# QR3.8.7 The Uncertainty Principle

Heisenberg’s uncertainty principle is that one can’t know both a quantum entity’s exact position and momentum at the same time. These facts are said to be complementary, to be separately knowable but together unknowable. This isn’t expected of physical objects but quantum theory insists that measuring either one fully denies all knowledge of the other entirely.

This result, which has been verified experimentally, can be understood if measurement is an information transfer:

… a measuring instrument is nothing else but a special system whose state contains information about the “object of measurement” after interacting with it:(Audretsch, 2004) p212

Quantum realism adds that every measurement is an overload interaction between quantum waves. Figure 3.25 shows a simple case of two waves interacting to overload in two nodes:

a. If they are in phase, one node overloads to give a position exactly but the wavelength is unknown.

b. If they are out of phase, both nodes cancel to define the wavelength exactly but there is no position information.

The interaction can reveal position or wavelength but not both, with no repeats. If the result gives position there is no wavelength data and if it gives wavelength there is no position data. In both cases, the observed wave has given all the information it has to the interaction. It follows that one wave “observing” another can give position or wavelength information but not both.

The quantum uncertainty principle follows from the nature of wave interactions based on De Broglie’s equation of momentum and wavelength (Note 1). The information change in any photon interaction can’t be less than a quantum process so position plus momentum can’t be less than Planck’s constant (Note 2).

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Note 1. If p is momentum, λ is wavelength and h is Planck’s constant, then p = h/ λ

Note 2. Mathematically δx.δp ≥ ħ/2 where x is position, p is momentum and ħ is Plank’s constant in radians.