ScienceWeek

6. HISTORY OF PHYSICS: ON ERNST MACH (1838-1916)

The following points are made by Frank Wilczek (Physics Today 2004 April):

1) Ernst Mach (1838-1916) cleansed the intellectual atmosphere of his time by making simple observations, obvious in retrospect, that unsettled conventional wisdom. Mach's close critical analysis of the empirical value of physical concepts and his insistence that they must justify their use helped produce the atmosphere in which special and general relativity, and later quantum theory, could be conceived.

2) Mach's masterpiece is The Science of Mechanics.(1) It is fascinating to read, even today, and every physicist ought to have that pleasure. In an annotated narrative, Mach dissects the conceptual innovations and presuppositions that marked the history of the science of motion, from its prescientific roots through the late 19th century. He was especially critical of Newton's concepts of absolute time and space:

"Absolute time can be measured by comparison with no motion; it has therefore neither a practical nor a scientific value; and no one is justified in saying that he knows aught about it. It is an idle metaphysical conception."(1)

2) Here's what Albert Einstein (1879-1955), in his self-styled "obituary", said about Mach's book:

"Even [James Clerk] Maxwell and [Heinrich] Hertz, who in retrospect appear as those who demolished the faith in mechanics as the final basis of all physical thinking, in their conscious thinking adhered throughout to mechanics as the secured basis of physics. It was Ernst Mach who, in his history of mechanics (Geschichte der Mechanik), shook this dogmatic faith. This book exercised a profound influence upon me in this regard while I was a student. I see Mach's greatness in his incorruptible skepticism and independence."(2)

3) Special relativity puts all spacetime frames that move with respect to one another at constant velocity on an equal footing. It thereby renders moot the notion of a unique "preferred" value for any single object's velocity. Mach's deconstruction of motion, however, went much further. It culminated in a concept of total relativity, Mach's principle, which remains provocative to this day.

4) Here is Isaac Newton's original formulation of his concept of absolute space:

"If a bucket, suspended by a long cord, is so often turned about that finally the cord is strongly twisted, then is filled with water, and held at rest together with the water; and afterwards by the acceleration of a second force, it is suddenly set whirling about the contrary way, and continues, while the cord is untwisting itself, for some time in this motion; the surface of the water will at first be level, just as it was before the vessel began to move; but, subsequently, the vessel, by gradually communicating its motion to the water, will make it begin sensibly to rotate, and the water will recede little by little from the middle and rise up at the sides of the vessel, its surface assuming a concave form. (This experiment I have made myself.) ... when the relative motion of the water had decreased, the rising of the water at the side of the vessel indicated an endeavor to recede from the axis; and this endeavor revealed the real motion of the water.(3)

5) Mach insisted that the relative motion of bucket and distant stars is responsible for the observed concave surface. In Mach's own words:

"Newton's experiment with the rotating vessel simply informs us that the relative motion of the water with respect to the sides of the vessel produces no noticeable centrifugal forces, but that such forces are produced by its relative rotation with respect to the mass of the Earth and the other celestial bodies. No one is competent to say how the experiment would turn out if the sides of the vessel increased in thickness and mass until they were ultimately several leagues thick."(1,4,5)

References:

1. E. Mach, The Science of Mechanics: A Critical Historical Account of its Development, Open Court, La Salle, IL (1893).

2. A. Einstein, in Albert Einstein: Philosopher-Scientist, P. Schilpp, ed., Harper and Row, New York (1949), p. 1.

3. I. Newton, Mathematical Principles of Natural Philosophy, I. B. Cohen, A. Whitman, trans., U. of Calif. Press, Berkeley (1999).

4. A. Einstein, Annalen der Physik 49, 769 (1916); Eng. trans. in The Principle of Relativity, Dover, New York (1952), p. 111.

5. D. Lindley, Boltzmann's Atom: The Great Debate That Launched a Revolution in Physics, Free Press, New York (2001)

Physics Today http://www.physicstoday.org

--------------------------------

HISTORY OF PHYSICS: ERNST MACH (1838-1916) AND RELATIVE MOTION

The following points are made by H.I. Hartman and C. Nissim-Sabata (Amer. J. Phys. 2003 71:1163):

1) Physicists and philosophers have debated many topics under the heading of "Mach's principle".(1) The authors restrict their discussion to Mach's related criticisms of Newton's interpretation of his rotating bucket experiment and of the prevailing view that the Copernican system describes reality. The authors focus on statements by Ernst Mach (1838-1916) that often preface discussions of Mach's principle,(2) and examine the internal consistency of Mach's views and their validity in the light of classical physics that Mach knew(3) in 1912, but without using special relativity (SR), which Mach rejected.

2) Isaac Newton (1642-1727) had stated, "The effects which distinguish absolute from relative motion are the [centrifugal] forces. If a vessel filled with water is whirled about [for a while] the surface of the water will be plain; but after that [the water] will revolve and from a concave figure till it becomes relatively at rest in the vessel. The true and absolute motion of the water, which is here contrary to the relative [motion with respect to the vessel] may be measured by this endeavor." (4) Here, absolute motion means motion with respect to absolute space.

3) In the rotating bucket the water is accelerated. Galilean and special relativity are relevant only to uniform rectilinear motion. Pre-SR electrodynamics posited that one could measure both velocity and acceleration with respect to a luminiferous ether, and acceleration with respect to the ether was taken to be identical to acceleration with respect to absolute space. Calling absolute space a "monstrous conception"(5), Mach rejected the notion of absolute space, but not that of the ether. He claimed that the centrifugal force in the bucket could be due to the water's motion with respect to the masses in the Universe. He thus sought to extend to rotational motion the notion that motion is purely relative. The authors present a critique of Mach's arguments for the relativity of rotational motion.

4) In summary: By maintaining the relativity of all motion, especially rotational motion, Mach denied the existence of absolute motion and of absolute space. Accordingly, he maintained the equivalence of the Ptolemaic and Copernican systems and the equivalence of rotating-system/fixed-Universe and Universe-rotating/fixed-system situations. An analysis of the Foucault pendulum shows that Mach's relativity principle implies that there cannot be a fixed bucket in a rotating universe. Also, Mach's views violate the physics that he espoused: noninertial experiments, for example stellar aberration and electromagnetic effects, distinguish between a rotating bucket in a fixed Universe and a fixed bucket in a rotating Universe, between a Copernican Universe and a Brahean or Ptolemaic Universe, and establish that one cannot ascribe all pertinent observations solely to relative motion between a system and the Universe.

References (abridged):

1. Mach's Principle: From Newton's Bucket to Quantum Gravity, edited by Julian Barbour and Herbert Pfister (Birkhauser, Boston, MA, 1995), p. 530 where 21 different formulations are listed.

2. Denis W. Sciama, The Unity of the Universe (Anchor Books, New York, 1961).

3. Ernst Mach, The Science of Mechanics (Open Court, LaSalle, IL, 1960), 6th ed. Originally published as Die Mechanik in ihrer Entwicklung Historisch-kritisch Darstellt, 9th ed.

4. Isaac Newton, The Mathematical Principles of Natural Philosophy (University of California Press, Berkeley, CA, 1960), pp. 10-11.

5. Reference 3, p. xxviii.

Amer. J. Phys. http://www.kzoo.edu/ajp

--------------------------------

KURT GOEDEL, ERNST MACH, AND THE VIENNA CIRCLE

The following points are made by J.L. Casti and W. DePauli (citation below):

1) The period between World War I and World War II marked the peak of Vienna's most productive cultural period. In the autumn of 1924, Kurt Goedel (1906-1978) settled in Vienna, the city of twelve-tone music, Jugendstil art, and the socio-linguistic critiques of Ludwig Wittgenstein (1889-1951) and Karl Kraus (1874-1936), to continue his studies.

2) Philosophy, logic, and mathematics were the topics that absorbed the young Goedel. And as he moved deeper into these realms, he increasingly confronted the limits of language for expressing the truths of even such a pristine, simple realm as arithmetic, the relationships among numbers. Here Goedel was beginning to touch upon the work of the famed Vienna Circle.

3) One of the main goals of this group was to promote the ideas of Ernst Mach (1838-1916). Mach had argued that conceptually analyzing contradictions between theories leads to progress in our understanding of the natural world. His analytic method --presented in books such as /The History of Mechanics/ and /Analysis of Sensations/ -- had fruitful consequences for both science and culture. In particular, by explaining and deconstructing physical concepts, Mach paved the way for Einstein's theory of relativity. His critique of Newtonian mechanics, with its notion of absolute time and space and the invariance principle of inertia, was of special historical importance. But Mach's theoretical approach also influenced artists, philosophers, and economists, thus shaping Austro-German discourse at the turn of the century. (V. Lenin (1870-1924) feared Mach's influence on the cultural and political scene enough to publish in 1909 the polemic tract "Materialism and Empirico-Criticism", which ultimately denounced Mach's ideas.)

4) One of the outgrowths of The Ernst Mach Society, founded in Vienna in 1922, was the "Schlick Circle", named after its leading figure, Moritz Schlick (1882-1936), professor of mathematics at the University of Vienna and one of Goedel's philosophy teachers. With the appearance of its manifesto on "The Scientific World View" in 1928, the group became more publicly visible.

5) If Plato's Academy in Athens served as the geographical focal point for Greek philosophy and its view of the world, then its twentieth-century counterpart can only be a small seminar room in the Mathematics Institute of the University of Vienna, where a group of physicists, mathematicians, and philosophers met every Thursday evening for several years in the 1920s and 1930s to debate the relationship between the theories of science and objective reality. This group, christened the Vienna Circle in 1931, eventually came to what amounts to the instrumentalist position that the only meaningful statements are those for which we can give a definite prescription (method or algorithm) for their verification. Thus, using a word like "yellow" would be equivalent to specifying a procedure for verifying that any particular object possessed the property of being yellow. In this way, the meaning or reality of "yellow" became equivalent to the statement of the procedure for its verification. This, in essence, forms the basis for the notorious "Verification Principle", which lay at the heart of the school of logical positivism, the term later applied to the philosophy expounded by the Vienna Circle. The triangle formed by language, world, and science was the focal point of the Vienna Circle's overall concerns.

Adapted from: J.L. Casti and W. DePauli: Goedel: A life of Logic. Perseus Publishing 2000, p.8. More information at: http://www.amazon.com/exec/obidos/ASIN/0738205184/scienceweek

ScienceWeek http://scienceweek.com