#### I believe that the existence of the classical "path" can be pregnantly formulated as follows: The "path" comes into existence only when we observe it. --Heisenberg, in uncertainty principle paper, 1927

Cartoon by John Richardson for Physics World, March 1998

Heisenberg realized that the uncertainty relations had profound implications. First, if we accept Heisenberg's argument that every concept has a meaning only in terms of the experiments used to measure it, we must agree that things that cannot be measured really have no meaning in physics. Thus, for instance, the path of a particle has no meaning beyond the precision with which it is observed. But a basic assumption of physics since Newton has been that a "real world" exists independently of us, regardless of whether or not we observe it. (This assumption did not go unchallenged, however, by some philsophers.) Heisenberg now argued that such concepts as orbits of electrons do not exist in nature unless and until we observe them.

There were also far-reaching implications for the concept of causality and the determinacy of past and future events. These are discussed on the page about the origins of uncertainty. Because the uncertainty relations are more than just mathematical relations, but have profound scientific and philosophical implications, physicists sometimes speak of the "uncertainty principle."

#### "In the sharp formulation of the law of causality—if we know the present exactly, we can calculate the future—it is not the conclusion that is wrong but the premise."

—Heisenberg, in uncertainty principle paper, 1927

Heisenberg also drew profound implications for the concept of causality, or the determinacy of future events. Schrödinger had earlier attempted to offer an interpretation of his formalism in which the electron waves represent the density of charge of the electron in the orbit around the nucleus. Max Born, however, showed that the "wave function" of Schrödinger's equation does not represent the density of charge or matter. It describes only the probability of finding the electron at a certain point. In other words, quantum mechanics cannot give exact results, but only the probabilities for the occurrence of a variety of possible results.

Heisenberg took this one step further: he challenged the notion of simple causality in nature, that every determinate cause in nature is followed by the resulting effect. Translated into "classical physics," this had meant that the future motion of a particle could be exactly predicted, or "determined," from a knowledge of its present position and momentum and all of the forces acting upon it. The uncertainty principle denies this, Heisenberg declared, because one cannot know the precise position and momentum of a particle at a given instant, so its future cannot be determined. One cannot calculate the precise future motion of a particle, but only a range of possibilities for the future motion of the particle. (However, the probabilities of each motion, and the distribution of many particles following these motions, could be calculated exactly from Schrödinger's wave equation.)

Although Einstein and others objected to Heisenberg's and Bohr's views, even Einstein had to admit that they are indeed a logical consequence of quantum mechanics. For Einstein, this showed that quantum mechanics is "incomplete." Research has continued to the present on these and proposed alternative interpretations of quantum mechanics.

One should note that Heisenberg's uncertainty principle does not say "everything is uncertain." Rather, it tells us very exactly where the limits of uncertainty lie when we make measurements of sub-atomic events.

Heisenberg's uncertainty principle constituted an essential component of the broader interpretation of quantum mechanics known as the Copenhagen Interpretation.