## How Gravity Works at Microscopic Scales

### The Greatest Unsolved Problem of 20th-Century Theoretical Physics Is the Construction of a Quantum Theory of Gravity.

Isaac Newton understood gravity in a rather mechanical way. (1) Objects with mass simply attract each other. The more mass they have, the stronger the attraction. (2) The force weakens as the separation between bodies increases. (This, by the way, explains why distant stars do not produce a significant pull on us on Earth -- they are too far away.) (3) Gravity is a very weak force. Hence, only very massive objects such as the Earth and the Sun can produce a sizeable gravity.

Einstein understood gravity in a more natural way. The essential idea is that space is dynamic. This means that space can stretch, bend and be deformed. But what causes space to change its shape? The answer is mass. Massive objects cause space to curve. Now a second body moving in this curved space will not move in a straight line. By definition, it must be accelerating. Acceleration is the change in speed or the change in direction of motion. But since forces are things that cause accelerations, the first object must be producing a force. In this way, Newtonian gravity is reproduced by the Einsteinian viewpoint. In summary, gravity is the consequence of the curving of space. There is a simple analogy used in the book The Bible According to Einstein that illustrates how this works. If you take a bowling ball and place it on a bed, then the surface around the bowling ball will depress. If you then toss a marble onto the bed, the marble will roll toward the bowling ball. It is as though the marble is attracted to the bowling ball. In this analogy, the surface of the bed is like physical space, the bowling ball is like the Earth and the marble is like an apple. When tossed, the apple heads toward the Earth, just as the marble does toward the bowling ball. See animation.

#### What Are Some of the Unusual Features of Quantum Mechanics?

An important discovery of the early twentieth century is quantum mechanics. It governs the behavior of microscopic entities such as atoms and electrons. Uncertainty is a feature of these tiny worlds. An electron circling an atom is never at a definite position. Rather, there is a "probability cloud" associated with it. The electron has a certain chance of being at a particular position, another chance at being at another position and so on. The denser regions of the probability cloud represent regions where the electron is most likely to be found. Another feature of quantum mechanics is fluctuation, which is closely related to the above uncertainty. The position of an electron or atom in the microscopic world seems to fluctuate, being here and there like the motion of a leaf in a wind.

#### What is the Difficulty?

When theorists try to construct a microscopic extension of gravity, that is, a description of gravity at tiny, tiny distances, they must do so in obeisance with the rules of quantum mechanics. Such a theory is called a quantum theory of gravity. Although many suggestions have been made for such a theory, including the most promising candidate of superstrings, no proposal has gained universal acceptance. Almost all ideas encounter difficulties. It is easy to understand why -- the marriage of quantum mechanics and Einstein's gravity theory requires space itself to fluctuate, a mind-boggling concept. How can it be that space has certain probabilities of having certain shapes? If there are a variety of spaces, which one do we live in? The answer must be all of them if the probabilistic nature of quantum mechanics is to be implemented. Although these issues seem philosophical, mathematical difficulties also arise. The construction of a quantum theory of gravity is one of the greatest unsolved problems of theoretical physics.

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