One measurement disturbs the other

In classical physics, the properties of a physical system exist independently of the observer. For example, a particle has a certain position and a certain momentum irrespective of whether we have observed it or not. We can in principle measure its position without disturbing its momentum, and vice versa. It makes no difference if one or the other of these parameters is measured first, or if position and momentum had been measured simultaneously.

The rules of described by Equations (12.1) and (12.2) say something quite different. They say that measuring position after momentum is not the same as measuring momentum after position. The difference is quantified using the language of matrices, and is expressed in terms of Planck's constant, h. This constant of nature plays a much more mysterious and deeper role than Planck ever imagined!

Although it is possible in principle to measure the momentum or the position of a particle to an arbitrary accuracy, it is not possible to measure these two observables simultaneously. Position and momentum are complementary properties of a system but the theory does not permit knowledge of the two at the same time. This idea goes very much against intuition, what we 'feel' the laws of physics should be. But our intuition is based on our experience of the everyday 'household' world; the world of electrons and atoms is definitely not 'household'.

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