What is the principle that states the position and velocity of a particle cannot both be precisely measured at the same time?

The principle that states the position and velocity of a particle cannot both be precisely measured at the same time is known as the Heisenberg Uncertainty Principle. This principle is a fundamental concept in quantum mechanics, formulated by Werner Heisenberg in 1927. It highlights the inherent limitations in measuring certain pairs of complementary variables, such as position and momentum (which is closely related to velocity).

According to this principle, the more accurately you measure one of these properties, the less accurately you can know the other. This is not just a limitation of measurement tools but a fundamental property of matter itself at the microscopic scale, arising from the wave-particle duality of particles. The mathematical formulation involves the idea that the product of the uncertainties in position and momentum is always greater than or equal to a constant known as reduced Planck’s constant divided by 2.

This principle has profound implications for quantum mechanics, emphasizing that at a quantum level, certainty is replaced by probability. Understanding this principle is crucial for interpreting phenomena in quantum systems, such as electron behavior in atoms or the properties of subatomic particles.