An essay presented to the Spring, 1997 meeting of the Minnesota Area Association of Physics Teachers

on the St. Paul Campus of the University of Minnesota.

Space-time and motion are not unrelated, nor continuous. "Continuous" means "infinitely divisible," however, motion and space-time are actually quantized (or finitely divisible), just as matter, electricity, and light are generally recognized to be since the beginning of this century. In fact, space-time and motion not only are quantized, they also are so inseparably related as to be more accurately described as identical, according to the Reciprocal System of physical theory of Dewey B. Larson.^{1}

However, motion and space-time appear neither identical nor quantized, according to the way physics ordinarily has been taught. On the contrary, most physicists usually have assumed that space-time and motion are infinitely divisible and unrelated. A consequence of adopting these questionable assumptions has been an unquestioning adopting of the unprovable paradigm that motion is merely a property of matter. So then, the universe is modelled as an infinite universe of matter and energy, contained within a four-dimensional envelope of space-time. Aristotle earlier put the matter this way in his Physics, "Now motion is supposed to belong to the class of things which are continuous, and the infinite presents itself first in the continuous."^{2}

A universe of matter paradigm also implies that matter is prior to motion. This dogmatic postulate was introduced into natural science centuries ago, during which it remained unquestioned. Aristotle put it this way, "Again, there is no such thing as motion over and above things." I, myself, and I dare say you, were brought up to think that motion is impossible unless some thing is moving. I have never meant to say that undisplaced space-time progression at unit speed (the speed of light) is nothing; but only that it is no thing, but rather simply motion.

The Reciprocal System of physical theory retires the universe of matter paradigm, replacing it with the more evidentially sustained paradigm that motion is prior to matter. This theory postulates that the physical universe is composed of one component, motion, existing in three dimensions, in discrete units and in two reciprocal forms, space and time.

Larson's discovery that the physical universe is a universe of motion provides a much more cogent account of the expanding universe than the Big Bang hypothesis. Dewey Larson agrees with Paul Davies, "The expanding universe is not the motion of the galaxies through space, but is the steady expansion of space."^{3}

While orthodox physics teaches that no finitely divisible units of motion, space and time can or do exist, Larson deduces from his fundamental postulate that the steady speed of scalar outward space progression with time progression is Nature's finitely divisible unit of speed. Its scalar magnitude is the speed of each light photon's physical location. Larson defines motion as the relation between two uniformly progressing, reciprocal quantities, Space and Time. Motion, as defined, is measured by speed, the scalar magnitude of the relation between space and time. By reason of the postulated reciprocal relation between space and time, each individual unit of motion is a relation between one unit of space and one unit of time, motion at unit speed. If Larson's Reciprocal Theory is correct, the whole physical universe is constituted from nothing but these individual units of motion. Photons, electrons, atoms, all physical entities are simply different compounds of these same units of motion.

Although undisplaced outward uniform space-time progression at the speed of light easily is as important a motion as gravitational, magnetic, electrical, or light motion, hitherto it has been ignored and so remained undiscovered until Larson first called attention to it in 1959.^{4} Space-time undisplaced progression Larson distinguishes as "the primary motions," which he defines as those motions which can exist independently of displaced space-time progressions, such as light and gravitation.

### Questioning the Truth of the Space-Time Continuum Postulate

Is there evidence that space and/or time is each continuous?

Is it enough that physicists from Aristotle through Newton to Einstein have assumed that both space and time are continuous or infinitely divisible?

Is the truth clinched when a competent modern physicist, such as Dr. French of M.I.T., teaches, "Both space and time are assumed to be infinitely divisible--to have no ultimate structure?"^{5}

Is the truth further clinched when the distinguished modern author of the relativity theory space-time continuum postulate, Dr. Albert Einstein, in his later years wrote, "I am tending to believe that it is impossible to continue further with this continuum theory?"

Or when Dr. Einstein retires the space-time continuum postulate, as follows, "One can give good reasons why reality cannot at all be represented by a continuous field. From the quantum phenomena it appears to follow with certainty that a finite energy can be completely described by a finite set of numbers (quantum numbers). This does not seem to be in accord with a continuum theory and must lead to an attempt to find a purely algebraic theory for the description of reality. But nobody knows how to obtain the theory. (italics mine)"^{7}

Is this truth questionable when the competent Nobel prize-winning physicist, Dr. Richard Feynman, doubts that space is a continuum? "I believe that the theory that space is continuous is wrong, because we get these infinities and other difficulties, and we are left with questions of what determines the size of all particles. I rather suspect that the simple ideas of geometry, extended down into infinitely small space, are wrong."^{8}

It is unfortunate that Larson's Reciprocal Theory about the quantum nature and structure of the universe of space-time or motion was first published in 1959, only after Einstein died. Dewey Larson completely agreed with Albert Einstein that the physical universe is entirely finite and not at all in any way continuous. The finitude of the whole physical universe, enormous though it be, is an essential general corollary of Larson's Reciprocal System of physical theory. He put it this way to me:

"Infinity is excluded from the physical universe, since we are defining motion, as a relation between a time magnitude and a space magnitude, and we deduce that the quantity of motion is finite. Since all physical entities and phenomena are manifestations of motion, they are all measured in terms of 1/n and n/1, where* n* is finite. No infinities are possible."

Applying the Larson and Feynman finitude criterion to measure physical truth rules out the Big Bang hypothesis, since it postulates infinite density to begin with. The essence of Big Bang has been well stated by Silk, "The central thesis of Big Bang cosmology is that about 20 billion years ago, any two points were arbitrarily close together. The density of matter at this moment was infinite."^{9}

### Questioning the Truth that Motion and Space-Time are Unrelated

What evidence is available, as Newton claims, that "absolute, true and mathematical space in and of itself remains always the same and immovable?"

Does Einstein's support of Newton's opinion that the idea of motion is inapplicable to space constitute evidence of the opinion's truth?

What is the evidence for Isaac Barrow's opinion that motion and time are unrelated, that time does not imply motion?

To what extent is it evidence for the above opinions being true that competent modern physics teachers continue to accept and teach them? For example, Dr. K.W. Ford, "While fields and particles come and go, space and time lie inert, providing the stage upon which the actors come and go."^{10}

Can these above opinions be summed up to mean that space, especially, but also time, is stationary, four-dimensional space-time constituting what used to be called a "stationary ether"?

Probably Herman Minkowski, who formulated the 4-dimensional space-time reference frame of the Einstein relativity theory, has asked the question most relevant to the issue of the relation of motion to space-time. Minkowski asked how "we may overcome the difficulty of never being able to decide from physical phenomena, whether space, which is supposed to be stationary, may not, after all, be in a state of uniform translation?"^{11} Larson's answer to this question is that the unprovable supposition that space is or ever was stationary has been erroneous, just as the geocentric theory that our planet Earth must be immovably located at the center of the universe was wrong. Space will not be, is not, has not been stationary. Space has been, is, and will be in scalar uniform translation or progression with time progression at a steady unit speed, at light speed rate of one natural unit of space per one natural unit of time.

Whether space is stationary (immovable), as Isaac Newton postulated or an aspect of motion, a progression with time progression at the speed of light, as Dewey Larson later postulated, has been settled for some time by the Michelson-Morley experiment. As reported by Albert Michelson, the outcome of the experiment by 1881 was unequivocal, "The interpretation of these results is that there is no displacement of the interference bands. The result of the hypothesis of a stationary ether is thus shown to be incorrect and the necessary conclusion follows that the hypothesis is erroneous."^{12}

### How Larson Identifies Motion, Time and Space Quanta

In Larson's Reciprocal Theory, the speed of light in vacuo is not the steady speed of the photon of light through an immovable, stationary space, but rather the uniform speed of its physical location, in which each photon remains throughout its whole existence.

Larson learned how to measure Nature's smallest time interval and shortest space length, after he discovered how to depict each physical location as an equable progression, at the rate of a natural unit of space per a natural unit of time, whose magnitude is that of the speed of light.

Mathematical unity, unit speed (the speed of light), not mathematical zero is the true physical zero, the reference origin Nature prefers. Unit speed involves equivalence between space and time quanta, both as to magnitude and dimensionality. Mathematical unity is the true physical zero, because the reciprocal character of the space-time relation also implies that all physical entities, beginning with the photon of radiation, result and emerge only from speed displacements below or above unit speed.

Larson thinks that the natural quantum of time is computable^{4}, if and when information is available about a unit photon, that is, one whose vibrating frequency involves an outward motion unit, followed by an inward unit, constituting a full cycle of oscillation in a measureable time interval. If the frequency of this photon is counted with the cgs unit of cycles per second, the duration of the time quantum is computed as follows:

Choosing cycles/second as the frequency unit assumes that frequency is a function of time only. Now frequency is equivalent to velocity, a ratio of space to time. So the natural unit of frequency is a ratio of space to time. Therefore, the natural unit of frequency is a space quantum divided by a time quantum. This is equivalent to a half cycle per time quantum, since the full cycle includes one outward motion unit and one inward. Larson finds that the frequency of the specified photon has been measured and given by Rydberg^{13}. Larson reports this frequency value as 3.2880×10^{15} cycles/second. This measured value of the Rydberg fundamental frequency will be expressed as 6.576×10^{15} half cycles/second. Larson goes on to say, "Expressing the frequency, which is actually a velocity, in terms of reciprocal time in this manner is equivalent to using the natural unit of space in combination with the cgs unit of time as the cgs unit of frequency. In other words, omitting consideration of the space term in selecting the unit of measurement has the same effect as giving it unit value. The natural unit of time in cgs terms is therefore the reciprocal of the Rydberg frequency, or 1.52×10^{-16} seconds.

"We may now multiply this figure by the natural unit of velocity, 2.9979×10^{+10} cm/sec to get the natural unit of space, 4.55×10^{-6} cm/sec."^{4}

### Conclusion

Astrophysical advocates of the accepted prevalent explanation of the expanding universe claim that the evidence for their hypothesis, irreverently referred to as the "Big Bang," is so ample as to exclude all need for any alternative. But this theory rests on two unverified guesses: First, that the original state of the physical universe just before it began, was one of infinite density, since all physical stuff before exploding is located at a single, infinitely divisible physical location, and secondly, after exploding, the galaxies forming, move outward away from each other through an immovable or inert space-time.

Natural philosophers and physicists postulating that, since something should stay put in the universe of motion, space-time must be immovable, stationary, inert, or at rest, reminds me of our ancestors, obviating the necessity of the Copernican Revolution, because they had abundant evidence that our planet Earth is immovably located at the center of God's Universe.

Abundant evidence questions whether the prevalent "inertness" postulate of space-time with respect to motion and the space-time continuum postulate of relativity physics are true. Larson's physics discloses that the expanding universe of motion primarily is a relation between two uniformly progressing reciprocal and discrete quantities, space and time, at unit speed, the speed of light in vacuo.

### References

- Larson, D.B.,
*The Universe of Motion*(North Pacific Publishers, 1984). - Aristotle,
*Physics*(Great Books, 1952), Book III, Chapter 1. - Davies, Paul,
*Edge of Infinity* - Larson, D.B.,
*The Structure of the Physical Universe*(North Pacific Publishers, 1959), p. 25. - French, A.P.,
*Newtonian Mechanic*s (W.W. Norton, 1971), p. 45. - Einstein, A., quoted by L. Infeld,
*Upsekli Fizicheskihk Nauk*(1956), Volume 59, p. 171. - Einstein, A.,
*The Meaning of Relativity*(Princeton University Press, 1955), p. 165. - Feynman, R.,
*The Character of Physical Law*(M.I.T. Press, 1990), pp. 166-167. - Silk, J.,
*The Big Bang*(W.H. Freeman & Co., 1980), p. 61. - Ford, K.W.,
*The World of Elementary Particles*(Blaisdell, N.Y., 1963), p. 212. - Minkowski, H.,
*Uber Raum und Zeit*. - Michelson, A.,
*American Journal of Science*, 3^{rd}Series, Volume 22, (August 1881), pp. 120-122. *Handbook of Physics*(Condon & H. Odishaw, McGraw-Hill, 1958), Table 10.5.In the ...maxim that space and time are infinitely divisible, we pass to an axiom the truth of which is extremely doubtful, even in the physical world. Specious space and time (that is, extension and duration as given in intuition, and space and time as defined geometrically) are indeed infinitely divisible. Scale in them is elastic and utterly unsubstantial, so that there is room for the most elaborate ideal event or object within the smallest fraction of time and space. But this hardly seems to be true in the chemical or animal or astronomical spheres, where scale is not variable fantastically.

George Santayana, The Realm of Truth.