A Brief History of Time | Study Guide

Stephen Hawking

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A Brief History of Time | Chapter 2 : Space and Time | Summary



Stephen Hawking starts out this chapter pitting Galileo Galilei and Sir Isaac Newton against Aristotle by explaining how their later observations led to theories in contradiction with Aristotle's theories. Galileo's measurements of the speed of objects of different weights falling to Earth showed that not only do they hit the ground at the same time, but that the rate at which they fall accelerates uniformly. Based on this, Newton later discovered the laws of motion, which dictate that there is no unique state of rest and thus no absolute, static position any object can have—contrary to Aristotle's understanding.

Hawking explains this idea of relative, rather than absolute, space using the example of a table tennis ball bouncing up and down on a moving train, which would appear to happen differently for someone on the train than for someone standing outside the train as it passes. Relative space was a troubling idea for Newton, and he refused to accept it. Similarly, Newton and Aristotle both believed in absolute time, the idea that different observers would measure time uniformly and independent of space, which would later be refuted.

Although the measurement of time at slow speeds is not problematic, it becomes more complex when considering extremely fast speeds. This realization stemmed from the discovery of the finite, unchanging speed of light in 1676. Hawking points out that James Maxwell succeeded in bringing together partial theories on electricity and magnetism in 1865 to prove that short waves (such as radio or light waves) must travel at a fixed speed the same for all observers at all distances regardless of how fast they themselves move. The idea of a fixed speed, however, does not fit well with a model of motion that rejects absolute space. How can something move at the same speed relative to all observers? While it seemed impossible, an 1887 experiment measured the speed of light to be identical in both the direction of Earth's movement and perpendicular to it.

For nearly 20 years, scientists puzzled over how this could be, until a 1905 paper by Albert Einstein proposed that the difficulty in understanding the fixed speed of light can be removed by rejecting the idea of absolute time. A few weeks later, this idea was given greater credence by the French mathematician Henri Poincaré, who came to a similar conclusion by different means. This new idea, called the theory of relativity, asserts that "the laws of science should be the same for all freely moving observers, no matter what their speed," and also led to Einstein's famous equation, E = mc2 (energy equals mass times the speed of light squared). Nothing can travel faster than the speed of light because the amount of energy it would take to push an object past the speed of light (which has no mass) increases its mass. Thus, as an object approaches the speed of light, its mass proportionally increases so that the energy required to accelerate it also increases.

The theory of relativity revolutionized our conceptions of space and time, tying the two together into what we now call space-time. Space-time is four-dimensional, adding the element of time to the traditional three-dimensional understanding of space. Relativity also enables much more accurate measurements of distance (in terms of how long it takes light to travel that distance) with the creation of new measures such as light-year distances (the distance light would travel in one year). If a star is four light-years away from us here on Earth, it means the light observed at a specific time on Earth had left its point of origin four years in the past.

One difficulty with the new theory, which we now call the special theory of relativity, is that it is not consistent with the Newtonian concept of gravity. Newtonian gravity works instantaneously, or with infinite velocity, but relativity states that nothing can move faster than the speed of light. Einstein wrestled with this problem for several years, eventually finding a solution in 1915 with his general theory of relativity. In this model, gravity is not a force but rather a consequence of the bending of space-time by the distribution of mass and energy within it.

Early confirmations of Einstein's general relativity theory came through its more accurate predictions of planetary orbits compared to Newton's models. Rather than moving in curved orbits, the planets move in straight lines over curved space-time, which appears to be curved movement in three-dimensional space. It was later found that the movement of light also bends with space-time. An even more amazing confirmation came with the discovery that time moves more slowly near large bodies of mass, such as planets. This has practical applications for modern technologies, such as the navigation of artificial satellites.

Einstein's general theory of relativity has changed our conception of space and time from absolute, unchanging attributes of reality into dynamic quantities. That is, space and time are relative to motion, speed, and position. They affect and are affected by the happenings within the universe. This new dynamic understanding of reality also points toward a possible beginning and end to the universe; thus general relativity would shape scientific pursuits in the following decades.


In this chapter, Stephen Hawking immediately sets forth explaining the dual nature of scientific exploration as one of observation supported by speculation, and vice versa. Although Aristotle believed that pure thought alone could reveal the laws of the universe, his ideas of absolute rest and an immobile Earth surrounded by the sun and planets did not hold up under progressively acute observations made by Galileo Galilei and Sir Isaac Newton.

In addition, Hawking sets the stage by which each new discovery leads us toward the idea that nothing can be "fixed" or static—neither the thing being observed nor the position of the observer. While the speed of light is always and in all conditions the same, relativity states that observers would not be able to agree on determining the actual distance that light from distant stars has traveled before reaching them.

Charting an event, therefore, becomes a task of a four-dimensional positioning in space-time. This means that charting light as it spreads out from an event produces a light cone (a configuration that traces the expanding ripple of a light wave outward from the starting point of the event across time). Hawking lays out for the reader, with the aid of illustrations, how to visualize four-dimensional space-time. This new understanding is critical to the advances in physics going forward.

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