Heisenberg’s uncertainty principle is that one can’t know both the exact position and momentum of a quantum entity at the same time. These facts are called complementary, separately knowable but together unknowable. This isn’t expected of a particle but quantum theory insists that measuring either property fully denies all knowledge of the other entirely.
To understand this, first recognize that every 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.
Now if every measurement is physical event triggered when quantum waves interact to overload a point, a measurement is one wave gaining information from another. Figure 3.25 then shows a simple case of two waves interacting over two points of space, where their combined strength overloads a point:
a. If they are in phase, one of the points must overload to give a position exactly, but no length information is provided.
b. If they are out of phase, both points overload to give a length exactly, but no position information is provided.
In the second case, the length given is the measuring wave wavelength. It follows that a known wave interacting with an unknown one can reveal position or length but not both, with no repeats. If the result gives a position, there is no length data and if it gives a length, there is no position data. In both cases, the observed wave has given all the information it can to the interaction, so one wave observing another can give position or length data, but not both. Since length is needed to define momentum, this is equivalent to the uncertainty principle.
The quantum uncertainty principle follows from the nature of wave interactions based on De Broglie’s equation (Note 1). In this model, the information transferred in any interaction can’t be less than a quantum process, so position plus momentum can’t be less than Planck’s constant (Note 2). The uncertainty principle then implies that every observation is an interaction of waves that have a fundamental unit.
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.