The Uncertainty Principle: What It Is & How It Works

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What is the uncertainty principle? Why is it impossible to predict the position and velocity of a subatomic particle with absolute certainty?

Stephen Hawking, in his book A Brief History of Time, discusses the origins and basic principles of quantum mechanics. He shows how quantum mechanics gives rise to the uncertainty principle and explains how uncertainty can limit the accuracy of predictions in physics.

Read more to learn about the uncertainty principle.

The Uncertainty Principle

Quantum mechanics provides probabilistic solutions instead of deterministic ones, and that limits scientific determinism. And there’s another limitation on determinism that comes from quantum mechanics: the uncertainty principle.

What is the uncertainty principle? As Hawking explains, the principle states there is always at least a certain amount of uncertainty in your measurement of the position and velocity of a particle. This is important because, to predict where a particle will go (or is most likely to go) in the future, you need to know where it was and which way it was going at some point in the past or present. Uncertainty about the present creates greater uncertainty about the future.

(Shortform note: Hawking explains how uncertainty can limit the accuracy of your predictions in physics, but this general concept is applicable to other areas as well, especially in fields like the social sciences where outcomes are harder to measure or quantify. In his book Superforecasting, Philip Tetlock discusses the importance of measurement in predicting the future. In particular, he points out that many political and economic forecasters’ predictions are never actually checked against measurements after the fact. This makes it difficult to assess the credibility of the forecaster or the accuracy of their methods.)

To understand how the uncertainty principle works, you need to understand a few things about quantum mechanics. For one thing, as Hawking notes, a basic premise of quantum mechanics is that certain quantities like energy and frequency have to be incremented by at least a certain minimum value. (Shortform note: This minimum unit is called a “quantum” of energy, which is where “quantum mechanics” gets its name.)

To explain this phenomenon, it’s helpful to consider how quantum mechanics was discovered, so let’s discuss its origins. Then, we’ll show how quantum mechanics gives rise to the uncertainty principle.

The Origins of Quantum Mechanics

Hawking recounts that circa 1900, scientists realized that their theories of radiant heat transfer predicted that any hot object should radiate an infinite amount of energy, which was obviously not the case. The reason was that in these theories, radiation could have any frequency, and objects were thought to give off radiation uniformly over a range of frequencies.

For example, a hot object might give off radiation at 10 Mhz, 10.1 MHz, 10.01 Mhz, and so on. Mathematically, there are an infinite number of frequencies between 10 and 11 MHz (or any two frequencies), so if the object radiates energy at every possible frequency, then it will give off an infinite amount of energy. 

Hawking explains how, to resolve this problem, Max Planck hypothesized that physical quantities like the frequency of radiation are “quantized,” meaning they can only have certain distinct values. If frequency could only be incremented by a finite value, then an object would only give off a finite amount of radiation because there would only be a finite number of frequencies at which it could give off radiation. This solved the problem and led to the development of the theory of quantum mechanics.

Shortform Note: Standing Waves and Quantization

As Hawking recounts, Planck was the first to recognize that electromagnetic energy was quantized, and Planck may have coined the term “quantum.” However, in Planck’s day, it was already common knowledge that certain physical quantities were “quantized,” in the sense that they could only have certain values.

The Uncertainty Principle: What It Is & How It Works

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  • The search for a theory that explains the history and evolution of our universe
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Elizabeth Whitworth

Elizabeth has a lifelong love of books. She devours nonfiction, especially in the areas of history, theology, and philosophy. A switch to audiobooks has kindled her enjoyment of well-narrated fiction, particularly Victorian and early 20th-century works. She appreciates idea-driven books—and a classic murder mystery now and then. Elizabeth has a Substack and is writing a book about what the Bible says about death and hell.

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