Is Einstein Wrong

Scientific Paper
Title	Is Einstein Wrong
Read in full	Link to paper
Author(s)	Charles Lane Poor
Keywords	Einstein, Theory of Relativity
Published	1924
No. of pages	12

Read the full paper here

Abstract

Forum, V71, N6, pp. 705-716 (June 1924). A Professor of Celestial Mechanics maintains thay Einstein's theory of relativity has not been proved, unless we accept on faith the special pleadings and assumptions of his followers. He calls attention to the wide divergence between stellar positions predicted by Einstein and the actual positions observed at the time of eclipses, and he argues that Newton's conclusions can be equally well vindicated if Newtonians permit themselves similar liberties in explaining away embarrassing facts.

Overview

This is the first half of a two-part debate staged by The Forum in 1924 under the running head "Is Einstein Wrong? — A Debate". Poor's contribution is subtitled "The Errors of Einstein"; the reply, "The Triumphs of Relativity" by Archibald Henderson, was promised for the July issue and is not part of this document. Poor was Professor of Celestial Mechanics at Columbia and wrote as a working orbit-computer rather than as a theorist, and the piece is addressed to the general reader: it contains no equations, only two star-displacement diagrams from the 1922 eclipse and a photograph of the 1923 eclipse taken at Yerbaniz, Mexico.

Poor's target is not the mathematics of General Relativity as such but the claim that the theory has been observationally verified. He argues that the two celebrated astronomical tests — the anomalous perihelion motion of Mercury and the deflection of starlight at a solar eclipse — do not do the work claimed for them. On his account the Mercury result is an artefact of applying a formula written in relativistic ("proper") time to observations reckoned in ordinary astronomical time, and the eclipse result is a number extracted by a reduction procedure that already assumes the effect it reports. His constructive alternative is the older one: unmeasured diffuse matter inside Mercury's orbit for the perihelion, and ordinary atmospheric and coronal refraction for the light-bending.

The argument

Gravitation replaced by geometry

Poor opens by contrasting the two schemes. Newton gave "the law of universal attraction of particle for particle, of body for body", and from it a law of motion for the heavenly bodies. Einstein's law of motion is one "in which, however, gravitation, or attraction, plays no part, for the basic principle of the generalized relativity theory is a denial of gravitation" — there is on this view no force between earth and moon, and no force made the apple fall. In its place stands "a transcendental conception of warped space and of geodesic lines along which a body freely rolls", set in a non-Euclidean geometry in which "the area of a square varies as it is transported from place to place".

The complaint that follows is partly one of style and partly one of method. Newton's law "can be expressed as simply as the Commandment, 'Thou shalt not steal'"; the Einstein theory is "as complicated and involved as a tariff bill". More substantively, Poor objects that the derivation proceeds by "difficulty after difficulty", each surmounted by "some new mathematical device", and that operations an engineer would call approximations are relabelled "substitutions, or transformations of coordinates" and their results then called exact. His specific example is the treatment of the separation between two particles: instead of the exact distance between centres, "the relativitist adds a small, a very small factor to this distance" and then uses the modified distance as if it were the true one.

The time objection and the 43 seconds

The core of Poor's case is a units argument. Classical mechanics treats time as universal — "a minute is a minute the world around". Relativity denies this: each planet carries its own "proper" time, which itself varies around the orbit as the planet's speed changes. Poor's claim is that the relativistic equation of motion therefore "does not represent the motion of a planet about the sun in the ordinary astronomical units of distance and of time" but in a different system, and that Einstein's formula "can be derived directly from the Newtonian formula by merely changing the system in which the motion is measured". Strip out the special system and use ordinary astronomical measures, he says, and the Einstein formula becomes Newton's; put the relativistic measure into Newton's formula and it becomes Einstein's. The two are the same motion "expressed as so many francs, or so many dollars".

From this he draws the conclusion that the celebrated 43 seconds of arc per century is "a mere mathematical illusion due to the use of an approximate, or mystical system of time in the relativity equations": Einstein computes a century of Mercurial time and reports it as a century of earthly time, and in those different intervals "Mercury will travel different distances in its orbit".

He then attacks the comparison itself. Leverrier found in 1859 not a clean perihelion motion but "a combination effect", a coupled pair of small wobbles — one in the perihelion, one in the eccentricity — that he could not disentangle; within limits any value could be assigned to the perihelial motion, with a matching eccentricity wobble for each. Leverrier's most probable figure was 38 seconds of arc per century; Newcomb in 1895 made the perihelion motion somewhat larger and the eccentricity change correspondingly smaller, and found "several other small discrepancies, or wabbles" in Mercury and in the other planets besides. Poor's charge is that relativity claims the one residual it fits and is silent about the rest, quoting Einstein's assertion that "The perihelial motion of Mercury is the sole anomalous one in our planetary system, which has been sufficiently attested." Leverrier's own explanation — an undiscovered planet or "scattered masses of matter" between Mercury and the sun — remains available, Poor says, because such scattered matter has in fact been seen and photographed in just those places; what is missing is any method of measuring how much of it there is.

Light bending: nothing new but the factor 2

Poor grants that the idea of light being bent by the sun is old. Newton suspected that bodies might act on light at a distance, and in 1801 von Soldner computed the deflection on the corpuscular theory, obtaining what is now called the Newtonian value: 0.87 seconds of arc for a ray grazing the solar limb. The corpuscular theory was afterwards displaced by the wave theory, and Poor notes that it is "not definitely known" what a great gravitating mass does to a wave.

His objection is that relativity helps itself to both pictures. Under the principle of equivalence the track of a ray "agrees with that of a material particle moving with the speed of light", so the bending is computed corpuscularly while the experiments that killed the corpuscular theory are answered by appeal to waves. "Somewhere, however, in the computations under the principle of equivalence, Einstein introduces a factor 2 and makes the deflection 1.75 seconds instead of the 0.87 seconds of the simple corpuscular theory." What is genuinely new in the prediction, on Poor's reading, is only the number 1.75; and he reports that recent work suggested that even on Einstein's own formulas the figure should be 0.87.

The 1922 eclipse plates

The observational section is the most concrete part of the article. Poor stresses first that a star ray reaching a telescope in Australia or Mexico has crossed the solar corona and then the earth's atmosphere, and that terrestrial refraction is "usually many times greater than the minute quantity predicted by Einstein, sometimes many hundreds of times larger" and varies sharply with air temperature. During totality the sun stops warming the air, the temperature falls suddenly, the refraction changes, and the star appears to move — a change no thermometer records and no computation anticipates.

Against this background he examines the Lick Observatory expedition to Australia for the eclipse of 21 September 1922. In April 1923 W. W. Campbell announced a deflection of 1.72 seconds, "agreeing almost exactly with the Einstein prediction of 1.75 seconds", and the announcement was carried everywhere as the final stamp of verification. Less than three months later, Poor notes, Campbell described that as a preliminary announcement and gave a more probable figure of 2.05 seconds — "some 17 per cent greater than the Einstein prediction" — attributing the excess to abnormal refraction in the earth's atmosphere. (2.05/1.75 = 1.17, so the arithmetic of the quoted percentage is right.)

Poor's two figures then compare the predicted and observed displacements of the same 92 stars, drawn from Campbell's own chart and data in Lick Observatory Bulletin No. 346, with the deflections magnified some 2100 times. The predicted pattern is radial: every star pushed outward from the sun's centre by an amount falling off with distance from the limb. The observed pattern, Poor says, is not. "Only fifteen stars show bendings even approximately in the directions predicted by Einstein: and twenty-six stars, or nearly one-third of the entire number, show deflections in a general direction opposite to that called for by the relativity theory." The published mean, he adds, was obtained by formulas and methods which "presuppose the existence of the Einstein effect" and treat every departure in direction or amount as accidental error of measurement. And no check at all was made on the question he regards as vital — whether the bending happened at the sun or in our own air. The Sproul Observatory party carried instruments to test exactly that at the 1923 eclipse, but was clouded out.

The caption to the closing photograph carries a further charge: the corona is "very tenuous matter", and Einstein "neglects this matter in all his theories", asserting that it can have neither refractive effect on light passing through it nor gravitational effect on Mercury.

Assessment

The strongest material here is observational and remains interesting. Poor is right that the 1922 Lick reduction was model-dependent — the deflection was fitted as a radial 1/r term with the coefficient free, so departures from radiality could only appear as noise — and right that a plate-scale change of a few parts in 10⁵ mimics the signal almost exactly, which is why the eclipse method never got below about 10 per cent accuracy in half a century of attempts. His insistence that nobody had shown where the bending occurred, and his pointing to the abrupt cooling of the air during totality, are legitimate systematic worries, and the fact that Campbell's own published value moved from 1.72 to 2.05 seconds within three months of a triumphant press announcement is a fair thing to put on the record. The scatter diagrams are the article's best weapon: reproducing the predicted and measured displacements side by side for all 92 stars is a more honest presentation than a single quoted mean.

The time argument, which Poor treats as his decisive point, does not survive scrutiny. A perihelion advance is a secular quantity — the orbit's line of apsides rotates by a fixed angle each revolution, and the count of revolutions is the same in any time variable. Rescaling time changes how fast the planet is said to move, not how far the ellipse has turned after a given number of returns to perihelion; the number of orbits per Julian century is itself an observed quantity, not a theoretical one. Poor's claim that the Einstein formula is obtainable from Newton's "by merely changing the system in which the motion is measured" would, if true, mean the relativistic orbit was a closed ellipse in disguise, which it is not: the extra term is a genuine non-closure, not a reparametrisation. Nor is the appeal to intra-Mercurial matter free: any distribution of dust dense enough to give 43″/century would perturb Venus and the Earth by amounts already excluded by Newcomb's own tables, which is precisely why the Vulcan hypothesis had been abandoned rather than merely unconfirmed.

On light bending, the "factor 2" is treated as an unexplained interpolation, and here Poor is arguing against a version of the theory he declines to follow through. The two contributions are separately identifiable — one from the time component of the metric, matching the Newtonian 0.87″, one from the spatial curvature — and the second is exactly what distinguishes the two predictions observationally. The report that "even under his own fundamental formulas" the answer should be 0.87 is asserted without a source or a derivation, and it is the single place where the article most needs the mathematics it has renounced. The question was settled by methods Poor could not have anticipated: radio interferometry of quasars occulted by the sun, which is free of both the corona-refraction and the plate-scale problems because refraction at radio wavelengths has the opposite sign and a known dispersion, and later the Cassini Doppler-tracking experiment, which fixes the coefficient to about one part in 10⁵ of the full relativistic value. His specific complaint about optical eclipse work was well founded; his conclusion about the effect was not.

Finally, the rhetorical frame — relativity as a tariff bill, its practitioners as special pleaders — is doing more work in the article than the evidence does, and the piece nowhere states what observation would have satisfied its author. It is best read as what its own title says it is: one side of a debate, and a useful record of how much genuine slack remained in the 1919-1923 eclipse measurements at the moment they were being announced as decisive.

See also

• Charles Lane Poor
• Perihelion Precession of Mercury
• Gravitational Lensing
• General Relativity
• Equivalence Principle
• Time Dilation
• Simultaneity
• Speed of Light