A Brief History of Time | Study Guide

Stephen Hawking

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A Brief History of Time | Chapter 4 : The Uncertainty Principle | Summary



Stephen Hawking begins this chapter with comments on scientific determinism, which proposes that if we had enough information, we could predict all events based on scientific laws. Some extreme versions of this idea assert that this could extend to human behavior. Scientific determinism stems from the extraordinary success of Newtonian physics, but discoveries in the 20th century would call it into question.

Moving from the staggering vastness of space, Hawking turns his attention in this chapter to advancements made in the realm of subatomic particles, or quantum mechanics. The word "quantum" (meaning the smallest amount) is used by the German scientist Max Planck, who proposed that light and X-rays were emitted in tiny packets called quanta. This coincided with observations, but it also meant that in order to predict a particle's future position and velocity as it is emitted from hot bodies, scientists would have to be able to measure where it is to begin with, where it goes, and how fast it moves.

Werner Heisenberg, another German scientist, discovered that if the position of a particle can be calculated with accuracy, any attempt to measure its velocity became correspondingly less accurate, and vice versa. This peculiar correlation became known as the uncertainty principle, which also supports Planck's constant that the uncertainty in a particle's position times uncertainty of velocity times the particle's mass cannot be infinitely small.

The uncertainty principle put an end to any hopes of a viable model of a completely deterministic universe in which the future could, if one knew all the laws, be predicted. Scientists instead examine a "quantum state" that combines both position and velocity for a prediction of a number of possible outcomes and their relative probability. Both Planck's constant and the uncertainty principle mean that particles sometimes behave like waves, and other times waves behave like particles, depending on which the observer is measuring. The realization of the wave-particle dualism of subatomic particles opened up an avenue to understanding how atoms work, generating subsequent advances in many fields.


As shown in the previous chapter, revolutionary discoveries in science are not always welcomed with open arms. Among those disturbed by the randomness and unpredictability of quantum mechanics was Albert Einstein, even though he had been instrumental in its development. He objected, asserting that "God does not play dice."

In a surprising development, the acceptance of randomness and unpredictability that comes with quantum mechanics has actually opened up greater levels of control and accuracy for modern technologies. Stephen Hawking points out that advances in quantum mechanics have provided a foundation for understanding subatomic structures, which enabled the development of transistors, integrated circuits, and the electronic devices upon which many of our daily activities now depend. In fact, the field of quantum mechanics is so integral to modern science, prior theories that do not account for uncertainty (such as general relativity), are now called "classical" theories.

An understanding of quantum mechanics highlights a troubled relationship with the theory of relativity. Points of singularity at both the event of the big bang and in black holes suggest a possible meeting ground at which both quantum mechanics and the theory of relativity indicate that the incompatible laws governing the very large and the very small break down.

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