According to the Heisenberg uncertainty principle, it is not possible to simultaneously determine the exact position and momentum of a quantum particle with arbitrary precision. The uncertainty principle is a fundamental principle of quantum mechanics that places a limit on the precision with which certain pairs of physical properties, such as position and momentum, can be known.
Mathematically, the uncertainty principle is expressed as:
Δx * Δp >= h/2π
where Δx represents the uncertainty in position, Δp represents the uncertainty in momentum, and h is the reduced Planck's constant. The principle states that the product of the uncertainties in position and momentum must be greater than or equal to a specific value.
This means that the more precisely you try to measure the position of a quantum particle, the less precisely you can know its momentum, and vice versa. The uncertainty principle arises due to the wave-particle duality of quantum objects. Quantum particles exhibit both particle-like and wave-like properties, and their behavior is described by wave functions that are inherently probabilistic.
If one were to somehow determine the exact position of a particle, the uncertainty principle implies that the uncertainty in momentum would be infinite. Similarly, if one were to measure the momentum of a particle with absolute certainty, the uncertainty in its position would be infinitely large.
The uncertainty principle is a fundamental aspect of quantum mechanics and is supported by experimental evidence. It sets a fundamental limit on the precision with which certain properties of quantum particles can be simultaneously known. Thus, it is not possible to determine both the exact position and momentum of a quantum particle at the same time.