String Theory For Dummies. Andrew Zimmerman Jones

distance between them stays the same. (See the sidebar “A matter of mass” for clarification of this relationship.)

      A MATTER OF MASS

      When we 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 fall 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 a soccer ball off a building (which we don’t recommend), they would accelerate at the exact same rate (ignoring air resistance) — approximately 9.8 meters per second squared.

      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 is identical for the two balls.

      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 (like in a vacuum), shows that the objects fall at the same rate, regardless of their 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 from each other, 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. If two objects get extremely close to each other — and we’re 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.

      We delve a bit deeper into Newton’s work, both in gravity and in related areas, in Chapter 5.

      Despite the success of Newton’s theory, he had a few nagging problems in the back of his mind. First and foremost among them was the fact that although he had a model for gravity, he didn’t know why gravity works. 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 see gravity. Instead of thinking of gravity as a force acting between objects, Einstein 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 the net effect of gravity. Instead of being a force, gravity was actually the result 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 Hermann Minkowski, Einstein’s former professor, 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 1915, he was able to include gravity in his explanation 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 Chapter 6, and the major implications of relativity to the evolution of the universe are covered in Chapter 9. The space-time dimensions are discussed in Chapter 15.

Describing Matter: Physical and Energy-Filled

      Einstein helped to revolutionize our ideas about the composition of matter as much as he changed our understanding of space, time, and gravity. Thanks to Einstein, scientists realize that mass — and therefore matter itself — is a form of energy. This realization is at the heart of modern physics. Because gravity is an interaction between objects made up of matter, understanding matter is crucial to understanding why physicists need a theory of quantum gravity.

      Viewing matter classically: Chunks of stuff

      The study of matter is one of the oldest physics disciplines, going back to the ancient philosophers who tried to understand what made up the objects around them. Even fairly recently, a physical understanding of matter was elusive as physicists debated the existence of atoms — tiny, indivisible chunks of matter that can’t be broken up any further.

      

One key physics principle is that matter can be neither created nor destroyed, but can only change from one form to another. This principle is known as the conservation of mass.

      Though it can’t be created or destroyed, matter can be broken, which led to the question of whether there was a smallest chunk of matter, the atom, as the ancient Greeks had proposed — a question that, throughout the 1800s, seemed to point toward an affirmative answer.

      As an understanding of thermodynamics — the study of heat and energy, which made things like the steam engine (and the Industrial Revolution) possible — grew, physicists began to realize that heat can be explained as the motion of tiny particles.

The atom had returned, though the findings of 20th-century quantum physics would reveal that it wasn’t indivisible, as everyone thought.

      Viewing matter at a quantum scale: Chunks of energy

      With the rise of modern physics in the 20th century, two key facts about matter became clear:

       As Einstein had proposed with his famous E = mc² equation, matter and energy are, in a sense, interchangeable.

       Matter is incredibly complex, made up of an