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Einstein and Eddington: a film

Joseph Sykora sent me a link to a 94-minute-long 2008 BBC Two film about Eddington and Einstein:



It's no documentary. Expect a drama movie that may be watched by those not too interested in physics as well. I liked it a lot (despite the artistic license to modify the history) and you should watch it, too.




Beware: the text below may contain spoilers. All of them.

The movie begins in 1919 when poetic Arthur Eddington and his assistant try to measure the bending of light during the solar eclipse at Principe, an island off West Africa (it was shot near the Adriatic beaches of Croatia; the rest was shot in Cambridge and the Hungarian Academy).

However, we quickly return to 1914. Eddington apparently beats Novak Jock Itch but they say that the ball was out. He thinks that the ball was in. He is hired (by Sir Oliver Lodge, his "boss") at the Cambridge observatory and informed about the minimal height of men who would be recruited for the military. Note that the Great War is just getting started and it will influence most of this film, too.




His important job is to defend the pride of Great Britain and its great Isaac Newton and their status quo against the attacks by the Germans, particularly a man called Albert Einstein. This task sounded a bit comical to me but I can't prove that it is historically inaccurate.

Meanwhile, we're shown a highly relaxed Albert Einstein lying on the boat's floor and interacting with two kids, apparently his sons Hans Albert (*1904) and Eduard (*1910), in a boat in a Swiss lake. Once the boat hits the shore, Einstein jumps and performs a sock-free performance that clowns in a circus wouldn't be ashamed of. While throwing the socks to the viewers on the bank, he explains that the velocities of the socks and the boat add up as \(u+v\). But what about the light? A kid guesses \(c+v\). Not. Why not? The course on relativity is interrupted and replaced by some joy in the Swiss house. Well, the wife is worried about the female viewers of Albert's performance and the reasons why he was talking relativity to the kids and not herself. ;-)

Mileva decides to leave but a sock-free Albert on the staircase is as fast as the elevator. The physics-flavored argument of the couple softens a bit when Max Planck suddenly appears in the corridor. The wife is upset that Planck doesn't even remember her name but he screams: "Mileva!" It doesn't help, however. She's running away. ;-)

Planck is annoyed that Einstein had worked on gravity for 9 years and he only has questions, not answers. Zurich probably sucks as a place for physics. Planck suggests Einstein needs a help. Self-confident Einstein with a cigar doesn't need any help, smiles, and ignores Planck's comments about the life in obscurity. ;-)

Well, up to the moment when Planck offers 12,000 marks in Berlin and the Prussian Academy of Sciences. Einstein's "No" is fast but a serious Planck gives Einstein a lecture on sacrifices in sciences along with a ticket to Berlin. Einstein accepts the ticket as a backup.

We return to the great defender of the English pride against the attacks by the Wehrmacht led by Mr Einstein, to Mr Arthur Eddington. ;-) Everything is ordered and has a reason. Newton explained the cause but was worried because you can't "touch" gravity, Eddington said. So what causes gravity? At the moment when you're already expecting Eddington to defect to the German army, he says that Newton actually found the missing cause behind gravity. It was God's will! ;-) Everything is fine again.

Einstein is leaving by the train. His wife is calm while waving her hands and one of the kids is really sad and annoyed. Jump elsewhere. Eddington goes to the library and orders something by Einstein, Albert, an enemy of God. He is only offered one thing, "On Electrodynamics of Moving Bodies". It's 9 years old, the librarian says, but there's nothing newer over there.

The enemy of God looks happy in Berlin, too. Planck welcomes him to the greatest university in Europe. Albert meets Fritz Haber in a uniform – he looks less Jewish than last time, Albert points out. Well, Haber says that he denounced his judaism and became a Christian. No problem with that. Einstein wants to know what Haber works on – a gas, ammonia. Einstein adds "explosives!" and smiles. ;-) Planck wants Einstein to meet someone.

The "someone" is the person who made those 12,000 marks possible. Einstein doesn't like this encounter because he was promised complete freedom. Einstein is giving an entertaining lecture on the relativistic justification why Einstein has to be tautologically late but the male "someone" seems annoyed. Well, relaxed Einstein crisply articulates the reasons behind the incompatibility of special relativity with gravity (gravity propagates immediately, faster than light) and the annoyed sponsor asks: "This is what I am paying for? What did you say?" LOL. Smiling Einstein says "thank you very much for all the money you're giving to me" while both Planck and the sponsors look really disgusted. "Good-bye," Einstein improves his performance, and leaves. "This is the Einstein you'd speak so highly of?" the sponsor asks Planck. "Yes. He has a truly original probing mind." But questions don't help wars, the sponsor replies. Planck is trying to explain that Einstein is a theorist and what's the difference between pure and applied research. At the end, Planck manages to say that Einstein could at least prove the Englishman Isaac Newton wrong. I guess that this observation has improved the situation somewhat. ;-)

Eddington biking with a friend William Marston – 2,000 miles per year, it's pretty much exactly like your humble correspondent. A happy conversation on miles is interrupted by their disagreement about the war. William goes to fight; the Quaker Eddington can't. He cries a little bit. (Quakers are the democratic protestant "Religious Society of Friends" with some strange silence-dominated unplanned worship and desire to unify all Christians. Eddington was really quite important in these circles.)

Over in Berlin, Einstein is dining with his older relatives, uncle Rudolf and aunt Fanny, along with their daughter Elsa Einstein. Einstein clarifies that he denounced his German nationality and has no attachment to any land, so he may leave any place. Now he's Swiss, what difference does it make? After all, there's no such thing as the aether; light doesn't slow down. What else is there? Elsa, Einstein's cousin, says "freedom". Einstein adds "imagination" and these two relatives fall in love with one another. A subtle event that is less subtle due to Mileva's hysterical scenes in Switzerland. Elsa's father's comment that "Einstein's imagination is overexcited" cannot calm the growing relationship. Einstein gets excited later when he hears his cousin sing and play the piano. Especially because Einstein likes Franz Schubert (but not Beethoven who makes Einstein feel naked). Music and physics are nourished by the same... She doesn't know anything about physics... "Good!" Einstein replies, "so it will have to be music in between us." His cousin is a bit scared.

Defender of the British pride Eddington is reading and reproducing Einstein's calculations, suggesting to his sister (and housekeeper) Winnifred Eddington that there's something about it. Is it good or bad? ;-) Englishmen must take an enlightened approach, the sister wisely quips. Eddington has to see his friend William's leaving train. He's late – and his boss wastes more of his time – so Eddington with his bike tries to catch up with the train, really obsessed about William's journey. They don't state it explicitly at this point but Eddington was probably gay (even in the real world).

At any rate, he is telling some folks that Einstein has no respect for the conventions and even invents his own mathematical symbols. ;-) Eddington was able to decode [time dilation] from the papers, anyway. Nine years after the publication of special relativity, everyone still finds it weird and new. A proud English potentate asks what are Einstein's references and acknowledgements. None. Can it be tested? Isn't it [relativity] "not even wrong"? Eddington says that the testing isn't really the point. "What is the point if it can't be tested?" others ask. And "What does he say about gravity?" Nothing. "What controls everything, life of the Universe etc.?" An overwhelmed Eddington replies "Gravity."

The old potentates and sourballs victoriously smile and say that "this Einstein has nothing to say about the real world." I was laughing out loud – the makers of this film must have had a hidden agenda to make fun out of various Peters Shmoits and their idiotic populist ideology because the way how these folks "debunk" relativity is isomorphic to the Shmoits' "debunking" of string theory.

Eddington surrenders and agrees, "It [relativity] is not real". LOL. However, unlike the smiling old potentates, Eddington is frustrated when he has to pronounce this bullshit. To make his detachment from the primitive English nationalism even clearer, he de facto saves the life of a German family, the Müllers, from a violent anti-German mob. He has to hug a pretty girl, too, which is probably a greater sacrifice than Eddington's broken nose.

His conscience is bad. He didn't say one thing. Einstein hasn't written it explicitly but the pride of Isaac Newton could be in trouble: Newton said that gravity was instantaneous but it can't be the case according to special relativity. He's worried by the very same point that made Einstein's sponsor in Berlin complain "Why do I pay this guy?". Eddington realizes that either Einstein or Newton is wrong. His sister tells him that only the truth matters and he must get after it. I guess that they improved the history a bit.

A snoring Einstein is visited by Mileva and the kids whom he was expecting a day later. Is the work finished? Einstein is showing what his work is about, throwing stones or eggs from the staircase. Gravity, that's what he is struggling with. Mileva is not hysterical but observes that Einstein moved away from her a lot. Einstein plays the piano (not the violin) and Elsa suddenly enters, screaming that she bought Schubert. A family crisis. Mileva sort of calmly understands and starts to talk divorce. They're leaving Einstein. He is screaming that he would explain what the work means when he's finished.

Eddington is speaking like a Quaker priest. Everyone must be welcome to England, including foreign-born folks. Nationalist mobs are screaming outside. A minute later, these violent men spit in the face of the "stinking coward" Eddington who accepted the German family. At this moment, I guess, Eddington already knew whom he wanted to be right: It was Einstein.

A presentation of the effects of ammonia on innocent poultry and birds takes place in a Berlin lecture hall; the annoying sponsor offers would-be important remarks about a shorter war. Einstein arrives and nearly crying, he is devastated by the dead pigeons etc. "What're you doing?" Planck takes him away and explains the new pride to be German that he learned from his son in the army. The annoying sponsor appears in the pub and brings good news: Einstein's membership in the Academy has consequences, he is a citizen of Germany again, and Kaiser himself has signed it. "Then the whole Kaiser should have asked me first," Einstein reacts. ;-) Planck shows a list of 93 celebrities who wrote a manifesto to support the German army. Einstein should be honored to become the 94th. A smiling, witty Einstein asks: "Is Goethe going to fight Shakespeare?" LOL. Einstein won't sign. "You are an expensive addition to the university," Einstein is told by the sponsor. Einstein recognizes: "Are you threatening me?" Planck peacefully tries the "love of God" and "duty for the country". Einstein points out that he has a contract which implies that he is not belonging to anyone and they won't have his name.

Now, Eddington returns for Einstein's paper in the library – he started to like it, his face shows. Not available, the librarian says: All German papers were taken out of the circulation. He finds the paper somewhere, anyway. A woman catches him which is not a problem. His boss says that Eddington has already done a great job about the paper. Eddington stresses that the German science isn't a part of the German artillery. But he is shown the manifesto with 93 celebrities. The German nation is one object, Eddington is told. Signed are Haber, Planck, and others. "Einstein is not there!" Eddington finally observes and shouts. Eddington's waterproof argument is countered by the comment that "moving to Berlin is enough". ;-)

Eddington is showing "die Sonne", Uranus, Neptune, and other models to the cute German girl. Eddington says that Newton could predict everything, it works, but there's a discrepancy for Mercury. Eddington is determined to write Einstein and ask him for predictions concerning Mercury! ;-)

Meanwhile, Einstein is openly dating Elsa. Up to the DNA overlaps, it works excellent. Einstein's actor's deep voice makes him sound like Benjamin Netanyahu (but the actor, Andy Serkis, is actually of Armenian descent). Elsa observes that they spent all day talking about bullshit and music so Einstein must be stuck. Einstein replies that she knows nothing about physics so let's keep it this way.

Haber et al. are stunned that he brings Elsa to the "Senior Common Room" even though she is just a woman. Albert and Elsa leave and laugh: she dared to enter the Senior Common Room and they were chastised for that but they were already sure they wanted to have sex just meters away from it and Einstein actually announced the intent to the colleagues in a scrambled message! ;-) Einstein doing funny things with food. Suddenly, he opens the letter from Eddington. Einstein realizes the importance of the Mercury comment.

At the university, a superhappy Einstein meets a devastated Planck. His son died (in reality, one son of Planck was taken prisoner in 1914 and the other one was killed in action in 1916). Planck says that Einstein will be able to see his sons again. Einstein totally changes the topic and requires Planck helps him with Mercury and mathematics.

They work together. Above lots of papers, Planck asks what Einstein would do if God told him that Newton was right and Einstein is wrong. Einstein would thank God for His point of view and would point out that their opinions differ. ;-) "Don't you believe in God," Planck asks. Einstein says that he is not believing in any God similar to ourselves. Einstein can't see individuals who survive their death, either. Suddenly, an answer for Mercury's orbit emerges and they send a letter to Eddington, England. I doubt that the real-world Planck has participated in the calculation of Mercury.

Eddington gets the letter, compares the predictions with the known data (it's suggested that Einstein didn't know the required answer) and it works, Eddington's sister is told. Do you know what it could mean? Einstein may be beginning to close in on gravity. Meanwhile, they tell Eddington that the English army was obliterated (by ammonia?). Eddington's romantic idol William was killed, too. "I am so sorry, William was a good friend, wasn't he?" – "Yes, he was," Eddington is trying to reply calmly.

Einstein undergoes an annoying German passport check, enters the Senior Common Room and angrily and rightfully screams how it is disgusting that they discuss how to optimize the poisoning by lethal gases instead of science. Haber tells him to be quiet. Einstein complains about the hypocrisy – one can't be loud at this great university but killing thousands of people by a chlorine-based gas from this school is just OK! What are we doing? What is this madness?

A sad Eddington visits the tree where they had the happy discussions on the bike mileage. After his sister requests it, he cries and reveals he has loved William so much. She says she knew it. There's no reason for his death. Where was God?

A British committee plans to sever all ties with the German scholars – not so shocking given those 15,000 people gassed by the Germans in one day. "Who killed my son," the boss asks? German science! The old men request an unanimous vote. Eddington rebels: It's the f*cking war that has killed all of them, it's all of us. Expelling German scientists will do no good. Science transcends national boundaries, takes us beyond our anger etc. "What does your Einstein want, to kill all morality etc.?" Eddington answers that Einstein wants the same thing as Eddington: a new theory of gravity. Eddington votes against the motion. "My son is dead," Eddington is told by Sir Oliver Lodge again (his real-world son Raymond was indeed killed in 1915 which made Lodge start with Spiritualism – along with Arthur Conan Doyle whose son had the very same fate). "I will not allow his death to be in vain." Eddington counters: "Mercury!" But the old man doesn't like it: "We've had this discussion before. Uranus didn't work. But there was Neptune, exactly where Newton predicted it to be. Everything happens for a reason!" A strong shouting match.

A seemingly routine passport check; but he was not allowed to enter. Soon afterwords, Einstein meets Planck who just says that Einstein was cutoff for his "anti-German outburst". It was a pretty stupid moment for them to fire Einstein! Einstein is depressed and sick. He visits Elsa who tells him he looks horrible. "But you look beautiful," Elsa learns, "I love you". But Elsa leaves him; she made up her mind about him.

Einstein is asked to go. He goes and is nearly killed by cars. That was badly needed because his devilish smile returns: Einstein has another essential idea to complete GR! He needs Planck's help for his letter to Eddington to avoid the censors. "You hired me and I did what you wanted: my theory of gravity is finished!"

Eddington receives the letter and shortly afterwords, he is already presenting the general theory of relativity to his environment. The dishes have to be removed from the table to explain the spacetime curvature; an apple orbits a bread as they hold the tablecloth. "The curved space is directing the matter, the matter tells the space how to get curved." An English experimenter wants to prove a German theorist right. Opposition due to politics follows. "I love my country but this is so much more." The sister seems proud.

Eddington figures out that the light bending needs an eclipse – lots of money for an expedition. His new aide argues that whether they prove Einstein right or wrong, it will be a victory for the British experimental science. Eddington's boss "doesn't believe Eddington and his open mind." Eddington replies that he was hired exactly because he's the best measuring guy in England. "This is my moment. This is what my science life was all about. I would never allow a bias or a prejudice." Eddington also assertively replies to his boss: "And what about your mind? Is it open?" Of course. "So then we will have our money." ;-)

As Germany surrenders, Eddington learns that the officials have agreed and they are going to Africa (they went to islands off West Africa). Eddington and his sister talk about the victory in the war; she is going to Berlin to help the poor Germans who may be victims of a revenge. The leaving sister seems hysterical about Eddington's apparent loss of the faith in God.

Principe, West Africa. We saw this environment at the beginning. They worry about the weather – the visibility. Clouds aren't good news. The Sun emerges behind the clouds. Look! Now it looks good, the clouds cleared (maybe it was done by God). Totality: they have 5 minutes to take photographs by their pretty nice apparatus. Two pictures out of eight look fine. Comparisons with the normal British skies will be done at home.

Einstein sees his son(s) and Mileva again. She hopes that the results were worth the sacrifice. "My theory is too beautiful to be wrong, someone will prove it," Einstein claims. The promised explanation to the son is that "the space is curved, full of curves and wonderful shapes". – "Are you going to Berlin again?" crying Einstein is asked by a son again. The answer is Yes. (The real-world younger son of Einstein, Eduard, suffered from schizophrenia and was apparently overdrugged or damaged by the electric shock therapy during the treatment. Once the illness began, he told his father that he hated him and they would never meet again. His mother would take care of him until her death in 1948. He continued to live in an asylum for 17 more years before he died of stroke. The older son Hans Albert was an achieved engineer who did some important research on sediment transport.)

Eddington decides to compare the photographic place in the public. A hundred of viewers in a hall looks at Eddington. They somewhat incorrectly say that Newton predicts that the star locations should agree. Well, it depends what Newton's theory for light you choose. Newton actually believed in light corpuscles that would be affected by gravity as well (50% of the angle change predicted by Einstein). On the other hand, James Clerk Maxwell would probably expect his equations to be unaffected by the gravitational field so the light rays should be straight. Will the locations of the stars agree? "A gap," Eddington announces. He begins a good historical speech making it clear that he would back Einstein.

His boss and other English nationalist potentates immediately leave the hall. After a short break, Eddington finishes a good speech about the way in which the world has changed. "I could hear God thinking" is a bonus sentence that makes his sister smile really happily. Applause.

Max Planck likes Einstein again when the journalists storm the building in Berlin. "The word has reached us from England," Planck says as he is showing the headlines about the revolution in science published by the Times. "You're famous." Elsa returns at this very moment and agrees to live with him assuming that he will fix his appearance instead of looking like a lunatic. "A kind of a genius looks like you," Elsa observes. This encourages Einstein to improve himself to a "lunatic on steroids" right before he appears in front of the journalists. He sticks his tongue out, too.

One year later, Einstein visits Eddington in Cambridge. The war has been nearly forgotten. Einstein is smiling and is greeted as a hero, Eddington looks calm and unfriendly when he sees Einstein for the first time. They say "Eddington – Einstein" to each other – they shake their hands and restore some smile on Eddington's face. Now, lots of it.

Captions remind us that Eddington has transformed Einstein from an obscure scientist to a celebrity. (It is weird that Einstein was an obscure scientist 10 years after his miraculous year and special relativity but it's sort of true, too.) Eddington didn't like the spotlight, we are told, and spent the rest of his life by reconciliations of his faith and science. His work is largely forgotten today, the filmmakers bizarrely claim (numerous other Eddington's results have become standard toolkits of cosmology and astrophysics).

I think it was a powerful movie. The idea that GR was all about Einstein, Eddinngton, and Planck is an oversimplification but it probably increased the dramatic qualities of the movie considerably.

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reader Uncle Al said...

Eddington versus Chandrasekhar. Respect the future when it arrives. It will not go away.


reader Luboš Motl said...

Sorry for that, a blogger bug. It's being said that they're working on a fiix, see:

https://productforums.google.com/forum/?hl=en#!searchin/blogger/dynamic$20views/blogger/tdvbtpaR4PE/POuuWYAXo0wJ



So they should ultimately return.


I will have to remove and replace the (paid) Neocounter etc. because it came out of business today. I liked it so that I paid $50 every year!


reader biff33 said...

Thanks for the explanation! And Happy Birthday (Thursday)!


reader lucretius said...

This is a very interesting thread but at the moment I have no time to participate seriously so I will only remark that Sanskrit is a far more interesting language than Portugese unless, of course, you think that the only or main valid reason for learning a language is to use it on your holiday trips.

On the one hand, ancient Hindu texts written in Sanscrit are among the intellectually most complex and fascinating products of human mind in the “literary” sphere - for example some of them have even three independent interpretations (often one of them describing something universal and the other related to human sexuality) and decoding these is comparable to other highly non-trivial intellectual pursuits, like mathematics or theoretical physics.


On the other hand, Sanscrit is the closest language to the hypothetical ancient language of the Indo-Europeans, and by studying it you can discover surprising connections with a variety of Indo-European languages. You can, for example, find Polish words that are similar to those in Sanscrit and you can find them in Greek and German yet the corresponding words in these languages are not necessarily similar to each other. You can even find words in Japanese that are similar to Slavic ones and the explanation for this very surprising link can be found in Sanscrit.

OK, you may say, but what’s the practical use of that, does it help with shopping on a trip to Dehli? Actually, it might, but if you need this kind of justification for studying something I wonder what you really think of String Theory?


reader Bee said...

Steve Hsu clearly has a complex ... He is no Feynman ... He will accomplish less in the field of physics than Feynman ... No one will ever say he is in the same league ... He will, however, demonstrate he is more concerned about indirect measures of intelligence than pushing physics forward ... Pathetic


reader Barbara said...

It's a science-fiction movie set in the past :)


Funny that Eddington says he has no bias and that he is the best measuring guy in England.


In the end the measuring was more of a publicity stunt, the best part of Eddington's work are mostly contained in his “The Internal Constitution of the Stars”, which was a milestone towards understanding stellar physics.


reader Luboš Motl said...

LOL, sci-fi based in the past is a great concept by itself.


reader lucretius said...

A very minor quibble: the German Army in the first world war was not called the Wehrmacht.
A pretty good film without any serious nonsense as far as the science is concerned (well, at least I can't find any). Pity they could not find a place for Karl Schwarzschild.


reader Luboš Motl said...

LOL, I know, it was a joke - to highlight the idea that the Jew Einstein was supposed to be critical for the existential interests of Germany.


reader lucretius said...

Rather embarrassing to have missed this (that is what the Internet does to one's sense of irony). Still I think my other point is O.K. : they could have made good use of the 40 year old Schwarzschild volunteering for the front and doing physics in the trenches... At least they could have showed Einstein reading a letter from him which would have made for another historically accurate scene...


reader thefuturist said...

If I remember rightly Feynman had a counterpart, who independently 'rediscovered ' much of western mathematics from scratch- Ramanjuan


reader lucretius said...

No, you are quite wrong. There is almost no relation or similarity between the two: except that they both deserve to be called a genius.

It’s hard to even to start describing the difference. Perhaps the main point is that Feynman was a fully and properly educated American physicist. Ramanujan had some basic training in mathematics but he could not enter into university in India because he could not pass the required English exams. Thus, when Feynman chose do “rediscover” things he did it by choice but Ramanujan simply did not know most of the basic mathematics. For that reason, he worked almost exclusively in the field of number theory and closely related areas, where a great many discoveries could be made without knowing almost any existing theories. Of course he new nothing at all about topology, differential geometry, algebraic geometry, and so on and so on, subjects that you can’t just study without any proper training.

Moreover, Ramanujan never learned the Western concept of “a proof”, so while he discovered many remarkable and sometimes amazing formulas, he never really proved them (except as part of joint work with Hardy and Littlewood).

Another difference from Feynman was, of course, that while Feynman was a man of great curiosity with interest in many aspects of the world around him, Ramanujan was entirely absorbed in mathematics and other than that a very conventional Hindu (in fact a Brahmin). He could not have even travelled to the West at the invitation of Hardy and Littlewood if his grandmother did not have a convenient dream…

Ramanujan is probably the only example in the history of mathematics of pure genius, who owed very little to education. Hardy rated his talent at 100, Hilbert’s at 80, Littlewood’s at 30 and his own at 20. Nevertheless Ramanujan’s contribution to mathematics is certainly smaller than Feynman’s to physics. As Hardy himself observed, had Ramanujan been properly educated he would have achieved far greater things. Nobody has ever claimed that about Feynman.


reader Leo Vuyk said...

Lubos did you observe the photographic presentation of eddington at the end of the movie?
Don't you think the number of stars and star shifts was over done?


reader Luboš Motl said...

Yes, I do think. The angular size of the Sun is 0.54 degrees i.e. 9.44 mrad, while the shift of the stars near the Sun is by 1.75 arc seconds if I remember well, 8.48 microrad, almost 1,000 times smaller. The ratio was less extreme than 1,000 over there. Also, the number of relevant visible stars near the Sun is smaller.


reader Leo Vuyk said...

Thanks Lubos,

So i presume you are sure that this shift photo is artificial manipulated and not by accident a very recent product of a clever experimentalist.

Leo Vuyk


reader Luboš Motl said...

No, I am not sure. I am not sure even about my original answer to you.


reader Leo Vuyk said...

It would be very interesting if the photo is real, because THEN the gravity field of the Sun should be inhomogenous.
Inhomogenous, If you look at the displacements of the different stars related to the centre of the sun!


reader Leo Vuyk said...

I made some rough lines to show these differences in displacements.