The Elegant Universe

by Brian Greene

In fact, Einstein realized that the principle of relativity makes an even grander claim: the laws of physics—whatever they may be—must be absolutely identical for all observers undergoing constant-velocity motion.

The Speed of Light

Truth and Consequences

The Effect on Time: Part I

The constancy of the speed of light requires that we give up the age-old notion that simultaneity is a universal concept that everyone, regardless of their state of motion, agrees upon.

The Effect on Time: Part II

For this purpose we introduce the world's conceptually simplest (yet most impractical) clock. It is known as a "light clock" and consists of two small mirrors mounted on a bracket facing one another, with a single photon of light bouncing back and forth between them (see Figure 2.1). If the mirrors are about six inches apart, it will take the photon about a billionth of a second to complete one round-trip journey. "Ticks" on the light clock may be thought of as occurring every time the photon completes a round-trip—a billion ticks means that one second has elapsed.

Life on the Run

Time elapses more slowly for an individual in motion than it does for a stationary individual.

Who Is Moving, Anyway?

Motion's Effect on Space

Motion through Spacetime

Einstein proclaimed that all objects in the universe are always traveling through spacetime at one fixed speed—that of light.

Thus light does not get old; a photon that emerged from the big bang is the same age today as it was then. There is no passage of time at light speed.

What about E=mc2?

Chapter 3

Of Warps and Ripples

Newton's View of Gravity

Gravity dictates the rhythm of the cosmic dance that is tirelessly and meticulously executed by billions upon billions of cosmic inhabitants, from asteroids to planets to stars to galaxies.

Newton's view of gravity might be called the great equalizer. He declared that absolutely everything exerts an attractive gravitational force on absolutely everything else. Regardless of physical composition, everything exerts as well as feels the force of gravity.

Newton deduced that the strength of the gravitational attraction between two bodies depends on precisely two things: the amount of stuff composing each of the bodies and the distance between them.

In words, these equations state that the gravitational force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them.

The Incompatibility of Newtonian Gravity and Special Relativity

Nothing outruns photons.

In a vacuum.

Einstein's Happiest Thought

By what means does gravity execute its mission? This is a problem of which Newton himself was well aware.

Newton accepted the existence of gravity and went on to develop equations that accurately describe its effects, but he never offered any insight into how it actually works. He gave the world an "owner's manual" for gravity which delineated how to "use" it—instructions that physicists, astronomers, and engineers have exploited successfully to plot the course of rockets to the moon, Mars, and other planets in the solar system; to predict solar and lunar eclipses; to predict the motion of comets, and so on. But he left the inner workings—the contents of the "black box" of gravity—a complete mystery.

Einstein realized that hundreds of years of experimental confirmation notwithstanding, special relativity implied that in some subtle way Newton's theory was "broken" and that its repair required coming to grips with the question of the true and full nature of gravity.

Einstein called the indistinguishability between accelerated motion and gravity the equivalence principle. It plays a central role in general relativity.2

Einstein's 1907 insight now shows us how to embrace all points of view—constant velocity and accelerating—within one egalitarian framework. Since there is no difference between an accelerated vantage point without a gravitational field and a nonaccelerated vantage point with a gravitational field, we can invoke the latter perspective and declare that all observers, regardless of their state of motion, may proclaim that they are stationary and "the rest of the world is moving by them," so long as they include a suitable gravitational field in the description of their own surroundings.

Acceleration and the Warping of Space and Time

Time is warped if its rate of passage differs from one location to another.

Gravity, according to Einstein, is the warping of space and time.

The Basics of General Relativity

These links between gravity, accelerated motion, and curved space led Einstein to the remarkable suggestion that the presence of mass, such as the sun, causes the fabric of space around it to warp, as shown in Figure 3.4.

According to this radical proposal, space is not merely a passive forum providing the arena for the events of the universe; rather, the shape of space responds to objects in the environment.

In Einstein's view, the gravitational tether holding the earth in orbit is not some mysterious instantaneous action of the sun; rather, it is the warping of the spatial fabric caused by the sun's presence.

Einstein fully agreed with Newton's statement that "Gravity must be caused by an agent" and rose to Newton's challenge in which the identity of the agent was left "to the consideration of my readers." The agent of gravity, according to Einstein, is the fabric of the cosmos.

A Few Caveats

As the eminent physicist John Wheeler has often said in describing gravity, "mass grips space by telling it how to curve, space grips mass by telling it how to move."8

(In fact, the mathematics of general relativity shows that in the case of a relatively slow-moving body like the earth revolving around a typical star like the sun, the warping of time actually has a far more significant impact on the earth's motion than does the warping of space.)

Conflict Resolution

Einstein's formulation thereby resolves the conflict; gravitational disturbances keep pace with, but do not outrun, photons.

The Warping of Time, Revisited

Experimental Verification of General Relativity

Aesthetics aside, the ultimate test of a physical theory is its ability to explain and predict physical phenomena accurately.

You said it, Brian!

This is both good and bad. It is good because any theory purporting to supplant Newton's theory of gravity had better closely agree with it when applied in those arenas in which Newton's theory has been experimentally verified. It is bad because it makes it difficult to adjudicate between the two theories experimentally. Distinguishing between Newton's and Einstein's theories requires extremely precise measurements applied to experiments that are very sensitive to the ways in which the two theories differ.

Einstein's general relativity predicts that the sun will cause the surrounding space and time to warp and such distortion will influence the path taken by the starlight.

In November of 1915, Einstein used his new understanding of gravity to calculate the angle through which starlight signals that just graze the sun would be bent and found the answer to be about.00049 of a degree (1.75 arcseconds, where an arcsecond is 1/3600 of a degree).

On November 6, 1919, after some five months of analysis of the photographs taken during the eclipse at Principe (and of other photographs of the eclipse taken by a second British team led by Charles Davidson and Andrew Crommelin in Sobral, Brazil), it was announced at a joint meeting of the Royal Society and the Royal Astronomical Society that Einstein's prediction based on general relativity had been confirmed.