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,
