REFERENCE SYSTEMS As reported in the October 1977 issue of The first point to be noted is that whether or not an object
is in motion, and the amount of that motion, if any, depends on the reference
system. An object which is stationary in one reference system is moving
in any reference system that is in motion relative to the first system.
Whether we see the motion of the object as a complex motion, a simple
motion, or no motion at all depends on the reference system to which we
relate it. One of the important findings of modern physics, confirmed
by the Reciprocal System, is that there is no Another significant finding is that a reference system
for motion necessarily includes a time datum as well as a space datum.
For most ordinary purposes we refer changes in spatial position to the
surface of the earth, but we realize that these motions would have some
very different aspects if we adopted a different reference system, one
based on the sun, for example. The development of the Reciprocal System
of theory now shows that for a complete definition of a motion we must
also specify position in time relative to some selected reference system,
This is the fundamental fact that has heretofore gone unrecognized because
it has been assumed (”without examination,” as one prominent
physicist puts it) that time always progresses uniformly at the rate indicated
by a clock. On the basis of this assumption, the time registered by a
standard clock is the same at all points in space. This makes it possible
to represent motion in a coordinate system which provides only for variability
in the three dimensions of space; that is, a The point that we now need to realize is that when we select some physical object, such a, the earth, to define a spatial reference system, we are, by the same act, utilizing the position of the earth in time to define a temporal reference system. If an object A is ejected from the earth with a speed x this means that the change in the position of that object in space relative to the earth‘s location in space divided by the elapsed clock time plus or minus the change of position of that object in time relative to the earth‘s location in time is x. If a similar object B is ejected from Mars at speed x, the same statements apply to the motion of that object relative to the reference system defined by Mars. But if it is now desired to express the velocity of B in terms of the reference system defined by the earth, everyone realizes that the change in the relative spatial position of Mars and the earth must be taken into account. What was not realized before the development of the Reciprocal System is that there is also a change in the relative position of these two planets in time, and whenever the magnitude of this change is significant it too, must be taken into consideration. The true measure of the speed is the amount of change of position in space divided by the total time including the amount of change of relative position in time. Clock time is a correct measure of the total time only at low relative speeds. Much of the difficulty that some students of the theory
are having in understanding the motion of photons of radiation could be
avoided if it is recognized that although the photon motion is inherently
scalar once a direction has been imputed to it in the context of the spatial
reference system, the photon moves in the same manner as any other object.
The object A in the preceding paragraph could just as well be a photon
as anything else. A photon emitted from the earth moves away As in the preceding illustration which referred to the motion
of material objects, if we want to express the nation of a photon emitted
from Mars in terms of a reference system defined by the earth, the spatial
distance traveled by the Mars photon in the reference system during~ one
unit of clock time will be 1+a, where a is the effect of the relative
motion of Mars and the earth. However the distance component a is traversed
during a time a, which is separate and distinct from the one unit of time
registered on the clock. The total time involved in the motion is there
1+a and the speed is 1+a/(1+a) = 1. Thus the speed of the photon motion
is independent of the reference system, but the No doubt some of the misunderstanding that I am now trying
to correct is due to my use of the term “natural reference system.”
Even though I have continually emphasized that space and time do not constitute
a setting or background for physical action, and that there is no absolute
reference system, it has been widely assumed that this “natural reference
system” is such a setting. As one correspondent puts it, “Whenever
you talked about the progression of space...we instinctively assumed you
were talking about the expansion of some background space...Objects not
participating in such an expansion would emit photons by simply ‘cutting
them adrift in the expansion.” The term “natural reference system,”
as I am using it, has no such implications. A spatial reference system
can be stationary, in which case the distances between its various parts
remain the same as time progresses. Or it can he a moving system, in which
case the distances between its various parts increase as time progresses.
Inasmuch as each of the primitive undifferentiated nations that are the
fundamental units of the physical universe involves one unit of space
in association with one unit of time the datum for physical activity —
the The concept of an expanding system of reference is applicable
only to scalar motion. It is unfamiliar because the existence of inherently
scalar motion was not recognized prior to the development of the Reciprocal
System, notwithstanding the fact that motions such as those of spots on
an expanding balloon are obviously different For the purpose of explaining the relation of such a reference
system to the more familiar types, let us assume an object A to be motionless.
A sphere centered at A then constitutes a stationary system of reference
(magnitudes in which can, of course, be expressed either in polar or rectangular
coordinates). A sphere centered at object B which is not moving relative
to A is part of the same reference system. A sphere centered at object
C, which is in motion relative to A is Generalizing the principle brought out in the foregoing
paragraphs, we may say that scalar motion can be represented in a stationary
three-dimensional system of reference only if Inability to represent change of position in tin,e in a
spatial reference system is another case of the same kind. I am continually
receiving letters from individuals who :ay that they need help because
they are having difficulty in “drawing a diagram” to represent
some motion in which change of position in time is involved, according
to the theoretical findings. I cannot give any help in these cases, because
motion in This is not something that is peculiar to the Reciprocal
System. The The two-photon case that I have frequently discussed in my publications demonstrates this point. In this illustration, we assume two photons, A and B, emitted simultaneously from an object 0 in opposite directions. At the end of one unit of clock time, A and B are separated by two units of distance, and x/t = 2/1 = 2. But experiments show that the speed of A relative to B is only 1. Clearly, either the distance entering into the determination of the speed differs from that measured in the reference system, or the time differs from the uniform rate of progression that has to be assumed in order to make it possible to represent motion in a spatial coordinate system. In either case, the spatial reference system is not capable of representing the motion accurately. Current physical theory, based on Einstein assumptions, simply says that the coordinate positions have no meaning at high speeds. As expressed by Moller, “In accelerated systems of reference the spatial and temporal coordinates thus lose every physical significance; they simply represent a certain arbitrary, but unambiguous, numbering of the physical events.” Those who insist ihat we should be able to represent every
motion by a spatial diagram are demanding something that has long been
known to be impossible. Perhaps some day a device may be invented whereby
change of position in three dimensions of space and change of position
in three dimensions of time can be accurately represented in a diagram
that can be comprehended by the human mind. In the meantime, we will sin,ply
have to recognize that some natural phenomena are not amenable to our
cherished diagramatic modes of representation, regardless of what kind
of a theory we may use in our attempt to understand them. The only difference
between the Reciprocal System and other theories, so far as this point
is concerned, is ihat this new theoretical system has clearly identified
the phenomena that the conventional systems of reference are unable to
handle, including sonre phenomena such as scalar motion that have heretofore
been overlooked, largely There is no good reason, however, why we should be disconcerted
because nature refuses to make things easy for us. If we start with the
basic units of motion and build the possible combinations of these units
step by step in accordance with the rules specified in the fundamental
postulates of the Reciprocal System, we define the physical universe,
the universe of motion, in alt of its detail. The universe as thus defined
is rational, logical, and |