6.7 The Heisenberg uncertainty principle (1927)

The Heisenberg uncertainty principle (1927)

Heisenberg’s uncertainty principle states that there are pairs of physical properties for which simultaneous determination of both values is impossible. The more accurately one property is measured, the less accurately the other property can be known. The probability distribution of both values is related. This concept is also referred to as the indeterminacy relation. For further insights, refer to the section on the Schrödinger equation.

Δx = uncertainty about the location

Δp = uncertainty about the momentum

The reduced Planck constant is often used for this purpose

When we persist in thinking of particles as isolated entities, we will not find a resolution here. But a ‘particle’ can also be viewed as a set of shared information, representing a superposition of probability distributions. During measurement/observation, one of the entanglements of the ‘particle’ collapses and is shared with the observer. The observer thus gains knowledge about this aspect of the ‘particle’.

Heisenberg’s Uncertainty Principle is also related to the ‘measurement problem’: How does the collapse of the wave function occur?

During an interaction/event, shared information is redistributed in the most likely direction. When differences in probability are small, this equates reversibility. This can be compared to Feynman’s path integral formulation: Elements can be found in different places and in various forms. Or, in terms of the Copenhagen interpretation: Elements exist within the probability distribution of a wave function. They are in superposition.

In an observation or measurement where differences in probability are very large, improbable options can be neglected, making the event irreversible. This irreversibility, caused by significant differences in probability, parallels the collapse. Both participants in the observation are no longer in the original superposition, but have acquired a new state/value (such as location). Both participants have changed, as well as their neighbors, and the neighbors of their neighbors, and so on. During measurement, the entire system undergoes a change. Hence, collapse is a description of the transition from the quantum level (probability distribution) to the macro level (a concrete value/state).

There is also an uncertainty relation for energy and time:


Hence, one of the conclusions we can derive from our thought experiment is that Heisenberg’s uncertainty is the ultimate origin of change.