The essence of this doctrine was presented to the Fall Meeting of the Minnesota Area Association of Physics Teachers,

October 25, 1997 in the Physics Building, Room 210, of the University of Minnesota, Minneapolis campus.

### Dewey B. Larson's Reciprocal System of General Physics

The best evidence that motion is a *reciprocal* relation between space and time, is the everyday way physicists all over the Earth use *speed* to **measure** motion. All agree that speed of a motion is given by a multiplicatively inverse relation between space and time and/or between time and space. The physical universe is entirely composed of one component, *motion*, existing in three dimensions, in *discrete units* and in two *reciprocal* forms, space and time.

Until and unless motion exists, neither space nor time exists nor can exist. Time and space are the only two essential aspects of all motion as such. That is, space and time not only are the necessary conditions, they are the sufficient conditions of motion of the material and cosmic sectors of our physical world. Space and time do not exist at all, apart from motion. Space and time have no properties but those they have in relation to one another.

### Is the Space-Time Continuum Postulate True or False?

The two allegedly modern physical theories--relativity physics theory and quantum physics theory--share two ancient, questionable fundamental axioms:

- Space-time and motion are infinitely divisible or continuous and have no structure.
The MIT teacher of Physics, Professor A. P. French

^{1}speaks for both relativity and quantum physicists when he writes in his text on*Newtonian Mechanics*: "Both space and time are assumed to be infinitely divisible--to have no ultimate structure." - Space-time is inert, stationary, immovable, different from and not closely, if at all, related to motion.

The elementary particle physicist, Professor K. W. Ford^{2} speaks for both quantum and relativity physicists when he says in his treatise on elementary particles: "While fields and particles come and go, space and time lie inert, providing the stage upon which the actors play their roles."

The consensus among the present physics profession, as I understand us, is that motion, space and time are *not* quantized or finitely divisible but continuous or infinitely divisible.

Few modern physicists, including most quantum physicists, have questioned the space time continuum postulate of relativity physics. One who has is the Nobel-prize winning physicist, Professor Richard Feynman^{3}: "I believe that the theory that space is continuous is wrong, because we get all these infinities and other difficulties... I rather suspect that the simple ideas of geometry, extended down into infinitely small space are wrong."

Another Nobel-prize winning physicist, who began in his later years to question the space-time continuum assumption, is Dr. Albert Einstein^{4}: "One can give good reasons why reality cannot be represented by a continuous field. From the quantum phenomenon 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."

The writer considers that this testimony of Drs. Feynman and Einstein is strong evidence that the space-time continuum postulate can be false or mistaken, and therefore wrong.

What appears to make the modern physics profession very reluctant to question this postulate is that this is not merely a modern assumption, but an very old one together with the assumption that *motion also must be continuous*. Aristotle^{5} never dreamed that time and space might not be continuous, because he believed time to be an aspect of motion and he assumed *motion to be continuous*: "Now motion is supposed to belong to the class of things which are continuous, and the infinite presents itself in the continuous. ...Again, there is no such thing as motion over and above things."

From Aristotle, Newton^{6} probably derived his attitude that motion, space and time are continuous, and have little to do with one another. From Aristotle, Newton's contemporary, Isaac Barrow^{7} perhaps derived his attitude that motion does not apply to time. From Newton, Einstein^{8} probably got his idea that motion does not apply to space.

### Are Space and Time An Inert Stage or An Uniform Progression At Unit Speed?

When the teacher, Albert Einstein, died in 1955, he died believing 'nobody knows how how to obtain the theory' that space and time are quantized or finitely divisible, instead of being continuous or infinitely divisible, as was taken for granted for more than 25 centuries. Four years later, in 1959, an Engineer, Dewey B. Larson^{9}, published the theory that space and time are **not** continuous, but rather finitely divisible or quantized. This new theory has so far been dismissed without examination as "amateurish" by the physics profession.

The Larson Reciprocal System of physics not only challenges the space-time continuum assumption. It also challenges an even more intrenched and more ancient platitude of the natural science of yesterday. This plausible platitude is variously expressed: Motion is impossible without things; there is no such thing as motion over and above things; motion is only a property of matter. Also, it challenges the materialist metaphysical proposition that matter is prior to motion. Blind acquiescence in these propositions has had much to do with precluding natural scientists, until now, from examining the hypothesis that the physical universe is a universe of motion, rather than one of matter and energy.

One can obtain a cogent physical theory about the universe of motion, as Larson has done, by excluding infinite divisibility from the physical and rejecting the dogma that *motion is impossible without matter.* Think of the physical world as a universe of motion, where and when *motion is possible without matter*. For example, the photon of light is not matter, but rather is simply a compound unit of motion. Furthermore, the *physical location* of a photon is no *thing*, it is an outward translating unit of motion, progressing uniformly *in vacuo* at unit speed (the speed of light), whether or not occupied by a photon. Note how our account of this phenomenon compares with Einstein's^{8}.

We postulate that this universe of motion is composed *entirely* of one component, *motion*, existing in three dimensions, and in discrete units. Motion is defined to be the relation between two uniformly progressing, reciprocal quantities, space and time. By reason of the reciprocal character of the 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. Since we are defining motion as a relation between a time magnitude and a space magnitude, we deduce that the quantity of motion is finite and conserved. Since all physical entities and phenomena are expressed in terms of 1/n and n/1, where n is finite, **no infinities are possible**.

In the universe of motion space and time play a quite different role from that assigned to them in the conventional universe of matter. In the universe of motion, space and time progress together at unit speed. They are the sole constituents of the units of motion, from which all physical entities and phenomena are integrated. Because of the reciprocal character of the relation between space and time, two consequences flow: 1) The unit of space of length 4.55 × 10^{-6} cm is equivalent to the unit of time 1.52 × 10^{-16} sec, their ratio giving the speed of each unit of motion the magnitude of the speed of light *in vacuo*. 2) The multiplicative inverse relation between space and time also implies that all physical entities result from **finite** speed displacements, from below *or above* unit speed. Units of motion combine so that 1 unit of space can associate with *n* units of time, resulting in motion in *space* of the material sector and also 1 unit of time can associate with *n* units of space, resulting in motion in *time*, in the reciprocal sector, which Larson calls the Cosmic sector.

A fair test to find out if space-time is inert and stationary, as the conventional universe of matter perspective views them, or whether space progresses with time progression at the speed of light, as the universe of motion perspective views them, is available to learn which perspective is more truthful.

Few physicists have yet considered that space-time can progress together, independently of matter. One who has is Dr. Minkowski, Einstein's partner in composing the 4-dimensional mathematics of Einstein's relativity theory. In his famous essay,* Raum und Zeit*, Minkowski asked how "we may **overcome** the difficulty of never being able to decide from physical phenomena, how *space*, which is supposed to be stationary, may not after all, *be in a state of uniform translation*?"

Another who has considered that space-time involves *a progression of* *space* rather than an immovable or stationary space is Professor Paul Davies^{11}: "The expanding universe is not the motion of the galaxies through space, but is the *steady expansion of space.*"

The steady expansion of space is represented in Larson's Reciprocal System of physics as an outward uniform scalar progression of *physical* *locations*, space with time progression at unit speed (the speed of light).

At relatively short distances gravitation predominates, and the net motion is inward. Since the gravitational motion decreases with distance, while the outward progression remains constant, the opposing motions reach equality at some greater distance, which Larson has named the *gravitational limit*. Beyond this distance the net motion is outward, *increasing with distance* and approaching unit speed (the speed of light) at extreme distances.

This theoretical pattern of net speeds is verified observationally by measurements of the Doppler shift in the radiation received from the distant galaxies.

This is the alternative explanation of the "expansion of the universe" to the Big Bang hypothesis offered by the astronomers' about the observed recession of the distant galaxies. An advantage of the reciprocal physical theory over the Big Bang hypothesis is that the latter does not avoid invoking and importing infinities into its mathematical structure; while the reciprocal system avoids infinities when dealing with the physical.

The essence of the Big Bang has been well stated by Silk^{12}: "The central thesis of Big Bang cosmology is that 20 billion years ago, any two points were arbitrarily close together. The density of matter at this moment was infinite."

The Reciprocal System of general physics implies that no infinities are possible, that is, no infinities can occur in the physical universe, as has been previously discussed. Therefore, unless the reciprocal physics is mistaken, the central thesis of the Big Bang cosmology is not true.

Unity, that is unit speed, c, the speed of light, is the true physical zero of Nature. The scalar space-time progression is **always** *away from unity*, and gravitational motion is **always** *toward unity *. In the macroscopic physical region, gravitation plays the role of the universal force of attraction, since "toward unity" generally occurs outside the unit of space of 4.55 × 10^{6} cm length, while space-time progression away from unity plays the role of the universal force of repulsion.

In the sub-microscopic physical regions, the roles of the two universal forces reverse. This is the world of the solid state of matter and solid cohesion. Three centuries ago, Newton theorized that the newly discovered gravitational force must be the force of attraction between the atoms in a crystal of matter. Newton postulated that when God made atoms, he made them absolutely hard and impenetrable and so this constituted the repulsive force of solid cohesion. Newton's solid cohesion theory was ruled out at the beginning of this century when X-ray crystallographers discovered that when atoms approach each other quite closely in crystals, coming much closer generally than 10^{-6} cm, they do not touch each other. However, in the light of the reciprocal physical theory, it turns out that Newton was not altogether mistaken when believing that gravitational force should have a role in solid cohesion as well as cosmology. What Newton did not and could not know, and what Dewey Larson has discovered, is that solid cohesion is an affair that occurs **inside the natural unit of space**. *Toward unity* inside the unit of space assigns gravitational force the role of the force of repulsion, while *away from unity *assigns the role of attraction force to the space-time progression force in solid cohesion.

### References

- French, A. P.,
*Newtonian Mechanics*(W.W. Norton,1971), p. 45. - Ford, K. W.,
*The World of Elementary Particles*(Blaisdell, N.Y., 1963), p. 212. - Feynman, R.,
*The Character of Physical Law*(M.I.T. Press,1990), pp 166-167. - Einstein, A.,
*The Meaning of Relativity*(Princeton University Press, 1955), p. 165. - Aristotle,
*Physics*(Great Books, 1952), Book III, Chapter 1. - Newton, I.,
*Principia scholium*: "Absolute true and mathematical space, in its own nature and without relation to anything external, remains always the same and immovable." - Barrow, I.,
*The Geometry Lectures*, (1670, 1916), pp. 35-37:"But does time not imply motion? Not at all, I reply, as far as its absolute, intrinsic nature is concerned; no more than rest; the quality of time depends on neither essentially, whether things run or stand still, whether we sleep or wake, time flows in its even tenor. Imagine all the stars to have remained fixed from their birth; nothing would have been lost to time; as long would that stillness have endured as has continued the flow of this motion."

- Einstein, A.,
*Sidelights on Relativity*, (Dover, N.Y., 1922, 1983), p. 223:"Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity, space without an ether is unthinkable; for in such space there would be not only no propagation of light, but also no possibility of existence for standards of space and time (measuring rods and clocks), nor therefore any space-time intervals in a physical sense. But this ether may not be thought of as endowed with the quality of ponderable media, as consisting of parts which may be tracked through time.

*The idea of motion may not be applied to it*[italics mine]." - Larson, D. B.,
*The Structure of the Physical Universe*, (North Pacific Publishers, 1959). - Minkowski, H.,
*Raum und Zeit*in*The Principles of Relativity*, (Dover, 1923), pp. 75-91. - Davies, P.,
*The Edge of Infinity*, p 137. - Silk, J.,
*The Big Bang*, (W. H. Freeman & Co., 1961), p. 61.