Friday, April 17, 2015

A wonderful 100th anniversary gift for Einstein

This year, Einstein’s theory of General Relativity celebrates its 100th anniversary. 2015 is also the “Year of Light,” and fittingly so, because the first and most famous confirmation of General Relativity was the light deflection on the Sun.

As light carries energy and is thus subject of gravitational attraction, a ray of light passing by a massive body should be slightly bent towards it. This is so both in Newton’s theory of gravity and in Einstein’s, but Einstein’s deflection is by a factor two larger than Newton’s. Because of this effect, the positions of stars seem to slightly shift as they stand close by the Sun, but the shift is absolutely tiny: The deflection of light from a star close to the rim of the Sun is just about a thousandth of the Sun's diameter, and the deflection drops rapidly the farther away the star’s position is from the rim.

In the year 1915 one couldn’t observe stars in such close vicinity of the Sun because if the Sun does one thing it’s shining really brightly, which is generally bad if you want to observe something small and comparably dim next to it. The German astronomer Johann Georg von Soldner had calculated the deflection in Newton’s theory already in 1801. His paper wasn’t published until 1804, and then with a very defensive final paragraph that explained:
“Uebrigens glaube ich nicht nöthig zu haben, mich zu entschuldigen, daß ich gegenwärtige Abhandlung bekannt mache; da doch das Resultat dahin geht, daß alle Perturbationen unmerklich sind. Denn es muß uns fast eben so viel daran gelegen seyn, zu wissen, was nach der Theorie vorhanden ist, aber auf die Praxis keinen merklichen Einfluß hat; als uns dasjenige interessirt, was in Rücksicht auf Praxis wirklichen Einfluß hat. Unsere Einsichten werden durch beyde gleichviel erweitert.”

[“Incidentally I do not think it should be necessary for me to apologize that I publish this article even though the result indicates that the deviation is unobservably small. We must pay as much attention to knowing what theoretically exists but has no influence in practice, as we are interested in that what really affects practice. Our insights are equally increased by both.” - translation SH]
A century passed and physicists now had somewhat more confidence in their technology, but still they had to patiently wait for a total eclipse of the Sun during which they were hoping to observe the predicted deflection of light.

In 1919 finally, British astronomer and relativity aficionado Arthur Stanley Eddington organized two expeditions to observe a solar eclipse with a zone of totality roughly along the equator. He himself travelled to Principe, an island in the Atlantic ocean, while a second team observed the event from Sobral in Brazil. The results of these observations were publicly announced November 1919 at a meeting in London that made Einstein a scientific star over night: The measured deflection of light did fit to the Einstein value, while it was much less compatible with the Newtonian bending.

As history has it, Eddington’s original data actually wasn’t good enough to make that claim with certainty. His measurements had huge error bars due to bad weather and he also might have cherry-picked his data because he liked Einstein’s theory a little too much. Shame on him. Be that as it may, dozens of subsequent measurement proved his premature announcement correct. Einstein was right, Newton was wrong.

By the 1990s, one didn’t have to wait for solar eclipses any more. Data from radio sources, such as distant pulsars, measured by very long baseline interferometry (VLBI) could now be analyzed for the effect of light deflection. In VLBI, one measures the time delay by which wavefronts from radio sources arrive at distant detectors that might be distributed all over the globe. The long baseline together with a very exact timing of the signal’s arrival allows one to then pinpoint very precisely where the object is located – or seems to be located. In 1991, Robertson, Carter & Dillinger confirmed to high accuracy the light deflection predicted by General Relativity by analyzing data from VLBI accumulated over 10 years.

But crunching data is one thing, seeing it is another thing, and so I wanted to share with you today a plot I came across coincidentally, in a paper from February by two researchers located in Australia.

They have analyzed the VLBI data from some selected radio sources over a period of 10 years. In the image below, you can see how the apparent position of the blazar (1606+106) moves around over the course of the year. Each dot is one measurement point; the “real” position is in the middle of the circle that can be inferred at the point marked zero on the axes.

Figure 2 from arXiv:1502.07395

How is that for an effect that was two centuries ago thought to be unobservable?


  1. Thanks for sharing this among your readers.
    Maximal learning curve here.

  2. Two centuries. The paper is from 1804.

  3. What about
    some refraction in the suns atmosphere?
    And why are there much more points
    in the lower part of the circle in
    that VLB data?

  4. Yes.
    I understand your reply.

    I meant I learned from your retrospective view of scientific progress. Your reply is meant to convey scientific progress is slow when reading:

    Two centuries. The paper is from 1804.

    The learning curve for me was faster than two centuries. I did not know all of this before.

  5. George,

    Not sure what experiment your question is referring to. The one in the paper I mentioned, the sources are not actually very close to the Sun. It's 3° or so, which is (if I recall correctly), about a hand's width at arm length? Yes, the quality of the VLBI data depends on Coronal activity for all I know.

    Regarding the dots - I suppose it's weather correlated. This is data from about 10 years. Clearly there isn't a dot for every day. I don't know when they measure this particular object and why, but I suppose if the weather is too bad, then no dot. I'm just guessing here of course, but maybe the upper rim of the circle corresponds to a season where bad weather is more likely? Best,


  6. Dear Georg and Sabine,
    this circle is illustration of light deflection which predicted by Einstein. There is no influence of any weather issues, like refraction and simply because of weather has neglectible influence and has very good reductions in VLBI techincs, nor the Sun corona effects also counted in VLBI observations. Just because these points were gathered as the best from all data set of VLBI observations.

  7. Anastasiia,

    Thanks for your comment. The question was why there are more dots in the lower part of the circle than in the upper part? Best,


  8. This plot shows quasar's coordinates changes from unshifted point (zero), which is quasar's coordinates without influence Sun's gravitational field. The maximum amplitude achieves during several day (1-2), when angular distance shrinks to several degree, and coordinate shift represents as circle. That is light deflection discovered by Einstein. Because of close approaches go on several day and during the whole other time quasars coordinates almost unshifted, we can see more points on lower part of plot than upper part.

  9. "the “real” position is in the middle of the circle..." "The question was why there are more dots in the lower part of the circle than in the upper part?"

    It's a bit unclear from the wording of the paper, because they say Fig 2 shows TWO sources, and they say "The non-deflected
    positions are at the reference origin...", which I assume is at (0,0) on the plot, which is at the bottom of the circle. This would make sense, because there is very little deflection for most of the year, so most points would be clustered near the origin, i.e., the bottom part of the circle.

    The confusion comes because the paper goes on to talk about FOUR sources: "The ecliptic latitude of the four sources are different... As a result... for the former radio sources the reference origin is in the middle of the ring... In contrast, for the latter case... the reference origin lies near the edge of the ring." I'm not sure what four sources they are talking about, but maybe the two sources shown in Fig 2 are the "latter case", so the non-deflected positions are near the edge of the circle.

  10. Ummm .... 1606+106 is a BLAZAR not a radio pulsar.

  11. Jay,

    Thanks for pointing out - or should I say poynting? - I fixed that. Best,


  12. Amos,

    Yes, you are right - that makes sense. I thought it's the first part of the sentence that referred to the figure. Best,


  13. That I would live to see this...


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