In everyday life, calculating the speed and position of a moving object is relatively straightforward. We can measure a car traveling at 60 miles per hour or a tortoise crawling at 0.5 miles per hour and simultaneously pinpoint where the objects are located. But in the quantum world of particles, making these calculations is not possible due to a fundamental mathematical relationship called the uncertainty principle.

Formulated by the German physicist and Nobel laureate Werner Heisenberg in 1927, the uncertainty principle states that we cannot know both the position and speed of a particle, such as a photon or electron, with perfect accuracy; the more we nail down the particle's position, the less we know about its speed and vice versa.

In other words, if we could shrink a tortoise down to the size of an electron, we would only be able to precisely calculate its speed or its location, not both at the same time.

Though the Heisenberg uncertainty principle is famously known in quantum physics, a similar uncertainty principle also applies to problems in pure math and classical physics—basically, any object with wave-like properties will be affected by this principle. Quantum objects are special because they all exhibit wave-like properties by the very nature of quantum theory.

To understand the general idea behind the uncertainty principle, think of a ripple in a pond. To measure its speed, we would monitor the passage of multiple peaks and troughs. The more peaks and troughs that pass by, the more accurately we would know the speed of a wave—but the less we would be able to say about its position. The location is spread out among the peaks and troughs. Conversely, if we wanted to know the exact position of one peak of a wave, we would have to monitor just one small section of the wave and would lose information about its speed. In short: the uncertainty principle describes a trade-off between two complementary properties, such as speed and position.

_{The rollercoaster above serves as an analogy for how the uncertainty principle works at scales much smaller than this. Left: When the rollercoaster car reaches the peak of the hill, we could take a snapshot and know its location. But the snapshot alone would not give us enough information about its speed. Right: As the rollercoaster car descends the hill, we can measure its speed over time but would be less certain about its position. The uncertainty principle is a trade-off between two complementary variables, such as position and speed.}_{Credit: Lance Hayashida/Caltech}

The fundamental law comes into play in the quantum world because subatomic particles can behave like waves. A common misconception about the uncertainty principle in quantum physics is that it implies our measurements are uncertain or inaccurate. In fact, uncertainty is an inherent aspect of anything with wave-like behavior.

Dive Deeper

The more general uncertainty principle, beyond quantum