Understanding the uncertainty principle

People often talk of the Heisenberg uncertainty relation, but what many don't realise is that the term is actually used to refer to two completely different principles in quantum physics. Our presentation aims to dispel this misunderstanding. We introduce the two principles and clarify the differences between them. Confusingly, they both also go by various other names, but for the purposes of this introduction they will be referred to as:

1) The Robertson Uncertainty Relation

This is the most general form of the fundamental uncertainty principle due to the wave-particle duality inherent in quantum mechanics. It is formulated in terms of standard deviations. It can be derived mathematically from the postulates of quantum mechanics and no experiment has ever shown it to be false.

2) Heisenberg's Measurement-Disturbance Relationship

This is the formulation that Heisenberg published in 1927. It describes the uncertainty in a measurement of one variable (for example, momentum) introduced by the disturbance created when measuring another variable (for example, position).

One of the reasons that these two principles are so often confused may be due to the fact that, mathematically, they look almost identical. The only difference is that the first talks of standard deviations, whilst the second talks of uncertainties in individual measurements.

In 2003, 76 years after Heisenberg first devised his uncertainty principle, Ozawa proved mathematically that his formula was not universally true. He reformulated the principle and showed that the disturbance introduced by a quantum measurement need not be as large as Heisenberg originally thought. Ozawa also suggested an experiment that would demonstrate this.

In 2012, two different teams carried out independent experiments which confirmed Ozawa's work and showed for the first time that Heisenberg's Measurement-Disturbance Relationship is not a fundamental limit on the information we can gain through measurement. Of course, the Robertson Uncertainty Relation continues to hold and quantum mechanics remains our best description of nature.