|
A Revaluation of Time
(and
Velocity)
by Miles
Mathis
I would like to offer here a definition of time that is
as little abstract as possible. What we want, I think, is a
definition that describes time as something that we measure. Only
that. One might call it an operational definition. This
definition is not an explanation of what time means (or has come to mean)
philosophically or epistemologically. It is an explanation of what
time is in our experimental or everyday use of it.
I
maintain that time is simply a measurement of movement. This is its
most direct definition. Whenever we measure time, we measure
movement. We cannot measure time without measuring
movement. The concept of time is dependent upon the concept of
movement. Without movement, there is no time. Every
clock measures movement: the vibration of a cesium atom, the swing of
pendulum, the movement of a second hand.
In this way time
can be thought of as a distance measurement. When we measure
distance, we measure movement. We measure the change in
position. When we measure time, we measure the same thing, but give
it another name. Why would we do this? Why give two
names and two concepts to the same thing? Distance and Time. I
say, in order to compare one to the other. Time is just a second,
comparative, measurement of distance.
~~~~~~~~
The
measurement of time is necessary to the measurement of velocity. It
may be that time was not even "invented," in the modern sense, until
someone first thought of the idea of velocity. Velocity is the
measurement of the change in position of one thing (the object in
question) relative to the change in position of another thing (the cesium
atom, or the pendulum, etc.). Once you have conceived of the
idea of velocity in this way, you realize that it can be measured in only
one way: Compare the unknown movement to a known movement.
That is, find something in your world that moves as uniformly as possible,
and let that be your clock. Then compare your unknown movement to
the movement of your clock. That is what velocity is.
You may
say, how can I know that something moves "as uniformly as possible"
without already having an idea of time? You cannot. But I
maintain that this idea of time-- as simply a commonsense idea of
uniformity of movement-- is the only operational idea of time we have ever
had. The initial idea of time, historically, or instinctively, is
the idea of uniform movement. The first clock must have been chosen
on this basis, just as the very latest atomic clock is chosen on this
basis.
Also notice that there has never been any way to test
the uniformity of a clock, except relative to another clock. The
first clock must have been chosen based mainly on instinct. The
ancient who chose the swinging pendulum because it swung the same number
of times per day was comparing it to another clock-- the sun. If he
was smart he counted his pendulum swings from sunup to sunup, rather than
sunup to sundown, and so avoided the variation in length of
daylight. And if he was very smart, he continued to look for even
better natural clocks to fine-tune his measurements by. But
notice that as long as the sun was his standard, he had to assume that the
sun was a good clock-- he took for granted that one day was the same
length as the next.
In judging the uniformity of natural
clocks, like the sun or the stars, our ancient would resort to comparing
them to his pendulum clock. How did he know that the sidereal clock
was more accurate than the solar clock? By comparing it to his
pendulum. He corrected his pendulum by the sun and corrected the sun
by his pendulum.
In this way you can see that there never was an
idea of "absolute time." Time was always a relative
measurement. It had to be. It was relative to a given clock, a
clock chosen mostly by instinct. For there was never any way to
prove that the given clock was absolutely uniform. It was only more
uniform relative to clocks that were already relative to other
clocks.
So time is not a measurement of "time." Time
is a measurement of the movement in or on a given clock. And this
given clock is uniform only by definition. It is uniform relative to
a standard clock. One that has been defined as uniform.
This standard clock cannot be proven to be uniform. It is only
believed to be more uniform, based on previous definitions and previous
clocks.
In this sense, time is not absolute. There is not,
and cannot be, a clock that is known to be absolutely uniform.
This is a statement of logic. A clock known to be absolutely uniform
is a reductio ad absurdum. For us to know the clock was
absolutely uniform would require us to have a previous clock by which to
measure it. A clock may be defined as absolutely uniform. That
is, we may decide, quite freely, to define some vibration of the
background radiation of the big bang to be absolutely uniform. But
we cannot know the truth of that definition.
Every
measurement of time is a relative measurement, in this sense. It is
relative to a standard clock, defined as standard. Time is also a
relative measurement in the sense that it is dependent upon a measurement
of distance. The time concept is relative to the distance
concept.
~~~~~~~~
Now that we have an operational definition
of time, we may proceed to an operational description of the calculation
of velocity. As I said above, velocity is a relative
measurement. It is the change in position of an object relative
to the change in position of (the internal workings of) a clock.
We usually write this as distance-over-time. d/t.
I maintain that this is exactly the same as distance-over
distance. If we had written miles per hour, we might have written
miles per miles. For we might have remembered that our clock is a
little something in movement, and the movement inside the clock might be
expressed in our denominator just as easily as the "time" on the
clock. A pendulum travels some distance each second, and so
does a cesium atom or a pulse of light. In calling the distance
traveled a "second" instead of a mile or a foot or an angstrom, we are
simply choosing terminology that suits us. But the fact remains: in
terms of measurement, what is being measured by a clock is
distance.
In the calculation of velocity, one makes one basic
assumption. One must assume that there is indeed a relationship
between the measurement of the object in question and the measurement of
the clock. If I am comparing two things, I must assume that the two
things are comparable. I must assume that the distance I am
measuring with my object is the same sort of distance I am measuring with
my clock. In my velocity equation, what I have is really
distance-over-distance. For the equation to make any sense at all, I
must assume that the concept in the numerator is equivalent to the concept
in the denominator. That is, I must assume continuity. I
must assume that the measuring rod of the object-distance is the same
measuring rod of the clock-distance. I must assume that the
background is the same for the clock and the object. In mathematical
terms, I must assume that the clock and the object are in the same
co-ordinate system. If they are not, then it would be foolish to
compare them. It would be foolish to put one over the other in an
equation.
Think of it this way. A velocity equation
states that the object (of the numerator) moves a certain distance
relative to the movement of another object-- the workings of a clock (the
denominator). "Relative to" means that the first thing is related to
the second thing. If they are in different co-ordinate
systems, they are not related to eachother, and it would be senseless to
put them in the same equation.
So the basic assumption of a
velocity equation is that the object and the clock are related. They
are in the same co-ordinate system. Or, to put it another way, space
is continuous from the object to the clock. If it were not,
there could be no velocity equation.
If time is actually a
measurement of distance, then wherever space is continuous, time is also
continuous. This being true, it follows that wherever there is an
attempt to measure velocity, there is an assumption that time and space
are continuous. There is an assumption that all local measurements
are equivalent. Without this assumption, no equations are
possible.
In this sense, time is absolute. Time
is assumed to be invariable from point to point, throughout space.
This assumption is what allows for the measurement of velocity.
[This says nothing about measuring moving clocks. As I have shown in
another place, the findings of Einstein's Special Relativity are valid, in
the main. But in order to calculate the slowing of moving clocks,
from a distance, one must assume they are not slow,
locally.]
~~~~~~~~
It is said that Einstein did not make
this assumption-- of absolute time-- when he began his calculations in
Special Relativity. It is said he did not make the Newtonian
assumption of absolute and continuous space and time (one big co-ordinate
system); nor did he make the assumption in a more limited sense, as I have
above. He did not assume the equivalence of local time. It is
said that he proceeded without this assumption, and by proceeding without
it proved that local time, in my sense, is meaningless. According to
the canon, one may now speak of ones own local time. But speaking of
the local time in another place is a faux pas.
I will show that
Einstein hid his assumption very well, but that it was there
nonetheless. What is the only assumption that most people will admit
that Einstein carried into Special Relativity? What was his "only"
given? The constancy of the speed of light. But if
the speed of light is the same in every co-ordinate system, then that, by
itself, implies that the local time of every co-ordinate system is equal
to that of every other. If light goes 300,000 km/s in every system,
then the kilometers and the seconds in every system must be equal.
Either that, or the statement "light has a constant speed" has no
meaning.
If you say, "Yes, light has a
constant speed, but the time in another system may be different than
ours," then I don't see what light has a constant speed means. It
does not matter that their time is "different than ours." When they
measure the speed of light, they will not be using our watches. What
their watches are relative to ours will not enter into the velocity
equation they use at all. When they measure the speed of light, they
will divide the distance light goes in their system by the distance their
little cesium atom wobbles. The relationship of light to a
cesium atom in their system is the same as in ours, so they will not only
see the light go the same speed, they will see it go the same distance we
do. Notice this has nothing really to do with cesium atoms. It
has to do with the relationship between distance and time in their
system. You say "their time is different." But what does that
mean? If their time is slow relative to ours, it surely doesn't mean
that they will measure it differently. What I mean is, Einstein said
they will get the number 300,000 km/s, just like us. You say,
perhaps their second is slower, so that the distance must be shorter than
300,000 kilometers in order to equal the same speed. But this is not
looking at it from their perspective. They are not going to divide
the distance they see light travel by one and a half pendulum swings, for
instance, or by 1.5 seconds, or by some extra number of cesium
wobbles. They are going to divide the distance by one second, just
like we do. And they are going to call it one second, no
matter what you or I think of the matter-- no matter how long or short
that second looks to us. Einstein says that according to them, light
will be going 300,000 km/s. They define one second as being one tick
of their own clock, just like we do. Therefore, they will see light
travel 300,000 kms during that tick.
It is
true that if we could see the light in their system from our system (which
we can't-- by the time we see it, it is in our system) it would appear to
have traveled a shorter (or longer) distance-- since those clocks over
there are slow (or fast). But that is not the question. The
question is what do they see. They see the same thing we do.
This is not of the nature of a guess. It is a deduction. If
the speed of light is given as a constant in every system, then every
system must have equivalent local time.
Conclusion
I was asked by a
reader of another paper whether I ultimately thought time was absolute or
not. You can see that this is not such a simple question. I
had to ask, "absolute in what sense?"
As I have shown, time
is assumed to be absolute in the sense of being equivalent from one system
to another. We must make this assumption in order to calculate
velocities, among other things. This does not mean that it is
absolute, of course. It means that we must define it as
having continuity from our immediate vicinity to any vicinity we want
information about. If we do not assume time and space
continuity, we cannot hope to build meaningful equations. A universe
without continuity is a universe without equations, without mathematics,
and without science.
But time is not absolute in the sense of
absolutely precise, or absolutely known. It is a concept based on
the idea of uniform movement, but the concept allows of only relative
measurement. A movement can be known to be more or less
uniform, but not absolutely uniform.
Likewise, time is not
an absolute in the sense that many "classicists" appear to mean when they
mean by it that Special Relativity is wrong. Objects moving at a
distance, including of course clocks, look different than objects at
hand. And velocity and acceleration influence the appearance of
distant objects in quantifiable and dramatic ways. Time dilation is
a fact. A poorly interpreted fact-- up to now-- but a fact
nonetheless.
Time is also dependent upon, and therefore relative
to, movement. In a sense, time is nothing. Or it is
nothing but a second measurement of movement. Displacement is
movement. Time is movement. Time is displacement. Time
is the displacement of the reference body. |
|
