The *Heisenberg uncertainty principle* is a fundamental statement of [[Quantum Mechanics|quantum physics]]. It states that certain quantities cannot be measured simultaneously with any desired degree of accuracy. The best-known example of this is position-[[Momentum|momentum]] uncertainty. It limits the accuracy with which the location and speed of a particle can be measured simultaneously. Concretely, the *Heisenberg uncertainty principle* is formulated as a [[inequality]]: $\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$ Let's break this expression up into its different parts: $\Delta x$ is the uncertainty in the position. If you know that someone is standing somewhere on a square in your town, $\Delta x$ might be $50\,\text{m}$. That means that we know their position up to $50\,\text{m}$. The same goes for $\Delta p$, it is the uncertainty in [[Momentum|momentum]]. On the right hand side of the inequality, we have a very small constant $h$, [[Planck's Constant]]. This constant ensures that the *Heisenberg uncertainty principle* only applies at very small scales. Let's consider an example: wouldn't it be nice to get out of your next police control after speeding by quoting Heisenberg. The argument could be as follows: we usually know quite precisely where we are. Could we use the *Heisenberg uncertainty principle* to argue that a police officer can't measure the car's speed very accurately? If we assume that we can determine the car's position with an inaccuracy of $1\,\text{m}$ and that the car weighs approximately $2000\,\text{kg}$ (momentum is speed multiplied by mass), then the speed uncertainty is unfortunately only $0.000\, 000\, 000\, 000\, 000\, 000\, 000\, 000\, 000\, 000\, 000\, 1 \,\text{km}/\text{h}$. That is not really helpful for an argument... However, if we change the scale to single [[Atom|atoms]] and [[Electron|electrons]], then we suddenly get quite a strong effect: When an [[electron]] is bound to a specific [[atom]], it has a relatively small spatial uncertainty. The typical size of an atom is approximately $0.1\,\text{nm}$ (nanometers). This results in a spatial uncertainty of $0.05\,\text{nm}$, half the size of an atom. If the spatial uncertainty was larger, the electron would already belong to the next atom. If we insert this spatial uncertainty into the *Heisenberg uncertainty principle*, it means that the speed of the electron can only be measured up to $4,168,000\,\text{km}/\text{h}$. With such a high degree of uncertainty, we know nothing about the electron's speed. >[!read]- Further Reading >- [[Quantum Mechanics]] >- [[Measurement]] >- [[Superposition]] >- [[Entanglement]] >[!ref]- References >- W. Heisenberg, Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik, Z. Physik **43**, 172 (1927).