Wednesday, 25 November 2015

General Relativity, 100 Years On

by Elliot Ebert

The current best theory we have for explaining the force of gravity has its 100th birthday today, 25th of November. This theory, known as Einstein’s General Theory of Relativity, conceived by Albert Einstein in 1915, describes, with the use of ten field equations, how mass and energy exert an attractive force on all matter.

Einstein’s General Theory of Relativity was preceded by his Theory of Special Relativity which was published in 1905. The Special Theory of Relativity describes the implications of a finite, uniform speed of light (proved by Mickelson and Morley in 1887) for all observers, irrespective of their motion, on the laws of physics. Einstein’s Special Theory of Relativity leaves us with some implications which are rather counter-intuitive. These include the following: the faster you move, compared to a stationary friend, your watch will run slower than theirs and to them, you will appear contracted in the direction of your motion. Just to illustrate this, if we imagine a 4-metre-long, rocket-powered F1 car moving past you at 90% of the speed of light, you will perceive it to be just 1.74m long. Just by moving fast, its length has decreased by over two metres. Of course, these effects are only noticeable at large proportions of the speed of light (so fast that with the naked eye you would have no chance of actually measuring the effect). However, this is no optical illusion as the F1 car is actually shrinking from your point of view. This effect has been tried and tested repeatedly and it has yet to fail any of the challenges it faces. Furthermore, now that two observers of one event could have different measures of time depending on the speed they are travelling, there cannot be one universal ‘clock’. Every observer must have their own clock and so this leads to the creation of a four-dimensional space-time, consisting of the normal three spatial dimensions plus one time dimension.

Anyway, enough about Special Relativity. Its centenary has already been and gone. General Relativity is, so far, science’s best attempt at explaining the large-scale structure of the Universe and how gravity shapes it to be the way we observe it. Newton’s Theory of Gravitation was the first attempt at explaining the gravitational force and, in most cases, it serves perfectly well and can provide us with incredibly accurate models of orbits and gravity. However, in certain cases, Newton’s theory does not work, namely in particularly strong gravitational fields. This can be observed in the orbit of Mercury, which hardly varies from Newton’s theory’s predictions. However, if a scientific theory disagrees with observations even slightly, it must either be amended or abandoned. This is where Einstein’s General Theory of Relativity steps in.

The General Theory of Relativity is Einstein’s attempt at incorporating acceleration into the Special Theory of Relativity (since Special Relativity only describes the effects of uniform motion). Einstein devised some thought experiments, including one with an astronaut in a spaceship free from the gravitational pull of any other celestial objects. Einstein said that, if the ship were stationary or moving at a constant velocity, the astronaut would feel weightless. However, if the spaceship were to accelerate, the astronaut would feel a force like that of gravity and be pushed against a wall/floor (depending on the direction of the acceleration). If the spaceship were to accelerate at the acceleration due to gravity that we feel here on Earth, the astronaut would be unable to distinguish whether or not he was still on the surface of the Earth (assuming the spaceship is windowless), as he would feel the same force acting upon him as he would if he were in the Earth’s gravitational field. Einstein called this the Principle of Equivalence. This showed there was a deep relationship between systems that are accelerating and systems that are in gravitational fields.

Einstein then used some geometry he was introduced to by Carl Friedrich Gauss and Bernhard Riemann to calculate how his space-time would be affected by the energy (and mass, although they are interchangeable through Einstein’s E=mc2) it contains. He found that the presence of energy curves space time and that other objects feel a gravitational pull because they pass through these curved regions. It is much like placing a bowling ball in the centre of a trampoline and rolling a golf ball in a straight line through the deformed part of the fabric. The golf ball will roll towards the bowling ball. All objects try to follow a straight line through space-time. However, when passing through curved space time, they trace out lines called geodesics. This is what we perceive to be the force of gravity. Light can also be affected by this gravity, as it too follows a geodesic path through space-time, so Einstein’s theory was proved during the eclipse of 1919, when a star that would normally be hidden behind the sun was sighted due to its light being bent around the sun by the sun’s gravitational field. These observations agreed with Einstein’s predictions, so strengthening the support of his theory.

The General Theory of Relativity succeeds where Newton’s theory failed and correctly predicts Mercury’s orbit. It also says that time flows slower in a stronger gravitational field. It is thanks to Einstein that we have such accurate GPS systems today: the time-slowing effect caused by the satellite’s fast orbit and the time-quickening effect caused by the weaker gravitational field in which the satellite orbits do not cancel each other out. In fact, the clocks on the satellites run faster than the earth-bound clocks by 38 microseconds per day. If this were not adjusted, this would cause the GPS system to become less accurate by 10km per day.

Although Einstein’s theory is much more complex than Newton’s, in the vast majority of cases they predict the same thing. For that reason, Newton’s theory is used more regularly than Einstein’s theory. However, Einstein’s theory gives us a better understanding of the true nature of the gravitational force, a force that has had such an instrumental part to play in the shape and structure of the Universe we observe today. For that reason, I believe it should be placed among the most important discoveries mankind has ever made. 

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