I) History of Gravity

A) Early ideas

The very earliest ideas regarding gravity must have been based on every day experience. For example:

• Objects fall unless they are supported.
• "Down" is different from "across".
• Climbing a hill is harder work than walking on a level.

We still use these very basic ideas and properties of objects every day without further thought. Because we live on a large Earth and are not familiar with gravitation from any other object, we tend to equate gravity with "down". (If we lived on a planet the size of the asteroid in The Little Prince we might have different instincts.) This is one of the basic points we want to get across: gravity is "together" not down.

B) Ancient Greeks: Aristotle

It was with the Ancient Greeks, and in particular Aristotle, that these disparate observations began to be unified into one idea. For Aristotle, physics was the investigation of "causes" in the widest possible sense. While "Gravity" was not yet a concept in itself, Aristotle realized that these various properties of objects must be related.

To Aristotle, the cause of falling was heaviness. The heavier the object, the more it falls - a large rock plummets to the earth, a leaf ambles along downward slowly and a dandelion fluff barely falls at all and frequently rises higher into the sky instead. But what was the connection between heavy objects and falling? To understand this, one must have an idea of the Aristotelian worldview.

To Aristotle, all Matter was made of four elements, Earth, Water, Air and Fire. Earth, the basest and least noble, was in the center. This was the ground we walk on. Next was the sphere of Water, followed by the sphere of Air and then of Fire. The eternal and perfect Celestial spheres of the stars and planets surrounded and limited the Universe. Everything under the moon was composed of some mixture of the four elements. Clouds for example were considered to be mostly air with a bit of water and fire.

The natural place for heavy objects (made principally of Earth) was back in the center. If one removed a heavy object, say a stone, from its natural place (i.e. by lifting it) it would tend to return to its "proper" place. In a similar way, fire tended to rise, because it was trying to return to its natural place above the sphere of air. Intermediate objects, such as the leaf or dandelion fluff, were made of less Earth and more Air (or Fire) and hence fell more slowly, or perhaps not at all.

C) Middle Ages

Medieval physics (and astronomy) was largely based on the ideas of Aristotle. Since the teachings of Aristotle had been given the seal of approval by the Church, they were taken to be the revealed truth and essentially unquestioned in the Universities. In general, this didn't work too badly: most objects work more or less in the manner described by Aristotle. This is not surprising since his work was essentially the codification of day to day experience and is very commonsensical. In certain cases, however, serious discrepancies might have been noted. One example of this was the medieval view of cannonball trajectories. In the Aristotelian view, when a cannonball's initial upward and forward impetus was exhausted it would fall vertically to the Earth, its natural place. This indeed should be true of any object shot or thrown into the air. Anyone who had watched a rock thrown into the air could tell this was not true. The trouble was that the people teaching the theories and the people dealing with the real world objects were different. Furthermore, until the beginning of the Renaissance, experimentation was discouraged and considered beneath the dignity of philosophers. The way to truth was considered to be pure thought and the scriptures.

D) Renaissance: Galileo

Galileo's work represents the beginnings of a modern understanding of Gravity. Ironically, to achieve this, Galileo began by disavowing any interest in "causes". Instead of trying to answer the question "why do objects fall?" he explored "how do objects fall?" This is an extremely important step. Even today we do not fully understand the "why" of gravity although we understand the "how" very well indeed.

Galileo began his exploration of how objects fall by comparing the rates at which objects fall. He also tried to figure out how fast they fall. His basic conclusions were the following:
• objects of different weight fall at the same speed,
• falling starting from a complete stop, objects move more and more quickly the longer they have been falling.
• the distance an object falls is proportional to the square of the elapsed time.

He arrived at these conclusions through a beautiful series of experiments. The first thing he realized was that he would need to slow down the motion of objects to be able to measure their fall. He did this by allowing the objects he studied to roll down a tilted board instead of falling straight down. He had to assume that this procedure was valid... fortunately it was. Second, he knew that he had no accurate clocks for measuring times. Instead he used his natural sense of rhythm (he was a very musical man). In the path of the objects he rolled down the plane he placed little bumps. Every time the object went over a bump it made a click. By arranging the bumps so that the clicks came in a regular series he knew the time between the bumps was the same. The story of Galileo dropping cannonballs of different weights off the Leaning Tower of Pisa is probably apocryphal. If he did this, it was certainly less important to him than his controlled experiments.

Galileo's contribution to the understanding of gravity was threefold. First, he subtly changed the question being asked. Second he based his answers on careful experimentation and measurement. Third, he gave a mathematical quantitative description of his results and gave the limits within which he had verified this description.

E) Enlightenment: Newton

Newton, born in the year Galileo died, developed the modern concept of gravity. Instead of simply exploring how objects fall, he posited a force of gravity that was responsible for a variety of effects.

Newton started from Galileo's law of falling objects and applied it to an unlikely object: the Moon. Why, he asked, did the moon not fall to the earth? Other unsupported objects (like rocks, sticks etc.) fall immediately to the ground. The Moon seems to flout the law of gravity. That's the trick, however. The moon only seems to be immune to gravity. Newton realized that the Moon is not immune to gravity... it is continuously falling towards the Earth, but it keeps missing it! A little explanation of this somewhat outrageous sounding statement is in order.

Imagine standing on a tower on a flat earth. Throw a rock sideways out the window. Eventually, the rock will fall to the ground. Now throw the rock harder. It will hit the ground farther from the tower. On a flat earth this can be continued, throwing the rock harder and harder with the impact farther and farther away. But not so on a spherical earth. On a spherical Earth, the earth curves away under the falling rock. When the rock is thrown with only a little speed, the distance is small and the surface of the Earth the distance spans is almost flat. But if the rock is thrown hard enough, the ground will drop a great deal. In fact, if the rock is thrown very, very hard indeed it will never hit the ground because the earth keeps receding beneath it! This is what is called being in orbit. The secret to flying is falling but missing the ground!

Newton thus realized that gravity was not something special to the Earth. Gravity also acts in space. This was a profound, even revolutionary idea. According to Aristotle, the laws governing the heavens were considered to be completely different from the laws of physics here on Earth. Now, however, if the moon was affected by gravity, then it made sense that the rest of the Solar System should also be subject to gravity. Newton found that he could explain the entire motion of the Solar System from the planets to the moons to the comets with a single law of Gravity:

All bodies attract all other bodies, and the strength of the attraction is proportional to the masses of the two bodies and inversely proportional to the square of the distance between the bodies.

A modern mathematical way of saying this is:

where G (Newton's Constant) is a constant value equal to 6.67x10-11 m3/s2/kg, M is the mass of one object, m is the mass of the other object, R (radius) is the distance between the objects and F is the resulting gravitational force pulling the objects together. This is called the Universal Law of Gravity. Universal because it applies to all bodies in the Universe regardless of their nature. Gravity is not just about falling, it is about attraction! As I write this, the keyboard in front of me pulls ever so slightly on the phone to my right, the penny I left at home gently tugs at the umbrella I lost in San Diego and the flight of a bird above the Adler makes me fractionally lighter! All objects pull on all other objects! What a fantastic statement! Of course, for most objects, the force of attraction is incredibly tiny and not noticeable, but it is always there.

Despite its power in explaining the orbits of the Solar System, Newton (and his critics) were unhappy with the lack of a mechanism by which gravity worked. Until then, all forces were believed to be "contact" forces. That is to say, to push an object one had to be touching it. I push a pen across the table using my hand directly. Even if I blow a piece of paper, I am really moving the air with my lungs which then moves across to the paper and pushes it along. Almost everything in our experience works this way - except for gravity. The Newtonian concept of "action-at-a-distance" was profoundly disturbing to his opponents, who attacked his theory as "occult" and explaining nothing.

F) Post Enlightenment - 1700s,1800s

From the period immediately following Newton's discovery of his Universal Law of Gravitation, to about the turn of the last century (1900), the theory of gravitation stayed essentially unchanged. More sophisticated mathematical tools for understanding the interplay of the planets were developed, but the underlying theory remained stable. As in the earlier Aristotelian world-view, gravitation was intricately connected with the structure of the Universe. The moons revolved around the planets, the planets revolved around the Sun, the Sun floated through space passing other stars, all with clockwork precision. The Universe was orderly and controlled by gravity and the laws of motion.

The excitement during this period mainly came from the systematic application of the theory of gravity to the heavens. For example:

1) Comets: an understanding of how objects orbited the Sun allowed predictions of the path of comets. The best known case of this was Halley's prediction of the return of the comet that now bears his name.

2) Discovery of Neptune: In the time of Newton, only six of the nine planets had been discovered. While the discovery of the planet Uranus was by and large accidental, the discovery of Neptune was a triumph of the Newtonian theory of gravity.

After the discovery of Uranus, great attention was paid to this newest of planets. Its orbit was carefully mapped out in great detail. And something strange was found... The orbit of Uranus did not seem to follow Newton's laws precisely! The motion across the skies was just slightly different from the motion predicted on the basis of the theory of gravity. Astronomers were presented with a choice. Either Newton was wrong, or their calculations were somehow incomplete. Many influential scientists thought that perhaps the law of gravitation did not apply so far from the Sun.

In the period 1843-1846 John Adams and Urbain Leverrier independently came to the conclusion that the perturbations of Uranus's orbit were due to an eighth planet. Shortly thereafter, the new planet was discovered precisely where Adams and Leverrier had predicted. Newton was spectacularly vindicated!

3) Binary Stars: William Hershel's observations of binary stars during the early 1800s showed that the Newtonian laws of gravity also applied to the stars. They also allowed, for the first time, the calculation of the mass of stars other than our Sun.

4) Rings of Saturn: The law of gravitation also illuminated the origin and nature of the rings of Saturn. The rings could not be thin solid sheets as previously thought. James Maxwell showed that such rings would break apart under the combined actions of their own motion and the gravity of Saturn. He suggested instead that the rings were made up of many individual particles.

Of course, other advances were made. Among the most important were the experiments of Cavendish. Cavendish directly demonstrated the gravitational force between two objects in the laboratory. Indirectly, this was equivalent to the first measurement of the mass of the Earth.

G) Twentieth Century: Einstein

The twentieth century was a time of tremendous progress in physical science. For the understanding of gravity, the century began with two puzzles.

The first of these puzzles concerned the orbit of the planet Mercury. In the Newtonian theory of gravity, the orbit of a single planet around the Sun should be a perfect ellipse. In the real world however, the planet is subject to the gravitational forces from the other planets in the Solar System, and hence, does not move in a perfect ellipse (This is how Neptune was discovered). In the case of Mercury, the motion was expected to look almost like an ellipse, but the point of closest approach to the Sun (perihelion) was expected to slowly revolve around the Sun. This is called the "perihelion advance of Mercury". Astronomers carefully measuring the position of Mercury over a period of time came to a startling conclusion: The perihelion advance was there, but it was occurring too quickly.

At first, astronomers assumed this was due to the influence of another undiscovered planet. But after extensive searches, no new planet was found. What was going on? Nobody knew.

The second puzzle was related to a series of experiments performed by the Hungarian physicist Roland Eotvos at the end of the 19th century. Eotvos was intrigued by a curious fact about Newton's laws of gravity and motion. Newton's laws can be written:

Newton's law of gravity says that the gravitational force felt by an object is proportional to its "mass". Newton's law of motion also involves a "mass". But why should both laws involve the same quantity? After all, motion and gravity seem to be two very different things. Why should they both depend on the same property of an object? One might imagine a world where the force of gravity depended on how green an object was, or perhaps some other property. Scientists call the mass in the law of gravity "gravitational" mass and the mass involved in motion "inertial" mass. Amazingly, Eotvos' experiments showed that the gravitational mass was the same as the inertial mass to at least a few parts in a hundred million. One consequence of this is that all objects fall towards the Earth at the same rate. A larger mass is pulled with a larger force, but a larger mass also needs a larger force to get it moving. If one calculates the acceleration of an object, the mass cancels out entirely. Nobody had any idea why this should be the case.

Both of these puzzles were solved by the epochal work of Albert Einstein. Earlier, in the first years of the 20th century, Einstein had proposed his Special Theory of Relativity. This is the theory that sets the maximum speed as that of light and gives the famous relationship between energy and matter (E=mc²). Einstein then turned his thoughts towards gravity. His greatest insight can be illustrated by a very simple "thought experiment". Imagine you are sitting inside a room on a comfortable chair with a desk full of equipment in front of you. You are then told that one of two situations is true:

a) the room is sitting on the Earth.
b) the room is in space (far from the Sun) being accelerated by a powerful rocket.

You are told to figure out which is true without leaving the room or obtaining information from outside. Einstein's realization was that your task is impossible. There is no observable difference between acceleration and gravity. The reason that the inertial mass and the gravitational mass are identical is that acceleration and gravity are really, on some deep level, the same thing. This can be turned around. Imagine one is in the same room, but now the room is weightless. Are you in space far from a source of gravity, or are you in an elevator whose cable has been cut (freely falling)? No experiment that you do can help you decide. What is going on, and why is this helpful in understanding gravity?

Einstein realized that one doesn't really need to deal with gravity directly - one can always cancel it out by moving in the right way. If one moves in the right way (falling), then one doesn't feel any gravity - in fact one is weightless. This is called being in an inertial frame. But physicists know all about doing physics in inertial frames: it's what we do best! But the way you have to move is different in different locations (see image). It's not possible to cancel out gravity everywhere by motion, only locally. Einstein's great achievement was to show how to connect, to patch together, the inertial frames in different locations.

In doing so, Einstein showed that space itself is bent by the presence of matter. Objects don't feel a force of gravity, they simply move in straight lines - but the space they move through is bent and so it appears that they move in arcs. An example may help to clarify things. Imagine an ant walking on the surface of a table. Being lazy, it wants to walk straight ahead. If the surface is perfectly flat, then its path will be a line. But what if the table has an inverted bowl in the middle? The ant walking along will reach the bowl and then continue walking along its side. But the side of the bowl is curved so when it reaches the other edge it may not be going in the same direction as before. It looks like a force acted on the ant to change its direction, but in reality the ant continued to walk as straight as it could, and it was the geometry of the table that changed the direction the ant walked. So in the Einsteinian world picture, matter affects space and space affects matter. They are inextricably tied together.

Extraordinary claims require extraordinary proof, and General Relativity is no exception. The statement that space itself is dynamic and that time and distance are dependent on matter is a very strong claim. Luckily, the support for Einstein's claims is equally strong. It ranges from measurements of the bending of starlight around the Sun to the slowing down of clocks in airplanes to the indirect detection of gravitational waves in a binary pulsar system.

One of the most exciting consequences of General Relativity is the existence of black holes. These are objects so massive and so dense that nothing can escape! Even light, moving at the absolute speed limit, cannot escape the gravitational pull of a black hole. This is where a black hole gets its name: if light cannot escape, then it is truly black! It is interesting to note that the concept of a black hole was not first introduced by General Relativity. As long ago as the late1790s, the French mathematician Laplace conjectured that a sufficiently massive object might have an escape velocity greater than that of light:

"A luminous star, of the same density of Earth, and whose diameter should be two hundred and fifty times larger than that of the Sun would not, in consequence of its attraction, allow any of its rays to arrive at us; it is therefore possible that the largest luminous bodies in the Universe may, through this cause, be invisible."

The black holes of Laplace however, are strictly Newtonian constructions. If they existed, nothing would be particularly strange about them except for the strong gravity. With a strong enough rocket ship one could leave anytime one wished. True black holes are much stranger objects. One might imagine that if one had a strong enough pitching arm one could throw a ball faster than light and it would escape... But hold on, Einstein tells us that nothing can go faster than light! So such a ball is impossible! But what about a rocket ship, or even better having someone from the outside pulling you back up! Couldn't you escape from a black hole that way? General Relativity says no! Not only is the escape velocity that of light, but it would require infinite force to move out from a black hole! Actually, things are even weirder than this! Look in the modern concepts section for more about black holes.

Cosmology

While black holes are very weird objects, they are perhaps not the strangest consequence of General Relativity. Stranger still are the singularities hidden deep in the heart of every black hole. Singularities are regions of space where the density of matter becomes infinite, and the very concepts of matter, space and time lose their meaning. In their vicinity, time travel becomes possible, and the laws of physics break down completely. Luckily for us, black holes' event horizons shield us from the hidden singularities. They clothe the singularities in a one-way surface that would allow hapless astronauts in, but not out. As long as an object remains outside the event horizon, it would be possible to get pulled back out of the vicinity of the black hole. But the event horizon marks the point of no return. Thus, there is no way for the madness of the singularity to get out to infect the rest of the Universe. But what if a singularity could be formed without a surrounding black hole? This would be a Bad Thing! It is an open question whether such "naked" singularities can be formed. Relativists conjecture that the formation of a naked singularity is forbidden by "Cosmic Censorship", but no one has proved this to be the case.

H) Future Directions

General Relativity is perhaps the most beautiful physical theory yet created. It is powerful, pleasing to the aesthetic sense and well-tested. It is one of the crowning glories of modern physics. At about the same time General Relativity was born, another theory was being created. This was Quantum Mechanics. If General Relativity deals with very massive objects, then Quantum Mechanics deals with the interactions of very small objects, such as electrons and protons. Quantum Mechanics has been verified to a stunning degree of accuracy. It is perhaps the most successful theory in all of physics. So what would happen if one had a very massive, but small, object? Both GR and QM would apply. This seems reasonable... until one tries to do the math! It turns out that the two theories are incompatible. I don't mean that they predict different results (that would be straightforward to test), but rather that we don't even know how to express a theory that combines both GR and QM! The usual method for obtaining a quantum theory of a physical process is to take the classical theory and to "quantize" it. But if one does this to General Relativity, the answers to all calculations become infinite! Nothing makes sense anymore. Most physicists believe that a true combination of GR and QM is possible, but it won't be found as merely an extension of GR. The search for a theory that combines GR and QM is called the search for the Theory of Everything (TOE).

Recently a theory known as "string theory" has gained a lot of support as a candidate TOE. What is different about string theory? Normal Quantum Mechanics treats all particles as points of zero size. This leads to a lot of problems when distances get small or energies get large. String theory says that particles are not points after all, but instead small little loops. The size of these loops are about 10-34 cm-- so very, very small indeed. But not zero! Most of the problems reconciling GR and QM go away when one uses this theory. The full consequences of string theory have not been worked out yet (the mathematics is incredibly complex); but, so far it seems very promising. But we don't know yet, and the final theory of gravity may be something else entirely. Whatever it is, however, we can be certain that the attempts to understand it will have profound consequences for our understanding of the Universe.