Gravity

The one holdout, the one force for which we do not have a successful theory, is gravity. We have come a long way since Newton’s law of gravity. After Einstein developed his theory of relativity in 1905, he spent the next 12 years working on a relativistic theory of gravity. The result, known as general relativity is a theory of gravity that is in many ways similar to Maxwell’s theory of electricity. Einstein’s theory predicts, for example, that a planet in orbit about a star should emit gravitational waves in much the same way that Maxwell’s theory predicts that an electron in orbit about a nucleus should emit electromagnetic radiation or light.
One of the difficulties working with Einstein’s theory of gravity is that Newton’s theory of gravity explains almost everything we see, and you have to look very hard in places where Newton’s law is wrong and Einstein’s theory is right. There is an extremely small but measurable correction to the orbit of Mercury that Newton’s theory cannot explain and Einstein’s theory does.
Einstein’s theory also correctly predicts how much light will be deflected by the gravitational attraction of a star. You can argue that because light has energy and energy is equivalent to mass, Newton’s law of gravity should also predict that starlight should be deflected by the gravitational pull of a star. But this Newtonian argument leads to half the deflection predicted by Einstein’s theory, and the deflection predicted by Einstein is observed.
The gravitational radiation predicted by Einstein’s theory has not been detected directly, but we have very good evidence for its existence. In 1974 Joe Taylor from the University of Massachusetts, working at the large radio telescope at Arecibo discovered a pair of neutron stars in close orbit about each other. We will have more to say about neutron stars later. The point is that the period of the orbit of these stars can be measured with extreme precision.​

Einstein’s theory predicts that the orbiting stars should radiate gravitational waves and spiral in toward each other. This is reminiscent of what we got by applying Maxwell’s theory to the electron in hydrogen, but in the case of the pair of neutron stars the theory worked. The period of the orbit of these stars is changing in exactly the way one would expect if the stars were radiating gravitational waves.
If our wave-particle picture of the behavior of matter is correct, then the gravitational waves must have a particle nature like electromagnetic waves. Physicists call the gravitational particle the graviton. We think we know a lot about the graviton even though we have not yet seen one. The graviton should, like the photon, have no rest mass, travel at the speed of light, and have the same relationship between energy and wavelength.
One difference is that because the graviton has energy and therefore mass, and because gravitons interact with mass, gravitons interact with themselves. This self interaction significantly complicates the theory of gravity. In contrast photons interact with electric charge, but photons themselves do not carry charge. As a result, photons do not interact with each other which considerably simplifies the theory of the electric interaction.
An important difference between the graviton and the photon, what has prevented the graviton from being detected, is its fantastically weak interaction with matter. You saw that the gravitational force between the electron and a proton is a thousand billion billion billion billion times weaker than the electric force. In effect this makes the graviton a thousand billion billion billion billion times harder to detect. The only reason we know that this very weak force exists at all is that it gets stronger and stronger as we put more and more mass together, to form large objects like planets and stars.

Not only do we have problems thinking of a way to detect gravitons, we have run into a surprising amount of difficulty constructing a theory of gravitons. The theory would be known as the quantum theory of gravity, but we do not yet have a quantum theory of gravity. The problem is that the theory of gravitons interacting with point particles, the gravitational analogy of quantum electrodynamics, does not work. The theory is not renormalizable, you cannot get rid of the infinities. As in the case of the electric interaction the simple calculations work well, and that is why we think we know a lot about the graviton. But when you try to make what should be tiny relativistic corrections, the correction turns out to be infinite. No mathematical slight of hand has gotten rid of the infinities.
The failure to construct a consistent quantum theory of gravity interacting with point particles has suggested to some theoretical physicists that our picture of the electron and some other particles being point particles is wrong. In a new approach called string theory, the elementary particles are view not as point particles but instead as incredibly small one dimensional objects called strings. The strings vibrate, with different modes of vibration corresponding to different elementary particles.
String theory is complex. For example, the strings exist in a world of 10 dimensions, whereas we live in a world of 4 dimensions. To make string theory work, you have to explain what happened to the other six dimensions. Another problem with string theory is that it has not led to any predictions that distinguish it from other theories. There are as yet no tests, like the deflection of starlight by the sun, to demonstrate that string theory is right and other theories are wrong.
String theory does, however, have one thing going for it. By spreading the elementary particles out from zero dimensions (points) to one dimensional objects (strings), the infinities in the theory of gravity can be avoided.