Einstein's Ether: D. Rotational Motion of the Earth
| Scientific Paper | |
|---|---|
| Title | Einstein's Ether: D. Rotational Motion of the Earth |
| Read in full | Link to paper |
| Author(s) | Galina Granek |
| Keywords | stationary ether hypothesis, nonstationary ether hypothesis |
| Published | 2001 |
| Journal | Apeiron |
| Volume | 8 |
| Number | 2 |
| No. of pages | 13 |
Read the full paper here
Abstract
Prof. Ludwig Kostro is the most influential historian and philosopher of science who has written about Einstein's post 1916 return to the ether concept (1988, 1992). He has endeavored to show that (Kostro, 1988, p. 239): "the notion of the ether was not destroyed by Einstein, as the general public believe." In addition, Kostro showed (1988, p.238): "Lorentz wrote a letter to Einstein in which he maintained that the general theory of relativity admits of a stationary ether hypothesis. In reply, Einstein introduced his new nonstationary ether hypothesis."
In parts A, B and C I suggest a new view of the problem tackled by Kostro. I ask the following question: Did Einstein respond to Poincaré too when returning to the ether concept? In parts A and B I first introduce the problem by re-examining the problems that had been occupying Poincaré from Einstein's point of view.
Overview
This is the fourth and final instalment of Galina Granek's Apeiron series on Einstein's ether, written from the Department of Philosophy at Haifa University. It is a work of history and philosophy of science rather than of physics: no new equation is proposed and no measurement is disputed. The question it pursues is why Einstein, having declared in 1905 that "the introduction of a 'light ether' will prove to be superfluous" and in 1910 that "the first step to be made [...] is to renounce the ether," was speaking of the ether again by his 1920 Leyden lecture.
Granek's answer runs through Henri Poincaré. Building on Ludwig Kostro's work — which established that Hendrik Lorentz wrote to Einstein arguing that general relativity admits a stationary ether, prompting Einstein's non-stationary alternative — she asks whether Einstein was also answering Poincaré. Her earlier parts identified four problems that kept Poincaré from abandoning the ether: stellar aberration and its constant; action at a distance, since a signal delayed in transit implies a medium; the fact that rotational motion violates the relativity principle, so that a body may rotate absolutely with respect to absolute space; and the failure of Poincaré's own conventionalist escape. The claim advanced here is that in 1905 Einstein could dispense with the ether only for aberration and only inside special relativity, and that "he could not treat action-at-a-distance and uniform rotations without retaining some kind of ether." This paper focuses on the rotation problem, and on the two thought experiments — the elevator and Einstein's variant of Newton's bucket — by which Einstein is held to have answered it.
The argument
Why Poincaré could not let the ether go
The rotation problem is set out precisely. The relativity principle applies to rectilinear uniform motion; rotation escapes it, so a rotating body appears to rotate absolutely with respect to absolute space. The ether provided a way out: by treating it as a ponderable body one could say the body rotates relative to it, converting an absolute motion into a relative one. Poincaré's alternative was philosophical — the conventions "the earth rotates and the sky is at rest" and "the earth is at rest and the sky rotates" would be logically and experimentally equivalent for inhabitants of a planet permanently veiled in cloud. Granek rejects this as a solution: one may imagine a being standing outside the cloudy planet who decides from experience whether it rotates, and for that observer the earth rotates with respect to absolute space. The ether is therefore still needed.
Einstein's 1905 objection was different in kind. He renounced the ether precisely because it was a body to which absolute rest could be applied, so that motion with respect to it would be absolute motion; and, following Ernst Mach on admitting only observable quantities, he judged the ether not to be a fact of experience. Granek notes his 1934 formulation that "the concept of absolute space, comprised that of absolute rest."
The elevator and the bent light ray
The 1911 weak equivalence principle states that a uniformly accelerated frame K′ far from all matter is exactly equivalent, for all physical processes, to a frame K at rest in a homogeneous gravitational field — a claim grounded empirically in the equality of gravitational and inertial mass. Granek develops the elevator case (in the Einstein–Infeld 1938 presentation) as a rotation-type problem in disguise, structurally similar to Newton's bucket: two observers, two irreconcilable descriptions.
The threat is sharp. A horizontal light ray entering a side window will, according to the outside observer, meet the far wall slightly below the entry point, because the elevator rises while the light crosses; relative to the elevator the path is curved. The inside observer, believing only a gravitational field acts, reasons that light is weightless and so unaffected, and predicts a straight path meeting the wall exactly opposite. If both are right the equivalence fails, and worse, the bend becomes a detector of absolute motion: "whenever an observer finds a bent light ray he knows that the reference frame under consideration is in absolute motion." That is exactly the bucket dilemma — flat surface versus curved surface as a marker of absolute rotation.
Einstein's 1911 resolution is that the inside observer reasoned wrongly. By special relativity a light beam carries energy, and energy has mass; the increase in gravitational mass is E/c2, equal to the increase in inertial mass. Since every inertial mass is attracted by a gravitational field, light bends in one "exactly as a body would if thrown horizontally with a velocity equal to that of light." The two accounts coincide, and the essential assumption is the equivalence of gravitational and inertial mass.
Granek then applies the same reasoning to the daily rotation of the Earth. Whether the Earth turns or the heavens revolve becomes "no more than an argument over the choice of reference frames." In frame 1 the centrifugal force is a consequence of the Earth's motion relative to the heavens and flattens the poles; in frame 2 the rotating heavens generate a gravitational field that produces the same flattening. There is no frame from which the flattening is not seen, and the two explanations are equivalent because inertial and gravitational mass are.
Einstein's bucket: the two fluid globes
The final section reconstructs Einstein's 1916 argument, which fuses Mach's reading of the bucket with Newton's revolving-globes experiment from the Principia. Two fluid bodies of identical size and nature revolve about the line joining them, far from all other masses, with no internal relative motion and constant separation. Each co-moving observer measures the other as rotating uniformly. Yet S1 is measured to be a sphere and S2 a flattened ellipsoid.
Newtonian mechanics attributes the difference to absolute rotation of S2, making the privileged inertial space R1 the cause. Granek presses the epistemological objection: "To take space as a cause does not satisfy the requirements of causality," since we have no indication of that space's existence other than the very centrifugal forces it was introduced to explain. The law of causality applies to experience only when observable facts appear as causes and effects, and R1 is not observable. Nor, she adds, is the premise itself observable — we cannot observe two bodies in an otherwise empty universe, so we cannot marshal facts to support the claim that they would behave differently there; "a valid mechanics should rather exclude this assumption."
The cause must therefore lie outside the two-body system. The correct systems are S1 + R1 and S2 + R2, where R now means the distant masses — which are observable, in the form of the fixed stars. Those stars, at enormous distances and moving slowly relative to one another, act "as a whole" like a solid mass containing a cavity in which the body sits; they curve space-time and thereby condition the body's behaviour. This is Mach's inertial interaction combined with gravitation and, finally, with curved space-time. The laws of mechanics then apply to both systems, with no frame privileged a priori.
Assessment
The paper's genuine value is that it takes seriously a fact usually treated as an embarrassment or a curiosity: that Einstein returned to ether language after 1916, and did so for reasons Poincaré would have recognised. Granek's structural insight — that the elevator experiment is the bucket problem in another costume, with a bent light ray in place of a curved water surface as the tell-tale of absolute motion — is a real contribution, and it explains why the 1911 light-bending result mattered to Einstein philosophically as well as observationally. Her reconstruction of the two-globes argument is careful, correctly separating Newton's version, Mach's critique and Einstein's synthesis, and the epistemological objection she highlights (that absolute space is supported only by the phenomenon it was invented to explain) is stated in Einstein's own terms rather than imposed. For a wiki that treats the aether as a live question, the point that the founder of relativity himself judged some medium indispensable once rotation and action at a distance were on the table is worth having documented from the primary sources — and the source apparatus here is exact, citing the 1905, 1910, 1911, 1916, 1920 and 1934 texts by page.
The difficulties are those of the genre. The paper does not actually deliver the answer its own framing promises: having asked whether Einstein was responding to Poincaré, it ends on Einstein's globes without returning to Poincaré at all, so the thesis is set up and then left for the reader to complete from parts A–C. More substantively, the claim that Einstein's metric-tensor ether does the work Poincaré wanted is asserted rather than argued. Granek raises the decisive question herself — "Was Einstein's ether endowed with any properties independent of the masses in it? For if it did possess such properties then there was actually no difference between Einstein and Poincaré's ether" — observes that Einstein gave no definitive answer in 1920, and then does not pursue it, though a century of subsequent work bears on it directly: vacuum solutions of the field equations, in which the metric is non-trivial with no matter present at all, are precisely a case of the ether having properties independent of the masses in it, and they tell against the Machian reading she presents as Einstein's settled view. Nor does the paper register that Einstein's own hopes for Mach's principle were later disappointed, or that the "fixed stars as a solid shell" picture is a heuristic that general relativity does not in fact reproduce. Finally, the dismissal of Poincaré's cloudy-planet convention by invoking an outside observer is quicker than it looks: Poincaré's point was about what could ever be established by the planet's inhabitants, and postulating a privileged external viewpoint concedes the question rather than answering it. These are limits of scope in a short historical paper rather than errors, but they mean the title question — did Einstein answer Poincaré? — remains open at the end.