The jumping apple

According to tradition, Newton's hypothesis of universal gravitation was prompted by the fall of an apple. Whether this is a fiction or not, it represents a way in which Gravitation nicely fit into people imagination. Following this pictorial approach, Einstein realized that an apple placed in the vicinity of a pair of orbiting stars would oscillate, like a sort of jumping apple. Indeed, one of the consequences of the Einstein’s theory of Gravitation is that a pair of orbiting stars generates ripples in space, the so called gravitational waves.

A gravitational wave impinging perpendicular onto a ring of particles, forces them to oscillate in a "cruciform" manner, as shown in the above animation. If we consider two particles, we can see that their relative distance changes periodically, and that in the reference frame of one particle, the other particle is seen to be jumping up and down. Strictly speaking, in the case of extended bodies, the situation is more complicated. If an apple is located on ground, we definitely would not see it jumping. The system Earth-apple responds to gravitational waves as in the animation on the right.

However, if the apple is orbiting around the Earth, or it is attached to its own tree, in this case we would definitely see it jumping up and down when gravitational waves are impinging on it. At this point, during a public conference, a smart child said: "Whow ! that's why the Newton's apple fallen! It was shacked by a gravitational wave, and so it was detached by the tree, and fallen down!"