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WERNER HEISENBERG (1901 - 1976)
The Uncertainty Principle is a property of quantum states, corresponding to the statistical properties of measurement in quantum mechanics. To clarify this point, consider the Heisenberg microscope experiment again.
Suppose that a physicist has a way to prepare an electron in a particular quantum state. The physicist repeats this procedure 200 times, and for 100 times measures the position, and 100 times measures the momentum. The answers will be different in each of the first 100 and second 100 experiments, and they will cluster around some mean with some spread, measured by the standard deviation.
The standard deviation of the position times the standard deviation of the momentum is never less than .
Richard Feynman gives a simple argument for understanding the uncertainty in momentum and position. He starts with a particle which passes through a small hole, and then encounters a N detectors, covering each possible exit direction arranged in concentric hemispheres. He notes that when the innermost hemisphere of those counters records a particle, then the momentum of the particle and its past trajectory is known, in particular, it may be deduced that the particle left the small hole with the momentum that will be inferred later.
This is actually not in contradition with the uncertainty relation. Rather, once the detector detects the particle, the next detection involves a different counter further out, and to determine which one is impossible. This is the Heisenberg uncertainty relation, and the uncertainty translates to an uncertainty of prediction.
In quantum physics, the Heisenberg uncertainty principle is the statement that locating a particle in a small region of space makes the momentum of the particle uncertain; and conversely, that measuring the momentum of a particle precisely makes the position uncertain.
In quantum mechanics, the position and momentum of particles do not have precise values, but have a probability distribution. There are no states in which a particle has both a definite position and a definite momentum. The narrower the probability distribution is in position, the wider it is in momentum.
Physically, the uncertainty principle requires that when the position of an atom is measured with a photon, the reflected photon will change the momentum of the atom by an uncertain amount inversely proportional to the accuracy of the position measurement. The amount of uncertainty can never be reduced below the limit set by the principle, regardless of the experimental setup.
A mathematical statement of the principle is that every quantum state has the property that the root-mean-square (RMS) deviation of the position from its mean (the standard deviation of the X-distribution).
