Impossible Inexactness

"Inexactness" or the "uncertainty" principle, as formulated by physicist Werner Heisenberg, is an end often seen as the beginning. It reflects T.S. Eliot's observation: "what she gives, gives with such supple confusions that the giving famishes the craving".

In 1927, Heisenberg showed that uncertainty is inherent in quantum mechanics. It is impossible to simultaneously measure certain properties—position and momentum. In the quantum world, matter can take the form of either particle or waves. Fundamental elements are neither particles nor waves, but can behave as either and are merely different theoretical ways of picturing the quantum world.

The profound beauty of Inexactness transects science, mathematics, method, philosophy, linguistics and faith.

Inexactness marks an end to certainty. In seeking to measure one property more precisely and accurately, the ability to measure the other property is undermined. The act of measurement negates elements of our knowledge of the system.

It undermines scientific determinism, implying that human knowledge about the world is always incomplete, uncertain and highly contingent.

Inexactness challenges causality. As Heisenberg observed: "'If we know the present, then we can predict the future', it is not the consequences, but the premise that is false. As a matter of principle we cannot know all determining elements of the present".

Inexactness questions methodology. Experiments can only prove what they are designed to prove. Inexactness is a theory based on the practical constraints of measurement.

Inexactness and quantum mechanics challenge faith as well as concepts of truth and order. They imply a probabilistic world of matter, where we cannot know anything with certainty but only as a possibility. It removes the Newtonian elements of space and time from any underlying reality. In the quantum world, mechanics are understood as a probability without any causal explanation.

Albert Einstein refused to accept that positions in space-time could never be completely known and quantum probabilities did not reflect any underlying causes. He did not reject the theory but the lack of reason for an event. Writing to Max Born, he famously stated: "I, at any rate, am convinced that He [God] does not throw dice." But as Stephen Hawking later remarked in terms that Heisenberg would have recognised: "Not only does God play dice, but…he sometimes throws them where they cannot be seen."

Allusive and subtle, the power of Inexactness draws on its metaphorical property which has allowed it to penetrate diverse fields such as art theory, financial economics and even popular culture.

At one level, Heisenberg's uncertainty principle is taken to mean the act of measuring something changes what is observed. But at another level, intentional or unintentionally, Werner Heisenberg is saying something about the nature of the entire system—the absence of absolute truths, the lack of certainty and the limits to our knowledge.

Inexactness is linked with different philosophical constructs. Nineteenth-century Danish philosopher Søren Kierkegaard differentiated between objective truths and subjective truths. Objective truths are filtered and altered by our subjective truths, recalling the interaction between observer and event central to Heisenberg's theorem.

Inexactness is related to linguistic philosophies. In the Tractatus Logico-Philosophicus, Ludwig Wittgenstein anticipates Inexactness arguing that the structure of language provides the limits of thought and what can be said meaningfully.

The deep ambiguity of Inexactness manifests itself in other ways: the controversy over the term itself and Heisenberg's personal history.

Heisenberg's principle is various referred to as Ungenauigkeit (meaning inexactness), Unschärfe (blurred or lacking clarity) or Unbestimmtheit (indeterminate). In translation, the ambiguity and differences in meaning are accentuated. Playwright Michael Franyn suggested: indeterminability. It was not until the publication of the 1930 English-language version of Heisenberg's textbook, The Physical Principles of the Quantum Theory that the term uncertainty (Unsicherheit) was used and widely adopted.

In 1941, during the Second World War, Werner Heisenberg and Niels Bohr, the Danish Physicist and his former teacher, met in occupied Denmark. In Michael Franyn's 1998 play Copenhagen, Margrethe, Bohr's wife, poses the essential question, which is debated in the play: "Why did he [Heisenberg] come to Copenhagen?"

The play repeats their meeting three times, each with different outcomes. As Heisenberg, the character, states: "No one understands my trip to Copenhagen. Time and time again I've explained it. To Bohr himself, and Margrethe. To interrogators and intelligence officers, to journalists and historians. The more I've explained, the deeper the uncertainty has become."

In his 1930 text The Principles of Quantum Mechanic. Paul Dirac, a colleague of Heisenberg, contrasted the Newtonian world and the Quantum one: "It has become increasingly evident… that nature works on a different plan. Her fundamental laws do not govern the world as it appears in our mental picture in any direct way, but instead they control a substratum of which we cannot form a mental picture without introducing irrelevancies."

There was a world before Heisenberg and his Inexactness principle. There is a world after Heisenberg. They are the same world but they are different.