Died: 1976, Munich, Germany
Major Works: Development of quantum mechanics (1925), the Heisenberg uncertainty principle (1927)
Anomalous experimental results in microscopic physics can be explained through the use of matrices. There is an unsurpassable limit to the accuracy with which certain properties (position and momentum) of subatomic particles can simultaneously be determined.
Every measurement of a subatomic entity necessarily involves the substantial interference of an observer, so physics must focus on describing the experimental setup, which includes a relationship between an observer and the object observed; hence, statistical descriptions are the most accurate possible descriptions for such systems.
Werner Heisenberg is largely responsible for the twentieth-century revolution in physics known as quantum mechanics. He is most famous for his development of the Heisenberg uncertainty principle (also called the "indeterminacy principle" or "uncertainty relations" ) and his espousal of radical philosophical conclusions drawn from it. Prior to the advent of quantum mechanics, the origination of which is often credited to Heisenberg, physical science was proceeding in the direction initiated by Isaac Newton achieving greater and greater precision in the description of nature. It was the view of Newton and the majority of his followers that there was no theoretical reason why one could not approach an absolutely precise description of physical bodies and their motions. Many under Newton's influence were determinists in that they thought that sufficient knowledge of current physical conditions in the universe would enable the precise prediction of all future physical conditions. This Newtonian edifice was still s tanding when Werner Heisenberg was born in 1901 and it was weakened only slightly by the ideas of James Clerk Maxwell and Max Planck.
The foundations of Newton's idealized world were shaken by the work of Einstein in the years around 1905, but it was the work of Heisenberg and many of his peers that brought the walls crashing down. The Newtonian picture of a world of empty space filled with discrete, accurately representable physical bodies was shown by Heisenberg and others to be a myth. He showed that precise mathematical description of individual microscopic bodies was impossible, not due solely to the limitations of contemporary experimental technique, but for all time.
Influenced by philosophers such as Plato, Aristotle, Kant, and the positivists, and physicists such as Planck, Einstein, Sommerfeld, and Bohr, Heisenberg began to elaborate the meaning of his discoveries for wider arenas of science and philosophy. His exposure to philosophy and the classics (his father was a university professor) allowed him to see very quickly that his ideas, when fully grasped, could send shock waves jolting through practically every area of human thought.
Heisenberg was recognized early in his life as a gifted mathematician and theoretician. He had a healthy dose of the theoretician's disdain for experimental work, a condition shared and encouraged by fellow student Wolfgang Pauli (to the dislike of their teacher Arnold Sommerfeld). Heisenberg received his Ph.D. in 1923 and proceeded to a number of teaching positions in theoretical physics. He won the 1932 Nobel Prize for his work in quantum mechanics. He helped found the Max Planck Institute for Physics in Gottingen in 1946 and directed the Planck Institute for Physics and Astrophysics in Munich for many years, working for its advance until he fell too ill to do so. He died in 1976.
Heisenberg was an amiable man, well liked by all who came in contact with him. Practically the only personal criticism directed toward him comes from those who lament his less-than-vociferous defiance of the Nazis during the 1930s and 1940s. Heisenberg was a sensitive but apolitical person and hence suffered inwardly for the millions who suffered more noticeably from the Nazi abuses.
The Discovery of Quantum Mechanics
Many things about the state of physics in the early 1920s disturbed the young Heisenberg. He particularly abhorred the conceptual model of the atom that described atoms joined to one another by means of hooks and eyes. If the structure of the atom is this complex, he thought, then there must be more fundamental units from which they are constructed. Heisenberg was familiar with the atomic theories of the ancient Greeks and found their mathematical and logical beauty compelling but could not tolerate their complete lack of experiential corroboration. Especially intriguing to him were the theories of Plato in the Timaeus. Plato's description of the ultimately small in terms of geometrically simple forms was aesthetically pleasing to Heisenberg, and even though he could find no physical reason to describe atoms in this way, Plato's description seemed more tenable than the hooks-and-eyes model. Heisenberg's inability to settle upon a satisfactory model for the portrayal of atoms would lead him to a description so abstract that it would befuddle and put off many of his peers.
In addition, there were myriad inexplicable experimental results that Heisenberg felt compelled to resolve. There were also several unusual theories, proposed by Niels Bohr, Wolfgang Pauli, and others, that matched experiments, though no one knew why. Poised in the background behind these questions was the older question concerning the nature of electromagnetic radiation (including light). The wave propagation of light and the absorption of light in discrete packets (quanta) were experimental facts that could not be explained away. Was this radiation ultimately wavelike or particlelike? All attempts to explain the situation in terms of models that made clear sense had failed.
By the time of Heisenberg's preoccupation with these matters, in the period from 1923-25, Bohr, Heisenberg's mentor, was already developing his ideas on complementarity, the view that both kinds of descriptions (wave and particle) must be employed in the characterization of atomic phenomena. Any description of atomic phenomena that used exclusively the wave picture or the particle picture was doomed to fail, according to Bohr. Heisenberg saw that an entirely new conceptual scheme was called for. Bohr's freedom from restrictive thought pictures and Heisenberg's dissatisfaction with the same led to the first quantum mechanics, developed with the help of mathematical matrices.
In early 1925, no one had been able to find a mathematical tool that consistently accounted for the anomalies mentioned above. And Heisenberg had suffered a particularly severe attack of hay fever. He went to the island of Heligoland to recuperate and to ponder the numbers from the results of the perplexing experiments. Here it occurred to him that numbers handled in arrays, with their own mathematical peculiarities, sufficed to explain and to predict the hitherto befuddling experiments. It was pointed out to him that what he had used was matrix mathematics, whose properties had been known for several decades. A few physicists were adept at manipulating matrices, and with their help Heisenberg formulated the first consistent and widely applicable quantum theory. Max Born, Pascual Jordan, and Heisenberg collaborated on a paper that publicized these ideas. The paper was completed in mid-November of 1925 and became a crucial nail in the coffin of the classical (Newtonian) understanding of physical reality.
The ideas promulgated under the rubric "matrix mechanics" were very abstract, far removed from straightforward analyses of physical reality, and the language of matrices was largely unknown to the physicists of the day. To many it seemed quite absurd to describe physical particles in terms of an arcane branch of mathematics. Those close to the project were well aware of its rigor and precision, but it did not gain its widest acceptance until it became clear that Heisenberg's matrix mechanics was operationally equivalent to Schrodinger's wave mechanics, developed only a few months later. By then it was clear that quantum events, whether described by matrices or waves, did not behave anything like the classical particles they had been assumed to be. There remained a serious question concerning the application of the mathematical formalism created by Heisenberg to the physical reality that it somehow represented. These questions persist today. Physicists cannot say how subatomic particles, in themselves, behave , but Heisenberg was instrumental in defining just what physicists can say.
The Uncertainty Principle
Much of the reason that Heisenberg favored the matrix1 explanation of quantum events was his refusal to speculate about the existence or behavior of some ill-defined atomic "thing-in-itself." He bad an ongoing dispute with Erwin Schrodinger over this very issue. Schrodinger insisted that there must be an underlying continuity and lawfulness in atomic processes even if such could not be observed in current experiments Heisenberg thought it unbecoming of physics to ruminate over anything but observable quantities and, those observable quantities displayed discontinuities and apparent lawlessness.
This emphasis on the observable, along with certain peculiarities of matrix mathematics (noncommutativity), led Heisenberg to the formulation of his uncertainty principle. The seminal paper in famous which this principle was announced was published in the Zeitschrift fur Physik in 1927. This publication assured Heisenberg's fame and provided him with a starting point from which much of his career would proceed. The principle, wrote Heisenberg three years later in "The Physical Principles of the Quantum Theory," centers around the fact that "the interaction between observer and object causes uncontrollable and large changes in the system being observed. because of the discontinuous changes characteristic of atomic processes." He continued by explaining the scope and significance of this discovery: "This lower limit to the accuracy with which certain variables can be known simultaneously may be postulated as a law of nature (in the form of the so-called uncertainty relations)." And further: "These uncertainty relations give us that measure of freedom from the limitations of classical concepts which is necessary for a consistent description of atomic processes."
The classical mechanics of Newton did recognize, of course, that the observer interfered in certain measurements and hence that there arose various means of compensating for this interference, which, when accomplished, would lead to results that were held to be true "objectively." It was assumed by most physicists that the refinement of experimental technique would eventually lead to greater precision of measurement and that the effect of the observer's interference could be minimized to the point of insignificance. Heisenberg's principle of uncertainty summarily demolished this Newtonian hope.
Heisenberg showed that it would be impossible to determine simultaneously both the position and momentum of an electron. Because of observer interference and the unpredictable behavior of individual quanta of radiation, there would always remain a haziness about either momentum or position, or both.
Specifically, Heisenberg showed that the greater the accuracy with which one determines the position of an electron (or other subatomic particle), the greater the inherent inaccuracy in the determination of its momentum, and vice versa, If one would measure precisely the momentum, then the position would be entirely unknown. Definite determination of the position produces inescapable and complete uncertainty about the momentum. More precisely, the uncertainty principle states that the product of the uncertainties regarding position and momentum must be greater than or equal to Planck's quantum of action divided by twice [pi] (pi): If x is position, p is momentum, [delta] is amount of indeterminacy, and ["h bar" sign] ("h bar") is Planck's constant divided by 2[pi] then the formula reads [delta]x[delta]p [greater than or equal to]h.
Much of Heisenberg's theoretical work in this area was driven by his realization that Bohr's electron orbits were unobservable. Electrons were held by most thinkers to be classical particles, obeying Newtonian laws of motion, but they were not directly observable (as classical particles were observable). The effects that could be seen painted a much more complicated picture. Heisenberg chose to focus on what could be observed and demonstrated the existence of permanent limits on the accuracy of that observation.
The accuracy of any measurement is always a function of the wavelength of the light used in the observation. Visible light has a wavelength much too long to allow the resolution of items as small as subatomic particles. Hence, if it were possible to observe individual electrons with visible light, then there would be a high degree of uncertainty in measurement. It might be suggested, Heisenberg postulated, that radiation of a shorter wavelength be used in order to arrive at more accurate measurements. Though this course of action may sound promising, Heisenberg indicates its inadequacy by proposing a thought experiment employing a gamma-ray microscope. Gamma radiation has a much shorter wavelength than visible light, so if a microscope could be constructed to utilize gamma radiation, the measurements it yielded should be more accurate. However, Heisenberg says, this smaller wavelength is necessarily accompanied by a higher energy This increase in energy leads to a greater perturbation of the object under inv estigation, and an accurate measurement again becomes impossible. Any observation requires the exchange of at least one quantum (the smallest possible amount) of radiation between observer and object. For the low energy--large wavelength quantum, the observation cannot be precise due to poor resolving power. For the high energy--short wavelength quantum, the observation cannot be precise due to the increased interference affecting the observed object. Combine the notion of this perturbation with the fact that when the subatomic particle is disturbed it leaps discontinuously and unpredictably, and the result is a permanent and fateful inability to characterize accurately the behavior of microscopic phenomena. "Our knowledge then of this class of objects," says Heisenberg, "is limited to irreducible statistical distributions and correlations."
As the experimental prowess of modern physics approached analysis of the smallest particles of matter, where it seemed possible that physics would reach the precision of the classical ideal, Heisenberg pointed out the inherent impossibility of attaining the goal. This realization was bound to change not only the physicists' way of viewing nature but the very mind-set engendered by Newtonian successes, a mind-set shared by all persons educated in the nineteenth- and twentieth-century Western world. As Heisenberg himself said in a 1955 article, these changes in twentieth-century physics must "be considered as expressions of changes in our very existence and thus as affecting every realm of life."
Philosophical Interpretation of Uncertainty
Heisenberg spent untold amounts of time trying to fathom the full philosophical consequences of his uncertainty principle. In this effort he showed a degree of philosophical sophistication that outstripped most of his colleagues in the physical sciences. He began his career with very strong positivist leanings (believing that language has meaning only when it refers to potentially observable states of affairs) and later moved to a more highly nuanced Kantian-style rationalism (believing that certain a priori thought structures are prerequisite for the intelligible experience of nature).
Though he was originally opposed to both, Heisenberg eventually came to affirm the value of Schrodinger's wave mechanics and Bohr's principle of complementarity. These notions aided Heisenberg tremendously in his endeavor to develop a cogent philosophical understanding of his physical principles. Throughout the adjustments and refinements of his ideas, Heisenberg always held to what he and others have called the "Copenhagen interpretation" of quantum mechanics. This interpretation espoused the relative finality of the quantum mechanical description of the microscopic realm and forthrightly abandoned the classical notions of causality, determinism, and old-style materialism. Changes in atomic physics, says Heisenberg, "have made us abandon the world-view of ancient atomic philosophy. It has become clear that the desired objective reality of the elementary particles is too crude an oversimplification of what really happens, and that it must give way to very much more abstract conceptions."
Many physicists were vehemently opposed to the Copenhagen interpretation's dismissal of crucial explanatory notions such as causality and objective existence of physical bodies, but the experiments have vindicated Bohr, Heisenberg, and all the others who insisted that the statistical description of reality was the most complete description possible. The Copenhagen interpretation today is also called the orthodox interpretation.
This view, now so widely accepted in one form or another, was forged in an atmosphere of heated debate. Some of the most interesting literature in the history of science was born out of the correspondence between opponents and proponents of the Copenhagen interpretation. It seems wise to describe Heisenberg's understanding of certain elements of this position in light of some of the objections raised against it.
The Copenhagen interpretation as understood and spread by Heisenberg was essentially opposed to what he called the "ontology of materialism." He believed that this ontology, or ultimate understanding of existence, rested upon the illusion that concepts applicable to the everyday world of tangible and visible objects could be extrapolated into the world of the microscopic. As Heisenberg states in his 1958 monograph "Physics and Philosophy," the Copenhagen interpretation "starts from the fact that we describe our experiments in the terms of classical physics and at the same time from the knowledge that these concepts do not fit nature accurately. The tension between these two starting points is the root of the statistical character of quantum theory." This passage indicates many of the important features of the Copenhagen interpretation and indicates the abstract course that must be followed.
The statistical nature of the methods used to define quantum events calls into question perhaps the most revered principle of classical physics, the principle of causality. Heisenberg thinks that this is the most important of the traditional notions that must be abandoned. In quantum physics, one can make no sense of the idea that "natural phenomena obey exact laws." The principle of causality rests on the assumption that "it is possible to observe the phenomena without appreciably influencing them." So one element of the Copenhagen interpretation is an ineluctable subjectivity that renders inapplicable the traditional notion of complete causality. Subatomic reality, discontinuous and subject to uncontrollable observer-related perturbations, cannot be said to obey precise laws. This conclusion was anathema to many physicists, the most illustrious of whom were Planck, Einstein, and Schrodinger.
These three men, who have a minority following still, proposed that there is an underlying continuity in nature, that cause and effect are just as inexorable in the microscopic realm as they are at the level of the visible. They argued that the mere inability of humans to penetrate the mystery of elementary particles is no evidence in favor of the renunciation of causality.
Heisenberg's answer to these critics was twofold: First, no positive evidence has been produced in favor of such "hidden variables" (invisible causal connections); second, no experimental scheme has been devised in which the uncertainty principle can be shown to be anything but complete.
Heisenberg's opponents then created a series of thought experiments intended to illustrate a scenario in which Heisenberg's limits could be transcended. None of these thought experiments succeeded. Hidden-variables theories have not gained a substantial following, and various persons claim to have demonstrated their impossibility as consistent descriptors of microscopic nature. More advanced physical experiments in the 1970s and 1980s have served to corroborate further Heisenberg's contention that the quantum mechanical statistical description, involving the strange notions of acausality, complementarity, and subjectivity is the most complete that can be given (short of another scientific revolution akin to quantum mechanics in its impact).
Though Heisenberg's fame as a scientist and thinker is secure, there is still much controversy concerning the proper interpretation of his theories. He is accused of wavering between the view that the discontinuity and immeasurability of subatomic reality is subjective and the view that it is objective. A large amount of difficulty remains still surrounding this point, not the least of which surrounds the meaning of the terms "objective" and "subjective." For the early positivistic Heisenberg, questions about some unapproachable objective reality are meaningless. For the later, more rationalistic Heisenberg, it makes sense to speak of an objective world "out there," but its features are so far removed from the world of everyday experience that only metaphors suffice to point to it.
At least one thing cannot be doubted--quantum mechanics is an unqualified experimental and technological success. The electronic lifeblood of contemporary society is a fruit of the labor of many astute and daring quantum physicists. None from this group was more astute and daring than Werner Heisenberg.
Gribbin, John. In Search of Schrodinger's Cat. New York: Bantam Books, 1984. One of the better popularizations of quantum physics. Gribbin is as precise as possible given his nonmathematical presentation of the ideas. His writing is engaging and lucid.
Heelan, Patrick. Quantum Mechanics and Objectivity: A Study in the Physical Philosophy of Werner Heisenberg. The Hague: Martinus Nijhoff, 1965. A revised Ph.D. dissertation that includes a wealth of information on the conceptual foundations of Heisenberg's thought.
Jammer, Max. The Conceptual Development of Quantum Mechanics. New York: McGraw-Hill, 1966. An unparalleled historical source that recounts the theoretical development of quantum theory from its inception through the various debates about its proper interpretation.
__. The Philosophy of Quantum Mechanics. New York: John Wiley and Sons, 1974. An in-depth analysis of the philosophical interpretations and implications of quantum theory. The rigor is sustained by the author's refusal to shy away from the pertinent mathematics.
Mehra, Jagdish, and Helmut Rechenberg. The Historical Development of Quantum Theory. 5 vols. New York: Springer-Verlag, 1982. An exhaustive narration of the events leading to the development of quantum theory. The authors begin with an analysis of nineteenth-century physics and the difficulties that caused the twentieth century to begin on such a radical note. The final volume deals with the rise and interpretation of Schrodinger's wave mechanics.
Polkinghorne, J. C. The Quantum World. Princeton, N.J.: Princeton University Press, 1984. An excellent, brief popularization of quantum theory. His combination of a lively writing style and specific details of quantum theory is rare among such popularizations.
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|Author:||AUSTIN, D. BRIAN|
|Publication:||Great Thinkers of the Western World|
|Date:||Jan 1, 1999|
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