## CHAPTER 7## High Speed MotionAs brought
out in Chapter 3, the “space” of our
ordinary experience, extension space, as we have called it, is simply
a reference system, and it has no real physical significance. But the
Einstein calls this a “metrical” meaning; that is, a connection between the coordinate differences and “measurable lengths and times.” To most of those who have not made any critical study of the logical basis of so-called “modern physics” it probably seems obvious that this kind of a meaning exists, and it is safe to say that comparatively few of those who now accept Einsten's relativity theory because it is the orthodox doctrine in its field realize that his theory denies the existence of such a meaning. But any analysis of the logical structure of the theory will show that this is true, and Einstein’s own statement on the subject, previously quoted, leaves no doubt on this score. This is a
prime example of a strange feature of the present situation in science.
The members of the scientific community have accepted the basic theories
of “modern physics,” as correct, and are quick to do battle
on their behalf if they are challenged, yet at the same time the majority
are totally unwilling to accept some of the aspects of those theories
that the At any rate, the present general acceptance of the relativity theory as a whole, regardless of the widespread disagreement with some of its component parts, makes it advisable to point out just where the conclusions reached in this area by development of the consequences of the postulates of the Reciprocal System differ from the assertions of relativity theory. This chapter will therefore be devoted to a consideration of the status of the relativity concept, includes the extent to which the new findings are in agreement with it. Chapter 8 will then present the full explanation of motion at high speeds, as it is derived from the new theoretical development. It is worth noting in this connection that Einstein himself was aware of “the eternally problematical character” of his concepts, and in undertaking the critical examination of his theory in this chapter we are following his own recommendation, expressed in these words:
In spite of all of the confusion and controversy that have surrounded the subject, the factors that are involved are essentially simple, and they can be brought out clearly by consideration of a correspondingly simple situation, which, for convenient reference, we will call the “two-photon case.” Let us assume that a photon X originates at location O in a fixed reference system, and moves linearly in space at unit velocity, the velocity of light (as all photons do). In one unit of time it will have reached point x in the coordinate system, one spatial unit distant from 0. This is a simple matter of fact that results entirely from the behavior of photon X, and is totally independent of what may be done by or to any other object. Similarly, if another photon Y leaves point O simultaneously with X, and travels at the same velocity, but in the opposite direction, this photon will reach point y, one unit of space distant from O. at the end of one unit of elapsed time. This, too, is entirely a matter of the behavior of the moving photon Y. and is independent of what happens to photon X or to any other physical object. At the end of one unit of time, as currently measured, X and Y are thus separated by two units of space (distance) in the coordinate system of reference. In current practice some repetitive
physical process measures time. This process, or the device, in which
it takes place, is called a In 1887, an experiment by Michelson and Morley compared the velocity of light traveling over round trip paths in different directions relative to the direction of the earth’s motion. The investigators found no difference in the velocities, although the accuracy of the experiment was far greater than would be required to reveal the expected difference had it been present. This experiment, together with others, which have confirmed the original findings, makes it necessary to conclude that the velocity of light in a vacuum is constant irrespective of the reference system. The determination of velocity in the standard manner, dividing distance traveled by elapsed time, therefore arrives at the wrong answer at high velocities. As expressed by Capek, the initial impact of this discovery was “shattering.” It seemed to undermine the whole structure of theoretical knowledge that had been erected by centuries of effort. The following statement by Sir James Jeans, written only a few decades after the event, shows what a blow it was to the physicists of that day:
After a quarter of a century
of confusion, Albert Einstein published his special theory of relativity,
which proposed a theoretical explanation of the discrepancy. Contradictions
and uncertainties have surrounded this theory from its inception, and
there has been continued controversy over its interpretation in specific
applications, and over the nature and adequacy of the various explanations
that have been offered in attempts to resolve the “paradoxes” and other
inconsistencies. But the Now that a new theory has
appeared, however, the defects in the relativity theory acquire a new
significance, as the arguments which justify using a theory in spite of
contradictions and inconsistencies if it is the only thing that is available
are no longer valid when a new theory free from such defects makes its
appearance. In making the more rigorous appraisal of the theory that is
now required, it should be recognized at the outset that a theory is not
valid unless it is correct both mathematically and conceptually. Mathematical
evidence alone is not sufficient, as What this means is that if we devise a theoretical explanation of a certain physical phenomenon, and then formulate a mathematical expression to represent the relations pictured by the theory, or do the same thing in reverse manner, first formulating the mathematical expression on an empirical basis, and then finding an explanation that fits it, the mere fact that this mathematical expression yields results that agree with the corresponding experimental values does not assure us that the theoretical explanation is correct, even if the agreement is complete and exact. As a matter of principle, this statement is not even open to question, yet in a surprisingly large number of instances in current practice, including the relativity theory, mathematical agreement is accepted as complete proof. Most of the defects of the
relativity theory as a The significance of this kind
of a discrepancy lies in the fact that when a theory makes certain assertions
of a general nature, if any In the usual statement of
the paradox, it is assumed that a clock Here we have
a situation in which a straightforward application of the special relativity
theory leads to a conclusion that is manifestly absurd. This paradox,
which stands squarely in the way of any claim that relativity theory is
conceptually valid, has never been resolved except by means which contradict
the basic assumptions of the relativity theory itself. Richard Schlegel
brings this fact out very clearly in a discussion of the paradox in his
book All of the
efforts that have been made by the professional relativists to explain
away this paradox depend, directly or indirectly, on abandoning the general
applicability of the relativity principle, and identifying the acceleration
of clock The impossibility of resolving the contradiction inherent in the clock paradox by appeal to acceleration can be demonstrated in yet another way, as the acceleration can be eliminated without altering the contradiction that constitutes the paradox. No exhaustive search has been made to ascertain whether this streamlined version, which we may call the “simplified clock paradox” has been given any consideration previously, but at any rate it does not appear in the most accessible discussions of the subject. This is quite surprising, as it is a rather obvious way of tightening the paradox to the point where there is little, if any, room for an attempt at evasion. In this simplified clock paradox we will merely assume that the two clocks are in uniform motion relative to each other. The question as to how this motion originated does not enter into the situation. Perhaps they have always been in relative motion. Or, if they were accelerated, they may have been accelerated equally. At any rate, for purposes of the inquiry, we are dealing only with the clocks in uniform relative motion. But here again, we encounter the same paradox. According to the relativity theory, each clock can be regarded either as stationary, in which case it is the faster, or as moving, in which case it is the slower. Again each clock registers both more and less than the other. There are
those who claim that the paradox has been resolved experimentally. In
the published report of one recent experiment bearing on the subject the
flat assertion is made that “These results provide an unambiguous
empirical resolution of the famous clock paradox.” This one clearly established
logical inconsistency is sufficient in itself, even without the many items
of evidence available for corroboration, to show that the special theory
of relativity is incorrect in at least some significant segment of its
conceptual aspects. It may be a useful theory; it may be a “good” theory
from some viewpoint; it may indeed have been the best theory available
prior to the development of the Reciprocal System, but this inconsistency
demonstrates conclusively that it is not the The question then arises: In the face of these facts, why are present-day scientists so thoroughly convinced of the validity of the special theory? Why do front-rank scientists make categorical assertions such as the following from Heisenberg?
The answer to our question
can be extracted from this quotation. “The theory,” says Heisenberg, has
been “confirmed by a large number of experiments.” But these experiments
have confirmed only the Like any other theory, special relativity cannot be confirmed as a theory unless its conceptual aspects are validated. Indeed, the conceptual aspects are the theory itself, as the mathematics, which are embodied in the Lorentz equations, were in existence before Einstein formulated the theory. However, establishment of conceptual validity is much more difficult than confirmation of mathematical validity, and it is virtually impossible in a limited field such as that covered by relativity because there is too much opportunity for alternatives that are mathematically equivalent. It is attainable only where collateral information is available from many sources so that the alternatives can be excluded. Furthermore, consideration
of the
The logical structure of both of these statements (including the implied assertions) is the same, and can be expressed as follows:
In the case of statement A,
this logic is irrefutable. It would, in fact, be valid even without any
such search for alternatives. Since the original solution yields the correct
answers, any other valid solution would necessarily have to be mathematically
equivalent to the first, and from a mathematical standpoint equivalent
statements are merely different ways of expressing the same thing. As
soon as we obtain Statement B is an application
of the same logic to a Furthermore, the need for
this additional evidence still exists as strongly as ever even if the
theory in question is the Here, then, is the reason
why the serious shortcomings of the special theory are currently looked
upon so charitably. Nothing more acceptable has been available (although
there are alternatives toEinstein's interpretation of the Lorentz equations
that are equally consistent with the available information), and the physicists
are not willing to concede that they could have overlooked the correct
answer. But the facts are clear. No new valid
”As an
emergency measure,” say Toulmin and Goodfield, “physicists have
resorted to mathematical fudges of an arbitrary kind.” Both the nature of the problem and the nature of the mathematical answer provided by the Lorentz equations can be brought out clearly by consideration of a simple analogy. Let us assume a situation in which the property of direction exists, but is not recognized. Then let us assume that two independent methods are available for measuring motion, one of which measures the speed, and the other measures the rate at which the distance from a specified reference point is changing. In the absence of any recognition of the existence of direction, it will be presumed that both methods measure the same quantity, and the difference between the results will constitute an unexpected and unexplained discrepancy, similar to that brought to light by the Michelson-Morley experiment. An analogy is not an accurate representation. If it were, it would not be an analogy. But to the extent that the analogy parallels the phenomenon under consideration it provides an insight into aspects of the phenomenon that cannot, in many cases, be directly apprehended. In the circumstances of the analogy, it is evident that a fudge factor applicable to the general situation is impossible, but that under some special conditions, such as uniform linear motion following a course at a constant angle to the line of reference, the mathematical relation between the two measurements is constant. A fudge factor embodying this constant relation, the cosine of the angle of deviation, would therefore bring the discordant measurements into mathematical coincidence. It is also evident that we
can apply the fudge factor anywhere in the mathematical relation. We can
say that measurement 1 understates the true magnitude by this amount,
or that measurement 2 overstates it by the same amount, or we can divide
the discrepancy between the two in some proportion, or we can say that
there is some unknown factor that affects one and not the other. Any of
these explanations When we compare these results
of the assumptions made for purposes of the analogy with the observed
physical situation in high-speed motion we find a complete correspondence.
Here, too, mathematical coincidence can be attained by a set of fudge
factors, the Lorentz equations, in This is exactly the answer to the problem that emerges from the development of the Reciprocal System of theory. We find from this theory that the conventional stationary three-dimensional spatial frame of reference correctly represents locations in extension space, and that, contrary to Einstein's assertion, the distance between coordinates in this reference system correctly represents the spatial magnitudes entering into the equations of motion. However, this theoretical development also reveals that time magnitudes in general can only be represented by a similar three-dimensional frame of reference, and that the time registered on a clock is merely the one-dimensional path of the time progression in this three-dimensional reference frame. Inasmuch as gravitation operates in space in our material sector of the universe, the progression of time continues unchecked, and the change of position in time represented by the clock registration is a component of the time magnitude of any motion. In everyday life, no other component of any consequence is present, and for most purposes the clock registration can be taken as a measurement of the total time involved in a motion. But where another significant component is present, we are confronted with the same kind of a situation that was portrayed by the analogy. In uniform translational motion the mathematical relation between the clock time and the total time is a constant function of the speed, and it is therefore possible to formulate a fudge factor that will take care of the discrepancy. In the general situation where there is no such constant relationship, this is not possible, and the Lorentz equations cannot be extended to motion in general. Correct results in the general situation can be obtained only if the true scalar magnitude of the time that is involved is substituted for clock time in the equations of motion. This explanation should enable
a clear understanding of the position of the Reciprocal System with respect
to the validity of the Lorentz equations. Inasmuch as no method of measuring
total time is currently available, there is a substantial amount of convenience
in being able to arrive at the correct numerical results in certain applications
by using a mathematical fudge factor. In so doing, we are making use of
an incorrect magnitude that we are able to measure in lieu of the correct
magnitude that we cannot measure. The Reciprocal System agrees that when
we need to use fudge factors in this manner, the Lorentz equations are
the correct fudge factors for the purpose. These equations simply accomplish
a mathematical reconciliation of the equations of motion with the constant
speed of light, and since this constant speed, which was accepted by Lorentz
as an empirically established fact, As P. W. Bridgman
once pointed out, many physicists regard “the content of the special
theory of relativity as coextensive with the content of the Lorentz equations.”
For those
who share this view, the results obtained from the Reciprocal System of
theory in this area make no change at all in the existing physical picture.
These individuals should find it easy to accommodate themselves to the
new viewpoint. Those who still take their stand with Einstein will have
to face the fact that the new results show, just as the clock paradox
does, that Einstein's interpretation of the mathematics of high speed
motion is incorrect. Indeed, the mere The status of an assertion
of this kind, a contention that there is no alternative to a given conclusion,
is always precarious, because, unlike most propositions based on other
grounds, which can be supported even in the face of some adverse evidence,
this contention that there is no alternative is immediately and utterly
demolished when an alternative is produced. Furthermore, the use of the “no alternative” argument constitutes a tacit admission that there is
something dubious about the explanation that is being offered; something
that would preclude its acceptance if there In contribution, in the form of the special theory, can be accurately evaluated only if it is realized that this, too, is a fudge, a conceptual fudge, we might call it. As he explains in the statement that has been our principal target in this chapter, what he has done is to eliminate the “metrical meaning,” of spatial coordinates; that is, he takes care of the discrepancy between the two measurements by arbitrarily decreeing that one of them shall be disregarded. This may have served a certain purpose in the past by enabling the scientific community to avoid the embarrassment of having to admit inability to find any explanation for the high speed discrepancy, but the time has now come to look at the situation squarely and to recognize that the relativity concept is erroneous. It is not always appreciated that the mathematical fudge accomplished by the use of the Lorentz equations works in both directions. If the velocity is not directly determined by the change in coordinate position during a given time interval, it follows that the change in coordinate position is not directly determined by the velocity. Recognition of this point will clear up any question as to a possible conflict between the conclusions of Chapter 5 and the constant speed of light. In closing this discussion
of the high speed problem, it is appropriate to point out that the identification
of the missing factor in the motion equations, the additional time component
that becomes significant at high speeds, does not merely provide a new
and better explanation of the existing discrepancy. It |