He is a master of astrophysics, but also a stumbling block to the development of the discipline?

Arthur Eddington made outstanding contributions in many fields of astronomy with his outstanding mathematical talent and solid physics foundation, and later became a master in the field of astrophysics. Eddington also became famous for his observational confirmation of the general theory of relativity, which directly pushed Einstein to the altar, so that people ignored his own achievements. However, due to some stubborn views, he was considered by some people to be a rude academic who hindered the development of stellar physics. After a report by the famous astrophysicist Chandrasekhar, Eddington directly criticized Chandrasekhar's theory because of his opposition. Is he really a stumbling block to the development of stellar physics? What important scientific contributions did he make?

Written by | Wang Shanqin

In the history of the development of astronomy and physics, Arthur Stanley Eddington (1882-1944) is an unavoidable figure. His main achievements are in astronomy, especially in the field of stellar physics.

However, because of his great reputation in verifying Albert Einstein's (1879-1955) general theory of relativity, many people have overlooked his great achievements and lofty status in the field of astronomy. Even more tragically, because of his stubbornness in studying white dwarfs, he was considered a rude academic who excluded dissidents and hindered the development of stellar physics.

So, what are Eddington's contributions to astronomy? Is he really a stumbling block to the development of stellar physics? This article introduces the legendary life of Eddington, a master of astrophysics.

Eddington. Image credit: Library of Congress Prints and Photographs Division Washington, DC 20540 USA

Miserable childhood

Eddington was born on December 28, 1882 in Kendal, Westmorland, England (now Cumbria). Eddington's father, Arthur Henry Eddington (1850-1884), graduated from the University of London in 1871 and later served as the headmaster of a Quaker school; his mother was Sarah Ann Shout Eddington (1852-1924). Eddington had an older sister, Winifred Eddington (1879-1954).

On February 14, 1884, Eddington's father died of a typhoid epidemic at the age of less than 34. At that time, Eddington was less than 2 years old and his sister was only 5 years old. Eddington's mother moved with her two children to Weston-super-Mare, living in a house called "Varzin" at 42 Walliscote Road. Here, Eddington's mother raised two children with great difficulty on a meager income. This miserable time was unforgettable to Eddington, and he often talked about it to his descendants after he became successful.

After moving, Eddington first studied at home, and then studied in a preparatory school for three years. At this time, Eddington had already developed an interest in the starry sky and often tried to count the stars, which planted the seeds for his later entry into the field of astronomy.

Math Honors Student, Senior Wrangler

In 1893, Eddington entered Brynmelyn School. He soon showed his extraordinary talent in mathematics and English literature.

Because of his excellent academic performance, Eddington received a scholarship and entered Owens College (now the University of Manchester) in Manchester at the age of 15 (October 1898). During his college years, he majored in physics and received scholarships many times.

In 1902, the 19-year-old Eddington graduated with first-class honors and received a scholarship from Cambridge University. In October of the same year, he went to Cambridge University to study for a master's degree. His supervisor was Robert Alfred Herman (1861-1927).

In 1904, Eddington took the Cambridge University mathematics course exam. This is an old academic tradition at Cambridge University. It is rumored that because early students had to sit on a three-legged stool to answer questions during the exam, the exam is also called the "Mathematical Tripos". It has always been known for its difficult questions and high intensity (testing for multiple days, 6-8 hours a day). The first-place student is awarded the title of "Senior Wrangler". They are hailed as the smartest people in the UK. Some of the winners' hometowns will organize their fellow villagers to celebrate on the streets. Many of the top few in the "Mathematical Tripos" exams over the years later became famous scientists. Eddington's mentor Hermann was the "Senior Wrangler" in 1882.

The 22-year-old Eddington won the first place in this exam, becoming the first person in the history of this exam to obtain the title of "Senior Wrangler" two years after entering the university. However, he had studied for four years as an undergraduate before entering Cambridge University and had more experience in various mathematical subjects than Cambridge undergraduates. Even so, being able to achieve this achievement in Cambridge University, which is full of experts, is enough to prove his extraordinary mathematical ability.

Because of Eddington's mathematical talent, the famous mathematical logician and philosopher Bertrand Russell (1872-1970) made him the central character in a short story he wrote in 1954 titled "The Mathematicians's Nightmare: the Vision of Professor Squarepunt".

Early astronomical career

In 1905, Eddington graduated from graduate school and immediately entered the Cavendish Laboratory to study thermal ion emission. At the same time, he also taught mathematics to engineering students. However, he was not interested in physical experiments or teaching.

Fortunately, with the recommendation of his colleague Edmund Whittaker (1873-1956), Eddington was awarded a position at the Royal Observatory Greenwich in early 1906 as the chief assistant to the Royal Astronomer William Christie (1845-1922).

From 1906 to 1917, Eddington studied stellar motions and cluster dynamics. His work on the dynamics of globular clusters was a breakthrough in the field.

During this period, he also observed the parallax of asteroids**[Note 1]**, comets and total solar eclipses. By comparing the photographic plates of the asteroid 433 Eros and combining them with the new statistical methods he developed, he measured the parallax of 433 Eros, for which he won the Smith's Prize in 1907 and a scholarship from Cambridge University. In 1908, Eddington made careful observations of Comet Morehouse (C/1908 R1) and published a related paper in 1910. In his paper, Eddington proposed that a large amount of ions emitted by the sun would affect comets. This idea was later developed by Eugene Newman Parker (1927-2022) into the important concept of "solar wind". (Editor's note: See "His Name is Worth $1.5 Billion: The Legendary Life of a Genius Boy")

Postcard image of Comet Morehouse. Image credit:
users.erols.com/njastro/barry/pages/postcd11.htm

In 1910, Frank Watson Dyson (1868-1939) became the Royal Astronomer, and Eddington continued to serve as the chief assistant. On October 10, 1912, Eddington and his colleagues observed a total solar eclipse in Brazil, which accumulated valuable experience for his later observation of the 1919 total solar eclipse.

Many outstanding achievements made Eddington a rising star in the field of astronomy. In 1913, at the age of 30, Eddington became the Plumian Professor of Astronomy and Experimental Philosophy at the Cambridge University Observatory.

In 1914, the 31-year-old Eddington became the director of the Cambridge University Observatory and a member of the Royal Society. In the same year, he published the book Stellar Movements and the Structure of the Universe, summarizing his mathematical research on the motion of stars and the dynamics of star clusters in the Milky Way.

Eddington (circa 1914). Image credit: Elliott & Fry. From Hutchinson's Splendour of the Heavens (1923).

Stellar physics

Starting in 1916, Eddington's main research interest shifted from the mathematical stellar dynamics to the physical stellar physics.

In the ten years from 1916 to 1926, Eddington achieved many groundbreaking results in stellar pulsations, radiation transfer and stellar energy, which brought his academic career into another glorious stage and established his historical position as a great astronomer.

First, Eddington studied the physical mechanism of Cepheid variables. The brightness of Cepheid variables changes periodically because they expand and contract periodically (pulsate). Eddington proved through calculation that the brightness changes of Cepheid variables come from changes in their opacity, which in turn comes from changes in temperature - changes in the proportion of helium ionized. This mechanism is called the "Eddington valve". Since the symbol for opacity is the Greek letter κ (kappa), this mechanism is called the "kappa mechanism" and was later used in the study of other pulsating variable stars.

The brightness evolution curve of the prototype star of Cepheid variable stars, Delta Cephei. Image source: Thomas K Vbg

In 1920, Eddington published a paper titled "The Internal Constitution of the Stars". He rejected the previously widely accepted stellar energy model, which holds that stars contract and convert part of the gravitational potential energy of matter into heat, which becomes the energy source of stars. This is the famous "Kelvin-Helmholtz mechanism" (KH mechanism). Eddington believed that according to the mass-energy relationship (E=mc2) in Einstein's theory of relativity, the mass of 4 hydrogens is slightly greater than that of 1 helium, and the lost mass will be converted into huge energy; even if the hydrogen in a star that can be used for fusion only accounts for 5% of the star's mass, the energy generated by its fusion is enough to keep the star shining. He also pointed out that helium-helium fusion and fusion between heavier elements may also occur inside stars. Modern research shows that Eddington's views are all correct.

Eddington also pointed out that thermal pressure is not enough to balance the star's own gravity, and that radiation pressure is necessary to prevent the star from collapsing. He was the first person to realize this, and more importantly, this conclusion still holds true today. In the process of calculating the radiation transfer of stars, Eddington gave an approximation, the "Eddington approximation".

In 1924, Eddington obtained the famous "mass-luminosity relation": the luminosity of a main sequence star is proportional to the nth power of the star's mass. Current observations show that the value of n ranges from about 2.3 to 4.

The mass-luminosity relationship of stars given in Eddington's 1924 paper. The horizontal axis is the logarithm of the star's mass, and the vertical axis is the logarithm of the star's brightness (apparent magnitude). Stars of different masses have different indices, so the slopes in the graph are different. Image source: Eddington, AS MNRAS, 84, 308-332

Eddington's research in stellar physics brought him great reputation. In 1924, at the age of 41, he won three major awards in the field of astronomy: the Gold Medal of the Royal Astronomical Society, the Henry Draper Medal, and the Bruce Medal. (Editor's note: For more information about the Draper Medal, see "She made a decision that went against her family's teachings and then advanced a discipline by decades")

However, on November 4 of that year, Eddington's 72-year-old mother passed away. His mother's departure made him extremely sad, and he felt even more sad when he recalled his childhood. Eddington could never forget the scenes of his childhood when he depended on his mother and sister.

In 1925, Eddington obtained the radiation limit of a spherically symmetric celestial body, namely the Eddington limit. When the brightness of a spherically symmetric celestial body exceeds this limit, the radiation pressure exceeds the gravity and the outer particles escape. The Eddington limit is proportional to the mass of the star; for the sun, its Eddington limit is 32,000 times the brightness of the sun.

In 1926, Eddington published his monograph "The Interior Structure of the Stars". This book became the standard textbook for a whole generation of astrophysicists. In 1928, Eddington was awarded the Royal Society Royal Medal.

Eddington's work quickly became the basis for studying stellar physics, and some of his classic conclusions are still the basic content of stellar physics textbooks. His research style also profoundly influenced subsequent stellar physicists.

Einstein on the altar

In addition to his groundbreaking contributions to stellar physics, Eddington also studied general relativity in depth during his graduate studies. During his graduate studies, his mentor Hermann taught a course on differential geometry, which is the main mathematical tool of general relativity. With his foundation in mathematics and physics, Eddington quickly mastered general relativity and became one of the British scholars who understood relativity best at the time.

General relativity makes several predictions, one of which is that light bends in a gravitational field by about 1.75 arc seconds. At Eddington's instigation, Dyson organized two expeditions for the total solar eclipse on May 29, 1919. The first expedition was led by Andrew Crommelin (1865-1939) and Charles Davidson (1875-1970) to Sobral in northern Brazil; the second expedition was led by Eddington and Edwin Cottingham (1869-1940) to Príncipe Island off the west coast of Africa.

The Sobral expedition ultimately determined that the light from the star was deflected by the sun's gravity at an angle of about 1.98 arc seconds, with a random error of no more than 6%. Although the observation process of the Principe Island expedition was somewhat bumpy, they determined that the light deflection angle was between 1.55 and 1.94 arc seconds, with an average of 1.61 arc seconds and an error of 0.3 arc seconds.

One of the photographs of the total solar eclipse of May 29, 1919. This photo appeared in a paper published by Dyson, Eddington and Davidson in 1920. Image credit: Frank Watson Dyson

On November 6, 1919, Eddington announced at a meeting of the Royal Society of London that the angle of starlight deflection observed during a total solar eclipse was consistent with Einstein's theory. This was the first time that human beings confirmed the predictions of general relativity through observation.

This result not only greatly enhanced Einstein's status in the physics community, making him the new leader of the physics community, but also caused a sensation in the media of various countries. Einstein, who had previously been unknown to the public, was immediately regarded by the public as a great physicist who surpassed Newton. It can be said that it was Eddington who put Einstein on the altar.

The movie "Einstein and Eddington", released in 2008, is based on the story of Eddington persuading his British colleagues to verify the general theory of relativity through a total solar eclipse. It tells the story of the precious transnational friendship between Eddington and Einstein during the war between Britain and Germany.

The DVD cover of "Einstein and Eddington". In this film, David Tennant (1971-) plays Eddington and Andy Serkis (1964-) plays Einstein. Image source: BBC.co.uk

Eddington also became famous among the public for verifying the general theory of relativity and became a household name. Moreover, Eddington was good at introducing the theory of relativity to his peers and the public in popular and precise language, which rapidly increased the influence of relativity in the English-speaking world. His observation of the total solar eclipse was therefore called the "Eddington experiment". Although some people later questioned the quality of the data obtained by Eddington, the results of subsequent total solar eclipse observations were consistent with the theoretical values ​​of general relativity. In addition, modern astronomers used modern measurement equipment and software to re-analyze the original images, which also confirmed that Eddington's results were relatively reliable.

Einstein and Eddington talking at the Cambridge University Observatory in June 1930. Image credit: Winifred Eddington

Eddington also made original contributions to the study of general relativity, especially the famous "Eddington-Finkelstein coordinates", which can be traced back to a study by Eddington in 1924, but neither he nor Finkelstein (David Finkelstein, 1929-2016) gave an expression.

Eddington in 1932. Image credit: Encyclopædia Britannica, Inc.

White dwarf debate

Eddington was not only proficient in relativity, but also in quantum mechanics. He introduced the concept of degeneracy pressure in quantum mechanics into stellar physics to describe dense stars such as white dwarfs, thus becoming one of the pioneers in the theoretical study of white dwarfs.

White dwarfs are the dense cores of some stars that are exposed in the late stages of their evolution. They appear "white" due to their high temperature, and are classified as dwarfs due to their low brightness. Sirius B is one of the most famous white dwarfs. It is the companion star of Sirius and its brightness is about one ten-thousandth of Sirius.

However, ironically, Eddington did not accept the combination of relativity and the concept of degeneracy pressure in quantum mechanics. He believed that: relativity is correct, and the formula of degeneracy pressure in quantum mechanics is also correct; however, the combination of the two is not "married" and is unfounded.

This view was the root of his conflict with Subrahmanyan Chandrasekhar (1910-1995, referred to as Chandra).

In 1930, Chandra considered both relativity and degeneracy pressure and used an approximate method to come to the conclusion that there is an upper limit to the mass of white dwarfs, and not all stars end their evolution as white dwarfs; white dwarfs with masses exceeding the limit will continue to shrink, and there is no force to resist this contraction. After that, Chandra proved his previous conclusions through precise calculations and submitted a report at the end of 1934.

Eddington could not accept the concept of "relative degenerate pressure", and could not imagine that some celestial bodies would collapse infinitely. In early 1935, after Chandra gave a report, Eddington opposed Chandra's conclusion and went to the podium to refute Chandra. The host also asked Chandra to thank Eddington for correcting his "mistake".
Later, they held another meeting in another place, and Eddington still openly opposed Chandra's research results. After the meeting, he found Chandra and said that this was just an academic debate and would not affect their personal friendship. Chandra asked: "Do you agree with my point of view now?" Eddington replied: "No." Chandra said depressedly: "What else can I say?" Then he turned and left. These things hit Chandra hard for a while, and he stopped studying white dwarfs. However, his personal relationship with Eddington was not damaged. The two traveled together until Chandra left England, and they kept communicating after that.

Later studies have shown that some stars will form neutron stars in their late evolution, with a maximum mass of 2-3 solar masses. If the mass of its debris exceeds about 3 solar masses, it will inevitably become a black hole. Observations to date have also shown that the mass of all white dwarfs is less than 1.4 solar masses. Chandra's calculation of the limit mass of white dwarfs is correct, although he did not consider the possibility of neutron stars. [Note 2]

Chandra said regretfully: "Eddington was already proficient in general relativity in the 1930s. He was fully capable of deriving the conclusion that stars would collapse when their mass was too large. If Eddington had really done this, he would have become the greatest astrophysicist of the 20th century."

Is he a stumbling block to the development of the discipline?

Chandra believed that Eddington's authority caused his erroneous views to affect the study of stellar physics, especially white dwarfs, for two generations. This evaluation makes people feel that Eddington is simply a stumbling block in this field. However, is this really the case?

In 2003, Hans Bethe (1906-2005) published an article titled "My Life in Astrophysics" in which he summarized his academic exploration in astrophysics. In the article, Bethe mentioned that he asked his doctoral student Robert Marshak (1916-1992) to study white dwarfs. "His thesis (on white dwarfs) was excellent. Many years later, a white dwarf expert at the California Institute of Technology told me that this thesis was still the basis for understanding white dwarfs at the time." Marshak received his doctorate from Cornell University in 1939, and the title of his thesis was "Contributions to the Theory of the Internal Constitution of Stars."

In 1940, Marshak published a paper titled "The Internal Temperature of White Dwarf Stars," and he explicitly stated that the main part of the paper was written during his doctoral studies at Cornell University. Marshak's 33-page paper deeply studied the internal temperature of white dwarfs and explicitly mentioned the "Chandrasekhar theory related to degenerate configurations."

Although Marshak is just an example, we can get a glimpse of the whole picture: Eddington's fierce opposition certainly destroyed Chandra's enthusiasm for continuing to study white dwarfs, and it is likely that it also hit the enthusiasm of Cambridge University and even the British astronomical community to study white dwarfs; however, white dwarf research outside the UK has not been interrupted, and it is likely that it has not been greatly affected (the citations and citations of Marshak's articles can indirectly prove this). Therefore, Eddington's obstruction to white dwarf research may be far less than Chandra and his descendants imagined. We should not overestimate Eddington's negative role in this regard.

Eddington's impact on the entire field of stellar physics was even smaller. In 1940, Marshak and Bethe published an article on the study of red dwarfs and subdwarfs, "The Generalized Thomas-Fermi Method as Applied to Stars". In the same year, Marshak also published "Note on the Point-Convective Model for the Sun". As for the work of others in stellar physics, it is too numerous to mention.

“Digital” Physics and Philosophy of Science

Since the 1920s, Eddington has also studied some problems related to quantum mechanics and space and time.

In 1936, Eddington published Relativity Theory of Protons and Electrons, which discussed quantum theory and studied the relationship between some constants. However, what he did were some patchwork-type number games. For example, when physics experiments showed that the fine structure constant α was about 1/136, he believed that the total number of protons in the universe should be 136×2^256-this number is called the "Eddington number", which would make α equal to 1/136; however, later studies showed that α was about 1/137, so he modified the total number of protons to make α equal to 1/137. (Editor's note: See "The Most Accurate Result of the 'Magic Number' in Physics") Such research has the characteristics of circular reasoning and has damaged Eddington's reputation in the physics community.

Eddington loved cycling, so he invented another much more reliable "Eddington number": a cyclist rides at least E miles every day for at least E days. His own Eddington number is 84 miles, which means that the number of days he rode more than 84 miles is 84. This concept is very similar to the later H factor: if a scholar's N papers are cited more than N times, his H factor is N.

In the field of philosophy of science, Eddington was an indeterminist. He believed that the uncertainty principle in quantum mechanics represented the essence of the microscopic world and that there was no hidden variable behind it. This view was in opposition to the deterministic view of his close friend Einstein and was consistent with the interpretation of the "Copenhagen School". Some of his scientific philosophy was reflected in his book Philosophy of Physical Science, published in 1939.

Death and remembrance

On November 22, 1944, Eddington died of cancer at Evelyn Nursing Home in Cambridge at the age of 61, and was buried in his mother's grave in Ascension Parish, Cambridge. He wrote his last letter to Chandra a week before his death.

The famous astronomer Henry Norris Russell (1877-1957) said at the beginning of his article mourning Eddington: "Sir Eddington's death has taken away the most outstanding representative in the field of astrophysics."

Chandra, who had a love-hate relationship with Eddington, also wrote a eulogy for him, saying that future generations would regard Eddington as the greatest astronomer of his time, second only to Karl Schwarzschild (1873-1916). The author's view is that Eddington's achievements and influence in the field of astrophysics are no less than Schwarzschild's.

Eddington and his colleagues in 1913. Schwarzschild is the third from the left, Dyson is the fourth from the left, and Eddington is the far right. Image source: AIP Emilio Segrè Visual Archives, Gift of Martin Schwarzschild

Schwarzschild and Eddington became good friends when they were young. After Schwarzschild's death, Eddington wrote a sad eulogy. At that time, Germany and Britain were still at war, and such a cross-border friendship was particularly precious. In 1933, Schwarzschild's daughter Agathe Thornton (1910-2006) fled Nazi Germany because of her Jewish ancestry and came to Cambridge, England. **[Note 3]** Thornton, who was penniless, received timely funding from an anonymous person and was able to continue her studies. Later, people found that the anonymous sponsor was Eddington.

In memory of Eddington, the Northwest Campus of Cambridge University was named "Eddington Quarter", and a memorial plaque was erected at his childhood home to record his contribution to science. In addition, a crater on the moon and the asteroid 2761 were both named "Eddington".

A plaque at Eddington's childhood home. Image credit: Peter Barrington

The Royal Astronomical Society of the United Kingdom established the "Eddington Medal" to reward astrophysicists or physicists who have made outstanding contributions to the field of theoretical astrophysics. This medal was first awarded in 1953 and has been won by many masters.

Interestingly, although Chandra won the Nobel Prize in Physics and many other awards, he did not win the Eddington Prize. It seems that the Royal Astronomical Society of the United Kingdom has not forgotten Eddington's "original intention". Even if Chandra's views on white dwarfs have been proven to be correct, it will never give the Eddington Prize to Chandra, whom Eddington opposed.

Gains and losses

Eddington lost his father at an early age and grew up in a poor environment. With his extraordinary talent, he quickly achieved success at a young age: he won the first place in the mathematics exam at Cambridge University at the age of 21, became a professor at the age of 30, became the director of the Cambridge University Observatory at the age of 31, and won three astronomy awards at the age of 41. His life was smooth after that. On April 16, 1934, the 51-year-old Eddington became the cover character of Time magazine.

Eddington appeared on the cover of Time magazine on April 16, 1934. Image source: Time

Although Eddington's life was not long, he was happy. Chandra recalled that when he was at Cambridge University, he often saw Eddington smoking a pipe and enjoying himself on the streets of Cambridge. Although Eddington was impatient at times, he was kind and warm, as shown by his anonymous sponsorship of Schwarzschild's daughter.

Eddington made contributions to varying degrees in stellar dynamics, stellar physics, interstellar matter, comets, solar eclipse observations, astronomical spectroscopy, and general relativity.

As a great astronomer, his pioneering research on stellar physics laid the foundation for human understanding of the physical properties of stars; the solar eclipse observation team he was in charge of verified Einstein's general theory of relativity, which not only put Einstein on the altar, but also directly promoted the timely acceptance of general relativity by the world. However, he was stubborn in the field of white dwarf research and resisted the correct conclusion, which objectively led to a certain impact on research in this field, but this impact was far less than most people think.

Like many great scientists in history, Eddington was not perfect. Future generations will criticize him for his negative influence, but they cannot deny his great contributions and noble character. Both his great achievements and his mistakes will be recorded in history forever; the former will be admired by future generations, and the latter will be a lesson for future generations.

However, one thing is certain: his merits far outweigh his faults.

Notes

[Note 1] When observing celestial bodies at different positions, you will see that the celestial bodies overlap with different background stars. Half of the angle between different lines of sight is the parallax. In order to measure the parallax, astronomers usually observe stars multiple times at different positions of the Earth's orbit to obtain multiple sets of parallaxes, and then use statistical methods to obtain the exact value of the parallax.

[Note 2] When a white dwarf rotates at high speed or has a strong magnetic field, its ultimate mass will increase significantly, that is, it can have a much larger mass. However, so far, even if the mass observed exceeds the ultimate mass of a white dwarf, it does not affect the correctness of Chandra's calculations, because his calculations do not take into account the effects of magnetic fields and rotation.

[Note 3] Schwarzschild had a daughter and two sons. His eldest son, Martin Schwarzschild (1912-1997), left Germany in 1936 and later became an outstanding expert in stellar physics. His second son, Alfred Schwarzschild (1914-1944), stayed in Germany and unfortunately died in the Nazi German genocide in 1944.

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