Uncertainty Principle

ORIGINAL: The Big View

At a time when Einstein had gained international recognition, quantum theory culminated in the late 1920’s statement of the Uncertainty Principle, which says that the more precisely the position of a particle is determined, the less precisely the momentum is known in this instant, and vice versa. The above phrasing of the principle is a succinct version of the mathematically precise uncertainty relation that Heisenberg published in 1927. Since the momentum of a particle is the product of its mass and velocity, the principle is sometimes stated differently, however, its meaning remains the same: The act of measuring one magnitude of a particle, be it its mass, its velocity, or its position, causes the other magnitudes to blur. This is not due to imprecise measurements. Technology is advanced enough to hypothetically yield correct measurements. The blurring of these magnitudes is a fundamental property of nature.

Click on this button to hear Heisenberg explaining his uncertainty principle. (.au, 176 kb)

The uncertainty relation describes the "blur" between the measurable quantities of a particle in mathematical terms. Like much of the math in quantum theory, it is not for the faint of heart, which is to say it is completely unintelligible to most people. Therefore we restrict ourselves to a brief account on the underlying ideas and how they developed into the "Copenhagen Interpretation", which Niels Bohr and Werner Heisenberg jointly elaborated as a complete and consistent view of quantum mechanics (the Copenhagen Interpretation refers to Bohr's place of birth).

Heisenberg: "What Schrödinger writes about the visualisability of his theory [...] is crap."

Around 1925 there were two competing mathematical theories that both attempted to explain electron orbits. Matrix mechanics developed by Heisenberg interprets the electron as a particle with quantum behaviour. It is based on sophisticated matrix computations, which introduce discontinuities and quantum jumps. In contrast, wave mechanics developed by Erwin Schrödinger interprets the electron as an energy wave. Because wave mechanics entails more familiar concepts and equations, it quickly gained popularity among scientists.

Schrödinger and Heisenberg were no too fond of each other's competing works. Schrödinger says about matrix mechanics: "I knew of [Heisenberg's] theory, of course, but I felt discouraged, not to say repelled, by the methods of transcendental algebra, which appeared difficult to me, and by the lack of visualisability." Heisenberg's comment on wave mechanics was: "The more I think about the physical portion of Schrödinger's theory, the more repulsive I find it. [...] What Schrödinger writes about the visualisability of his theory 'is probably not quite right,' in other words it's crap."

The Copenhagen Interpretation.

Despite the differences, Schrödinger published a proof in 1926, which showed that the results of matrix and wave mechanics are equivalent; they were in fact the same theory. According to the Copenhagen Interpretation, the wave and particle pictures of the atom, or the visual and causal representations, are "complementary" to each other. That is, they are mutually exclusive, yet jointly essential for a complete description of quantum events. Obviously in an experiment in the everyday world an object cannot be both a wave and a particle at the same time; it must be either one or the other, depending on the situation. In later refinements of this interpretation, the wave function of the unobserved object is a mixture of both, the wave and particle pictures, until the experimenter chooses what to observe in a given experiment.

The German physicist Werner Heisenberg (1901-1976) received the Nobel Prize in physics in 1932 for his work in nuclear physics and quantum theory. The paper on the uncertainty relation is his most important contribution to physics.

Werner Heisenberg

Heisenberg impressed his teachers with his ambition and brilliance. He never produced other grades than straight A's, except on one occasion: During his doctorate, professor Wien of the university of Munich gave him an F in experimental physics, because he handled the laboratory equipment clumsily. Reportedly this left Heisenberg so disconcerted that he did not speak to anyone for days. 

Fate had it that a few years later, Heisenberg demonstrated the very limitations of experimental physics, which unquestionably constituted a setback for its advocates, including Professor Wien.

The observer becomes part of the observed system.

The notion of the observer becoming a part of the observed system is fundamentally new in physics. In quantum physics, the observer is no longer external and neutral, but through the act of measurement he becomes himself a part of observed reality. This marks the end of the neutrality of the experimenter. It also has huge implications on the epistemology of science: certain facts are no longer objectifiable in quantum theory. If in an exact science, such as physics, the outcome of an experiment depends on the view of the observer, then what does this imply for other fields of human knowledge? It would seem that in any faculty of science, there are different interpretations of the same phenomena. More often than occasionally, these interpretations are in conflict with each other. Does this mean that ultimate truth is unknowable?

The results of quantum theory, and particularly of Heisenberg's work, left scientists puzzled. Many felt that quantum theory had somehow "missed the point". At least Albert Einstein did so. He was an outspoken critic of quantum mechanics and is often quoted on his comment regarding the Uncertainty Principle: "The Old One (God) doesn't play dice." He also said: "I like to believe that the moon is still there even if we don't look at it." In particular, Einstein was convinced that electrons do have definite orbits, even if we cannot observe them. In a conversation with Heisenberg he said:

A conversation between Einstein and Heisenberg.

Heisenberg: "One cannot observe the electron orbits inside the atom. [...] but since it is reasonable to consider only those quantities in a theory that can be measured, it seemed natural to me to introduce them only as entities, as representatives of electron orbits, so to speak."

Einstein: "But you don't seriously believe that only observable quantities should be considered in a physical theory?"

"I thought this was the very idea that your Relativity Theory is based on?" Heisenberg asked in surprise.

"Perhaps I used this kind of reasoning," replied Einstein, "but it is nonsense nevertheless. [...] In reality the opposite is true: only the theory decides what can be observed."

(translated from "Der Teil und das Ganze" by W. Heisenberg)

We can easily see the rift between Einstein's intuitive and Heisenberg's empirical approach. Although Einstein's argumentation appears tricky, it is clear that he believes in a reality independent of what we can observe, which is in essence the view of realism. Kant's "thing in itself" comes to mind. - In contrast, Heisenberg believes that reality is what can be observed. If there are different observations, there must be different realities, which depend on the observer. Insofar Heisenberg can be regarded as an advocate of philosophical idealism, which states that the objects of perception are identical with the ideas we have about them. The idealist view denies that any particular thing has an independent real essence outside of consciousness.

Is the moon still there when nobody is looking at it?

The two philosophies seem incompatible at first. Heisenberg is in good company with famous contenders of idealistic positions, such Plato, Schopenhauer, and Husserl, but so is Albert Einstein. If we take Heisenberg's view for granted, strict causality is broken, or better: the past and future events of particles are indeterminate. One cannot calculate the precise future motion of a particle, but only a range of possibilities. Physics loses its grip. The dream of physicists, to be able to predict any future event in the universe based on its present state, meets its certain death.

If we regard reality as that which can be observed by all, we have to find that there is no objective movement of an electron around the nucleus. This viewpoint would imply that reality is created by the observer; in other words: if we take Heisenberg literally, the moon is not there when nobody is looking at it. However, we must consider the possibility that there is a subatomic reality independent of observation and that the electron may have an actual trajectory which cannot be measured. The moon may be there after all. This conflict is the philosophical essence of the Uncertainty Principle.

Relativity and quantum theory are inconsonant up to the present day, despite great efforts in creating a unified theory capable of accommodating both views. After having published his papers on Relativity, Einstein dedicated the rest of his life to working on such a unified field theory, yet without success. The physicists who followed his lead developed a new model called string theory during the 1970s and 1980s. String theory was successful to some extent in providing a mathematical model that integrates the strong and the weak nuclear forces, electromagnetism, and gravitation. In spite of this, it cannot yet be called a breakthrough, because 

1. the theory has not been corroborated thoroughly by observational evidence; and 
2. there is not one, but five competing string theories. The latter point has recently been addressed by M-theory, a theory that unites existing string theories in 11 dimensions.

The Zen of Quantum Theory.

We shall leave the problem of theoretical unification to the physicists and instead briefly consider a philosophical unification of Relativity and quantum theory. Is this possible? Contemplating the subatomic realm seems like a Zen exercise. The nuclear reality embodies duality and multiplicity, such as is evident in the complicated structure of atoms and particles. It transgresses the narrow world of opposites. We have to realise that in spite of the different parts and components, the subatomic world in actuality is an undivided whole, where the boundary between the observer and the observed is blurred. Object and subject have become inseparable, spatial and temporal detachment is an illusion. When the American physicist J.R. Oppenheimer (1902-1967) describes the structure of probability clouds, he almost sounds like a Zen Master: "If we ask, whether the position of the electron remains the same, we have to say no. If we ask, whether the position of an electron changes with the course of time, we have to say no. If we ask, whether the electron is in a state of rest, we have to say no. If we ask, whether the electron is in motion, we have to say no."

[Read On]