By Steven J. Grisafi, PhD.
A biography of Karl Popper has reminded me of a story I learned as an undergraduate. A professor of mine voiced his opinion to our class that it was the misfortune of the Dutch people to have the renown of their two greatest scientists eclipsed by their contemporaries. He explained to us that Christian Huygens’ wave theory of light did not receive the recognition it warranted during Huygens’ lifetime because of the great authority bestowed upon the opinions of Isaac Newton. Although subsequent generations of scientists came to support Huygens’ wave theory, it was Newton’s corpuscular theory of light that many scientists supported simply because Newton himself proposed it. With the advent of quantum mechanics we have come to recognize the dual nature of not just light, but also of matter, as having both wave and corpuscular character. The professor was one of several whom I noticed seemed to doubt the validity of Einstein’s theory of relativity. He went on to explain that Einstein’s prediction of the bending of light by gravity could have been made by Issac Newton. Of course, there are always “could have” and “should have” moments in everyone’s life. But I found the assertion in the Karl Popper biography, “that light is deflected towards solid bodies, confirmed by Eddington’s experiments in 1919” to be so typical of the constant reaffirmation the public receives regarding the validity of relativity theory that I felt I need to explain this example
Regardless of whatever inaccuracies were made at the time of the measurement, Arthur Eddington’s measurement of the bending of starlight as it passed in the proximity of the Sun during a solar eclipse did confirm Einstein’s prediction. Our professor was asserting that such a calculation could be made using only Newton’s Laws of mechanics. The difficulty with Newton actually doing so himself was that he had no means by which to measure the mass of light. We believe our measurements indicate that the corpuscle of light, the photon, has no mass. Yet this fact should not deter Newton’s belief that gravity can deflect light. His experiments with the refraction of light provide all the insight one needs to recognize that gravity will bend light.
Although light has no mass, it has momentum. We know from quantum mechanics that the energy of a photon is the product of Planck’s constant with the frequency of the light. We also know that the momentum of the photon is the product of Planck’s constant with the wavelength of the light. Most people come to know Newton’s Second Law of Mechanics as force equals the product of mass with acceleration. Yet, the more general form of the law is that force equals the time rate of change of momentum. Since this relationship requires an understanding of the use of calculus, and most people do not learn calculus, most people learn the second law as f=ma. Newton believed that light was a particle. Yet he showed that light could be bent by a prism. Recognizing that the path of the light corpuscle had been bent, Newton could have understood that a force had been applied to cause a change in the momentum of the light. Perhaps it is the dispersal of white light into its component colors of the rainbow that distracts people’s attention to the fact that light is bent while passing through a prism because it is responding to a force acting upon it. So, let’s concentrate on another example of the refraction of light that almost everyone has seen.
If you have ever rowed a boat, or merely plunged a stick into water, you should have noticed that the oar appears bent as we look down at it in the water. The oar does not bend but the path the light takes traveling from the oar to our eyes does. So what force is it that causes this change in the momentum of light? The light is bent by the electromagnetic force exerted upon it by the molecules of water. Since the water molecules exert a slightly different force upon the photons than do the air molecules, within which we reside, we perceive the oar as bent. But it is not. This common example of light refraction is identical to the claim asserted in the Karl Popper biography and attributed to Einstein. We ought to recognize that the Sun does not have a sharp distinct boundary. Starlight passing through the corona of the Sun during a solar eclipse experiences not just the force of gravity from the Sun, but also the atomic and molecular forces of the particles within the Sun’s atmosphere. We recognize that there is the force of the solar wind caused by myriad particles ejected from the Sun’s corona and propelled towards the planets. So we know that starlight passing the Sun during a solar eclipse experiences much more than just the force of gravity.
Now the reader may be wondering: So who is the second Dutch scientist to suffer a fate similar to Christian Huygens? It was Hendrick Lorentz. Einstein’s general theory of relativity is built upon his special theory. His special theory of relativity is built upon the Lorentz transformations. Our teacher went on to explain, and I don’t know how he could have known this but the rumor persists, that Lorentz thought Einstein cheated. It was an incredibly laborious calculation for Lorentz to derive his transformations from Maxwell’s equations of electromagnetism. Einstein used simple geometric reasoning to propose the complicated forms of the transformations. Lorentz understood that his transformations meant abolition of Newton’s propositions of absolute time and space. Yet he was unwilling to take the bold step that Einstein took in suggesting that the transformations applied, not just to electromagnetic radiation, but to all forms of matter and energy. In due time Christian Huygens came to receive the recognition he deserved during his lifetime. Time will soon come for Hendrick Lorentz and we will recognize the virtue of his prudence.