# Understanding Two Schools of Thought on Gravity (String Theory)

Physicists are searching for a theory of quantum gravity because the current laws governing gravity don’t work in all situations. Specifically, the theory of gravity seems to “break down” (that is, the equations become physically meaningless) in certain circumstances that I describe later in the topic. To understand what this means, you must first understand a bit about what physicists know about gravity.
Gravity is an attractive force that binds objects together, seemingly across any amount of distance. The formulation of the classical theory of gravity by Sir Isaac Newton was one of the greatest achievements of physics. Two centuries later, the reinvention of gravity by Albert Einstein placed him in the pantheon of indisputably great scientific thinkers of all time.
Unless you’re a physicist, you probably take gravity for granted. It’s an amazing force, able to hold the heavens together while being overcome by my 3-year-old when he’s on a swing — but not for long. At the scale of an atom, gravity is irrelevant compared to the electromagnetic force. In fact, a simple magnet can overcome the entire force of the planet Earth to pick up metallic objects, from paper clips to automobiles.

## Newton’s law of gravity: Gravity as force

Sir Isaac Newton developed his theory of gravity in the late 1600s. This amazing theory involved bringing together an understanding of astronomy and the principles of motion (known as mechanics or kinematics) into one comprehensive framework that also required the invention of a new form of mathematics: calculus. In Newton’s gravitational theory, objects are drawn together by a physical force that spans vast distances of space.
The key is that gravity binds all objects together (much like the Force in Star Wars). The apple falling from a tree and the moon’s motion around Earth are two manifestations of the exact same fundamental force.
The relationship that Newton discovered was a mathematical relationship (he did, after all, have to invent calculus to get it all to work out), just like relativity, quantum mechanics, and string theory.
In Newton’s gravitational theory, the force between two objects is based on the product of their masses, divided by the square of the distance between them. In other words, the heavier the two objects are, the more force there is between them, assuming the distance between them stays the same. (See the nearby sidebar “A matter of mass” for clarification of this relationship.)

## A matter of mass

When I say that the force between objects is proportional to the mass of the two objects, you may think this means that heavier things fall faster than lighter things. For example, wouldn’t a bowling ball fall faster than a soccer ball?
In fact, as Galileo showed (though not with modern bowling and soccer balls) years before Newton was born, this isn’t the case. For centuries, most people had assumed that heavier objects fell faster than light objects. Newton was aware of Galileo’s results, which was why he was able to figure out how to define force the way he did.
By Newton’s explanation, it takes more force to move a heavier object. If you dropped a bowling ball and soccer ball off a building (which I don’t recommend), they would accelerate at the exact same rate (ignoring air resistance) — approximately 9.8 meters per second.
The force acting between the bowling ball and Earth would be higher than the force acting on the soccer ball, but because it takes more force to get the bowling ball moving, the actual rate of acceleration between the two is identical.
Realistically, if you performed the experiment there would be a slight difference. Because of air resistance, the lighter soccer ball would probably be slowed down if dropped from a high enough point, while the bowling ball would not. But a properly constructed experiment, in which air resistance is completely neutralized (such as in a vacuum), shows that the objects fall at the same rate, regardless of mass.
The fact that the force is divided by distance squared means that if the same two objects are closer to each other, the power of gravity increases. If the distance gets wider, the force drops. The inverse square relationship means that if the distance doubles, the force drops to one-fourth of its original intensity. If the distance is halved, the force increases by four times.
If the objects are very far away, the effect of gravity becomes very small. The reason gravity has any impact on the universe is because there’s a lot of it. Gravity itself is very weak, as forces go.
The opposite is true, as well, and if two objects get extremely close to each other — and I’m talking extremely close here — then gravity can become incredibly powerful, even among objects that don’t have much mass, like the fundamental particles of physics.
This isn’t the only reason gravity is observed so much. Gravity’s strength in the universe also comes from the fact that it’s always attracting objects together. The electromagnetic force sometimes attracts objects and sometimes repulses them, so on the scale of the universe at large, it tends to counteract itself. Finally, gravity interacts at very large distances, as opposed to some other forces (the nuclear forces) that only work at distances smaller than an atom.
I delve a bit deeper into Newton’s work, both in gravity and in other related areas, in topic 5.  Despite the success of Newton’s theory, he had a few nagging problems in the back of his mind. First and foremost among those was the fact that though he had a model for gravity, he didn’t know why gravity worked. The gravity that he described was an almost mystical force (like the Force!), acting across great distances with no real physical connection required. It would take two centuries and Albert Einstein to resolve this problem.

## Einstein’s law of gravity: Gravity as geometry

Albert Einstein would revolutionize the way physicists saw gravity. Instead of gravity as a force acting between objects, Einstein instead envisioned a universe in which each object’s mass caused a slight bending of space (actually space-time) around it. The movement of an object along the shortest distance in this space-time was gravity. Instead of being a force, gravity was actually an effect of the geometry of space-time itself.
Einstein proposed that motion in the universe could be explained in terms of a coordinate system with three space dimensions — up/down, left/right, and backward/forward, for example — and one time dimension. This 4-dimensional coordinate system, developed by Einstein’s old professor Hermann Minkowski, was called space-time, and came out of Einstein’s 1905 theory of special relativity.
As Einstein generalized this theory, creating the theory of general relativity in 1916, he was able to include gravity in his explanations of motion. In fact, the concept of space-time was crucial to it. The space-time coordinate system bent when matter was placed in it. As objects moved within space and time, they naturally tried to take the shortest path through the bent space-time.
We follow our orbit around the sun because it’s the shortest path (called a geodesic in mathematics) through the curved space-time around the sun.
Einstein’s relativity is covered in depth in topic 6, and the major implications of relativity to the evolution of the universe are covered in topic 9. The space-time dimensions are discussed in topic 13.