The Mathematics of Relativity for the Rest of Us

The Mathematics of Relativity for the Rest of Us provides a detailed explanation of relativity, particularly its mathematics, designed for the non-professional audience. The subject is developed from basic principles and observations in physics and mathematics, starting with algebra and geometry as taught in thorough high school courses. On the premise that this background suffices to build an appreciation and understanding of the subject, the crucial concepts are spelled out, and the key derivations are disclosed step-by-step.

The relativity of time, space, and mass is covered first, giving some attention to the history of the two main divisions of relativity, the special and the general. Once special relativity and its mathematics are established, general relativity is covered, beginning with its relationship to Newton's laws and advancing through its revolutionary concepts as well as its mathematics.

This process is carried all the way to the level of tensor equations. The Mathematics of Relativity for the Rest of Us treats topics such as: The constant speed of light, the invariant laws of physics, the basis and meaning of the equation E = mc², the nature of curved four-dimensional space-time, the importance of non-Euclidean geometry, the gravitational bending of light, experimental confirmation of relativity, the philosophical and intellectual appeal of relativity, the nature of black holes, and the cosmologic significance of relativity -- both as concepts and as mathematical issues.

As a result the sufficiently attentive reader is set at ease with the reputedly incomprehensible but essential details about relativity. Even subjects such as "tensor calculus" and the "covariant partially differential field equations of general relativity" will be clear. For instance such a reader will know just what a "tensor" is, why the equations are "covariant," why they are "partially differential," why they are "field" equations, why relativity can be "general," and most importantly just what is meant by "relativity." Furthermore, if a reader is shown the fundamental equation of general relativity,

R_ik - 1/2g_ikR = -XT_ik

he or she will understand what every term of this equation means, why each is included, what obstacles Einstein and his colleagues overcame to derive each term, what impact this equation has on modern science, and why this equation revolutionized our understanding of our universe.

The Mathematics of Relativity for the Rest of Us also devotes a chapter to the relationship between relativity and quantum mechanics. It reveals the limitations of relativity and the direction of future work in this branch of science. The chapter concludes with the role of string theory in reconciling relativity and quantum mechanics.

During the "Sputnik" era careers in engineering and mathematics were highly valued. Two of my uncles were mathematicians and engineers, and their convictions about the bright future of their profession induced me to enter a collegiate engineering program in 1957. To my disappointment, I found this field far less interesting and far more tedious than I had expected, and after two years I switched into pre-med, which suited me much better.

However one of my more thought-provoking engineering courses was relativity theory. Reputedly the topic was very difficult and frustrating, but by that time I had taken various background classes, and I found relativity quite logical and easy to grasp. I concluded that the main hurdle for most students was the absence of a satisfactory bridge between what is taught in high school math/science programs and the basic mathematics of relativity. I felt I could fill this void, but of course, once I started medical school and began building my practice, such a project was out of the question. Nevertheless, I undertook various forms of medical writing, and I published two books (no longer in print) on topics in my specialty, ophthalmology.

About fifteen years ago a flurry of news stories appeared about relativity. I noted how the press handled these - clumsily and naively in my opinion - and I decided it was time to fulfill my ambition. My first impulse was to write a short book, but my research indicated the need for a far more comprehensive work, one that spelled out the fundamentals as well as the mathematical basics of relativity. Since I only had limited time for writing, I did not finish until 2000.

I am amazed by how much literature continually emerges on the subject and on its various ramifications. For example, another biography on Einstein seems to sprout every few months, and I have found hardly any book or magazine or website on modern physical science that lacks at least some reference to relativity. However, the problem remains: No one I know of so far has taken what we are ordinarily taught about mathematics and science, and used it to explain what relativity is all about.