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 speed.

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 unity—one unit of space per unit of time—by 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 Einstein’s 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.