Why Does E=mc2_ - Brian Cox [11]
a current to flow in a wire, he might say, “because the battery causes there to be an electric field in the wire, and the field makes the current flow.” Or if you asked him why a compass needle deflects near a magnet, he might say, “because there is a magnetic field around the magnet, and this causes the compass needle to move.” If you asked him why a moving magnet causes a current to flow inside a coiled wire, he might answer that there is a changing magnetic field inside the coiled wire that causes an electric field to appear in the wire, and this electric field causes a current to flow. In each of these very different phenomena, the description always comes back to the presence of electric and magnetic fields, and the interaction of the fields with each other. Achieving a simpler and more satisfying view of many diverse and at first sight unrelated phenomena through the introduction of a new unifying concept is a common occurrence in physics. Indeed, it could be seen as the reason for the success of science as a whole. In Maxwell’s case, it led to a simple and unified picture of all observed electric and magnetic phenomena that worked beautifully in the sense that it allowed for the outcome of any and all of the pioneering benchtop experiments of Faraday and his colleagues to be predicted and understood. This was a remarkable achievement in itself, but something even more remarkable happened during the process of deriving the correct equations. Maxwell was forced to add an extra piece into his equations that was not mandated by the experiments. From Maxwell’s point of view, it was necessary purely to make his equations mathematically consistent. Contained in this last sentence is one of the deepest and in some ways most mysterious insights into the workings of modern science. Physical objects out there in the real world behave in predictable ways, using little more than the same basic laws of mathematics that Pythagoras probably knew about when he set about to calculate the properties of triangles. This is an empirical fact and can in no sense be said to be obvious. In 1960, the Nobel Prize-winning theoretical physicist Eugene Wigner wrote a famous essay titled “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” in which he stated that “it is not at all natural that laws of Nature exist, much less that man is able to discover them.” Our experience teaches us that there are indeed laws of nature, regularities in the way things behave, and that these laws are best expressed using the language of mathematics. This raises the interesting possibility that mathematical consistency might be used to guide us, along with experimental observation, to the laws that describe physical reality, and this has proved to be the case time and again throughout the history of science. We will see this happen during the course of this book, and it is truly one of the wonderful mysteries of our universe that it should be so.
To return to our story, in his quest for mathematical consistency, Maxwell added the extra piece, known as the displacement current, to the equation describing Faraday’s experimental observations of the deflection of compass needles produced by electric currents flowing in wires. The displacement current was not necessary to describe Faraday’s observations, and the equations described the experimental data of the time with or without it. Initially unbeknownst to Maxwell, however, with this simple addition his beautiful equations did far more than describe the workings of electric motors. With the displacement current included, a deep relationship between the electric and magnetic fields emerges. Specifically, the new equations can be recast into a form known as wave equations, which not surprisingly describe the motion of waves. Equations that describe the propagation of sound through the air are wave equations, as are equations that describe the journey of ocean waves to the shore. Quite unexpectedly, Maxwell’s mathematical description of Faraday’s experiments with wires and magnets predicted the