There are certain significant points of a general nature
that are immediate and direct consequences of the postulates. Before starting
to develop the more complex and specialized lines of thought leading to
the relationships in particular areas, we will take note of these general
- Neither space nor time has any independent existence. Each exists
only in association with the other as motion.
- But even though space and time do not actually exist independently,
we can isolate the space aspect or the time aspect of a particular
mation, or type of motion, and deal with it on a theoretical basis
as if it were independent. (This is the same thing that we are doing
in scientific practice when we work with such things as density, viscosity,
etc., even ghough they have no real existence, and are only
relations between certain realities).
- All units of space (or time) are alike, since each unit is equivalent
to a unit of time (or space).
- the only feature of either space or time that enters into the equation
of motion is the numerical value. The reciprocal relation is therefore
a general relation. Space and time are indistinguishable, except for
the fact that one is the reciprocal of the other.
- For this reason, the properties of one are likewise properties of
- Time, as well as space, is three-dimensional.
- More space in any physical phenomenon is equivalent to less time,
and vice versa.
- For every physical phenomenon, there is another phenomenon which
is an exact duplicate, except that space and time are interchanged.
- Motion can take place in time as well as in space.
- One of the kinds of motion that is possible within the limitations
is uniform translational motion in a straight line.
- Each unit of this motion involves a unit of space and a unit of
time. For convenience, let us call these units absolute locations
in space and time respectively, and let us call the combination of
a location in space and a location in time, a location in space-time.
Inasmuch as a single unit of space is the reciprocal of, and therefore
equivalent to, a single unit of time, it follows that when a motion
at unit speed has continued for a time x (that is, the absolute location
in time has moved forward x units in the context of a stationary reference
system), the corresponding absolute location in space has also moved
forward (outward in the direction of greater values) x units.
- The foregoing applies to every absolute location in space-time,
and we can therefore say that each such location is progressing outward
away from all other locations at unit speed. The basic framework of
a universe of motion is thus continually expanding (with respect to
a stationary system of reference) in a manner analogous to the expansion
of a balloon that is being inflated.
- We will call the uniform increase in space and time, with respect
to a stationary reference system, that takes place at unit speed the
progression of space and time, respectively. When both are
to be considered together, we will speak of the progression of
space-time. Every location in space-time, and consequently every
object that occupies such a location, is subject to the progression.
The progression of space-time is therefore one of the basic motions
(or forces) that determine the course of physical events.
- Even though space and time exist only in discrete units, according
to the postulates, the progression is a continuous process, not a
succession of jumps, and there is progression even within the units,
simply because these are units of progression, or motion.
Consequently, specific points within the unit--the midpoint, for example--can
be identified, even though they do not exist independently.
As an analogy, we may consider a chain. Although the chain exists
only in discrete units, or links, we can distinguish various portions
of a link. For instance, if we utilize the chain as a means of measurement,
we can measure 10½ links, even though a half link would not qualify
as part of the chain.
- If noting other than the continous expansion existed, the universe
would be merely a featureless uniformity. In order that there may
be physical phenomena that can be observed or measured, there
must be some deviation from this one-to-one space-time relation, and
since it is the deviation that is observable, the amount
of the deviation is a measure of the magnitude of the phenomenon.
The omnipresent expansion at unit speed therefore constitutes the
natural reference system, the datum from which all physical
NOTE: This is a significant point. We are accustomed to relating physical
phenomena to a stationary frame of reference. If an object has no
capability of independent motion, so that it must remain in its original
location unless acted upon by some outside agency, it has been assumed
that this means the same location with respect to a stationary reference
system. But, there is no reason why nature must necessarily conform
to the current beliefs of the human race, and the foregoing statement
of the implications of the fundamental postulates shows that a universe
of motion, of the kind specified in those postulates, does not
so conform. The natural system of reference for such a universe
is an expanding system in which each location is moving outward from
all others at unit speed. On this basis, an object with no independent
motion does not remain at rest with respect to a stationary reference
system, but moves outward at unit speed. The stationary reference
system to which motion is customarily related is not a natural
- A stationary three-dimensional system of reference may be defined,
either in the theoretical system or in the actual physical universe,
by arbitrarily assuming some location or physical feature to be stationary.
For most everyday purposes, positions are referred to the surface
of the earth in the immediate vicinity. Where it is necessary to take
the rotation of the Earth into account, the Earth's center is assumed
to be motionless. For some astronomical purposes, the sun is taken
as the stationary point of reference, while in other applications,
the astronomers utilize the center of the Galaxy. In this work, the
term location (as distinguished from absolute location)
will be used to designate position with reference to some stationary
system of this kind.
- Inasmuch as the space progression is simply outward, without any
inherent direction, its direction with respect to any stationary system
of reference is determined by chance. If a location y with reference
to a stationary, three-dimensional coordinate system is in coincidence
with absolute location Y at a given point in the progression, then
when x additional units of time have elapsed, absolute location Y
will have moved x units of space outward from location y, and will
be somewhere on the surface of a sphere centered at y.
- Representation of changes in absolute location in a three-dimensional
reference system is limited to translational motion and to the translational
effects (if any) of other types of motion.
- Since the movement of the absolute locations, as seen in the context
of a stationary reference system, is linearly outward without any
other qualification, except that imposed by the reference system,
the amount of this movement is inherently a scalar quantity.
It becomes a vector quantitythat is, it acquires a directiononly
by virtue of its relation to the stationary reference system.
- In current practice, the change of position resulting from motion
is expressed in terms of displacement, a vector quantity.
In this work, we will be dealing, to a large extent, with changes
of position that are either inherently scalar, as indicated in Item
19, or cannot be represented in a three-dimensional coordinate system.
For this reason, we will use the terms movement and change
of position, and will not employ the term displacement
in this sense. This term will, however, be utilized in a totally different
application, which will be explained later.