Minkowski enabled Einstein to supersede Newton. Today’s scientists must emulate them
When I was a teenager I asked my physics teacher why things travelled in a straight line unless acted on by outside forces, intending to inspire a discussion with this dull man. His inane response, “That’s Newton’s First Law,” convinced me the case was hopeless, but I tried. I pointed to Mach’s Principle that inertial mass and gravitational mass were equal (a body’s resistance to a push is proportional to its weight). I pointed to the gravitational curvature of space-time in general relativity, but all to no avail. He wasn’t interested. Newton had made the laws, and he was teaching them and their consequences.
Newton was indeed a man of astonishing genius, well expressed in Alexander Pope’s epigram:
Nature and nature’s laws lay hid in night;
God said “Let Newton be” and all was light.
But he had not designed the universe. His laws were empirical, based on results produced by people such as Galileo and Kepler, and he followed them up by inventing the mathematics to create what we call Newtonian mechanics. It reigned supreme until the late 19th century when new observations led to two new theories. One was the fact that small amounts of radiation seemed to be given off in tiny discrete quanta of energy — this led to quantum theory. The other was that bodies travelling very fast relative to one another seemed to measure time at different rates, and the Michelson-Morley experiment of 1887 showed that no matter what your velocity, light always went past you at the same speed. You couldn’t even begin to catch up with it. This led to Einstein’s relativity theory.
Yet in September researchers at CERN (the European Organisation for Nuclear Research) apparently clocked neutrinos — subatomic particles that barely interact with ordinary matter — at slightly more than the speed of light. If this result can be replicated elsewhere, does it undermine the current bedrock of physics, or is there another explanation? To provide an answer, let’s look at the history of relativity.
Philosophically speaking, the observation that time passes at different rates for different observers suggested it wasn’t external to the universe. Somehow the universe had to include time itself in a way that explained its dilation at rapid speeds and the limiting value of the speed of light. This was accomplished by the German-Lithuanian mathematician Hermann Minkowski in his four-dimensional space-time. In Minkowski’s four-dimensional world every particle, every body, every thing that existed in the universe traced out its own path, and the time it experienced was measured along this path. For a ray of light that time was zero. It was as if from the point of view of light itself, travel was instantaneous, and you can’t go faster than that.
This gave a fine mathematical basis for the special theory of relativity that Einstein had put forward in 1905 during his years working at the Swiss patent office in Bern. In his journeys to and from work he continued thinking deeply about these things, and asked whether the force you feel under a sharp acceleration, or under a change of direction in the line of motion, was any different from the force of gravity. He concluded it wasn’t, and this led him to his 1915 general theory of relativity, which gave an intrinsic curvature to Minkowski’s space-time in the presence of gravitational fields.
Four years later, during the solar eclipse of 1919, light rays were seen to curve as they passed the sun, so Einstein’s new theory was vindicated and he achieved undying fame. His results went beyond Newtonian mechanics to explain observed anomalies in planetary motion, and more besides. But the elephant in the room was quantum mechanics, which seemed to operate on quite different principles.
Attempts to unite general relativity with quantum mechanics have so far failed. The latest ideas using string theory — based on a concept of elementary particles being tiny strings whizzing through space-time — have not produced verifiable predictions, so some authors have condemned them as “not even wrong”. Yet now, suddenly, a strange anomaly has been measured, with neutrinos appearing to travel faster than light. To avoid an obvious conflict with Einstein’s relativity, some physicists have conjectured that the photons of light might be following a longer path involving the hidden quantum dimensions of string theory.
These hidden dimensions, all tightly curled up, extend four-dimensional space-time to ten or eleven dimensions. To get the idea, imagine adding just one further dimension, tightly curled up into a small circle. Doing this at each point of a one-dimensional line yields the two-dimensional surface of a cylinder. Doing it at each point of any space yields something one dimension higher, and doing it to four-dimensional space-time yields something five dimensional. This idea was propounded by Theodor Kaluza and Oskar Klein back in the 1920s in order to merge electromagnetism with gravity, but it came up with the wrong numbers and was abandoned. The point is that electromagnetic waves — of which light is one example — can be regarded as spinning round a tiny circle, and hence be thought of as barrelling down tiny cylinders, corkscrewing as they go. Neutrinos on the other hand are entirely unaffected by electromagnetism, so depending on how space-time is merged with the extra dimensions they may follow more direct paths, hence the apparent time difference.
Comparing the present confusion with the past, the astonishing experimental evidence of the late 19th century led to a new way of combining time with space, and hence to special relativity, but that was not the end of it. Einstein’s persistent willingness to ask questions led to the curvature of space-time in general relativity, helping us understand the strange phenomenon of black holes and much more.
What is now needed is not just a mathematical way of combining space-time with the extra dimensions of string theory — which may explain the anomaly — but the ability and willingness to ask some really probing questions.
Will it happen? Perhaps some clever young person, going to and from work on the Clapham omnibus, is looking out of the window and thinking…deeply. I do hope so.
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