THE TRAVELLING LIGHT

Imagine setting up an experiment inside such a lift to measure the behavior of a beam of light that crosses from one side of the lift to the other. In a lift moving at constant velocity, far from any planet or star, the light will travel in a straight line across the lift. But in the accelerated lift, the opposite wall has speeded up and moved forward (down) relative to the light beam in the time it takes the light to cross the lift. The only way in which it can look as if the light is following a straight line, from the point of view of the people in the lift, will be if the trajectory of the beam of light is bent by gravity.

Figure of Light

Since light has no mass, how can it be affected by gravity? The answer, as Einstein found with a little help from Grossman, is that what we think of as forces caused by the presence of lumps of matter, such as the Sun, are distortions in the fabric of space-time. The Sun, for example, makes a dent in the geometry of space-time, and the orbit that the Earth makes around the Sun is a result of trying to follow the shortest path (a geodesic) through curved space-time.

Figure of Bending of Light due to Gravity

‘Everybody knows’ that Einstein was the first person to describe the curvature of space in this way – but ‘everybody’ is wrong. Einstein was not even the second person to think about the possibility of space in our Universe being curved, and he had to be pushed along the path by others, including Grossman. He persuaded Einstein that the multidimensional geometry developed by 19th-century mathematicians might explain how light could be affected by gravity. While the geometry of the special theory of relativity is extended to four dimensions, it still obeys the rules which apply in flat space. What Grossman knew, but Einstein did not until Grossman told him in 1912, was that there is more to geometry (even multidimensional geometry) than good old Euclidean ‘flat’ geometry. Light follows the line of least resistance through space-time, but if space-time itself is curved, bent by the presence of matter, then these ‘geodesics’ are themselves curved. Einstein had the insight, and Grossman knew where to find the mathematics to describe the insight.

Figure of Experiment on Bending of Light

Euclidean geometry is the kind we encounter at school, where the angles of a triangle add up to exactly 180degree, parallel lines never meet and so on. The first person to go beyond Euclid and to appreciate the significance of what he was doing was the German Karl Gauss, who was born in 1777 and had completed all his great mathematical discoveries by 1799. But because Gauss did not bother to publish many of his ideas, non-Euclidean geometry was independently rediscovered by both the Russian mathematician Nikolai Ivanovich Lobachevski, who was the first to publish a description of such geometry in 1829, and by a Hungarian army officer, Janos Bolyai, who published in 1832. 

An Abstract from The Multidimensional Theory Research.