Total solar eclipse photographed on May 29, 1919 (Credit: F.W. DYSON, A.S. EDDINGTON, C. DAVIDSON)
Today, the rare "Golden Circle Eclipse" will appear in parts of the territory of our country, are you ready to watch? For physicists, eclipses are also the perfect "natural laboratory" that can help them test certain important theories. On May 29, 1919, the total solar eclipse experiment led by British scientist Eddington supported Einstein's theory of general relativity.
Now it seems that Eddington supported Einstein, made the general theory of relativity "famous in world war", and also made Einstein gain worldwide influence. However, some public opinion believes that this experiment was to ease the relationship between Britain and Germany after World War I, but the accuracy of the experiment at that time was not enough to prove that general relativity was correct. Is this perception justified? How was the experiment conducted at that time?
"Only 3 people understand general relativity"
It all started when Einstein wrote the gravitational field equations for Einstein's general theory of relativity.
In 1915, Einstein wrote the general relativistic gravitational field equation, which used the then-very advanced mathematics of the time, Riemannian geometry. In the process, Einstein, with the help of mathematicians Grossman and Hilbert, basically figured out all the mathematical problems in it - the remaining unsolved problems were physics experiments that needed to verify the correctness of the theory.
Einstein began to promote his own theory of general relativity. At this time, Einstein already had a certain reputation in the German scientific community (because of the strong recommendation of the German science master Planck after 1905, Einstein's academic status soared, and he had changed from a patent office clerk to a university professor at this time), but Einstein did not have academic influence in Britain, the United States and other places at that time.
It was during the First World War, which lasted from 1914 to 1918, and the whole of Europe was seriously injured. Einstein's general theory of relativity is not only too difficult mathematically, but also the worldview looks so strange that everyone has not yet worked hard to deal with it. In 1916, Einstein gave his German edition of The Foundations of General Relativity to his friend, Professor De Sitt of Leiden University in the Netherlands. Because the Netherlands was neutral during the war, and Professor DeSitter was secretary of the Royal Astronomical Society, DeSitter turned around and sent his paper to Professor Eddington of the University of Cambridge in the United Kingdom.
Arthur Eddington
Professor Eddington was then the director of the Royal Observatory. Although he didn't know Einstein yet, he could tell at a glance that if the paper was correct, it would be epoch-making. But at that time, the anti-German sentiment in England was so severe that it was impossible to publish a German report, so Eddington asked Desitt to write a series of articles introducing Einstein's theory, which were published in the proceedings of the Royal Astronomical Society.
Eddington read the English version of Einstein's paper and finally understood Einstein's train of thought.
One day, the reporter went to interview him and asked: "I heard that only 3 people in the world understand Einstein's general theory of relativity. ”
Eddington asked, "Who else but me?" ”
Eddington did understand Einstein's paper. In fact, in 1916, a German astronomer named Schwarzschild also understood Einstein's general theory of relativity and solved the static spherical symmetry solution of Einstein's gravitational field equation, which can accurately describe the gravitational field near the sun.
Light originally travels in a straight line, but in curved space-time, light is also deflected— similar to the refraction of light near the surface of the water, where distant starlight is bent by the sun's gravitational field as it passes by the sun, which can be tested experimentally.
Calculate ray deflection
Einstein actually thought that the gravitational field would bend the light, he began to do a lot of calculations from 1911, and then improved, and finally got the complete theory that light was deflected by the gravitational field when the general relativity theory was formed in 1916.
Simply put, Einstein's general theory of relativity puts time and space together to form a curved four-dimensional space-time, and gravity is equivalent to the curvature of space-time. Light is a light-like geodesic in this curved space-time.
Therefore, the mathematics behind this is very clear, mainly the geodesic equation in Riemann geometry.
At that time, for general curved space-time, this geodesic equation was difficult to solve. However, if it is in Schwarzschild space-time, then the deflection angle of the light is easy to find. The deflection angle of light very close to the Sun can be calculated using general relativity:
Here, G is Newton's gravitational constant, M is the mass of the star (the Sun), C is the speed of light, and R is the radius of the star.
For the Sun, we can substitute the values in, and the resulting deflection angle is 6.42×10-6. This is a very small number, which also means that the angle of the Sun's deflection of the light close to it is extremely small.
The deflection angle Δθ is a dimensionless quantity, which actually represents radians. We know that the radian of a circumference is 2π, so the sun's deflection angle towards light is about one millionth of a circumference. So, such a small amount of data, can it be measured at that time?
Seize the opportunity
In 1919, Eddington seized the opportunity of a total solar eclipse and led astronomers to use the starlight photographs of the total solar eclipse to declare that they had accurately measured the deflection angle of light passing near the sun, thus proving that general relativity was correct, and this time Einstein was sent to the altar. Media reports at the time were that "British scientists helped German scientists verify that general relativity was correct," and the article highlighted the repair of postwar relations between the two countries.
So why observe during a total solar eclipse? Because the moon at this time blocks the sun, only people on the earth can see the brilliant starry sky behind the sun and photograph the position of the stars in the sky when the sun exists. And then what? When the Earth orbits to another place (usually about half a year apart), the Sun moves away from the starry sky area (this starry sky will appear at night), and you can also photograph the position of the star in the sky when there is no Sun (that is, when there is no light deflection). Comparing the positions of the stars in both cases yields a light decinversion.
Of course, astronomers have predicted that a total solar eclipse will occur on May 29, 1919. So Eddington organized two observation teams to go to two observation sites. Eddington led the team to Principe, Africa, and another team, led by his assistant Dyson, went to Brazil to observe. The two teams each carried a 33-centimeter astrograph (actually a slightly larger camera) from the Royal Observatory of Greenwich, and the Brazilian observation team also brought an additional 10-centimeter optical telescope.
The Eddington Observation Team arrived in Principe in late April 1919 and spent more than a decade preparing for the sweltering heat, torrential rain and mosquito bites. On the morning of the eclipse, Principe was windy and rainy, but by the time of the eclipse, the wind and rain stopped and the weather changed. The Eddington Observation Team took several photos, but only two showed stars. The Brazilian observation team was very happy and took a lot of photos.
But in the end, the film was greatly disappointed, because the sun was too strong, the negative box was too hot, and the film was deformed. They had to do a certain amount of processing. Finally, the deflection angle measured by the Eddington group was 1.61 arcseconds, and the Brazilian group measured 1.98 arcseconds, and the deflection angle Δθ of both results was on the order of 10-6. The predicted value of general relativity is 1.74 arcseconds. The observations were close to the predictions of general relativity, so Eddington declared that the observations supported the predictions of general relativity.
Is the experiment reliable?
So, the most critical question is, is Eddington's experiment at that time really reliable?
Whether the deflection angle can be measured depends on the angular resolution of the telescope. We can look at the angular resolution of the Hubble Telescope. The Hubble Telescope has an aperture of 2.4 meters, and for visible light near 480 nanometers, the angular resolution that can be achieved is very high - just divide these two values to get the minimum angular resolution:
This shows that if you use the Hubble telescope to distinguish the deflection of the sun to the starlight, it is possible to distinguish it.
At the time, Eddington and others were using cameras with a diameter of 33 centimeters.
In terms of optical aperture, the 33 cm aperture camera of the Royal Greenwich Observatory is about an order of magnitude worse than the Hubble 2.4 m telescope, so at the visible wavelength, the angular resolution of the 33 cm aperture camera in Greenwich (at 660 nm) is:
This angular resolution is the same order of magnitude as Einstein calculated the deflection of light. Therefore, with this camera, if the experimental error is not considered, then it is theoretically possible to measure the deflection of the sun to the light.
Eddington, in their paper published at the time, can see that the schematic diagram they drew went like this – superimposing two photographs to compare the position of the stars:
Through the above theoretical analysis, it seems that Edddington's support experiment for Einstein's general theory of relativity is still relatively reliable. General relativity has since been verified by more and more experiments, such as the gravitational waves discovered by LIGO in 2015, which also show that general relativity is correct.
Eddington's paper that year was titled "A determination of the deflection of light by the Sun's gravitational field, from observations made at the total eclipse of May 29, 1919" If anyone wants to question the accuracy of this experiment, look at the 46-page paper. After all, the accuracy of Eddington's experiment is indeed very reluctant, and it is worth studying carefully.
Author: Zhang Hua