# Heisenberg’s Uncertainty Principle

The uncertainty relation is closely related to the quantum wave nature of things. It summarizes the impossibility for two complementary entities, such as position and momentum to be defined with arbitrary precision in the same experimental setting. This is summarized in the inequality:

$$\Delta x \cdot \Delta p_x \ge \frac{\hbar}{2}$$

• $$\Delta x$$ is the accuracy (standard deviation) to which the particle position is defined in the x-direction.
• $$\Delta p_x$$ is the accuracy (standard deviation) to which the particle momentum is defined in the x-direction.
• $$\hbar \simeq 1.1 \times 10^{-34} J s$$ is the reduced Planck quantum of action.

The prefactor of $$\hbar$$  depends on how you define the accuracy of position and momentum. But it is of the order of one.

We can demonstrate the effect and importance of the uncertainty relation in an experiment.