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RELATIVITY & ITS NEGLECTED IMPLICATIONS

Arthur M. Young

Sixty-two years ago, while an undergraduate at Princeton, I had the good fortune to have my request granted for a course in relativity, and for two years I became the sole student of Oswald Veblen, called by John Von Neuman the father of American mathematics. My debt to Veblen, with whom I kept in contact over the years until his death in 1960, was considerable. Even after his death I derived great help from an essay of his that I had not known about before his death. This essay, "A Mathematical Science," deals with the postulates of projective geometry. It and some of my other interactions with Veblen are discussed in Appendix II of my book, The Reflexive Universe.

But I also had another debt to relativity. When I started on my own theory in 1927 my dissatisfaction with relativity's treatment of time proved a stimulus to a different approach. What relativity did was to extend the geometrization of space to include time. This seemed to me to deprive time of its principal feature -- to introduce novelty and surprise, or as I then put it, discontinuity. This induced me to change my own theory, which I first called a theory of structure, to a theory of time structure, and eventually to a theory of process. At the time I did not know of Alfred North Whitehead's Process and Reality, published in 1929, nor did I know that Henri Bergson had made the same objection to Einstein in 1922.

I am still trying to do justice to time, but to keep to essentials I will confine myself here to my most recent effort to describe the difference between space, or the space-time of relativity, and time in its full implications. I would liken this difference to that between geography and history. The theory of relativity is an extension of geometry; by making time like an extra-space dimension, it implies a totality which can be surveyed in simultaneity. The extra dimension it supplies, while complicated by curvature, exists and is not essentially different from other dimensions. History, on the other hand, while it might enumerate events as does relativity, concerns itself not with events per se, or their location in space-time, but with the change of state that the events produce. It has to do with our experience of time as a process of change. We can think of the Civil War as an event, but to history the United States as a whole was different after the Civil War from what it was before. So too the American Revolution was an event, but its importance was that it created a new nation. This kind of difference, change of state, is not considered by relativity, which deals with location in time and space of events rather than with growth, or with changes of state. Relativity treats time as symmetrical.

One would not think of history as a science, perhaps because unlike science it does not follow the exact laws that are the basis of science. This certitude of science, the exactness of laws, was the basis of geometry in Greek times. Geometry is a collection of theorems and propositions whose truth could be proved. Newton, as I said, extended geometry, a science of position, to include motion, acceleration, forces, energy and other formulas used by science. Einstein went even further by treating force as a curvature of space-time, and the success of this approach to cosmology has led to an unfortunate situation: the geography department has taken over the history department.

It has taken me over sixty years to view the geometrization of space-time as a limitation. Even in school geometry had a mental fascination that was not supplied by history, whose appeal was temporary and emotional. The edifice of geometry, expanded and extended to include motion, is a permanent structure and object of veneration, whereas history, which changes day by day, year by year, depends on content for interest. But however impressive the laws of science, it cannot replace history. History's emphasis on change of state, with succession, gives importance to the direction of time. Relativity and its extensions - GUT (Grand Unification Theories) and TOE (theories of everything) - dismiss life as an epiphenomenon, evolution as chance, and do not stop to think that a theory of everything should apply to life. With the possible exception of fractals, mathematics has no conceptual tools for dealing with self-integration, with cumulative phenomena such as life, memory or consciousness, nor even with values and value judgment. Let that suffice for what I regard as the misinterpretation of time.

A point about the theory of relativity that has been noted by others, so I will not dwell on it here, is that it is not primarily about relativity, but is the search for invariants. The theory pointed out that position, a datum of sense experience, is relative. The position of an object is different for different observers; what is to my right may be to your left. Similarly with velocity; the passengers on a jet plane are at rest with respect to one another, they are moving 600 miles an hour with respect to the earth's surface, and the good old earth, in whose bosom we expect to rest, is moving through space at 18 miles per second.

On the other hand acceleration is not relative, and the gravitational constant which predicts the force between bodies due to their gravity is an invariant and thus is based on acceleration. Another invariant is the speed of light. Both of these are the same for all observers. But as I said, this has been noted before; the misconception in this case is the widely held public view of the theory as justifying the thesis that everything is relative.

 

Rotation

A consideration that to me is important is the invariance of rotation. This has been noted by Einstein and by Eddington, who don't make further reference to it. Percy Bridgeman wrote a book about rotation, but he doesn't seem to know what to do with it, and the invariance of rotation has not been incorporated in the theory of relativity. In my own effort to pursue the matter further I stumbled on a paradox. Yes, rotation is an invariant; if you get up from your chair and turn 360 degrees and sit down, you are not entitled to say the universe turned around you, because if the universe turned around you in the second or so it took you to turn, even the nearest stars, some six light years away, would have to travel X 6, or 36 light years per second - about 200 million times the speed of light. Because matter cannot travel faster than light, the remote stars establish rotation as an invariant. The paradox comes about because you are free to turn yourself as you please. So the invariance of rotation does not prevent your rotation! This can only mean that free choice is of a higher order than the invariants of relativity. In fact it is choice that can establish invariants. Thus the gold standard is an invariant by which the value of money is measured. But the president can decide to go off the gold standard, as Roosevelt did in 1933.

This is not so outrageous as might first be thought. To me it was another clue to the interpretation of the quantum of action, because it rotates, as freedom or choice. I mention rotation not as an error of science, but as a basic principle whose absolute nature, established by relativity, is neglected by science.

 

Mathematics, Physics and Reality

 

Mindfire