"In a changing room amidst an uneven field am I sitting"

"Susan Griffin explains it, but a way of narrating events that gives the listener ‘a path through those events that leads to some fragment of wisdom'."

Journey to Another Dimension

by Michio Kaku

Einstein in 1919, while explaining the unified aspects of his general relativity principle based on the field theory of Maxwell, received a letter from the mathematician, Theodor Franz Kaluza. In the letter was a remarkably far reaching insight. Elegant in its exquisite design and calculation, alas Kaluza had no experimental evidence for his conjecture. Yet the results of the formulas were so beautifully balanced that their vision was astonishing with respect to Einstein's suggestions that in addition to the three extensions of space as area and depth there is another dimension we inhabit called time.

Dr. Kaluza, with mathematically accurate, balanced and elegant proofs had shown how anyone with proficiency in the language of math could describe, in a formulaic way, Einstein's principle of general relativity about time in the fourth dimension as also a particular expression of gravity in another, or fifth, dimension. As physicist Michio Kaku says,"with his fifth spatial dimension, Kaluza had enough room to fit the electromagnetic force into Einstein's theory of gravity." (p.162) It is as if you lived in a room that expanded after you one started at a point, two stretched a measuring stick in a direction and three stretched the stick in a direction perpendicular to the previous measurement. Each of the moves from the point, to the line to the perpendicular would reveal a measure of the volume of the space you are in and we have called a room.

Sitting in such a room was Einstein reading Kaluza's letter and examining his proof. Because he was sitting in a measurable three dimensional room taking time, another dimension, to understand this letter, for him "The idea of five dimensions was so outlandish" Kaku suggests, that "Einstein held on to the paper, delaying its publication for two years." (IBID.)

There are clues to what Einstein thought in his letters to Kaluza. One was sent in April 1919, in which Einstein wrote "The idea of achieving" this outcome of brining together different physical concepts into one related whole "by means of a five-dimensional cylinder would never dawned on me." So excited was he over receiving Kaluza's ideas that Einstein wrote "I like your ideas enormously." (IBID., p. 163) Clearly it is challenging to anyone who senses three dimensions of length, width (or area) and depth, to consider the passage of time as a fourth dimension. But what on earth, better, where on earth is the fifth dimension?

Kaku tells us that what later became Einstein's life's obsession with respect to his work is based on this correspondence with Kaluza during the worst period of World War One's aftermath for Germans. Defeated and starving Einstein sat in Berlin reading a letter from Kaluza who had written from Konigsberg in eastern Prussia. How more dismal could a condition be for intelligent, urban, sophisticated people? Here in the dark, so to speak, of an abysmally destructive war, two brilliant thinkers exchanged letters containing a mathematically examined means of entertaining the existence of a fifth dimension! Weeks after receiving and responding to Kaluza's initial mail, Einstein wrote him again. In the letter Einstein explained, "the formal unity of your theory is startling."

The journey into the fifth dimension was brought about by Einstein's argument. Essentially Einstein posited that what the Greeks and Babylonians had called three dimensional space, is really spacetime. By that he meant that there is a fourth dimension of time obscured by our sense of space which we have, after Euclid, describe as length, width and depth. Further, Einstein revealed that because of this fourth dimension the human observer cannot tell the difference between acceleration and gravity. Finally as a consequence of this way of thinking Einstein suggested that gravity is best thought of as the curvature of space around very massive objects. Now in trying to reconcile gravity with electromagnetic energy, of which light is a particular bandwidth, Einstein gets a letter in the mail suggesting that in the fifth dimension, gravity can be uniformly related to time, light and space. It is a bit like someone saying, now that you have changed your mind about an experience, change it some more in the same manner to an even less acceptable way of thinking about everyday life. It is bad enough Germany surrendered, but in the cold and the dark of wartime two Germans encourage one another to think enough to look behind the curtain of our sensory experience that hides an underlying unity in the things we distinguish as separate entities and discover an additional measure of space.

As Kaku describes the unreal implications of Kaluza's conjecture and subsequent mathematical proof, many scientists rejected the idea because it was "devoid of physical content." Worse is the nagging ambiguity Kaluza's letter's contents raised for Einstein's life's work and our knowledge of the world we experience. On the one hand the journey embarked upon by Einstein and Kaluza conjoined at a fruitful but unhappy intersection near the edge of certainty and uncertainty. Kaku tells us that "If the unification of light with gravity requires five dimensions, but only four can be measured in our laboratories, then what happened to the fifth dimension?" Of course when Einstein departed the cosmos of Newton, where gravity is a constant force and attempted to unify the experimental findings of Maxwell concerning the unification of electricity and magnetism, he was walking down a well traveled path. The name of that pathway is the way of unification.

Now the way of unification is a path that Galileo, Newton, Lavoisier and Maxwell all traveled, marked out and extended into new territories of thought. In each extension of the road from demonstration and experience it was as if the voice and vision of mathematics as a language helped to guide the way. If higher math had not guided, then it surely in retrospect assisted in mapping the newly explored terrain to show this new territory's relationship to the previously discovered places on the journey.

Each of these explorers lived in three dimensions, until Maxwell decided to identify the relationships between two distinct experiences: magnetic attraction and electrical repulsion. While each of these fellows had used time and space as a means of resolving any sensory confusion by discovering an underlying relationship --and a mathematical means of describing and thus predicting that relation-- none had ever thought of time as a fourth dimension. What appears on the surface as differences, could at some deeper, or at least obscured, level emerge as a fundamental unity.

While Galileo and Newton had walked the fields to lay out the boundaries of gravity or the force of universal attraction among massive objects, they had begun but never fully described light and heat. Then, Lavoisier the French surveyor and chemist had described elements, such as the oxygen in the air we breathe, as a fuel for fire that gives off light and heat. He suggested that light and heat were elements in his field because they were produced by fire. His was a tentative, but unsatisfactory, reconciliation of the ambiguity between appearances and underlying simplicity. That is, light and heat seemed to be associated with electrical display, called discharges, just as they were displayed with fire. More confusing on the surface is the fact that in the absence of oxygen fires were extinguished,so it appeared that each element was distinct. Heat, light, oxygen and nitrogen, so Lavoisier wrote, were independent substances he called elements. Some elements, like iron were observed to behave near a magnet in ways that nitrogen or sulfur did not behave. So that on the level of appearances confusion persisted concerning the character of magnetic forces.

After each of these people's death, new information was discovered that allowed Maxwell to ponder the relationship between what appear to be distinct experiences. Magnetism is different from electrical discharges, or so it had seemed to investigators. Just as heat, light and chemical elements are different from one another and may have dimensions that are not so apparent to the naked eye, there are ways to use both experiments and mathematics to reveal hidden relations. This is particularly true of mathematical means used to show the meaning of, often unresolved, experimental findings about elements and electrical discharge. Why for instance do some elements like iron respond to magnetism, while gold does not?

So many questions and so little time. And every researcher who embarked on the journey dies, leaving it to those who follow the path to extend the way started by others. All investigators, leaving careful records, letters, or markers are really wayfarers on a journey into the unknown. So in the equations of Maxwell, who described the unification of electrical and magnetic effects as a field theory, there lay the intellectual seed for Einstein's discovery of how light moves through space. In describing how light is deflected by the warp of space, Einstein theorized that there exists a fourth dimension which he called space-time. Light emerges out of the electromagnetic spectrum, a feature of hidden space and over time it decays into heat which is also a vast portion of the lower frequencies found along the obscured electromagnetic spectrum. Like some depraved murder being investigated over a thousand years, Kaluza had discovered --through the application of mathematical formulas and proofs resembling Maxwell's equations for the unification of electromagnetism-- that another layer of confusion can be cleared up if we unify space-time with gravity!

So it is that here we are at the far distant intersection of attraction and expansion, bewildered, confused and ambiguously distraught because we are unable to unravel the riddle of the fifth dimension, which Einstein called the search for a unified field theory. We are ambiguously distraught, because as Kaku suggests, we have the mathematical ways, but lack the experimental means to test, examine and decide if space-time and gravity are unified in the fifth dimension. Intersections in the fifth dimension can be hazardous to your assumptions, if you are not careful. And like any intersection we have to cross, we may be hit by unseen obstacles if we don't carefully traverse the yawning abyss of time and gravity lying before us. Having left direct sensory experience as measured by a stick, far behind us at the intersection of Euclid's and Newton's corner we have only a map created in a foreign language of mathematical certainty to guide us through the present intersection of gravity and spacetime. Will we cross or linger here a bit longer to get our bearings?

Here standing at the corner we are sure of one thing, the longer we tarry the more likely we are to be hit by the unseen feature in the dimension of spacetime we call death. So we either wait here, or continue down the forking paths in search of an elusive order that as soon as we discover it, seems to recede into the distance beyond even our imagination's ability to see the next intersection. So we move to where Kaluza and Oskar Klein, a Swedish mathematician, conceived of a five dimensional world. As Kaku tells it "Klein suggested a possible solution to the problem." (IBID.) At the intersection of Kaluza and Klein the world we know is imagined to fold back into itself in a sort of infinite regress of interceding spaces. This is not at all like the room we have been sitting in, or the field we have been measuring, or is it? And we have yet to see what, indeed, it has become as it is always becoming?

JVS

9:01 Am, 11 June 2005

Beyond Einstein, by Kaku and Thompson ( New York: Random House,1995.) pp. 162-177.