Total Eclipse of the Sun and Deflection of light Rays

According to Einstein’s prediction, that is to say the deflection (bending) of light rays in the gravitational field of the Sun: those stars closest to the limb of the Sun during the eclipse are found to be displaced slightly by amounts that are inversely proportional to the distance of the stellar image from the Sun. The light from a star close to the limb of the Sun is bent inward, toward the Sun, as it passes through the Sun’s gravitational field. The image of the star appears to observers on the Earth to be shifted outward and away from the Sun.

The Universe and Dr. Einstein by Barnett (with forward by Einstein)

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In 1915 Einstein calculated the angle between the actual path of the starlight, the true position of the star, and the apparent path of the ray of light, the star seen during the eclipse. He obtained a result: 1.7” (seconds of arc).

However, in 1911 and 1913 he derived a different result, actually he had obtained half of this result: 0.84” (seconds of arc).

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Einstein’s letter to George Ellery Hale which illustrates starlight being deflected by the gravity of the Sun. Oct. 14, 1913. The Huntington Library, Art Collections, and Botanical Gardens. Here

During a total eclipse of the Sun, it is possible to take pictures of the field of stars surrounding the darkened location of the Sun, because during its occultation, the light emanating from the Sun does not interfere with visibility of fainter objects.

In the eclipse expedition of 1919 Sir Arthur Stanley Eddington and Charles Rundle Davidson went to find whether they could verify Einstein’s prediction of the deflection of starlight in the gravitational field of the Sun. Eddington and his assistant went to the island of Principe off the coast of Africa while Davidson and his assistant went to Sobral in North Brazil. In presenting their observations to the Royal Society of London in November 1919, the conclusion was that they verified Einstein’s prediction of deflection at the Sun’s limb to very good accuracy.

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Sir Arthur Stanley Eddington. Source (internet, unknown). If anyone knows the source please leave a comment.

The pictures taken during the solar eclipse are compared with pictures of the same region of the heavens taken at night. An astronomer compares his photographs taken during a total eclipse of the Sun with check plates, that is to say with comparison plates of the same stars (the eclipse field) when the Sun has moved away.

In 1919 Eddington examined the check field of stars that was photographed at Oxford Observatory. It was nearly the same as that of the total eclipse field of stars, which was photographed at the small island belonging to Portugal, Principe, at the same altitude as in Oxford in order to ensure that any systematic error, due to imperfections of the telescopes or other causes, might affect both sets of plates equally. There were differences in scale though between the compared photographs. Eddington determined these differences of scale between Oxford and Principe. The primary purpose of the comparison was to check the possibility of systematic errors arising from the different conditions of observation at Oxford and Principe.

After comparing the Oxford and Principe check plates, Eddington concluded that the Oxford photographs show none of the displacements which are exhibited by the photographs of the eclipse field taken under precisely similar instrument conditions. Eddington inferred that the displacements in the latter case could only be attributed to presence of the eclipsed Sun in the field and not to systematic errors.

Eddington’s four values of deflection in Principe were: 1.94, 1.44, 1.55 and 1.67 seconds of arc. He calculated the mean of these to be: 1.65” (seconds of arc). He added corrections due to experimental errors and due to the fact that the four determinations involved only two eclipse plates. The final Principe result was: 1.61±0.30 seconds of arc. Eddington calculated the final Sobral result: 1.98±0.12 seconds of arc and concluded: “They evidently agree with Einstein’s predicted value 1.75 seconds of arc.

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Photos taken at the Science Museum, London. Eddington’s original negative photo.

Final confirmation of Einstein’s prediction of the deflection of light near the Sun came from William Wallace Campbell and his assistant Robert J. Trumpler at the eclipse of September 22, 1922 in Australia. Campbell and Trumpler also compared the eclipsed plates with the photographs of the same stars taken at Tahiti four months before the eclipse. The observations with the first camera led to a stellar deflection of 1.82±0.15 seconds of arc for the light deflection at the Sun’s limb. The combined observations from the two instruments used by Campbell and Trumpler gave the value of 1.75±0.9 seconds of arc for the deflection at the Sun’s limb, which is in excellent agreement with the value predicted by Einstein’s theory.

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For more photos see here.

For more information on the history of eclipse expeditions and Einstein’s general theory of relativity see my books:

General Relativity Conflict and Rivalries: Einstein’s Polemics with Physicists

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Einstein’s Pathway to the Special Theory of Relativity (2nd Edition)

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אודיסאת איינשטיין ליחסות הכללית Einstein’s Odyssey to General Relativity

מאמר שלי על דרכו של איינשטיין לתורת היחסות הכללית: אודיסאת איינשטיין ליחסות הכללית

סיינטיפיק אמריקן ישראל

“Einstein’s Odyssey to General Relativity”, Scientific American Israel

את המונח “אודיסאה” ליחסות הכללית טבע פרופ’ ג’ון סטצ’ל מאוניברסיטת בוסטון והוא מייצג את המסע המפרך של איינשטיין בדרכו ליחסות הכללית. ראו המאמר של סטצ’ל למטה

Odyssey to general relativity is John Stachel’s memorable phraseology. See:

Stachel, John (1979). “Einstein’s Odyssey: His Journey from Special to General Relativity”. In Einstein from B to Z, 2002.

I am sorry but this piece is in Hebrew. You can read my book General Relativity Conflict and Rivalries, my papers on Einstein and general relativity and a short summary below.

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מפייסבוק: מארחים את ד”ר גלי וינשטיין לדבר על איינשטיין

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My drawing of Einstein:      האיור שלי של איינשטיין

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And the original (I tried as hard as I could to draw a young Einstein…):       המקור

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The article discusses the following topics:

1907. The Happiest thought of my life.

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1907-1911. The equivalence principle and elevator experiments.

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1911. Deflection of light and explaining deflection of light using an elevator thought experiment.

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1911-1912 (1916). The disk thought experiment, gravitational time dilation and gravitational redshift.

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1912. The disk thought experiment and non-Euclidean geometry.

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1912. Einstein to Marcel Grossmann: “Grossmann, you must help me or else I’ll go crazy!”. Grossmann searched the literature, and brought the works of Bernhard Riemann, Gregorio Curbastro-Ricci, Tullio Levi-Civita and Elwin Bruno Christoffel to Einstein’s attention. With Grossmann’s help Einstein searched for gravitational field equations for the metric tensor in the Zurich Notebook.

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1913-1914. The Entwurf theory. In 1913, Einstein and Michele Besso both tried to solve the new Entwurf field equations to find the perihelion advance of Mercury.

2October 1915. Einstein realizes there are problems with his 1914 Entwurf theory. November 1915. Einstein’s competition with David Hilbert.

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November 1915. Four ground-breaking papers: Einstein presents the field equations of general relativity, finds the advance of the perihelion of Mercury and predicts that a ray of light passing near the Sun would undergo a deflection of amount 1.7 arc seconds.