Standing The Test Of Spacetime

The greatest scientists, such as Einstein, often made their greatest discoveries by thought experiments

Mark Ronan

The great Scottish biologist D’Arcy Wentworth Thompson once said that Aristotle was the first person who “made [biology] a science, and won for it a place in Philosophy”. In a recent book on Aristotle’s biological work Armand Leroi even credits him with being the world’s first scientist, while disparaging Plato and modern physicists who come up with theories unjustified by experimental observation.

He has a point, yet quiet contemplation and thought experiments can play a huge role in physics, and Einstein was a master at it. Justifications can be sought later, and applications may appear later still. The modern GPS system is a great example. Facilitated by satellites orbiting the earth, it is essential their clocks be harmonised with those on earth, taking into account a 38-microsecond difference per day, otherwise you could soon find yourself standing in a muddy field rather than Piccadilly Circus. Why 38 microseconds? The clocks go seven microseconds slower because of the satellite’s speed — as predicted by Einstein’s Special Relativity — and 45 microseconds faster because of the weaker gravitational field — as predicted by his General Relativity. This raises the question of why there are two Relativity theories. But actually there is only one: the General subsumes the Special in the absence of gravity, but in order to explain both let us start at the beginning.

Aristotle formulated a theory, extended by the astronomer Ptolemy and much loved by the medieval Church, with the earth at the centre of the universe. Extraterrestrial bodies existed on various concentric spheres surrounding the earth, and the strange motion of the planets was explained using epicycles — each planet orbiting an invisible point that orbited the earth. Lovely stuff, but slight discrepancies with observation enforced added complications, and apart from divine dictate there was no obvious reason for this explanation.

During the Renaissance, attitudes started to change. Copernicus in Poland explained planetary motion as being centred on the sun, and the superbly detailed observations by Tycho Brahe in Denmark allowed his student Kepler to formulate a system in which the planets orbited the sun in ellipses. The sun lay at one focus of each ellipse and during the 17th century Kepler’s precise mathematical formulation finally found its natural basis in Newton’s law of gravitational attraction. As Pope wrote:

    Nature and Nature’s Laws lay hid in night:
    God said, “Let Newton be!” and all was light.

With Newton’s laws there was no longer a reason for everything to be centred on the sun. There was no point of absolute rest — the universe was not moored at the earth, the sun, or anywhere else. All motion was relative.

Fine — until electromagnetism caused a rethink in the 19th century. Electricity moving down a wire creates a magnetic field, and a moving magnetic field creates electricity. A synthesis of electric and magnetic fields emerged, mathematically formulated by James Clerk Maxwell. His equations involved electromagnetic waves moving at the speed of light, which had to be measured as the same by all observers no matter how fast they were travelling relative to one another.

This universal property of the speed of light, verified by experiment, had profound implications, notably providing the basis for Einstein’s Special Theory of Relativity, published in 1905. Here space and time were inextricably linked, and two years later Einstein’s erstwhile tutor Hermann Minkowski formulated a four-dimensional geometry embracing both. In this new geometry — spacetime — everything moves from past to future, and things such as spatial distance and time difference that were measured differently by different observers were jettisoned. Instead, Minkowski endowed spacetime with a new “distance” between any two events, invariant under changes of motion and measured as equal by any two observers, whatever their relative speeds.

Speeds less than that of light were of no consequence, so the previous notions of kinetic energy and momentum — vital in classical three-dimensional physics — had to be abandoned. They were replaced by something called energy-momentum in four dimensions, which for a body apparently at rest led to the famous equation E = mc², E being energy, m the mass at rest, and c the speed of light. The destruction of even tiny amounts of mass could potentially release huge energy, as the atomic bombs in World War Two made horribly clear.

Ten years after the Special Theory came the General Theory of Relativity, inspired by a famous thought experiment. Imagine yourself in a stationary elevator on earth, separated from the world outside. A force holds you to the floor, just as it would if the same elevator were accelerated upwards outside the earth’s gravitational field. Is there any difference? Einstein decided not, and by thinking in terms of the new spacetime this led him to an incredible conclusion.

To get the idea, forget four dimensions and picture just two: one for space, one for time. In this case spacetime looks like a sheet of graph paper with a time-axis and a space-axis. The graph for constant velocity is a straight line, and for accelerated motion it is a curve. So the person in the elevator accelerating in outer space follows a curved path, and the same must be true for a person standing still in a gravitational field. This implied that gravity must turn straight lines into curves, so a gravitational field literally bends spacetime.

To appreciate the idea, think of two ships at the equator sailing due north. They gradually get closer. No force draws them together, just the curvature of the earth. This is what Einstein said was happening with spacetime. The curvature produced by a massive body would cause other things travelling from past to future, including light, to veer towards it. In November 1915 Einstein finally had the mathematics to produce numbers explaining an anomaly in the orbit of Mercury, the planet closest to the sun, and observations during a solar eclipse in 1919 verified that the sun’s gravity bent light rays passing close to it, just as the General Theory predicted.

Yet although Einstein was awarded the 1921 Nobel Prize, it was not for one of the greatest intellectual advances ever in physics but as a backhanded compliment for other work, in 1905. Scientists can exhibit a marked preference for more practical work, such as Aristotle’s zoology, and be quite sniffy about theoretical physics.

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