## "Relativity" by Albert Einstein Albert Einstein was a genius, who understood the universe in ways that I will never completely grasp. In his book Relativity, he tried to explain his theories of relativity in a way that might make sense to mere mortals like me.

Einstein begins by discussing the concepts of relative position and velocity. The example to which he returns repeatedly is the person on a speeding train and a person on the ground next to the tracks. An object moving forward on the train would have a different velocity relative to each person. The math for this is relatively straightforward. Velocity is distance divided by time, and you can add or subtract vectors when determining relative velocities. However, Einstein posited that the velocity of light is constant (at least in a vacuum), so we must adjust our concept of relative velocities when dealing with light. In the example above, the perceived velocity of light is the same for both persons. To make the math work, we must modify either distance or time or both. This change in distance and time is negligible when dealing with most objects, but it becomes significant when objects approach the speed of light. This is the basis for Einstein's Special Theory of Relativity. A basic principle of this theory is that nothing can exceed the speed of light.

In the second section of the book, Einstein discusses his General Theory of Relativity, which builds on top of Special Relativity. This theory takes into account the effects of fields - particularly gravitational fields. Strong gravitational forces can actually bend the space-time continuum and may explain the physical limits of the universe. The math becomes more complex here and is significant only on a more macro scale.

Einstein concludes by discussing the structure of space itself. The universe appears to be expanding, to have no end, that there is a finite amount of mass and energy in the universe, and to be of approximately the same density everywhere. These three things seem to be inconsistent unless we consider the idea that space is curved on itself, much as a circle is curved on itself in 2 dimensions and a sphere curves on itself in 3 dimensions.  This would allow the universe to be both limitless and unbounded.

Although the book contains a lot of math, it does not include any calculus; so, if you are familiar with algebra and geometry, you can (mostly) follow the mathematics. Einstein builds on the work of scientists who preceded him, such as Newton and Lorentz, so it is helpful to be familiar with their ideas.

Some of the ideas presented herein sound like fudge factors to make the math work; however, a number of experiments were performed shortly after the Special Theory's publication and those experiments supported the theory. Experiments on General Relativity were difficult to perform at that time, but experiments since that time have supported this theory, as well.

This book was written in 1916, well before Albert Einstein became a worldwide household name. Despite its short length, this is not a simple book. But it is far simpler than reading academic papers and mathematical proofs on these topics. And it is a good introduction to ideas that shape our understanding of the universe.