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Impearls: Copernicus Dethroned

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Earthdate 2004-04-29

Copernicus Dethroned

Stimulated by NASA's Gravity B probe which went up the other day, designed to further test Albert Einstein's general theory of relativity, Impearls continues its recent series which began with a piece on competing theories of gravity to general relativity, followed by consideration of what scientific theories more generally are.

People often recall from undergraduate physics that Einstein's special theory of relativity (promulgated 1905) provides for the “relativity” or equivalence of motion between “inertial reference frames,” which is to say, between unaccelerated or “free falling” platforms or moving points of view in space.  Not included in typical undergraduate curricula — and thus gradually forgotten about by most, however — is Einstein's later general theory of relativity (1915), which removes the limitation of “inertial” on allowed viewpoints or reference frames, in order to permit relativity-equivalence of motion between accelerated as well as inertial points of view.  As Einstein put it: 1

We arrive at a very satisfactory interpretation of this law of experience, if we assume that the systems K and K′ are physically exactly equivalent, that is, if we assume that we may just as well regard the system K as being in a space free from gravitational fields, if we then regard K as uniformly accelerated.  This assumption of exact physical equivalence makes it impossible for us to speak of the absolute acceleration of the system of reference, just as the usual theory of relativity forbids us to talk of the absolute velocity of a system; and it makes the equal falling of all bodies in a gravitational field seem a matter of course.

All viewpoints, accelerated or not, are encompassed within Einstein's general theory, and since rotating points of view or reference frames are in actuality just another kind of accelerated viewpoint, rotating frames are fully instantiated under general relativity.  Thus, though it's frequently noted that Einstein's general relativity has displaced Newton's gravitation, a consequence less noticed by many, however, is that Copernicus has also been likewise dethroned.

Under general relativity, it's just as valid and “true” to consider the universe as rotating once a day about a fixed and stationary Earth (i.e., the Ptolemaic universe), as it is to regard a rotating Earth revolving about a Sun within a more or less stationary universe (the Copernican system).  When it is Earth that is considered motionless, it's gravitational fields induced by the universe spinning round it, rather than the inertia of a rotating Earth, that raises up the Earth's equatorial “bulge,” and so forth.  As Einstein pointed out in an illuminating 1913 letter to Ernst Mach, Foucault pendulums, hitherto regarded as nearly perfect and unassailable proof of the Earth's rotation, are swung about by such forces, known as “frame dragging,” thus neutering Foucault's perfect proof!  Einstein wrote: 2

[To Ernst Mach, concerning confirmation at an upcoming eclipse]
… If so, then your happy investigations on the foundations of mechanics, Planck's unjustified criticism notwithstanding, will receive brilliant confirmation.  For it necessarily turns out that inertia originates in a kind of interaction between bodies, quite in the sense of your considerations on Newton's pail experiment.  The first consequence is on p. 6 of my paper.  The following additional points emerge:  (1) If one accelerates a heavy shell of matter S, then a mass enclosed by that shell experiences an accelerative force.  (2) If one rotates the shell relative to the fixed stars about an axis going through its center, a Coriolis force arises in the interior of the shell; that is, the plane of a Foucault pendulum is dragged around (with a practically unmeasurably small angular velocity).

It's just this kind of general relativistic “frame dragging” that the new Gravity B experiment is designed to investigate.

Moreover, it's this sort of close uniting of seemingly contradictory, polar-opposite concepts (e.g., rotating universe vis-a-vis spinning Earth, matter = energy, light is both particles and waves, etc.) that is part and parcel of the basic process and progress of science, and what physicist Niels Bohr was talking about in the last century when he said, “A great truth is a truth whose opposite is also a great truth.”


References

1 A. Einstein, 1911, “Über den Einfluss der Schwerkraft auf die Ausbreitung des Lichtes,” Ann. Phys. (Germany) 35, 898-908.  English translation in H. A. Lorentz, A. Einstein, H. Minkowski, and H. Weyl, 1923, The Principle of Relativity: A Collection of Original Memoirs, Methuen, London; paperback reprint, Dover, New York.

2 “Albert Einstein's appreciation of Mach, written to Ernst Mach June 25, 1913, while Einstein was working hard at arriving at the final November 1915 formulation of standard general relativity.”  Quoted in Charles W. Misner, Kip S. Thorne, John Archibald Wheeler, Gravitation, 1973, W. H. Freeman and Co., San Francisco; pp. 544-545.


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