A
REVALUATION of
TIME
(and
VELOCITY)
by Miles Mathis
2002
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 show in other papers that Einstein hid his
assumption very well, but 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, assures 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 ratio of kilometers to
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.
The smartest scientists
have understood this, even when they were a bit unclear about
Relativity as a whole. Richard Feynman, for instance, who many
would call the smartest physicist since Einstein, explicitly
believed in what I am calling local time and distance. On page 94
of Feynman Lectures on Gravitation, he talks of "absolute
time separation" and "proper time". This was his
admission not only of local measurement, but of the universal
equivalence of local measurement. He understood that you cannot
link various systems with any transforms whatsoever unless you
assume the equivalence of all local time.
Four-dimensional Space
Minkowski is
known as the father of four-dimensional space. In his theory, time
becomes a fourth dimension, mathematically equivalent to x, y, and
z. In fact, by setting his quadratic equation equal to 1, instead
of to zero, Minkowski implied that time travels at a right angle
to all three of the other dimensions. It was therefore equivalent
to a spatial vector, travelling orthogonally. It so doing, it
created what mathematicians call symmetry. The t variable could
then be incorporated into matrices as an absolute equal to the
other distance variables.
This theory was appealing to
those who are attracted to mathematical esoterica, but
unfortunately it is completely false. As I have shown, time is a
measurement of movement. Without movement there is no time. But
this movement already has a direction, determined by x, y, z: it
cannot be given a secondary vector. All motion is a vector, and
that vector must coincide to some distance vector within the 3-d
continuum x, y, z. So to state that time has a vector outside this
continuum is false. If time is a measurement of motion and all
motion is contained in x, y, z, then time cannot be outside of or
external or superadded to x, y, z.
Nor can it be thought
of as mathematically symmetrical to the three distance variables.
It is a second measurement of distance, as I have shown, so it can
certainly be thought of as a distance variable. But it is not the
same sort of variable, theoretically. It is different because it
is not really a variable at all. It is a postulate. You may not
include it with the others simply because the others rely on it.
Meaning that you may not have all four variables as variables at
the same time. If time is unknown at the same time that x, y, and
z are unknown, then all four are unknowable. If x, y and z are
thought of as fields, then t is a subfield. If x, y and z are
thought of as axes, then t is a defining axis or "axiom
axis". It is not strictly equivalent to the other three.
Including it in matrices in the way that is now done is therefore
dangerous. Theory is lost, postulates are hidden from view, and
mathematical errors are the consequence.
If that critique
of Minkowski was a bit abstract for some, think of it this way:
Velocity is distance over time, right? Distance and time are both
vectors. They have direction. Well, you can't put orthogonal
vectors in a ratio or a fraction and expect to get a value for
your velocity vector. If you have one vector over another, and the
vector in the denominator is at a right angle to the vector in the
numerator, you have a serious problem. One of the first rules of
vector algegra tells us that you can't just divide one number by
the other; but this is what happens every time we find a velocity.
We simply divide the distance by the time. Which means one of two
things must be the case. Either all our historical velocities are
wrong, or Minkowski is wrong. The time vector is not at a right
angle to any possible distance vector.
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.
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mathematicians on the operational measure of time, and on the t
variable in the Lorentz transformation equations of special
relativity click
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