The Heisenberg Uncertainty Principle states that there is a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position and momentum, can be known simultaneously. It implies that it is not possible to determine both the position and momentum of a particle with arbitrary or unlimited precision.
The uncertainty principle arises from the wave-particle duality of quantum mechanics. According to quantum theory, particles such as electrons exhibit wave-like properties and their properties are described by wavefunctions. The position and momentum of a particle are related to the properties of its wavefunction.
Mathematically, the Heisenberg Uncertainty Principle is expressed as:
Δx * Δp ≥ h/4π
where Δx represents the uncertainty in position, Δp represents the uncertainty in momentum, and h is the reduced Planck's constant.
This inequality means that the product of the uncertainties in position and momentum must be greater than or equal to a certain minimum value. It does not imply that an object does not have a precise position or momentum in principle. Rather, it indicates that the more precisely one property (e.g., position) is measured, the less precisely the other property (e.g., momentum) can be known.
In other words, the uncertainty principle places a limit on the simultaneous precision with which position and momentum can be measured. It does not rule out the possibility of a particle having a well-defined position and momentum but rather limits our ability to know both of these properties simultaneously with unlimited precision.