Breakthrough Propulsion and Five-Dimensional Gravity:
An independent research odyssey
© 2007 L.L. Williams
This is a bloggish summary of my experiences doing research within the peer review system, but as an outsider. I have not attempted to explain any of the scientific jargon or define terms. The papers linked to below contain all that detail.
History of Five-Dimensional Gravity
Some years ago (late 1980s) I became enamored of a 1920's era unified field theory of gravity and electromagnetism. Then I went on in the 1990s to federally-funded research in a separate area of physics and, in 1996, to work in the private sector. After some time of dormancy in the private sector without any scientific problem to occupy myself, and the freedom to consider other areas of physics than the one I was paid to work in for many years, this old unified field theory again began to occupy my thoughts.
The old unified field theory was based on the simple tactic of writing the equations of general relativity in five dimensions. When this is done, one recovers the usual equations of general relativity as discovered by Albert Einstein, along with the equations of electromagnetism consolidated by James Maxwell in the 19th century. It turns out that Einstein's theory of general relativity can be written in any number of dimensions. These equations are merely the most general second-order differential equations which are Lorentz invariant. Without going into the details of what Lorentz invariance means, suffice it to say all equations of physics must have a basic mathematical property known as Lorentz invariance. The power of the unification was great while the underlying assumptions were modest, hallmarks of a truly great theory of physics.
The implications of five-dimensional relativity were realized almost immediately after Einstein and David Hilbert independently published the field equations of general relativity in 1915. In 1919 Einstein received a paper from a Polish mathematician named Theodor Kaluza proposing the five-dimensional theory, which was published in 1921. Einstein became intrigued by the five-dimensional theory, working on it on and off for some two decades. However, Einstein was always troubled by the fact that we don't see a fifth dimension and that therefore a five-dimensional (5D) theory must be abandoned. [1]
Aside from the assumption of five dimensions, the Kaluza theory was soon faced with a formidable obstacle: the discovery of the quantum theory. In 1925, Erwin Schroedinger and Werner Heisenberg independently published the basic theory of quantum mechanics. The quantum theory heralded an entirely new set of physical implications for reality that were not captured in general relativity or the Maxwell equations. The quantum theory dominated the very small, and somehow the microscopic quantum world added up to general relativity and electromagnetism on the large scale. These large-scale theories became known as “classical physics” to distinguish them from the radicalizing quantum theory which subsumed them.
At first, in 1926, Oskar Klein used the new quantum theory to try and explain Kaluza's fifth dimension in terms of an extra quantum degree of freedom. This would also explain why we didn't see the fifth dimension on the macro level: because it was a microscopic phenomenon. This hope was soon vanquished.
Gravity and electromagnetism were long known as fundamental forces of nature, but the quantum revolution added two more which only manifested at the micro level: the strong force which binds protons and neutrons together in the atom, and the weak force which allows protons to turn into electrons, thus allowing radioactive decay. It was clear the strong and weak forces would never have classical field equations. Furthermore, it was clear the Kaluza quantum world demanded more than five dimensions, as the Kaluza theory could not account for the strong and weak forces.
Although Klein's work was abandoned, he laid the groundwork for quantum-correct multi-dimensional unified field theories: the extra dimensions are presumed to be microscopic or, in the jargon, “compactified.” Once mainstream physics went in this direction, the idea of a macroscopic fifth dimension became all but lost to history. Bryce De Witt began attempts in 1963 to unify the new atomic forces using general relativity in higher dimensions. These dimensions beyond the four of space and time are always presumed compactified and their total number is, depending on the particular theory, around 10.
Today we now have a very nice quantum theory of electromagnetism which shows it to be unified with the weak force. Nobel Prizes were awarded both for “quantizing” electromagnetism and for unifying it with the weak force. This “electro-weak” theory, along with some basic ideas about the nature of the smallest particles, is called the standard model. We also have a quantum theory of the strong force. The mainstream view is that it is only a matter of time before all the four fundamental forces are unified in a single quantum theory; we have “only” to bring the strong force and gravity into the fold.
The Warp Drive
And that is where the mainstream scientific story of five-dimensional gravity would end. But a decade or so ago, the old flame of 5D relativity kindled again, for several reasons (besides the raw beauty and simplicity of the theory).
The first is that here we are, going on a century after Schroedinger and Heisenberg, and we still have not quantized gravity. General relativity, Einstein's classical masterpiece of gravity, has defied all attempts to bring it into the quantum fold. This is really saying something because electromagnetism also defied attempts at quantizing. For a long time, quantum electrodynamics would calculate infinities for known finite quantities. Finally, a mathematical breakthrough known as “renormalization” allowed the infinities to be explained (explained away, some would say). Yet general relativity confounds even renormalization.
The problem may be due in no small part to the fact that gravity, unlike the other forces, is closely tied to the nature of space and time -- spacetime. Indeed, gravity is an aspect of spacetime. It is a special kind of force in that people in freefall can't detect a gravitational field – until they hit bottom. The other equations of physics besides gravity tell us, for example, how the electric field or some other quantity behaves in space and time. But general relativity is how space and time behave in space and time.
Quantizing gravity would be indistinguishable from quantizing spacetime itself. That is a bold mathematical venture since the mathematics used to describe even the quantum theory, calculus, is based on infinitely smooth functions of space and time. The differential in calculus is defined in terms of a distance in space (or time) that goes to zero. With quantized spacetime, there would be minimum spacetime distances. Quantum gravity may exist, but we just may not have discovered its mathematics yet.
Another reason to revisit the classical 5D theory is that the field equations of Kaluza's theory were not fully discovered until 1948, by Yves Thiry [2]. The original theory as proposed by Kaluza had some unjustified assumptions which apparently went unnoticed at the time. When Thiry did publish his work, it was realized Kaluza had one apparently fatal assumption which seemed to add to the problems of the 5D theory. In fact, one of the key results of my own researches is that Kaluza's original equations were correct, just for the wrong reasons. This will be discussed more below. It is clear, however, that a fully self-consistent classical five-dimensional theory has not been popularized in mainstream science, since all the classical papers date from before 1948.
Still another reason is that there has never been any observational support either for or against the existence of a macroscopic fifth dimension [3]. The quantum assumption that higher dimensions are too small to observe is not philosophically superior to the classical assumption that our 4 dimensional world is the projection of a larger 5 dimensional reality. This then raises interesting implications about the nature of the 5th dimension which were discovered in the 1920s and then lost to history.
Perhaps the greatest reason for (me) revisiting the 5D theory was the impetus of the NASA Breakthrough Propulsion Physics Program. At the time, this program was funding research in breakthrough physics to address the problem of interstellar travel. Various far-out approaches were considered such as teleportation. The head of the BPP program, Marc Millis, proposed several approaches in his paper titled “Challenge to Create the Space Drive.” I am sympathetic to the objectives of this program (even though it has been discontinued by NASA) because I would like to see mankind realize the dream of becoming a truly spacefaring species. Yet our current understanding of propulsion is limited by the speed of light. It would take millenia just to explore our neighborhood in our galaxy. Whatever technology the realization of this dream will ultimately entail, let us call this archetypal dream of 21st century humanity “the warp drive.” It's a touch more dramatic than Millis's term, “the space drive”, but it captures the imagination.
Thinking about developing the warp drive, it seems clear to me that one can narrow down the area of physical law to look for technological leaps. The area to look for the key to the warp drive seemed to be at the conjunction of two parts of known physical law. One is general relativity. Since travel to the stars can be rephrased as mastery of space and time on interstellar distance scales, it must involve Einstein's theory which unifies space and time with gravity.
The other area must be electrodynamics. You see, all of human technology comes down to mastery of electromagnetic phenomena. It is the only force of the known four we truly wield. Electric power, telecommunications, and electronics are all fruit of our mastery of electromagnetism.
We are by no means masters of gravity, shuffling stars and planets around at will. Nor have we truly harnessed the strong and week forces at work in the atom. Modest advances have been made in harnessing the strong force through creation of nuclear energy and nuclear weapons but it is hard to see how nuclear power will revolutionize interstellar travel.
The warp drive must exist, then, at the intersection of general relativity and electrodynamics. The quantum laws of electrodynamics are responsible for electronics, but electric power and telecommunications are classical. While some key linkage may be uncovered between quantum electrodynamics and general relativity, the inability to develop a quantum theory of gravity prohibits us from finding it. However, should classical electrodynamics play a key role in the warp drive, and it seems reasonable that it might given that we would be forced to build our spacecraft from metal and power it with electric and magnetic fields, then we can begin our search for the key to the warp drive with the classical 5D theory.
And so, for all those reasons, I began my researches into Kaluza's theory with the hopes of finding the key to the warp drive, but realizing it would have been something that escaped the greatest minds of the 20th century when they considered Kaluza's theory. I hoped the benefit of a century of hindsight on physics might allow one to see what those great minds had missed in the 1920s and 1930s.
My Researches
The first step was deriving the standard results of Kaluza gravity but with the luxury of having Thiry and some other references. This means writing down the field equations and the equations of motion. All physical law breaks into one of these two categories. Field equations describe the force fields while the equations of motion describe how matter responds to the force fields. In Kaluza relativity, the field equations are the standard Einstein field equations written in 5 dimensions and the equations of motion are the geodesic hypothesis in 5 dimensions.
I worked though the mathematical implications of these equations and documented my findings here. All the standard results of interest are obtained: the simplification of the cylinder condition, the extension of the energy-momentum four-vector to an energy-momentum-charge five vector, the 5D equations of motion, and the extra scalar field. This is a working document which recapitulates the standard results of Kaluza relativity.
My first paper was submitted to Nature in 2003. It proposed the five-dimensional theory as the answer to one of the categories for breakthrough propulsion physics described in Millis's paper: “... develop a physics that describes inertia, gravity, or the properties of space-time as a function of electromagnetics that leads to using electromagnetic technology for inducing propulsive forces.” My paper also attempted to resolve one of the long-standing objections to Kaluza's theory: the problem of inconsistent assumptions about the electromagnetic field. However, this first paper was rejected by Nature without review.
In hindsight, the paper did have one problem which another reviewer helped me realize: equation 9 of the Nature submittal is not particular to the 5D theory. It turns out that 4D general relativity already includes electromagnetic sources for gravity. Every kind of mass energy generates curvature. The exact electromagnetic contribution to curvature is just a little easier to calculate in Kaluza theory and I mistakenly treated it as a new effect in my paper.
My second paper was essentially a reformatting of the first, this time for the journal Physical Review D in early 2004. It also approached the question of constant-time geodesics. This paper was rejected but this time with a referee review. I learned several things from the referee report. One, mentioned above, that 4D relativity already allows modification of gravity by electromagnetic fields. This result should not have been in a published article and my response, included with the referee review, was malformed. Another key concern of the referee, however, was that spacelike motion, which would be the crux of breakthrough propulsion physics, was too outrageous too consider. I disagree with this conclusion but the referee's statement that I was essentially identifying spacelike geodesics with the world lines of real particles does get to the heart of breakthrough propulsion within the 5D theory.
I then began to focus on the geodesics which I termed “isochronal”, equivalent to the spacelike geodesics which concerned my PRD referee. I felt this, then was the heart of the theory and drafted several papers on the topic such as this one. Presently I became unhappy with my approach and this work was never fully developed. I began to find that the role of the gravitational constant was important in the 5D theory; there were also some basic results that needed to be established before I could move on to consider the isochronal geodesics which were my ultimate goal. I felt that perhaps I would move in steps and win publication first of a paper readdressing the 5D framework and establishing some auxiliary results before moving on to the more-controversial (and more difficult) spacelike geodesics. So I turned my research efforts toward the field equations.
I undertook consideration of the implications of the 5D theory for cosmology. There were two key results I was trying to elaborate. One was that the variation of the scalar field was cosmological in scale if one were to maintain contact with the 4D theory. The other was that the gravitational constant evolved differently with cosmological time than the standard 4D result. I felt that perhaps the classical 5D theory could find some support in cosmological considerations.
Therefore, after 2 years and many rewrites (and a busy personal life), I submitted my third paper to the Astrophysical Journal Letters (ApJL) in 2006. I had high hopes that I could succeed with the ApJ since I already had a successful publication record in that journal and since the Letters format demanded short, succinct papers. The third paper focused on the cosmological implications of the 5D theory on the gravitational constant. I received a rejection letter for this paper on the grounds that ApJL was only for latebreaking results that directly impact observations.
I then turned around and resubmitted the same paper to the full Astrophysical Journal, which allows longer papers and papers not so oriented to current observational problems. The paper was again rejected, but after a lengthy correspondence with the Journal editor. The reason is that I calculated cosmological implications of the 5D theory, focusing on the gravitational field. I learned in my correspondence with the editor that cosmological observations constrain the gravitational constant to be approximately constant over the history of the universe. In that third paper, below equation 14, I solved for the dependence of the gravitational constant on cosmological time. Although the equations did allow a constant solution, I took the more-interesting solution of a variation with time and advertised it as a major result. This lengthy exchange may have obscured the fact that the 5D theory still allows a solution consistent with observation, at least for the parameters considered in the third paper.
My editor at the Astrophysical Journal was a fine example of the best of peer review. The ApJ editor reviewed my paper himself, instead of farming it out to a colleague, and then engaged in a lengthy discussion with me the on the technical merit of the paper. I had never seen a journal editor do this before when I worked as a research scientist, and greatly pleased he was doing it for an unaffiliated researcher to boot.
Based on the recommendation of the ApJ editor to submit to a journal oriented around relativity, I submitted my fourth paper to General Relativity and Gravitation. In this article, I generalized the treatment of the gravitational constant and its variation with cosmological time, learning the lesson of the ApJ review. However, GRG refused publication based on two reviews. I felt that the first reviewer had not really read or understood the paper, on one hand objecting to the historical mathematical problems of the classical theory which I was at pains to address as one of the primary purposes of the paper, and for its failures as a quantum theory, which I was not addressing. The second review was more thoughtful, echoing the concerns about the implications for cosmological nucleosynthesis, but it was the problem already raised by the ApJ editor and which I had rectified.
For this review, I did not seek reconsideration from the editor. At least for this review, I understand the referee objections so there is no point in seeking clarification. I have also tried to contact the few workers publishing on classical Kaluza theory and get a sponsor for the arXiv, but have not had any luck. I think it is safe to say I have done everything I can to publish this work and must accept the verdict of the single blind peer review system (and the sponsor system of the arXiv).
This project was a very interesting raw experience of the rigors of peer review. I found it very difficult to seek peer reviewed publication in an area where I did not have a previous publication or research record, was not working under a grant, and was not affiliated with a large research institution. I think the single blind peer review system, in which papers and grant proposals are not anonymous, while their reviewers are, is stacked against the sort of publication that may be necessary to encourage breakthrough physics. Based on responses from a letter to Physics Today on this topic, there are many who share my awe that 100 years ago, Einstein was able to publish earth-shattering papers on physics while working full time as a patent clerk and who wonder if it could happen again today. What do you think? Is there still room for the patent clerk?
Bibliography
1. Subtle is the Lord: The Science and Life of Albert Einstein, A. Pais, Oxford University Press, 1982.
2. Modern Kaluza Klein Theories, T. Applequist, A. Chodos, & P.G.O., Addison-Wesley, 1987.
3. Kaluza Klein Gravity, J. Overduin & P. Wesson, arXiv:gr-qc/9805018 v1, 1998.