Why Does E=mc2_ - Brian Cox [17]
At the heart of Einstein’s theory of special relativity lie two proposals, which in the language of physics are termed axioms. An axiom is a proposition that is assumed to be true. Given the axioms, we can then proceed to work out the consequences for the real world, which we can check using experiments. The first part of this method is an old one, dating back to ancient Greece. Euclid most famously deployed it in his Elements, in which he developed the system of geometry still taught in schools to this day. Euclid constructed his geometry based on five axioms, which he took to be self-evident truths. As we shall see later, Euclid’s geometry is in fact only one of many possible geometries: the geometry of a flat space, such as a tabletop. The geometry of the surface of the earth is not Euclidean and is defined by a different set of axioms. Another even more important example for us, as we shall soon learn, is the geometry of space and time. The second part, checking the consequences against nature, was not much used by the ancient Greeks. If it had been, then the world might well be a very different place today. This seemingly simple step was introduced to the world by Muslim scientists as early as the second century and took hold in Europe much later, in the sixteenth and seventeenth centuries. With the anchor of experiment, science was finally able to make rapid progress, and with that came technological advancement and prosperity.
The first of Einstein’s axioms is that Maxwell’s equations hold true in the sense that light always travels through empty space at the same speed regardless of the motion of the source or the observer. The second axiom advocates that we are to follow Galileo in asserting that no experiment can ever be performed that is capable of identifying absolute motion. Armed only with these propositions, we can now proceed as good physicists should and explore the consequences. As ever in science, the ultimate test of Einstein’s theory, derived from his two axioms, is its ability to predict and explain the results of experiments. Quoting Feynman more fully this time: “In general we look for a new law by the following process. First we guess it. Then we compute the consequences of the guess to see what would be implied if this law that we guessed is right. Then we compare the result of the computation to Nature, with experiment or experience, compare it directly with observation, to see if it works. If it disagrees with experiment it is wrong. In that simple statement is the key to science. It does not make any difference how beautiful your guess is. It does not make any difference how smart you are, who made the guess, or what his name is—if it disagrees with experiment it is wrong. That’s all there is to it.” It is a terrific quote from a lecture filmed in 1964, and we recommend looking it up on YouTube.
Therefore, our goal for the next few pages is to work out the consequences of Einstein’s axioms. We will begin by using a technique that Einstein himself often favored: the thought experiment. Specifically, we want to explore the consequences of assuming that the speed of light remains constant for all observers, no matter how they are moving relative to each other. To do this, we are going to imagine a clumsy-looking clock called a light clock. The clock consists of two mirrors, between which a beam of light bounces back and forth. We can use this as a clock by counting each bounce of the light beam as