Remember the example of traveling in a train at near the speed of light past a friend on a station platform. The friend sees time as slowing down and you as being thinner. Both space and time have changed in his perception. Remember also that the theory of special relativity combines both space and time into one, spacetime. What is this spacetime?

Mathematics is often called the language of science because many physical phenomena can best be expressed mathematically. For those of us who have trouble with high school algebra and geometry, describing scientific theories can be daunting and understanding them well-nigh impossible. We have to resort to crude analogies like the train traveling past the station. But using another everyday example lets us at least visualize spacetime.

Imagine a trampoline stretched taut in its frame. The surface is perfectly flat. This represents spacetime in the absence of any matter. If you roll a BB across the trampoline it will go in a straight line from one side to the other. Matter is composed of mass so let’s see what happens when mass is introduced into spacetime.

Now imagine placing a bowling ball in the middle of the trampoline. Spacetime becomes deformed as the trampoline sags to support the ball. If you now roll a tennis ball across the trampoline it will follow what appears to be a curved path caused by the indentation from the bowling ball. In fact, if you roll the tennis ball at just the right speed it will circle the bowling ball like a roulette ball circles the spinning wheel.

The bowling ball can be thought of as a star, our sun for example. The tennis ball is a planet orbiting that star, our earth or one of the other planets. The tennis ball makes its own slight indentation in the trampoline, just as the Earth makes its own indentation in spacetime. We can imagine a marble circling the tennis ball, following that indentation. In the same way the moon orbits the Earth.

This three-dimensional image of spacetime soon breaks down because friction of the tennis ball on the trampoline and air resistance slow the tennis ball and it drops into the indentation. However, that in itself is instructive because that is the ultimate fate of Earth: eventually the earth will spiral into the sun just like the tennis ball.

Einstein’s view of gravity is thus fundamentally different from Newton’s. Newton believed that gravity is a natural attraction of bodies for each other that is caused by a property inherent in mass. Einstein postulated that gravity is caused by a deformation of spacetime, which in turn is caused by the body. There is nothing inherent in mass that creates gravity. Instead it is the nature of spacetime that causes gravity.

Newton’s theories had served science well for nearly 400 years. It wasn’t enough for Einstein’s theory to predict the same thing as Newton’s. Einstein’s theory had to predict an observable event not predicted by Newton’s theory. Only in this way could Einstein’s theory be shown superior to Newton’s. This is how most theories are “proven.” In practice a theory can’t be proven right; it can only be proven wrong in the sense that it predicts something that is not observed or fails to predict an observation. Einstein’s problem was that for all situations on earth, including the orbit of the moon, both theories predicted the same thing with the same accuracy. Einstein’s theory predicted a difference in an extreme gravitational field. The only problem was finding such a situation where the two predictions could be observed and compared.

He finally found such a situation in the orbit of Mercury around the sun. Mercury’s orbit had long been observed as rotating. Mercury’s orbit is elliptical like the other planets’ but the ellipse itself rotates around the sun by 574 arcseconds per century. An arcsecond is 1/3,600 degrees. It takes Mercury over one million orbits of the sun and 200,000 years to return to the same orbit. Newton’s theory accounted for only 531 of the 574 arcseconds but Einstein’s theory account for exactly 574 arcseconds.

This was enough to put Newton’s theory in doubt but not enough for most scientists. Someone discovered that if, instead of r^{2 }in Newton’s formula for gravitational attraction there was r^{2.00000016} the two theories made the same prediction. This was just number fudging but it shows the lengths to which scientists will go to salvage pet theories. Einstein realized he would need something even more spectacular to win the controversy.