In quantum physics, the Heisenberg uncertainty principle states that certain pairs of physical properties, like position and momentum, cannot both be known to arbitrary precision. That is, the more precisely one property is known, the less precisely the other can be known. It is impossible to measure simultaneously both position and velocity of a microscopic particle with any degree of accuracy or certainty.

This is not a statement about the limitations of a researcher's ability to measure particular quantities of a system, but rather about the nature of the system itself and hence it expresses a property of the universe. In quantum mechanics, a particle is described by a wave. The position is where the wave is concentrated and the momentum is the wavelength.

The position is uncertain to the degree that the wave is spread out, and the momentum is uncertain to the degree that the wavelength is ill-defined. The only kind of wave with a definite position is concentrated at one point, and such a wave has an indefinite wavelength. Conversely, the only kind of wave with a definite wavelength is an infinite regular periodic oscillation over all space, which has no definite position.

So in quantum mechanics, there are no states that describe a particle with both a definite position and a definite momentum. The more precise the position, the less precise the momentum. The uncertainty principle can be restated in terms of measurements, which involves collapse of the wavefunction.

When the position is measured, the wavefunction collapses to a narrow bump near the measured value, and the momentum wavefunction becomes spread out. The particle's momentum is left uncertain by an amount inversely proportional to the accuracy of the position measurement. The amount of left-over uncertainty can never be reduced below the limit set by the uncertainty principle, no matter what the measurement process.

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