View source for Einstein's Ether: E. Annual Motion of the Earth

{{Infobox paper
| title = Einstein's Ether: E. Annual Motion of the Earth
| url = [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_787.pdf Link to paper]
| author = [[Galina Granek]]
| keywords = [[bucket experiment]], [[earth?s daily rotation]], [[Mach]], [[Poincar]]
| published = 2001
| journal = [[Apeiron]]
| volume = 8
| number = 3
| num_pages = 12
}}

'''Read the full paper''' [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_787.pdf here]

==Abstract==

In my paper &ldquo;Einstein's ether part A&rdquo; I mainly re-examined the bucket experiment and earth's daily rotation (the problems that had been occupying Mach and Poincar&eacute;) from Einstein's General Relativistic point of view. In this paper I further discuss Einstein's General Relativistic solution to the problems that had been occupying Mach and Poincar&eacute;.

==Overview==

This is the fifth instalment (part E) of Galina Granek's series in ''[[Apeiron]]'' on the persistence of the [[Aether|ether]] concept in [[Albert Einstein|Einstein]]'s own thought. Granek writes as a historian and philosopher of science at Haifa University; the paper is drawn from her doctoral dissertation, supervised by Mara Beller at the Hebrew University of Jerusalem. Its method is textual and conceptual rather than experimental: it works through three of Einstein's own thought experiments &mdash; the rotating disc, the freely falling elevator, and the annual motion of the earth about the sun &mdash; and asks what each of them commits Einstein to.

The conclusion is deliberately awkward for the standard story. General relativity is usually presented as the theory that finally disposed of the ether. Granek argues the reverse: that the route Einstein took to expel absolute motion led him straight back to a medium. Once absolute rotation is eliminated by a gravitational field, and once the gravitational field is identified with curved space-time, and once instantaneous action-at-a-distance is forbidden by the [[Equivalence Principle|strong principle of equivalence]] on the same grounds that [[Special Relativity|special relativity]] forbids absolute [[Simultaneity|simultaneity]], something must convey the gravitational and inertial interactions. Einstein himself, in 1920, named that something ether. In Granek's closing formulation: "the ghosts of absolute motion are expelled from physics, but the ghosts of the ether are still there."

==The argument==

===The rotating disc===

Granek begins where Einstein began in his 1916 review article "Die Grundlage der allgemeinen Relativit&auml;tstheorie," with a disc replacing Newton's bucket. A large disc carries two concentric circles, one small and one large. An outside observer K' is inertial; an inside observer K rotates with the disc. In K' 's frame Euclidean geometry holds and the ratio of the two circumferences equals the ratio of the two radii.

K now measures with a rod identical to K' 's. Three of the four measurements agree between the observers: both radii, because a rod laid along a radius moves perpendicular to its own length and does not contract, and the small circumference, because near the axis the speeds are low enough to ignore relativistic effects. The fourth does not. A rod laid along the ''large'' circumference lies along the direction of motion, and to K' it appears contracted. The large circumference therefore comes out differently for the two observers, and for K the ratio of circumferences no longer equals the ratio of radii. K "cannot confirm the validity of Euclidean geometry in his reference frame."

Granek stresses that Einstein read this breakdown as due to ''absolute rotation'' &mdash; and that this is precisely what he wished to be rid of. His remedy was the equivalence principle: the effect can equally be produced by a gravitational field directed outward from the disc's axis, deforming the rods. Non-inertial motion is then no longer absolute motion. She quotes Einstein and Infeld's own statement of the alternative from ''The Evolution of Physics'': "To save the Euclidean geometry, we should accuse the objects of not being rigid... If, however, we should not succeed in combining Euclidean geometry and physics into a simple and consistent picture, we should have to give up the idea of our space being Euclidean."

===The conventionalist fork: Einstein against Poincaré===

The heart of the paper is the observation that the disc experiment does not decide anything on its own. Einstein noted the alternative himself: an observer on the disc "could seek some physical reasons, say temperature differences, deforming his measuring instruments."

That alternative is exactly the choice [[Henri Poincaré|Poincaré]] made. Granek points out (citing her own 1998 dissertation) that Poincaré had proposed the same experiment with a disc heated at its centre, so that a temperature gradient deforms the rods, and had concluded that Euclidean geometry would always survive contact with experience. She quotes his ''La science et l'hypoth&egrave;se'' of 1902 on the astronomical case: if light were found not to travel in straight lines, "we could renounce the Euclidean geometry or, better, modify the laws of optics and admit that light is not rigorously propagated in a straight line... Euclidean geometry has therefore nothing to fear from new experiments."

Granek draws the fork sharply. Measurements alone "cannot determine what is the geometry of the world." Choose with Einstein that rods stay rigid, and the measurements show space is non-Euclidean. Choose with Poincaré that geometry stays Euclidean, and the very same measurements show that rods are non-rigid. The geometry of space is fixed by convention. But &mdash; and this is her qualification &mdash; ''once'' a convention is adopted, experiment does then verify a geometry. The conventional element sits at the choice, not afterwards.

Einstein took the first branch. From the measurements he deduced curved space-time itself; and curved space-time is what he later identified with a new kind of ether, one which is emphatically ''not'' at rest with respect to absolute space. Granek's point is that Einstein's cavity-with-bodies-in-it, once so read, makes the bucket and disc experiments "each exemplify the inevitable need for an ether."

===The falling elevator===

The next step is the strong equivalence principle, which Granek states in Einstein's 1911 terms: at each point of a gravitational field one can choose a local inertial frame in which, over a sufficiently small neighbourhood, all physical laws take the form they have in a non-accelerating frame with no gravitational field. The point of the principle is that it makes absolute acceleration and absolute rotation as unspeakable as [[Special Relativity|special relativity]] made absolute velocity.

The illustration is the Einstein-Infeld elevator. Its cable breaks; an observer inside drops a handkerchief and a watch. To the outside observer K all three &mdash; handkerchief, watch and elevator &mdash; fall with the same acceleration, "quite independent of their mass," which is precisely the equality of gravitational and [[Inertia|inertial]] mass. To the inside observer the two objects simply stay put. He may ignore the gravitational field, since its source lies outside his frame, and treat his frame as inertial.

Granek is careful about the limitation. The inertial character of the falling frame is bounded in space and time: "sooner or later the whole elevator will collide with the earth." A second elevator K<sub>0</sub>, moving uniformly relative to the falling one, is judged accelerated by K but inertial by an observer "born and brought up in the elevator." Both are locally inertial, all laws are the same in both, and the transition between them is a [[Lorentz Transformation|Lorentz transformation]].

===Copernicus and Ptolemy given equal justification===

The paper's title question is answered by carrying the same reasoning from the earth's daily rotation to its annual motion. Granek recalls [[Ernst Mach|Mach]]'s reading of the bucket: water fixed and the sky of fixed stars rotating is equivalent to water rotating and the sky fixed. Replace the water by the earth and the sky by the sun and the stars, and case 1 becomes the Ptolemaic system and case 2 the Copernican. "It makes no sense, accordingly, to speak of a difference in truth between Copernicus and Ptolemy."

Granek is explicit that this does ''not'' rehabilitate Ptolemy; it "contests the absolute meaning of either view." She grants Newton the dynamical argument that decided the historical case &mdash; his gravitational law explained the Copernican picture while Ptolemy's compound orbits fit no explanation at all. What general relativity adds is that it explains ''both'' as gravitational phenomena and so gives them equal dynamical justification. Under the strong equivalence principle the Copernican frame is one in which the earth freely falls toward the sun; and since we fall with it we feel no attraction, so an observer on earth "may ignore the sun's gravitational field, since its source lies outside his frame" and may regard his frame, locally and instantaneously, as Ptolemaic. Einstein and Infeld's own words are quoted: the two sentences "the sun is at rest and the earth moves" and "the sun moves and the earth is at rest" "would simply mean two different conventions concerning two different CS."

Granek's closing move is the one the series is built toward. Special relativity rejects absolute simultaneity; the strong equivalence principle then forces general relativity to reject instantaneous action-at-a-distance for gravity; and a rejected action-at-a-distance leaves a conveying medium as the only option. That medium is curved space-time, which Einstein named ether in 1920.

==Assessment==

The paper's strength is that it argues almost entirely from Einstein's own texts. The 1911 and 1916 ''Annalen'' papers, ''The Evolution of Physics'' and Poincaré's ''La science et l'hypoth&egrave;se'' carry the argument; Granek adds the connective reasoning rather than a new physical claim. That makes it unusually hard to dismiss. The Einstein-Poincaré fork in particular is set out with real clarity: two incompatible descriptions of one disc, neither refuted by measurement, differing only in which of geometry and rigidity is held fixed. Readers who know only the textbook slogan that relativity "abolished the ether" will find the 1920 Leyden address awkward, and Granek is right that it needs accounting for rather than embarrassed silence.

Three difficulties should be stated plainly. First, the word "ether" is doing a great deal of work across a wide gap. The medium Granek arrives at is a dynamical metric field with no state of rest, no rest frame, and no velocity that could be measured; that is exactly what the [[Michelson-Morley Experiment|Michelson-Morley experiment]] and its modern optical-resonator successors, which bound any preferred-frame anisotropy in the speed of light at the 10<sup>-17</sup> level, exclude for the ether of Lorentz and Fresnel. Einstein's 1920 usage was avowedly a redefinition. Granek acknowledges as much when she stresses that this ether is not at rest with respect to absolute space, but the paper's rhetorical force depends on the reader hearing the older word.

Second, the equivalence of Ptolemy and Copernicus is stated more strongly than general relativity supports. Coordinate freedom is genuine: any smooth coordinate system may be used, and the field equations take the same form in all of them. But the ''physical'' content is not coordinate-dependent. The solar system's dynamics are governed by a curvature distribution dominated by a body 333,000 times the earth's mass, and no change of coordinates alters which body dominates. A geocentric chart of the solar system is legitimate and useless; that is a weaker claim than "equal justification," and Granek's Machian framing tends to blur the two.

Third, the argument that a conveying medium is ''required'' does not follow as tightly as the paper suggests. Rejecting instantaneous action-at-a-distance requires a field with finite propagation speed; it does not require that field to be a material substratum in which anything moves. The direct detection of [[Gravitational Waves|gravitational waves]] by LIGO in 2015 confirmed the finite-speed field and, by the near-simultaneous arrival of GW170817 with its gamma-ray burst, fixed the propagation speed to that of light within about one part in 10<sup>15</sup>. That is a vindication of the field, not of a medium.

None of this touches the paper's historical thesis, which is its real content and which stands: Einstein did revive the word, he did so for reasons internal to his own argument, and Granek has traced those reasons carefully.

==See also==

* [[Galina Granek]]
* [[Aether]]
* [[Albert Einstein]]
* [[Henri Poincaré]]
* [[Ernst Mach]]
* [[Mach's Principle]]
* [[Equivalence Principle]]
* [[General Relativity]]
* [[Length Contraction]]
* [[Ludwik Kostro]]

[[Category:Scientific Paper|einstein 's ether e annual motion earth]]

[[Category:Aether|einstein 's ether e annual motion earth]]
[[Category:Relativity|einstein 's ether e annual motion earth]]
[[Category:Gravity|einstein 's ether e annual motion earth]]
[[Category:Philosophy|einstein 's ether e annual motion earth]]