5.1 Positivism & Physics

A Universe of Observations, Not Things

A new philosophic outlook was beginning to pervade physics. Deriding “metaphysical concerns” as beyond the realm of physics, advocates of this philosophy, called positivism, argued that the experimental evidence, our observations of reality, were of primary importance.

Austrian physicist and philosopher Ernst Mach (1836–1916) was about to take that a step further. “Properly speaking,” Mach argued, “the world is not composed of ‘things’ as its elements, but of colors, tones, pressures, spaces, times, in short what we ordinarily call individual sensations” [[i]].

Consider Mach's views on atoms and the atomic theory. “Atoms cannot be perceived by the senses;” he argued, “like all substances, they are things of thought” [[ii]]. In Mach's view, the purpose of such concepts as atoms is not to understand reality, but only to organize the contents of our consciousnesses. “The atomic theory... is a mathematical model for facilitating the mental reproduction of facts” [[iii]]. In other words, atoms are a mere mental construct that help us to organize the bundles of perceptions we obtain when we perceive that we have mixed what we perceive to be chemicals together and perceive that a reaction has taken place. What sounds like an Aristotelian demand to make sense evidence primary, is in fact a Platonic call to put the observer ahead of the observation.

There is no such thing as a “right” or a “wrong” theory in Mach’s view; the only possible distinction is whether the theory gives us a structure by which we can “economize” our sensation bundles by shrinking them down to shorter form using some mathematical formula. The only standard by which we can select between theories is to compare how economical they are. For instance, Mach argued:

...the motions of the universe are the same whether we adopt the Ptolemaic or the Copernican mode of view. Both views are, indeed, equally correct; only the latter is more simple and more practical [[iv]].

In addition, Mach argued there was no such thing as absolute space and time, only the relative motion of one perceived entity with respect to another:

No one is competent to predicate things about absolute space and absolute motion; they are pure things of thought, pure mental constructs that cannot be produced in experience. All our principles of mechanics are, as we have shown in detail, experimental knowledge concerning the relative positions and motions of bodies [[v]].

Figure 5.4: Newton’s bucket [[ix]].

Where Newton argued that fluid in a spinning bucket bows outward, demonstrating motion relative to absolute space [[vi], [vii]], Mach argued that inertia is due to an interaction between matter and the rest of the universe: “Try to fix Newton’s bucket and rotate the heaven of fixed stars and then prove the absence of centrifugal forces” [[viii]].

The Austrian-American mathematician, Karl Menger (1902–1985), writing in 1960 in the introduction to the sixth American edition of Science of Mechanics, described how Mach’s thinking was a precursor to the ideas of the influential Vienna Circle.

Mach’s operationalist, antimetaphysical, anticausal views, and his ideas on economy of thought pervade his presentation of the science of mechanics…. In its beginnings, the Vienna Circle was altogether Mach-oriented…. The philosophy of the Vienna Circle developed into logical positivism [[xii]].

Figure 5.5: Ernst Mach (1838–1916) [[x]], left, and James Jeans (1877–1946) [[xi]], right.

If we want to understand the impact of philosophy on physics, we must consider what physicists have to say about philosophy. In 1942, the British physicist, James Jeans (1877–1946), summarized the positivist school of thought pioneered by Mach:

The study of physics has driven us to the positivist conception of physics. We can never understand what events are, but must limit ourselves to describing the pattern of events in mathematical terms; no other aim is possible – at least until man becomes endowed with more senses than he at present possesses.... These [observations] will never describe nature itself, but only our observations on nature. Our studies can never put us in touch with reality; we can never penetrate beyond the impressions that reality implants in our minds [[xiii]].

To be clear, Mach did make important contributions to physics. Mach was a key contributor to the science of supersonic shock waves. In 1888, he succeeded in taking a photograph of the shockwave around a bullet, confirming the 1847 predictions of Christian Doppler (1803–1853) regarding the changes in frequency of sound waves from moving sources.

Figure 5.6: In 1888, Mach captured the first photo of the shock waves around a supersonic object [[xiv]], left, and Doppler’s original 1847 diagram of a supersonic shock wave [[xv]], right.

Almost contemporaneously, Waldemar Voigt (1850–1919) brought Doppler’s work to fruition with his 1887 demonstration of a transformation of variables to calculate the sound fields of moving sources from the field of a source at rest [[xvi]]. This anticipated what would come to be known as the Lorentz transform in relativity theory. Mach’s role in supersonic aerodynamics was aptly memorialized by German aeronautical engineer, Jakob Ackeret (1898–1981):

His [Ackeret’s] inaugural lecture at the ETH on 4 May 1929 was on drag at very high speeds. When defining the similarity properties of viscous compressible flow, he noted that it would be very convenient to have a special name for the important ratio of flow speed (or flight speed) v to sound speed a. He proposed the designation “Mach number” [[xvii]].

Although colored by Mach’s philosophy, The Science of Mechanics, is an excellent historical-based survey of classical mechanics (even if Mach does unfairly slight medieval science). By the beginning of the twentieth century, the philosophic stage was set for what some would call the most important discovery in the world of science since Newton’s theory of gravitation [[xviii]].

Next time, 5.2 Relativity: Top-Down, or Bottom Up?

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References

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[[i]]         Ernst Mach, The Science of Mechanics:  A Critical and Historical Account of Its Development, Third Paperback Edition, (Chicago:  Open Court, 1973), pp. 588-89.  Originally published 1893.

[[ii]]        Ernst Mach, Op. Cit., p. 589.

[[iii]]       Ernst Mach, Op. Cit., p. 579.

[[iv]]        Ernst Mach, Op. Cit., pp.294-5.

[[v]]        Ernst Mach, Op. Cit., pp.280.

[[vi]]        Newton, Isaac, Mathematical Principles of Natural Philosophy, (3^rd ed., Andrew Motte, trans., with notes by Florian Cajori), (Berkeley, CA: University of California Press, 1962), Book I Scholium, pp. 10-11.  Originally published, 1726.

[[vii]]       Ernst Mach, Op.Cit., pp.226.

[[viii]]      Ernst Mach, Op.Cit., p. 279. See: https://archive.org/details/scienceofmechani0000mach_o3q3/page/278/mode/2up?q=bucket

[[ix]]       Courtesy, Greta Schantz.

[[x]]        https://en.wikipedia.org/wiki/Ernst_Mach#/media/File:Ernst_Mach_01.jpg

[[xi]]       See: https://infogalactic.com/info/File:James_Hopwood_Jeans.jpg

[[xii]]       Ernst Mach, Op.Cit., pp. xiii, xvii, xix.

[[xiii]]      Jeans, James H., Physics and Philosophy, New York: Dover, 1981, p. 15.

[[xiv]]      This photo was taken by physicist Ernst Mach in 1888 in Prague, using Schlieren Photography on a 5 mm-diameter negative. It depicts the waves around a supersonic brass bullet. See: https://commons.wikimedia.org/wiki/File:Photography_of_bow_shock_waves_around_a_brass_bullet,_1888.jpg

[[xv]]       Rott, N., “Jakob Ackeret and the History of the Mach Number,” Annual Review of Fluid Mechanics, 17(1), 1985, pp 1–10. doi: 10.1146/annurev.fl.17.010185.000245

[[xvi]]      Rott, N., “Jakob Ackeret and the History of the Mach Number,” Annual Review of Fluid Mechanics, 17(1), 1985, pp 1–10. doi: 10.1146/annurev.fl.17.010185.000245

[[xvii]]      Rott, N., “Jakob Ackeret and the History of the Mach Number,” Annual Review of Fluid Mechanics, 17(1), 1985, pp 1–10. doi: 10.1146/annurev.fl.17.010185.000245

[[xviii]]     Anon., “Einstein Expounds His New Theory,” New York Times, December 3, 1919. “Indeed, there are German savants who believe that since the promulgation of Newton's theory of gravitation, no discovery of such importance has been made in the world of science.”