Motion in Time
When the uniform outward motion at unit speed
that constitutes the natural reference datum of the physical universe
is modified by a displacement of the space-time ratio from a normal
unit value, the resulting speed is either 1/n or n/1. A speed such
as n/m is excluded for reasons set forth in item E-13
If the displacement is in time, the speed is 1/n,
and in this case the change in spatial location due to the motion
is less than that which takes place at unit speed, whereas the change
in temporal location remains the same as at unit speed. From the
standpoint of the natural reference system, therefore, this motion
has resulted in a change of position in space. We may thus say that
motion at speeds less than unity is motion in space.
Inasmuch as the limiting value of the quantity 1/n
is 1/1, or unity, it follows that motion in space cannot take place
at speeds greater than unity (the speed of light). This agrees with
observation, but in interpreting the observations it has hitherto
been assumed that all motion takes place in space, and
on this basis, it has been concluded that no motion can
take place at a speed greater than that of light. According to the
present findings, this conclusion is incorrect.
It is generally believed that the conclusion as
to the impossibility of exceeding the speed of light has been proved
by experiment. The truth is, however, that the experiments have
all involved acceleration of particles by electromagnetic forces,
and what the results of these experiments actually show is not that
speeds in excess of that of light are impossible, but that they
cannot be produced by means of forces of this kind. As
will be seen later in the development, the deductions from the postulates
arrive at this same conclusion, but they also show that this does
not preclude production of higher speeds by other means, specifically
the release of large concentrations of energy by explosive processes.
From the reciprocal relation between space and time,
it follows that the statements in item 2 are also applicable in
the inverse manner; that is, motion can take place at speeds greater
than unity (v = n/1) but motion at such speeds results in change
of position in time. It is motion in time, rather than
motion in space.
The limiting value of the quantity n/1 is 1/1,
or unity. Motion in time therefore cannot take place at speed less
than that of light.
We will now want to recognize that when the equation
of motion is expressed in the form v = s/t, it is an equation
of motion in space. If stated in terms of velocity, v and s
are vector quantities, whille t is a scalar quantity.
In the inverse form, the equation is e= t/s,
where e and t are vector quantities, when the equation is stated
in vector form, and s is a scalar quantity. This is an equation
of motion in time.
If we begin with a speed 1/n approximating zero,
and add successive increments of space displacement, the result
is an increase in speed as the time displacement n-1 is gradually
neutralized by the addition of space displacement. This continues
until unit speed is reached. In the inverse situation, beginning
with unit speed, further additions of the same kind go into a direct
increase of the space displacement, reducing the inverse speed until
that quantity finally reaches the vicinity of zero. Addition of
successive increments of time displacement to any existing speed
similarly moves it in the opposite direction, toward zero spatial
When the speed is negligible in comparison with
the speed of light, the value of t in the equation of motion in
space is the same as that applicable to the object such as a photon
that has no motion at all in the natural reference system. The magnitude
of this quantity (in relative terms) can be determined by observation
of any repetitive physical process of a uniform nature. Such a process,
or the object in which the process is taking place, is called a
clock, and the time thus measured is clock time.
This clock time is the time of the progression, the time which corresponds
to motion at the speed of light.
At very low speeds or velocities, the relative speed
or velocity is the sum, or vector sum, of the individual values,
inasmuch as the paths of the progression in time for the two objects
are essentially coincident. For speeds a and b in opposite directions,
the relative speed is a+b.
At speeds significantly above zero the moving
object travels a distance of s in clock time t. By reason
of the equivalence of the unit of space and the unit of time, it
also moves an amount t in time equivalent to s, independently
of the time of the progression, and this additional time t
must be taken into account in determining relative speeds or velocities.
For example, if a photon is emitted from a stationary source, the
relative speed is 1+0=1. If it is emitted from an object moving
with speed a in the direction opposite to that in which
the photon is moving, the space separation at the end of one unit
of clock time is 1+a. But the moving object has also traveled an
equivalent distance a in time, so that the time separation between
the photon and the emitting object is now also 1+a. The relative
speed is 1+a divided by 1+a, or unity.
The absolute speed of light is unityone
unit of space per unit of timeby reason of the postulated
reciprocal relation between the two units. It now follows from item
11 that the speed of light (or any other radiation) relative to
any reference datum is also unity. This is the relationship
demonstrated by the Michelson-Morley experiment, and postulated
by Einstein as the principal basis of his special theory of relativity.
In the theoretical universe of the Reciprocal System, it is not
a postulate but a deduction from the general postulates
of the theory.
The inaccuracies due to the use of uncorrected
clock time in applications involving high speeds are the essence
of the problem that led to Einsteins formulation of the special
theory, and the lack of recognition of the true nature of the problem
is the reason why it has not been possible to extend this restricted
theory to motion in general.