Imagine that every time you weighed yourself you got a different result. At first it might seem quite convenient to know that if your weight looks a bit too high you can try again and get a better answer. But if you really want to know the right answer it can be a nuisance.
Physicists trying to measure gravity have a very similar problem. It is over 300 years since Newton, allegedly inspired by a falling apple, proposed his universal law of gravity. This states that all bodies of matter, including you, me, Newton’s apple and the planet earth, attract one another with a force that depends on how much matter is in each body (the mass), and their distance apart. The exact value of the gravitational force depends on a fundamental constant, G, known as “big G”. The problem is that the value of G seems to be slightly different every time it is measured.
An international meeting will be held in London in November 1998 to discuss gravity measurements. If the differences are real this could be really exciting, or even alarming. Gravity does more than make apples fall to earth. It does a range of things from holding the universe together to making the sun shine.
Newton’s law of gravity enabled him to explain the movements of the planets. Gravitational forces keep them orbiting around the sun and prevent them from flying off into deep space. In this century cosmologists and astrophysicists have shown that gravity also holds the sun in its orbit around the centre of the milky way, holds the universe together, and slows its expansion. It also forms the stars, by bringing together gas and dust, and sets them alight by generating the incredible pressures that set off nuclear reactions in their cores.
Despite all the wonderful things gravity does for us, it remains something of an enigma. There are two reasons. First, there is nothing in the rest of physics that predicts that gravity should exist. The other physical forces have been tied together in a unified theory that relates them to one another and predicts how strong each should be. But gravity remains on its own; there is no explanation for it and no way of predicting the value of G. Gravity’s enigmatic status is heightened by the fact that repeated measurements of G have failed to pin it down precisely.
In principle, measuring G is very straightforward. You calculate it from the gravitational attraction between two bodies of known mass a known distance apart. The calculation does not require a supercomputer. My niece Nicola, a bright 13 year-old, could do it with a pencil and paper. You multiply the gravitational attraction by two fractions whose numerator is the distance between the objects and whose denominators are the masses of the objects.
Unfortunately there is a practical problem. G is very small, so unless one of the objects has the mass of a planet, the attracting force is so small that it is hard to measure precisely. On the other hand, if one of the objects does have the mass of a planet it will also be the size of a planet, so measuring the distance between the centres of the objects is difficult.
These difficulties, which were overstated by Newton, deterred physicists from attempting to measure G for over 100 years. Henry Cavendish made the first measurement in 1798. He used a torsion balance, a beam with a weight at each end suspended from its centre by a fibre. Two extra weights were positioned close to the beam so that the gravitational attraction between them and the weights on the beam caused the beam to rotate slightly, twisting the fibre. Cavendish estimated the force of attraction from the amount the beam had rotated.
Modern attempts to improve on Cavendish’s measurement have refined his apparatus in different ways, mounting the dumbell in a vacuum, setting it spinning so that it forms a pendulum whose period is changed by the gravitational force, floating the weights on mercury to do away with the fibre.
The resulting measurements of G, each of them accurate to about one part in 100,000, differ from each other by up to 0.5 per cent. This is a huge error in physical terms. The problem according to Clive Speake of the University of Birmingham is that “this is a very difficult measurement to make… and we are still trying to make it with 200 year old technology.”
Speake’s personal mission is to apply 21st century technology to gravitational measurements. He is working with Terry Quinn of the International Office of Weights & Measures in Paris on a new torsion balance which will use a ribbon instead of a fibre to support the dumbell. This will make it possible to use much heavier weights that will produce a stronger gravitational force that can be measured more accurately. In the future he hopes to refine the technique further using magnetic levitation to support the weights.
Speake believes that the variation in the value of G is most likely to be caused by as yet unknown sources of error in the measurements. So if you really want your weight to change you had better rely on diet and exercise rather than on the changing value of G.