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Heisenberg Uncertainty Principle: Definition & Equation

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  • 0:01 Introduction
  • 1:01 The Uncertainty Principle
  • 3:59 The Equation
  • 5:29 Lesson Summary
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Lesson Transcript
Instructor: Amy Lange

Amy has taught university-level earth science courses and has a PhD in Geology.

The Heisenberg uncertainty principle is one of the core concepts in quantum mechanics. In this lesson, we define the uncertainty principle and learn more about its implications for physical science.

Werner Karl Heisenberg

At the young age of 26, a German physicist named Werner Karl Heisenberg published a landmark paper describing his theory of the uncertainty principle. Based on this work, in addition to his earlier theories that lay the groundwork of quantum mechanics, Heisenberg was awarded the Nobel Prize in Physics in 1932.

To understand why this work was deserving of the Nobel Prize, let's dive in a little deeper. Quantum mechanics is the area of physics that examines physical behavior at the nanoscopic scale. There are 1 billion nanometers in a meter. Particles at this scale, like individual atoms and molecules, are so small that they are impossible to image. This is what makes the field of quantum mechanics so difficult and so crucial. Because we cannot directly observe physical behaviors at this scale, they are exceedingly difficult to understand and predict.

The Uncertainty Principle

The Heisenberg uncertainty principle relates to how well we can know the position and the momentum of a nanoscopic particle with certainty at the same time. Remember that momentum is the mass times the velocity of a particle. Heisenberg summarized his uncertainty principle as the more precisely the position is determined, the less precisely the momentum is known, and vice versa. What this means is that you cannot accurately know BOTH the location and momentum of a nanoscopic particle.

You may have heard the Heisenberg uncertainty principle in popular media described as an observer effect. This refers to the changes that a particle undergoes as a result of being observed, or, put more simply, that the act of observing something changes it. The classic example is that if we try to measure an atom by using a super powerful gamma ray microscope, the gamma rays of the microscope would actually disrupt the tiny atom, making it impossible to image.

But the Heisenberg uncertainty principle is more complicated than this. It derives from the fact that all matter behaves as a particle and a wave. While particles have fixed locations, waves are disturbances that travel through space accompanied by a transfer of energy and do not have a fixed location. Think of the waves that form when you drop a rock in a puddle. We can describe certain features of the wave like wavelength, which is the distance between two successive wave peaks, but there is no actual location of the wave because it is always moving.

Wavelength is directly correlated with momentum, which, remember, is mass times velocity. This means that higher momentum has higher wavelengths and vice versa. An object with a large mass and a high velocity, like a moving car, has a huge momentum. Because the momentum is so large, the wavelength is very short. Thus, we can state that objects with high momentums have very small wavelengths. In the case of visible matter, the wavelength is always small, and that's why we can't observe the wave-like behavior. However, when we're dealing with very small nanoscopic particles, the mass, and thus the momentum, are exponentially smaller. This means that the wavelengths for nanoscopic particles can be larger.

So in its wave-state, we can determine the momentum of matter from its wavelength, but not the position. But remember that matter behaves both like a wave AND a particle. Particles, of course, have a known position, but they don't have momentum because they do not have a wavelength. This is the root of the Heisenberg uncertainty principle. To know both the position and momentum of nanoscopic particles, we must observe both the particle and wave behavior of the matter.

The Equation

So how do we mathematically define this principle? According to the Heisenberg uncertainty principle, there is an inverse correlation between the accuracy with which we can measure momentum and position. (In other words, as one measurement gets more accurate, the other measurement gets less accurate.) In this equation, position is x and momentum is p. So delta x is the uncertainty in position and delta p is the uncertainty in momentum:

Planck

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