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# Heisenberg's Uncertainty Principle

In 1927 the German physicist Werner Heisenberg (19011976) showed that quantum mechanics leads to the conclusion that certain pairs of quantities can never be measured simultaneously with arbitrarily high precision, even with perfect measuring instruments. For example, it is not possible to measure the position and the momentum of a particle with unlimited precision. If one denotes the uncertainty in the measurement of its position by Δ x and the uncertainty in its momentum by Δ p then Heisenberg's Uncertainty Principle states that the axioms of quantum mechanics require that

where h is Planck's constant
(h = 6.626 068 76 × 10-34 Js ).

The Uncertainty Principle is often presented as a manifestation of the fact that the act of measurement inevitably perturbs the state that is being measured. Thus, the smaller the particle being observed, the shorter the wavelength of light needed to observe it, and hence the larger the energy of this light and the larger the perturbation it administers to the particle in the process of measurement. This interpretation, while helpful for visualization, has its limitations. It implies that the particle being observed does have a precise position and a precise momentum which we are unable to ascertain because of the clumsiness of the measurement process. However, more correctly, we should view the Uncertainty Principle as telling us that the concepts of position and momentum cannot coexist without some ambiguity. There is no precise state of momentum and position independent of the act of measurement, as naïve realist philosophers had assumed. In large, everyday situations this quantum mechanical uncertainty is insignificant for all practical purposes. In the sub-atomic world it is routinely confirmed by experiment and plays a fundamental role in the stability of matter. Note that if we take the limit in which the quantum aspect of the world is neglected (so Planck's constant, h, is set to zero), then the Heisenberg Uncertainty would disappear and we would expect to be able to measure the position and momentum of any object with perfect precision using perfect instruments (of course in practice this is never possible).

The Uncertainty Principle has had a major effect upon the philosophy of science and belief in determinism. It means that it is impossible to determine the present state of the world (or any small part of it) with perfect precision. Even though we may be in possession of the mathematical laws that predict the future from the present with complete accuracy we would not be able to use them to predict the future. The Uncertainty Principle introduces an irreducible indeterminacy, or graininess, in the state of the world below a particular level of observational scrutiny. It is believed that this inevitable level of graininess in the state of matter in the universe during the first moments of its history led to the production of irregularities that eventually evolved into galaxies. Experiments are underway in space to test the detailed predictions about the variations left over in the temperature of the universe that such a theory makes.

Of the other pairs of physical quantities that Heisenberg showed cannot be measured simultaneously with arbitrarily high precision, the most frequently discussed pair is energy and time. Strictly, this pair is not a true indeterminate pair like position and momentum because time is not an observable in the way that energy, position, and momentum are in quantum mechanics. By using a time defined externally to the system being observed (rather than intrinsically by it), it would be possible to beat the requirement that the product of the uncertainty in energy times the uncertainty in time be always greater than Planck's constant divided by 4 π.

The physicist Niels Bohr (18851962) called quantities, like position and momentum, whose simultaneous measurement accuracy was limited by an uncertainty principle complementary pairs. The limitation on simultaneous knowledge of their values is called complementarity. Bohr believed that the principle of complementarity had far wider applicability than as a rigorous deduction in quantum mechanics. This approach has also been adopted in some contemporary religious apologetics, notably by Donald Mackay and Charles Coulson. There has also been an interest in using quantum uncertainty, and the breakdown of rigid determinism that it ensures, to defend the concept of free will and to provide a channel for divine action in the world in the face of unbreakable laws of nature.

The Uncertainty Principle also changes our conception of the vacuum. Quantum uncertainty does not allow us to say that a volume of space is empty or contains nothing. Such a statement has no operational meaning. The quantum vacuum is therefore defined differently, as the lowest energy state available to the system locally. This may not characterize the vacuum uniquely and usually a physical system will have more than one possible vacuum state. Under external changes it may be possible to change from one to another. It is therefore important to distinguish between the nonscientific term "nothing" and the quantum mechanical conception of "nothing" when discussing creation out of nothing in modern cosmology.

## Bibliography

barrow, john d. the book of nothing. london: jonathan cape, 2000.

heisenberg, werner. "'Über den anschaulichen inhalt der quantentheoretischen kinematik und mechanik." zeitschrift für physik 43 (1927): 127.

herbert, nick. quantum reality: beyond the new physics. london: rider, 1985.

jammer, max. the philosophy of quantum mechanics: the interpretations of quantum mechanics in historical perspective. new york: wiley, 1974.

pais, abraham. inward bound. oxford: oxford university press, 1986.

john d. barrow

# Heisenberg's Uncertainty Principle

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