ERNST MACH AND PIERRE DUHEM ON PHYSICAL THEORY
BOOK II - Page 4
The New Physics vs. the Old Philosophy
The history of philosophy of science has been greatly influenced by the history of physics. As twentieth-century physicists found themselves departing farther and farther from Newtonian physics, they also found themselves departing farther and farther from the positivist philosophy notwithstanding the positivists’ criticisms of Newtonian physics. At the beginning of the century positivism was not merely the academic philosophy it later became. It was for a time the working philosophy for many physicists including those who produced the revolutionary relativity and quantum theories. It achieved ascendancy in academia during the first half of the century, where it evolved into logical positivism with the introduction of the symbolic logic, which made it irrelevant to the practice of basic research in the sciences. But long before academia recognized positivism as a kind of latter-day decadent Scholasticism in the second half of the century, it had fallen into disrepute in the eyes of the physicists who encountered its fundamental inadequacy for the new physics.
In his “Autobiographical Notes” in Schilpp’s Albert Einstein (1949) Einstein stated that Mach’s History of Mechanics had exercised a profound influence on him when he was a student. He related that all physicists of the last century saw in classical mechanics a firm foundation not only for all physics but also for all natural science, and that it was Ernst Mach who with this book shook Einstein’s dogmatic faith. At sixty-seven years of age, when he was writing these autobiographical notes, Einstein saw Mach’s greatness in the latter’s incorruptible skepticism and independence, even though Einstein himself had since rejected Mach’s philosophy. Einstein was specifically influenced by Mach’s critique of the Newtonian concept of absolute space, time and motion, ideas that are also rejected in Einstein’s relativity theory. Initially Mach seemed to support Einstein’s views. But Mach and Einstein were fundamentally working at cross purposes: Mach attacked the Newtonian concepts of absolute space, time and motion as part of his critique of all theoretical physics, while Einstein discarded these Newtonian ideas as a means for developing a new theoretical physics.
Another influence on Einstein was a thought experiment that Einstein reports he imagined, when he was sixteen years of age. In this thought experiment Einstein wondered what would happen if an observer traveled at the speed of light, riding on a beam of light. The light would then be at rest relative to the rider, but Einstein concluded that the idea of a light beam at rest is self-contradictory. This thought experiment was imagined many years before Einstein was introduced to Mach’s book by his friend Besso, while they were students at Zurich, and Einstein reports that it contributed to his forming the idea that the velocity of light in a vacuum is constant in all reference systems. From the positivist view the constancy of light is no less objectionably absolute than the concepts of absolute space or time. Mach’s phenomenalist relativity states that all sensations are dependent on all other sensations, while Einstein’s relativity theory states that the velocity of light in a vacuum is independent of other phenomena.
Throughout Mach’s lifetime Einstein continued to view his relativity theory as a continuation of Mach’s philosophy, and in his obituary of Mach in 1916 Einstein expressed the opinion that Mach would have come across the theory of relativity, if when Mach was younger the constancy of the velocity of light had been accepted by physicists. In 1921 Mach’s son published his father’s Principles of Physical Optics. The preface of the book is dated July 1913, and in it the son reports that Mach opposed Einstein’s relativity theory, and he rejects the idea that his father was a forerunner of relativity theory. As it happens, in June of 1913 Einstein had sent Mach a preliminary draft of the general theory of relativity, which uses non-Euclidian geometry. But in the 1912 edition of his Science of Mechanics Mach had introduced a lengthy footnote (Ch. IV, Sec IV, 9) opposing Minkowski’s use of four-dimensional geometry in physics and stating that the space of sight and touch is three-dimensional. It is unlikely, therefore, that Mach was pleased when he received Einstein’s 1913 correspondence, and it may have provoked the comments in the 1913 preface to the book on optics. Eventually Einstein accepted the existence of basic differences between his relativity theory and the positivist philosophy of Mach, and he ultimately rejected Mach’s philosophy.
Einstein’s general theory of relativity departed even further from Mach’s philosophy than did the special theory of relativity, because in the general theory it is not possible to restrict the equations to relations among observable magnitudes. But as the theory became accepted among physicists, the positivists who followed Mach did not want to reject it, and instead they modified their philosophy. These later neopositivists or “logical” positivists, as the positivists of the Vienna Circle came to be known, replaced Mach’s rejection of theories with a less restrictive idea. They said that the language of science might contain theoretical terms referring to nonobservable entities and magnitudes, on condition that statements referring only to observables could logically be related to those that contain these theoretical terms referring to the nonobservable magnitudes or entities. This later positivist program is considered below in the discussion of the logical positivists including Rudolf Carnap. Mach eventually accepted Einstein’s relativity theory, and also persuaded Moritz Schlick, founder of the Vienna Circle and successor to the chair of inductive philosophy previously held by Mach at Vienna, to accept Einstein’s theory. With this acceptance of Einstein’s relativity theory one of the basic theses of the early positivist philosophy was changed.
Positivism was not without some influence on the contributors to the new quantum physics, whose views became known as the “Copenhagen interpretation.” Adherents to this Copenhagen interpretation included 1922 Nobel-laureate Niels Bohr, 1932 Nobel-laureate Werner Heisenberg, and 1945 Nobel-laureate Wolfgang Pauli. Its opponents included 1921 Nobel-laureate Albert Einstein, 1933 Nobel-laureate Erwin Schrödinger, 1918 Nobel-laureate Max Planck, 1929 Nobel-laureate Louis de Broglie and David Bohm. The member of Bohr’s Institute for Theoretical Physics in Copenhagen, Denmark, who was initially influenced by the positivist philosophy, was Werner Heisenberg. In his Physics and Beyond (1971) Heisenberg relates how Mach’s philosophy operated in his own thinking. In the chapter titled “Understanding in Modern Physics (1920-1922)” he described his positivist views during the years that preceded his development of his matrix mechanics. At that time he believed that true understanding in physics consists in using only language that refers to direct sense perceptions, and that while the ability to make correct predictions is often a consequence of this positivist kind of understanding, nonetheless making correct predictions is not the same as having true understanding. Because he accepted the positivist philosophy of science, Heisenberg rejected Bohr’s hypothesis of electron orbits, since the orbits are not observable, but unlike Mach he admitted the existence of the electron itself due to the observable tracks produced by the free electron in the Wilson cloud chamber experiments. The cloud chamber developed by C.T.R. Wilson in 1912 consists of a container with a saturated vapor under pressure. When the pressure is rapidly reduced, the vapor cools and becomes supersaturated, as the temperature drops below the dew point. The passage of a charged particle, i.e., an electron through the vapor causes ion pairs to form droplets. A string of these droplets produces the track of the charged particle.
In the chapter titled “Quantum Mechanics and a Talk with Einstein (1925-1926)” Heisenberg relates that on the day that he presented his matrix mechanics to the Physics Colloquium at the University of Berlin, Einstein, who was present in the assembly, expressed interest and invited Heisenberg to talk with him at his home that evening. The matrix mechanics does not postulate the existence of electron orbits around the nucleus of the atom, and when Einstein questioned Heisenberg about his positivistic views that evening, Heisenberg replied that he did not believe that postulates about orbits are appropriate, because the orbits are not observable. Heisenberg affirmed the view that the physicist should consider only observable magnitudes, and for that reason he developed the matrix mechanics, which treats only of the frequencies and amplitudes associated with the lines in the spectrum of the atom. Heisenberg also stated that he was using the same philosophy that Einstein had used, when the latter had rejected the concept of absolute space and time in developing relativity theory.
Einstein then replied that he no longer accepted the positivist view, because the physical theory decides what the physicist can observe. This idea that theory determines what is observed is philosophically very strategic, because it contradicts the underlying positivist assumption that there is a dichotomous distinction between the descriptive language about what is observable on the one hand, and the theoretical language about what is not observable on the other hand. When this dichotomy is denied, the positivist program of building science on firm foundations of observation is rendered untenable.
In the chapter titled “Fresh Fields (1926-1927)” Heisenberg describes the arguments between Niels Bohr and Erwin Schrödinger concerning the issue of the wave verses the particle views in microphysics and of the statistical approach taken by 1954 Nobel-laureate Max Born in 1927. Born maintained that Schrödinger’s wave function can be construed as the measure of the probability of finding an electron at a given point in space and time. Heisenberg accepted Born’s probability interpretation, but there still remained a problem in Heisenberg’s mind: Born’s interpretation did not explain how the trajectory of an electron particle in the cloud chamber could be reconciled with the wave mechanics. Particle trajectories did not figure in the matrix mechanics, and wave mechanics could only be reconciled with the existence of a densely packed beam of matter if the beam spread over areas much larger than the diameter of an electron.
With this problem in mind Heisenberg remembered his conversation with Einstein the previous year, specifically Einstein’s statement that it is the theory that decides what the physicist can observe. Einstein’s discussion with Heisenberg on the day in 1926, when Heisenberg had first presented his matrix mechanics in Berlin, led Heisenberg to recognize in 1927 that it was the classical theory that led him to think that the tracks in the Wilson cloud chamber represent the movement of a particle as having a definite position and velocity that defined its trajectory. Recognition of the interpenetration of theory and observation led Heisenberg to reconsider what is observed in the cloud chamber. He then rephrased his question about trajectories in terms of the quantum theory instead of the classical theory; he asked: Can the quantum mechanics represent the fact that an electron finds itself approximately in a given place and that it moves approximately at a given velocity?
In answer to this new question he found that these approximations could be represented mathematically, and he called this mathematical representation the “uncertainty relations”, also known as the “indeterminacy principle”. On this principle the limit of accuracy with which both position and momentum can be known is defined in terms of Planck’s constant. In the view of Heisenberg and those who advocate the “Copenhagen interpretation” this necessary degree of approximation is not merely a measurement inaccuracy, but is imposed by the nature of the universal quantum of action. Einstein’s semantical principle, that theory decides what the physicist can observe, became one of the cornerstones of the post-positivist philosophy of science as articulated both by Karl Popper and by the contemporary pragmatists; it led the contemporary pragmatist philosophers to reject the positivist separation of theory and observation.
Heisenberg also describes his thought processes in this discovery experience in his chapter on the history of quantum theory in his Physics and Philosophy (1958). There he says that he turned around a question: instead of asking how the known formalism of Newtonian physics could be used to express a given experimental situation, he asked whether or not only such experimental situations can arise in nature as can be expressed in the mathematical formalism of his matrix mechanics. This recounting of his thinking gives greater emphasis to the ontological commitment that characterizes the “indeterminacy principle”, according to which there does not simultaneously exist in reality both a determinate position and a determinate momentum for the electron. As it happens, Einstein was never willing to accept the ontology of the Copenhagen interpretation, even though Heisenberg attempted to do the same thing with his matrix mechanics that Einstein did with the Lorentz transformation, when the latter interpreted the Lorentz equation in non-Newtonian terms of actual time instead of apparent time and redefined the concept of simultaneity. Einstein maintained contrary to the Copenhagen interpretation that a more “complete” microphysical theory is needed, which would satisfy his own ontological criteria for physical reality. In imitating Einstein’s reinterpretation of the Lorentz transformation, Heisenberg was practicing scientific realism, i.e., ontological relativity according to which ontological commitment is extended to the most empirically adequate theory. The pragmatist philosophy of language implies this practice, in which it might be said that a carte blanche metaphysical realism is presumed, while the ontology describing reality is supplied by empirical science; it is a realism which is a blank check for which scientific theory specifies its cash value, and for which empirical criticism backs its negotiability.
Heisenberg did not escape the influence of positivism, even though he had departed from it in a very fundamental way to develop the indeterminacy relations. Another influence upon his thinking was Bohr’s philosophy of knowledge. Bohr did not explicitly embrace positivism, but in his view classical physics is permanently valid and must serve as the language of observation, in which all accounts of evidence in physical science must be expressed. Heisenberg’s attempt to reconcile the contrary influences of Einstein and Bohr resulted in his developing his semantical thesis of “closed-off theories.” This is his attempt at a systematic philosophy of language for science. It is different from the logical positivist philosophy, but due to Bohr’s influence it is more like positivism than the contemporary pragmatism. Einstein and Heisenberg had made very insightful criticisms of positivism, but neither produced a new systematic philosophy of language adequate to their insights in physics, however portentous these insights have turned out to be. The portended contemporary pragmatist philosophy of language and science was as great an intellectual revolution in philosophy as the revolutions in physics.
Comment and Conclusion
This chapter examined two variations on positivism formulated by two turn-of-the-twentieth-century physicists, and previewed the story of positivism’s rejection by the physicists who made the two great scientific revolutions in twentieth-century physics. This latter story will be given in greater detail below in the BOOK describing Heisenberg’s philosophy of quantum theory. But to appreciate these developments more adequately, it is helpful firstly to have examined the development of the pragmatist philosophy of language.
The next BOOK describes Carnap’s transformation of Mach’s positivism for his philosophy of semantical systems and then Quine’s transformation of Duhem’s positivist philosophy of mathematical physics into the contemporary pragmatism. Carnap and Quine were friends well known to one another, and both contributed insightfully to the linguistic-analysis tradition in philosophy. But Quine criticized Carnap’s positivism, and elaborated Duhem’s philosophy of mathematical physics beyond Carnap’s positivism into a new generalized philosophy of language now known as the Duhem-Quine thesis in contemporary pragmatism.