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Heisenberg’s Uncertainty Principle

Matthew Santos

Published Jan 1, 2013• 9 citations
OpenAlex

Abstract

In 1926 Werner Heisenberg’s Uncertainty Principle set the field of quantum mechanics on a trajectory riddled with indeterminacy, a trajectory which stood in stark contrast with the classical Newtonian world causality and origin. In doing so, Heisenberg effectively created a new standard by which physicists conducted their science, broadened the scope of that science, and altered the very worldview of those physicists. Such paradigmatic upheaval fits the philosophical model of scientific progress posited by Thomas Kuhn. However, in the ever-changing and still-evolving world of quantum mechanics, Heisenberg’s revolutionary work uniquely strays from Kuhn’s model in its further implications.

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In 1926 Werner Heisenberg’s Uncertainty Principle set the field of quantum mechanics on a trajectory riddled with indeterminacy, a trajectory which stood in stark contrast with the classical Newtonian world causality and origin. In doing so, Heisenberg effectively created a new standard by which physicists conducted their science, broadened the scope of that science, and altered the very worldview of those physicists. Such paradigmatic upheaval fits the philosophical model of scientific progress posited by Thomas Kuhn. However, in the ever-changing and still-evolving world of quantum mechanics, Heisenberg’s revolutionary work uniquely strays from Kuhn’s model in its further implications.
COGNITIVE ASPECTS OF THE HEISENBERG PRINCIPLE I T HE Heisenberg uncertainty principle, like its rival theory of relativity/ has been one of the truly crucial phases in the physics of our day~ It did not, like the discovery of a new element or the Maxwell equations, simply indent the story of classical physics for a new paragraph. It was not only a new chapter but a new book. Detected, in the words of Heisenberg himself, when physics became self-critical, the principle is a statement of what is observable-like its contemporary, the theory of relativity. It was anew advance in method, so revolutionary indeed that physics has virtually lost meaning as content and become synonymous , as logical empiricism amply indicates, with mere rules of procedure. That science is developing into a system of logic, combining the Cartesian stress on clearness with the Kantian regulative idea, actually confirms a contention of traditional philosophy. It reveals that once we deny the colors and sounds, the life, lights, and purpose in our universe-as pure scientific method actually does-we are fated to deny much more than quality. Quality is in the order of form, substance, and being. The moment quality is banished from the real world, by the same 1 That all is not as peaceful and unified in physics as the layman sometimes believes can be seen in the deep cleavage between quantum and relativity mechanics. For the first, the exact specification of space (position) and time (velocity, momentum) has no meaning, while in relativity theory such exact description is the only meaning that can be had. Despite the efforts 'of leading physicists, including Dirac, to unite the two theories, the contradiction is so profound that one of these systems must eventually be abandoned or, more probably, both of them will be superseded. The recent work .of Schroedinger and apparently also of Einstei~ himself are directed to extend the general theory of relativity, making the current theory a special case just as Newtonian physics is a special case of present relativity mechanics. 474 COGNITIVE ASPECTS OF THE HEISENBERG PRINCIPLE 475 decree being itself-because it is an immediate, non-inertial (formal) thing like quality-is driven into its only possible exile, nothingness. It is not surprising then that, after modern physics· has finished its task, the universe should not only be emptied of its lights, its fragrance, its sweetness, and its music but should also be without being and without existence. The uncertainty principle has been much debated in modern thought. Its impact has brought a sad end to the pride of 19th century science since it prevents a complete knowledge of anything at all by shading into the darkness at least one of the two major factors that specify it. Shortly after the principle was born it was hailed by various authors as a proof of free will, of the possibility of religion, and of non-mechanistic concepts in biology. In a more consistent and challenging sense, it has often been taken to refute what the physicist calls causality and what the philosopher calls the order of nature. The fact of the matter is that if the senses alone supply knowledge, truly only one thing at a time can be apprehended. If Hume was right in philosophy, so is Heisenberg. But when sensism yields to an intellectual insight into reality, it is easy to refute the scientist's claim to dethrone the doctrine of nature's order which he could never detect, even in classical physics, by pointerreadings .2 But whatever the fate of the Heisenberg principle in cosmology , it has had a most fruitful career in the field of physics. To Heisenberg himself, the principle was a point of departure for an original development of quantum mechanics based on the " uncertainty " of position and momentum,.: 3 If, for example, measurements are made, under a microscope, of the position of an electron, the photon (light-particle), which impinges on the eye and thus conveys the required knowledge to the physicist, has had to collide with the electron, thus imparting an impact known as the Compton recoil. When • For ·a discussion of the order of nature, cf. J. Marling: The...
The classical world, governed by classical physics, might have felt more intuitive and certain. However, the 20th century’s revolutionary birth of quantum mechanics opened a way to the “quantum world”. This chapter investigates the evolving concept of “world”, especially exploring the special and general theories of relativity, with Wittgenstein’s philosophical view that the world is composed of facts, or the existence of states of things. Quantum mechanics has two essential principles: The Heisenberg uncertainty principle and the new Heisenberg uncertainty principle, where the former indicates the inherent uncertainty within the quantum world and the latter uncovers the certainty under some circumstances such as quantum entanglement. Quantum mechanics, while having multiple interpretations, is considered a relatively complete framework; however, its “counterfactuals”—scientific facts that defy classical expectations—can be challenging for the classical understanding. Additionally, the potential for “backward causality” under time symmetry conditions adds another level of complexity. These counterfactuals and the possibility of backward causality don’t contradict existing facts, but rather signal the expansion of our scientific scope and, potentially, a new scientific paradigm.
A philosopher once said ‘It is necessary for the very existence of science that the same conditions always produce the same results’. Well, they don't! Richard Feynman Watching electrons We have seen that quantum mechanics does not allow us the comfort of being able to visualize the motion of a quantum particle. In a normal game of billiards we can imagine the paths taken by the individual balls (Fig. 1.1). Figure 2.1 shows the physicist George Gamow's attempt to give some impression of how the same game might look if played with quantum particles. Besides illustrating that the notion of a path is no longer valid in quantum mechanics, this cartoon also illustrates another significant difference between the quantum and classical worlds: the exact position of the white ball is not known. Uncertainty has entered physics and replaced the determinism of Newtonian mechanics. By the nineteenth century, physicists had been able to explain vast amounts of experimental observations on objects as different as planets and billiard balls. If an observation differed from the predictions of classical physics, they looked for something they had overlooked to explain the deviation. In 1864, physicists' confidence in the whole edifice of classical physics seemed to be spectacularly verified by an analysis of some irregularities in the orbit of Uranus. These were attributed to the existence of a then undiscovered planet – the subsequent discovery of Neptune was a triumph for Newtonian physics.
One of the most striking deviations of quantum mechanics from classical mechanics is that any measurement of a microscopic system involves the interaction with the measuring instruments. The interaction cannot be neglected and in fact leads to uncontrollable disturbance on the system. In 1927, Werner Karl Heisenberg in his celebrated paper established the quantitative expression for unavoidable momentum disturbance caused by any position measurement. The crucial word here is simultaneously. The uncertainty relation gives the lower bound on the product of the uncertainties of two pairs of variables. But it says nothing about the accuracy with which individual observables can be measured. The physical meaning of energy-time uncertainty is different from that of x-px uncertainty. Position and momentum are observables to which Hermitian operators are assigned and which are measured at a particular time. An important implication of the uncertainty principle is that quantum systems do follow classical trajectories which conflict with our everyday experience.