De Sitter double star experiment

According to simple emission theory, light thrown off by an object should move at a speed of c with respect to the emitting object.

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If there are no complicating dragging effects, the light would then be expected to move at this same speed until it eventually reached an observer. For an object moving directly towards (or away from) the observer at v metres per second, this light would then be expected to still be travelling at (c + v) ( or (c − v) ) metres per second by the time it reached us.

Willem de Sitter argued that if this was true, a star in a double-star system would usually have an orbit that caused it to have alternating approach and recession velocities, and light emitted from different parts of the orbital path would then travel towards us at different speeds. For a nearby star with a small orbital velocity (or whose orbital plane was almost perpendicular to our line of view) this might merely make the star's orbit seem erratic, but for a sufficient combination of orbital speed and distance (and inclination), the "fast" light given off during approach would be able to catch up with and even overtake "slow" light emitted earlier during a recessional part of the star's orbit, and the star would present an image that was scrambled and out of sequence.

De Sitter made a study of double stars (1913) and found no cases where the stars' images appeared scrambled.

Since the total flight-time difference between "fast" and "slow" lightsignals would be expected to scale linearly with distance in simple emission theory, and the study would (statistically) have included stars with a reasonable spread of distances and orbital speeds and orientations, deSitter concluded that the effect should have been seen if the model was correct, and its absence meant that basic emission theory was almost certainly wrong.

Notes

• De Sitter also dismissed the idea that light might travel at a fixed speed that was partially dependent on the original speed of the emitter (c + / − kv) - given the great distances of some of the stars surveyed, the absence of a scrambling effect meant that any hypothetical value of k would have to be absurdly small. It was simpler to assume that k was zero.

• Kenneth Brecher published the results of a similar double-survey in 1977, and reached a similar conclusion - that any apparent irregularities in double-star orbits were too small to support simple emission theory.

• Current theory does allow a correspondence between apparent timing irregularities in double-star orbits and the original speed of the emitter, as a consequence of the circling star throwing off gravitational waves that affect signal flight times. But the severity of this effect does not scale linearly with distance.

References

• W. de Sitter, "A proof of the constancy of the velocity of light," Proceedings of the Section of Sciences - Koninkijke Academie van Wetenschappen -- te Amsterdam 15 (2) 1297-1298 (1913).

• W. de Sitter, "An Astronomical Proof for the Constancy of the Speed of Light" Trans from Physik. Zeitschr. 14, 429, (1913)

• W. de Sitter, "On the constancy of the velocity of light," Proceedings of the Section of Sciences - Koninkijke Academie van Wetenschappen -- te Amsterdam. 16 (1) 395-396 (1913).

• W. de Sitter, "About the accuracy within which the independence of the speed of light from the movement of the source can be stated." Trans from Physik. Zeitschr. 14, 1267, (1913)

• Kenneth Brecher, "Is the Speed of Light Independent of the Velocity of the Source?," Phys. Rev. Letters 39 (17) 1051-1054 (1977).