# Uncertainty Principle In order to have confidence (and reduce uncertainty) about a *frequency* measurement, you need to have *long duration* observation. We can say: * Short signals correlate with a wide range of frequencies * Wide signals correlation with a short range of frequencies   The **uncertainty principle** is thus: a signal concentrated in time must have a spread out [Fourier Transform](Fourier%20Transform.md), meaning it correlates with a wide range of frequencies. ## Doppler Radar Imagine that you are in a aircraft control tower, trying to understand what planes are nearby and how fast they are moving. We understand their location based on their time space representation, and their velocity based on their frequency space representation. You have two options: 1. You can send out long duration frequency pulses. These will hit the aircrafts and return to you as echo's. However, the echo's will also be spread out over time—meaning that the echo's from multiple objects will overlap, making it less clear which echo corresponded to which object. 2. You can send out very short duration frequency pulses. These will hit the aircrafts and return to you, likely quite compressed and distinct in time. But can you guess the issue? The uncertainty principle states that a signal concentrated in time will correlate with a large range of frequencies! So, these echo's will overlap in *frequency space*. So, we will have a good idea of the objects location, but less certainty about their speed. Thus we can state the uncertainty principle again: > **Uncertainty Principle**: For a signal to be concentrated in frequency space, it necessarily has to be spread out in time.  ## Heisenberg Uncertainty ## Measurement in General Measurement in physics fundamentally involves waves because information transfer requires a physical interaction between the measuring object (A) and the measured object (B). To measure B, A must initiate a process — like sending out a probe — that interacts with B and returns information. Waves naturally serve this role because they are the primary carriers of information in physical systems, whether they are light waves, sound waves, or quantum matter waves. The Heisenberg Uncertainty Principle reflects this wave-based nature of measurement. To measure position accurately, short-wavelength (high-frequency) waves are needed, but short pulses are spread out in frequency space, increasing uncertainty in momentum (and thus velocity). This trade-off arises from the mathematical properties of Fourier transforms applied to waves. Even alternative measurement mechanisms, like particle-based or gravitational probes, reduce to wave-like behavior at a fundamental level. Quantum particles have wave properties, and even classical interactions (like touching an object) rely on electromagnetic or gravitational fields that behave as waves. Therefore, measurement in physics is inseparable from the wave-based nature of information exchange. --- Date: 20250311 Links to: Tags: References: * [The more general uncertainty principle, regarding Fourier transforms - YouTube](https://www.youtube.com/watch?v=MBnnXbOM5S4&t=3s)