This is one of the slimmest books that I bought in 2001, bargain priced, and I was sure it could tell me a lot about myself as well as about how Einstein thought. I spent 1964 through 1967 studying the kind of mechanics which Einstein is thought to have expanded into another dimension by making time an axis which allows consideration of systems moving at different speeds. E=mc-squared was a formula that I knew from high school. When I was learning calculus at the University of Michigan in the fall of 1965, it seemed to be the perfect mathematics for expressing what happens to objects in motion. In algebra, the big problem for those of us with a one track mind, capable of being surprised by solutions which didn't actually fit the problem, was solving equations in ways which did not involve a solution that required dividing both sides of an equation by zero. In calculus, major trends were often considered much more important than minor trends when everything was divided by quantities that were so small, they were like numbers approaching zero, and borderline concepts were subject to the kind of ambivalence that makes borderline psychological experiences such a booming field in the area of personality disorders, but the key thing about this book is the attempt to keep an eye on what can be learned from science. I thought that I was picking up what still made sense to me in the U of M introduction to Physics until there was a question on the final exam which asked for a mathematical manipulation of equations to produce the result E = mc-squared. I knew some equations, and wrote a few things down, but I didn't come up with that answer. I think I even looked in the textbook after the test, to see if I had forgotten something which was on one page, but I couldn't find that page. This book has what I should have known then.
The final section of the book, 7. AN ELEMENTARY DERIVATION OF THE EQUIVALENCE OF MASS AND ENERGY, from pages 70 to 73, claims to use the law of conservation of momentum, an expression for the pressure of radiation, and two coordinate systems, one of which is moving rapidly along the direction of the axis of a system which is fixed relative to a body that has equal radiation hitting it from both sides. I doubt if the professor for the Physics class expected me to think of this method of finding that E = mc-squared, and I'm still not sure that I believe this approach proves it. In the still system, the momentums of equal and opposite radiation complexes cancel each other completely, so the amount of energy which might be involved doesn't matter. For the system which is moving, the radiation is assumed to be hitting the body from some angle related to that speed, and the change of momentum added by the component along the axis of motion does not change the speed, so the additional momentum is considered an addition to the mass of the body. The mathematical solution depends on solving equations for the difference in the mass observed for using two different systems, one of which is observing zero momentum, and the other thinking, "We anticipate here the possibility that the mass increased with the absorption of the energy E (this is necessary so that the final result of our consideration be consistent)." I believe Albert Einstein wrote this book, but I still wonder what it is telling us.