though it requires reformulation to account for these discrepancies. I need to think about it. Suggestions by
readers will be welcome.
[1] Newton's first law of motion (also
known as the law of inertia) states that the velocity (speed and direction) of
a body remains unchanged unless a force is applied to that body.
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