About Gali Weinstein

I am specializing in the foundations of physics: special and general theories of relativity. Galina Weinstein.

Traversable ER = EPR wormholes are possible

In 2013 Juan Maldacena and Leonard Susskind demonstrated that the Einstein Rosen bridge between two black holes is created by EPR-like correlations between the microstates of the two black holes. They called this the ER = EPR relation, a geometry–entanglement relationship: entangled particles are connected by a Schwarzschild wormhole. In other words, the ER bridge is a special kind of EPR correlation. Maldacena and Susskind’s conjecture was that these two concepts, ER and EPR, are related by more than a common publication date 1935. If any two particles are connected by entanglement, the physicists suggested, then they are effectively joined by a wormhole. And vice versa: the connection that physicists call a wormhole is equivalent to entanglement. They are different ways of describing the same underlying reality.
Maldacena and Susskind explain that one cannot use EPR correlations to send information faster than the speed of light. Similarly, Einstein Rosen bridges do not allow us to send a signal from one asymptotic region to the other, at least when suitable positive energy conditions are obeyed. This is sometimes stated as saying that (Schwarzschild) Lorentzian wormholes are not traversable.
In 2017, however, Ping Gao, Daniel Louis Jafferis, and Aron C. Wall showed that the ER = EPR allows the Einstein-Rosen bridge to be traversable. This finding comes with implications for the black hole information paradox (of Stephen Hawking) and black hole interiors because hypothetically, an observer can enter a Schwarzschild black hole and then escape to tell about what they have seen. This suggests that black hole interiors really exist and that what goes in must come out and we can learn about the information that falls inside black holes.
Consider a light signal, traveling through the throat of the wormhole. In 1962, Robert Fuller and John Archibald Wheeler were troubled by the apparent possibility that a test particle, or a photon, could pass from one point in space to another point in space, distanced perhaps extremely far away, in a negligible interval of time. Such rapid communication of a particle or a photon, passing through an Einstein-Rosen bridge violates elementary principles of relativity and causality, according to which a light signal cannot exceed the speed of light.
Wheeler and Fuller, however, showed that relativity and causality, despite first expectations, are not violated. It is perfectly possible to write down a mathematical expression for the metric of a space-time which has simple Schwarzschild wormhole geometry. However, when we deal with the passage of light by the “long way” from one wormhole mouth to the other, both on the same space, the throat becomes dynamically unstable and the Einstein-Rosen bridge is non-traversable (see figure, middle).

What would cause an Einstein-Rosen bridge to be traversable? Recall that according to the ER = EPR, an Einstein Rosen bridge between two black holes is created by EPR-like correlations between the microstates of the two black holes. In 2017 scholars found that if one extends the ER = EPR conjecture by equating, not a Schwarzschild wormhole between two black holes and a pair of entangled particles, but a Schwarzschild wormhole and a situation which is somewhat analogous to what occurs in quantum teleportation (between the two sides of the wormhole), then the Einstein-Rosen bridge becomes traversable.
Entanglement alone cannot be used to transmit information and we need quantum teleportation because the qubit is actually transmitted through the wormhole say Gao, Jafferis and Wall: “Suppose Alice and Bob share a maximally entangled pair of qubits, A and B. Alice can then transmit [teleport] the qubit Q to Bob by sending only the classical output of a measurement on the Q-A system. Depending on which of the 4 possible results are obtained, Bob will perform a given unitary operation on the qubit B, which is guaranteed to turn it into the state Q”. But: “Of course in the limit that Alice’s measurement is essentially instantaneous and classical, the traversable window will be very small … — just enough to let the single qubit Q pass through. Therefore, we propose that the gravitational dual description of quantum teleportation understood as a dynamical process is that the qubit passes through the ER=EPR wormhole of the entangled pair, A and B, which has been rendered traversable by the required interaction”.
Next, say Alice throws qubit Q into black hole A. She then measures a particle of its Hawking radiation, a, and transmits the result of the measurement through the external universe to Bob, who can use this knowledge to operate on b, a Hawking particle coming out of black hole B. Bob’s operation reconstructs Q, which appears to pop out of B, a perfect match for the particle that fell into A. The new traversable ER = EPR wormhole allows information to be recovered from black holes. Thus, Gao, Jafferis and Wall write regarding the black hole information paradox:
“Another possible interpretation of our result is to relate it to the recovery of information … [from evaporating black holes]. Assuming that black hole evaporation is unitary, it is in principle possible to eventually recover a qubit which falls into a black hole, from a quantum computation acting on the Hawking radiation. Assuming that you have access to an auxiliary system maximally entangled with the black hole, and that the black hole is an efficient scrambler of information, it turns out that you only need a small (order unity) additional quantity of Hawking radiation to reconstruct the qubit. In our system, the qubit may be identified with the system that falls into the black hole from the left and gets scrambled, the auxiliary entangled system is … on the right, and the boundary interaction somehow triggers the appropriate quantum computation to make the qubit reappear again, after a time of order the scrambling time”. …
Thus, the Gao, Jafferis, Wall ER = EPR wormhole idea seems to extend to the so-called real world as long as two black holes are causally connected and coupled in the right way. If you allow the Hawking radiation from one of the black holes to fall into the other, the two black holes become entangled, and the quantum information that falls into one can exit the other. Thus, Gao, Jafferis and Wall conclude:
“Our example thus provides a way to operationally verify a salient feature of ER=EPR that observers from opposite sides of an entangled pair of systems may meet in the connected interior. … What we found is that if, after the observers jump into their respective black holes, a … coupling is activated, then the Einstein-Rosen [bridge] can be rendered traversable, and the meeting inside may be seen from the boundary. This seems to suggest that the ER=EPR wormhole connection was physically ‘real'”.
Finally the ER = EPR wormhole does not require energy-matter that violates the average null energy condition; the negative energy matter in the ER = EPR configuration is similar to the Casimir effect, and any infinite null geodesic which makes it through the ER = EPR wormhole must be chronal, i.e. the ER = EPR wormhole does not violate Hawking’s chronology protection conjecture. In addition, the ER = EPR wormhole does not violate the generalized second law of thermodynamics.
Therefore, the ER = EPR wormhole is not a configuration with closed time-like curves and it, therefore, does not permit one to travel faster than light over long distances through space; in other words, it cannot serve as a time machine and thus does not violate causality.


For further details:

Ping Gao, Daniel Louis Jafferis, Aron C. Wall (2017). Traversable Wormholes via a Double Trace Deformation.

Natalie Wolchover, Newfound Wormhole Allows Information to Escape Black Holes

Why did Einstein Reject his Field Equations of General Relativity in 1912 only to Come Back to them in 1915?

It has to do with Newton:


Sir Isaac Newton, by Sir Godfrey Kneller, Bt. oil on canvas, feigned oval, 1702.

In a forward from 1931 to Newton’s book, Opticks Einstein wrote: “In one person he combined the experimenter, the theorist, the mechanic, and, not the least, the artist of exposition”.

Starting in summer 1912, Einstein undertook a long journey in the search for the correct form of the field equations for his new gravitation theory. He began collaborating with his friend from school Marcel Grossmann.

In 1912 Einstein wrote a form of the Ricci tensor in terms of the Christoffel symbols and their derivatives. This was a fully covariant Ricci tensor in a form resulting from contraction of the Riemann tensor.

Einstein then considered candidate field equations with a gravitational tensor constructed from the Ricci tensor. This gravitational tensor was called by scholars the “November tensor”. It transforms as a tensor under unimodular transformations.

Setting the November tensor equal to the stress-energy tensor, multiplied by the gravitational constant, one arrives at the field equations of Einstein’s first paper of November 4, 1915.

Einstein hoped he could extract the Newtonian limit (i.e. the Newtonian gravitational field equation, Poisson’s equation for gravity) from the November tensor. Poisson’s equation for gravity: the Newtonian gravitational field equation for gravity; the potential at distance from a central point mass (the fundamental solution) is equivalent to Newton’s law of universal gravitation. But Einstein found it difficult to recognize that the November tensor reduces to the Newtonian limit. Thus, he finally chose non-covariant field equations, the so-called Entwurf field equations.

In 1913 Einstein and Grossmann wrote a joint paper in which they established the Entwurf field equations through energy-momentum considerations instead of the November tensor; these equations could also reduce to the Newtonian limit. Unfortunately, these equations were not covariant enough to enable extending the principle of relativity for accelerated motion and did not satisfy the equivalence principle.

Towards the beginning of November Einstein was led back to his starting point, namely to the November tensor of 1912. He gradually expanded the range of the covariance of his gravitation field equations. Every week he expanded the covariance a little further until, on November 25, he reached his fully generally covariant field equations.

Einstein explained to his colleagues that he had already considered the November tensor with Grossmann three years earlier (in 1912). However, at that time he had concluded that these field equations did not lead to the Newtonian limit. Einstein now understood that this was a mistake. In retrospect, he realized that it was rather easy to find these generally covariant equations but, it was not easy at all and even extremely difficult to recognize that they are a generalization of the Newtonian Poisson’s equation and that they satisfy the conservation of energy-momentum.

In 1915 Einstein explained this point of view to David Hilbert:


The Collected Papers of Albert Einstein, Vol. 8.

Einstein told Hilbert that the difficulty was not in finding the November tensor.

In my paper, “Why did Einstein Reject the November Tensor in 1912-1913, only to Come Back to it in November 1915?”,  published a year ago in May 2018, in the journal Studies in History and Philosophy of Modern Physics:

An ArXiv PDF version of this paper.


I ask three questions:

1) Why then did Einstein reject the November tensor in 1912-1913, only to come back to it in November 1915? Einstein explained that he found it difficult to recognize that the
November tensor reduces to the Newtonian limit.

2) Why was it hard for Einstein to recognize that the generally covariant equations are a simple and natural generalization of Newton’s law of gravitation?

3) Why did it take him three years to arrive at the realization that the November tensor is not incompatible with Newton’s law?

In my paper, I consider each of these three separate questions in turn. I examine these questions in light of conflicting answers by several historians: Michel Janssen, John Norton, Jürgen Renn, Tilman Sauer, and John Stachel.

Fast forward to the 1920s. In 1923 Élie Joseph Cartan provided a generally covariant formulation of Newtonian gravity (called the Newton-Cartan theory), though his formulation was much more complex than the generally covariant formulation of Einstein’s 1915-1916 general theory of relativity.

On a four-dimensional manifold, he introduced two geometrical objects the metric tensor and a symmetric affine connection. In general relativity, the metric tensor describes through the line element the behaviour of clocks (the chronometry) and measuring rods (the geometry) of space-time. We combine the one-dimensional chronometrical and the three-dimensional geometrical structures into the chrono-geometrical structure of space-time. In the four-dimensional version of Newtonian gravitation theory, the chronometry is represented by a scalar field on the four-dimensional manifold, called “absolute Newtonian time”, and the geometry by a degenerate metric field of rank 3. In the space-time formulation of Newton’s theory, proper time is not defined.

In Cartan’s formulation of Newtonian gravitation theory, the weak equivalence principle (Galileo’s law of free-fall) is taken as a principle: In a gravitational field, all local freely falling objects are fully equivalent. Free material particles follow the geodesic curve and a tangent vector field is parallel-transported along a geodesic curve. This is parallel transport of a tangent vector in an affine connection on a manifold.

Consider a freely falling particle moving in a gravitational field. We look first for the equation of the trajectory traced by the particle and then express this equation in geometrical language. A particle in free fall moves along a geodesic in space-time (in 3+1 space-time in Newtonian theory). The geodesic equation can be written in terms of the affine connection.

One cannot distinguish Newtonian inertial systems (material particles in free fall following geodesic lines in curved non-flat space-time) from local inertial systems (material particles in free fall following geodesic lines in flat space). We cannot, therefore, locally separate gravity from inertia. Gravity and inertia are described by a single inertio-gravitational field. We incorporate an inertio-gravitational field into the geometric formulation of Newtonian gravity theory. We cannot separate a flat affine connection of space-time from a field describing gravitation (a gravitational potential).

Cartan, therefore, found a general dynamical non-flat connection which represents both inertia and gravity. Rather than thinking of particles being attracted by forces, one thinks of them as moving along geodesic lines in curved, four-dimensional space-time. Therefore gravity is not a force anymore but is interpreted geometrically and should be considered as a curvature of space-time. The above non-flat affine connection defines the amount of curvature of geodesic lines. Cartan’s connection is still not the metric connection. The Christoffel symbols do not serve as the components of the connection (the Levi-Civita connection) and the connection is not written in terms of the metric tensor components.

Cartan introduced a Newtonian classical space-time: A four-dimensional manifold endowed with a Euclidean special metric and absolute time. Cartan then defined the total mass-momentum field associated with the matter field. To find the field equations he defined the Newtonian field equations similarly to the Einstein field equations: Field equations relate chrono-geometrical quantities and the non-flat connection to the matter distribution. Given the Newtonian Poisson equation (the mass density related to the gravitational field) the Poisson equation is now replaced with a generalized Poisson equation written in terms of the Ricci tensor and Cartan’s non-flat affine connection. The Ricci tensor is defined in terms of the Cartan connection. Finally, it turns out that the condition that space-time is flat is fulfilled.

The significance of Cartan’s formalism in general relativity is the following: Cartan’s affine connection is non-flat and cannot break up into a Newtonian flat affine connection and a gravitational potential. In a freely falling system, we cannot separate gravity from inertia. This embodies the inertio-gravitational field (equivalence principle). Accordingly, in the Newtonian limit, although we obtain Poisson’s equation and space-time is flat, Cartan’s affine connection remains non-flat, that is to say, the Ricci tensor is expressed in terms of Cartan’s non-flat connection. Thus, the four-dimensional formulation of the Newtonian Poisson field equation is a precise definition of the Newtonian limit of Einstein’s field equations. This actually finally solved Einstein’s problem of obtaining the Newtonian limit. Between 1912 and 1915 Einstein lacked Cartan’s formalism, i.e. more advanced mathematical tools and John Stachel argues that these could be responsible for inhibiting him for another few years. I extensively explain this in my second book: General Relativity Conflict and Rivalries: Einstein’s Polemics with Physicists

Did Einstein steal his theory of relativity from his first wife?

Allen Esterson and David C. Cassidy have published a new book: Einstein’s Wife. The Real Story of Mileva Einstein-Marić.

The last part of the book considers the question: Did Einstein’s first wife coauthor his 1905 path-breaking papers. In his book, the author Allen Esterson failed to mention my work on the subject probably because in 2013 I corrected his draft on Mileva Marić and Einstein and perhaps he didn’t like my comments…

Anyway, in 2012 I wrote the following paper:

Did Mileva Marić assist Einstein in writing his 1905 path breaking papers?

Shortly afterwards, the MIT Technology Review wrote a piece about my paper:

Did Einstein’s First Wife Secretly Coauthor His 1905 Relativity Paper?

I didn’t quite like the style and I have noticed that the paper required some corrections. In 2015 and 2017 I expanded on the aforementioned topic in my book:

Einstein’s Pathway to the Special Theory of Relativity (2nd Edition), Chapter E.

As to Allen Esterson’s book. His chapter begins with Desanka Trbuhovic-Gjuric’s biography of Mileva Marić: Im Schatten Albert Einsteins, das tragische Leben der Mileva Einstein-Marić (In the Shadow of Albert Einstein: The Tragic Life of Mileva Marić).


Esterson writes:



Esterson tries to refute one item after the other. While refuting  Trbuhovic-Gjuric’s thesis, Esterson tells in much detail how Marić was a good student and almost graduated the Polytechnic, she travelled to her parents’ home in Novi Sad to secretly give birth to a daughter, Liesel, in early 1902. Liesel was born before the couple’s (Einstein-Marić) marriage, and so forth.

Don Howard has written that Mileva Marić was a remarkably talented and ambitious young scientist, someone who expended tremendous personal energy to create for herself opportunities that normally would have been foreclosed to women at that time. Marić’s love affair with Einstein and her pregnancy with their illegitimate daughter Lieserl simply put an end to all of these dreams that had fired her soul. She was pregnant and scared about what the future would bring and she failed her final exams at the Zurich Polytechnic. The cultural norms of the era and the unhappy accident of the pregnancy and birth of Lieserl destroyed Mileva’s intellectual dreams and ambitions. However, Mileva was a very smart sounding board for Einstein’s ideas, in much the same way that Michele Besso, was a sounding board.

In his book, Esterson repeats John Stachel’s theme that Marić did not contribute to Einstein’s relativity paper of 1905 and Stachel’s altercations with feminists authors and with Evan Harris Walker (see, for instance, Esterson’s book, page 282 where he writes:


Esterson also analyses Peter Michelmore’s biography, Einstein, Profile of the Man and writes on page 107:


Yes, Michelmore mentioned the couple Einstein and Marić, writing that “Mileva checked the [relativity] article again and again, then mailed it. ‘It’s a very beautiful piece of work’, she told her husband” (Michelmore’s book 1962, page 46).

Michelmore interviewed Hans Albert Einstein. Michelmore wrote that Einstein’s son  “answered all my questions, and waited while I wrote down the answers. He did not ask to check my notes, or edit my book. He trusted me”. Thus, if Einstein’s son did not check Michelmore’s notes and the latter did not base his book on archival material, then Michelmore’s biography is not a primary source and we can consider it as almost pure imagination. See my book, Einstein’s Pathway to the Special Theory of Relativity (2nd Edition) for further analysis.

While refuting Trbuhovic-Gjuric’s and Michelmore’s theses Esterson bases himself on the Collected Papers of Albert Einstein and on secondary sources, such as Albrecht Fölsing’s biography of Einstein. He thus refers to biographies to make a point about Marić’s life and influence on Einstein’s 1905 ground-breaking papers. He refers to Walter Isaacson’s 2007 biography of Einstein and says that Isaacson “examined archival material newly released in 2006” (Esterson’s book 2019, page 136). This is absolutely true. Esterson explains in an endnote:


However, Isaacson inadvertently falls into the trap of Trbuhovic-Gjuric’s biography of Mileva Marić, which according to Esterson is a dubious source:


Isaacson writes in his biography of Einstein, page 136:

“In late summer 1905 Albert, Mileva and Hans Albert visited Belgrade, Mileva’s hometown Ujvidek (now Novi Sad). Walter Isaacson described Mileva Marić’s role in Einstein’s work: Albert and Mileva took a vacation together in Serbia to see her family and friends. “While there, Marić was proud and also willing to accept part of the credit. ‘Not long ago we finished a very significant work that will make my husband world famous’, she told her father, according to stories later recorded there […] and Einstein happily praised his wife’s help. ‘I needed my wife’, he told her friends in Serbia. ‘She solves all the mathematical problems for me'”.

The source is Dennis Overbye’s historical romance, Einstein in Love, in which Overbye has written (page 140):

“‘Not long ago we finished a very significant work that will make my husband world famous’, Mileva told her father in a conversation widely repeated through the years. To the villagers and relatives who remembered her as a childhood genius in mathematics, Mileva had a heroic aura, the local girl who had gone out into the world and made good. Now she had brought back a handsome, adoring husband. Albert knew how to play the crowd. ‘I need my wife’, he is reported to have said, ‘She solves all the mathematical problems for me'”.

Overbye quotes Trbuhovic-Gjuric’s biography of Marić, which was translated to English for him

Isaacson and Overbye simply fell into the trap of Desanka Trbuhovic-Gjuric’s biography of Mileva Marić.

This one minor fly in the ointment in Isaacson’s otherwise good intentioned book would pass unnoticed by the reader. But Esterson is citing Isaacson’s biography in a book the title of which is Einstein’s Wife. The Real Story of Mileva Einstein-Marić, and he thus has to rectify this trifling inadvertency.


Einstein’s 140th Birthday: this is not Einstein’s Legacy!

Yesterday the Einstein Archives (at the Hebrew University in Jerusalem) celebrated with much pomp and circumstance Einstein’s 140th birthday. It was overwhelmed with grandeur and was definitely Einstein’s “wishful thinking” (as you probably all know Einstein was so humble).
In 2004 my Ph.D. supervisor passed away from cancer. After her death, I learned from colleagues about the presence of overt or covert conflict between my mentor and another professor in her department of history and philosophy of science at the Hebrew University of Jerusalem (see my Hebrew posts). Not only did that professor cancel my mentor’s field of expertise after her death, but she would bend over backward to kick me off the academy. She would try to get rid of me plain and simple. And then with puppy dog eyes, people would tell me: don’t make a big mountain out of something small, we like you… People in the academy behave like thugs in the street and speak of both sides of their mouth.
But let us delve into Einstein’s 140th celebration. Ever since of my mentor’s death, Prof. Hanoch Gutfreund (celebrating on Einstein’s 140th birthday and is seen everywhere in the photos and interviews) would spin the web around me in such a way that he would do anything in his power to block me and not let me participate in any conference, project, any event organized by the Einstein archives/institute at the Hebrew University.
I am a well-known female scholar of the history of Einstein’s physics and mathematics. Prof. Gutfreund began to present my ideas as his own and use my ideas without mentioning my name. The organizers of the 2015 Berlin Century of General Relativity conference on Einstein failed to invite me to the conference (though I requested to lecture there) but Gutfreund gave the main plenary evening lecture at the conference and he made use of my works and failed to mention my name. He was feted by important people while presenting my ideas. But this was not the first and last time this would happen.
It’s not water under the bridge because the end result of this ordeal is that Gutfreund is celebrating with much pomp and circumstance with important people Einstein’s 140th birthday, and he’s presenting Einstein’s new documents. But here I am with no job and no money and I am ostracized by the entire academy. Something is way out of whack here because this is absolutely and unequivocally not Einstein’s legacy! Obviously, it is making a deal with the devil.


Photo from here

Einstein’s views on God and God Letter

I shall first briefly discuss Einstein’s views on God and then I will discuss Einstein’s God letter.

Einstein did not believe in an anthropomorphic concept of God but believed in a Spinozist conception of God. Spinoza believed that God exists and so did Einstein, but God according to Einstein and Spinoza is equivalent to the definition of nature. Nature reveals herself in the logical simplicity of the laws of science.

I first explain Einstein’s views on God and then quote from Spinoza.

Einstein’s general theory of relativity formulates the field equations in terms of partial differential equations. But to find a solution to these equations, and therefore to deduce results which can be compared with observations, we must integrate these equations. Einstein’s field equations are non-linear and finding exact solutions to these equations is a tedious and difficult procedure. But the logical chain from theory to observation consists mostly of this procedure of integrating differential equations. Here exactly lie the greatest technical difficulties. When Einstein’s assistants Leopold Infeld and Banesh Hoffmann had toiled for months over problems of this character in unified field theory Einstein used to remark: “God does not care about our mathematical difficulties; He integrates empirically”. What did Einstein mean? He believed that it was possible to reduce the laws of nature to simple principles. In special relativity, he reduced the laws of nature to two principles, the principle of relativity and the principle of the constancy of the velocity of light. In general relativity, we have the principle of equivalence and the generalized principle of relativity — the principle of general covariance. Unlike the technical difficulties in solving the field equations, the simplicity of these principles forms a criterion of the beauty of our theories and of nature, which we observe.

This is a Spinozist conception of nature. Einstein often repeated with variations to his assistants the phrase: “God created the world”. He thus believed that God exists. Second, if God exists, what is God? Infeld explained that in this phrase, was Einstein’s peculiar religious feeling that laws of nature can be formulated simply and beautifully. When Einstein felt he had a new idea, he asked himself: “Could God have created the world in this way?”. God is therefore equivalent to the definition of nature because of the inner consistency and beauty, logical simplicity of the laws of nature, and infinity in the world he created. Infeld called Einstein’s approach to God, “the realist’s approach to God” and one could add to this, the deterministic approach to God, and this is also the meaning of “God does not play Dice”.

(Leopold Infeld, Quest, An Autobiography; General Relativity Conflict and Rivalries: Einstein’s Polemics with Physicists)

Einstein, therefore, believed in Spinoza’s God. In a telegram to a Jewish newspaper from 1929 Einstein wrote:

“I believe in Spinoza’s God who reveals himself in the harmony of all that exists, but not in a God who concerns himself with the fate and actions of human beings”.

Einstein did not believe in an anthropomorphic concept of God, i.e. the use of anthropomorphism in the bible, descriptions such as the wrath of God and God’s flaming fiery, God is angry, a fire burns within His nose against His people for their disobedience, etc. This is God who concerns himself with the fate and actions of human beings. According to Einstein, God created the world and afterward, God does not intervene in human affairs and the world.

Baruch Spinoza explained in his treatise, “Short Treatise on God, Man and His Well-Being” from 1662 that God exists but in the simplicity and harmony of nature and not as an anthropomorphic God:

That God Exists

As regards the first, namely, whether there is a God, this, we say, can be proved…

If man has an idea of God, then God must exist formaliter;

Now man has an idea of God;


If therefore is an idea of God, then the cause thereof must formaliter, and contain in itself all that the idea has objective; …

What God Is

Now that we have proved above that God is, it is time to show what he is. Namely, we say that he is a being of whom all or infinite attributes are predicted, of which attributes every one is infinitely perfect in its kind. … in the infinite understanding of God no substance can be more perfect than that which already exists in Nature…

That in the infinite understanding of God there is no other substance than that which is formaliter in Nature. …

this can be, and is. proved by us: (1) from the infinite power of God, since in him there can be no cause by which he might have been induced to create one sooner or more than another; (2) from the simplicity of his will; (3) because he cannot omit to do what is good, … From all this it follows then: that of Nature all in all is predicted, and that consequently, Nature consists of infinite attributes, each of which is perfect in its kind. And this is just equivalent to the definition usually given of God.

Further, when once asked whether he had faith in life to come, Einstein replied:

“No, I have faith in the universe, for it is rational. And I have faith in my purpose here on earth. I have faith in my intuition, the language of my conscience, but I have no faith in speculation about Heaven and Hell”.

From: W. Hermann, Einstein and the Poet, 1983/Max Jammer, Einstein and Religion, Princeton, 1999, chapter 3.

Now I would like to speak about Einstein’s God Letter. Einstein wrote the God Letter to Eric Gutkind in response to his book, Choose Life: The Biblical Call to Revolt.

Einstein’s God Letter, 1954 (Reuters)

Einstein opens his letter by saying:

“What struck me was this: with regard to the factual attitude to life and to the human community we have a great deal in common. Your personal ideal with its striving for freedom from ego-oriented desires, for making life beautiful and noble, with an emphasis on the purely human element. This unites us as having an ‘unAmerican attitude’”.

What did Einstein mean when he said an “unAmerican attitude”? He meant that both he and Gutkind opposed Joseph McCarthy and the House Un-American Activities Committee. Einstein criticized U.S hydrogen bomb plans and tests and arms race with the Soviet Union; he criticized the U.S policy and he advised people under investigation by the Un-American Activities Committee to refuse to cooperate with the committee. This was his “unAmerican attitude”.

But Gutkind’s book was written in English and Einstein read German texts. Einstein, therefore, told Gurkind that his “book … is written in a language inaccessible to me”. And then he immediately declared:

“The word God is for me nothing more than the expression and product of human weaknesses, the Bible a collection of honorable, but still primitive legends which are nevertheless pretty childish. No interpretation no matter how subtle can (for me) change this. These subtilized interpretations are highly manifold according to their nature and have almost nothing to do with the original text”.

Einstein’s conception of God was based on firm belief in determinism: “God does not play dice”. He denied anthropomorphism in the notion of God; that is to say, making God into the form of a man: God exhibits human qualities such as beauty, wisdom, power, and sometimes human weaknesses such as hatred and uncontrollable anger.

Gutkind wrote in his book:

“The Judaistic elements with their ethical, monotheistic, anti-idolatrous radicalism are pushed into the background. Strangely enough, this church paganism has some features in common with naturalism, which means Assimilation the idolization of nature, nature as the absolute, all of it pagan. Only in contemporary science, in Einsteinian physics has this absolutism of nature been removed radically, even from the sciences”.

Einstein objected to this statement because all monotheistic religions, Judaism, Islam, and Christianity have a strong anti-idolatry stance. Ironically, Jewish and Christian theologians tend to portray or deem pagan deities of ancient Greek mythologies and polytheistic religion as anthropomorphic. Einstein, however, believes that Judaism and in general monotheism is based on an anthropomorphic conception of God. Therefore, nothing makes Judaism unique. This latter point is explained towards the end of the letter, see further below.

Einstein’s radical anti-anthropomorphism is a logical consequence of the second commandment of the Decalogue (Exodus 20:4/Deuteronomy 5:8):

“You shall not make for yourself a carved image or any likeness of anything that is in heaven above, or that is in the earth beneath, or that is in the water under the earth”.

According to Max Jammer in his book, Einstein and Religion, Einstein greatly respected Moses ben Maimon, commonly known as Maimonides, and also referred to by the acronym Rambam, the foremost Jewish philosopher of the Middle Ages.

Rambam (Maimonides) conceived God as follows:

“…our knowledge [of God] consists in knowing that we are unable to comprehend Him”.

People tend to give human characteristics to God and think that God relates to us in human terms. Thus, according to to the second commandment of the Decalogue, Einstein sees in the word God nothing more than the expression and product of human weaknesses.

Einstein objected to the biblical account of the creation of the world, as reported in the first chapter of Genesis. In the beginning, God created the heavens and the earth. Now the earth was formless and empty… The Lord God made man from the dust of the earth, breathing into him the breath of life. However, Einstein also objected to Genesis in physics, i.e. to the big bang.

George Lemaître pictured the very early universe as a “primeval atom”, a cosmic atomic nucleus, with the big bang as its spontaneous radioactive decay. André Deprit, a student of Lemaître, later noted that for the past fifteen years, since he proposed the big bang in 1931, Lemaître had been put on the defensive. The Big Bang (primeval atom) theory:

“…had been held in suspicion by most astronomers, not the least by Einstein, if only for the reason that it was proposed by a Catholic priest and seconded by a devout Quaker [Eddington], hence highly suspect of concordism”.

Actually, Einstein and Eddington both objected to the singularity in Schwarzschild’s solution, i.e. to black holes, and since Lemaître’s primeval atom big bang model had a singularity at time zero followed by rapid expansion, they also objected to this model. Indeed, Lemaître tried many times to convince Eddington of the big bang theory but Eddington remained firm in his objection to the big bang and to black holes.

Einstein thought that the bible was a collection of honorable historical stories. However, since Einstein firmly objected to descriptions such as the wrath of God and God’s flaming fiery, when he is angry, a fire burns within his nose against his people for their disobedience, etc., Einstein considered these descriptions in the Bible as legends which are nevertheless pretty childish.

Gutkind asked in his book:

“Can Judaism remain indifferent to the fact that modern man has to live in a world of machines and of ever-advancing science? But if this is so, why remain a Jew, why not simply be a scientist? What about Einstein and modern physics? Here arises the question as to whether science and technology are enough? Is there not something lacking in the scientific view of life? Perhaps the Jewish vision can redeem the grandeur of science and technology by integrating them with a meaningful life”.

Gutkind also wrote:

“Einsteinian physics is much nearer to truth than the pagan mythologies of nature, more scientific as we call it”.

Einstein objected to the view that Jewish vision has anything to do with his physics and that his physics is much nearer to religious truth as if his theory is derived from concepts of ethics and religion or else, has deep religious and ethical meaning.

And Gutkind glorifies Jewish science:

“We have already pointed to the three outstanding challenges: Einstein’s extreme mathematization of nature, Freud’s unmasking of the psychological substructures, Marx’s unmasking of the superstructures, namely cultures, religions, philosophies, the arts and social orders. The entire superstructure has proved to be utterly vulnerable, and the substructure too is analytically exposed. These three challenges the Jew too will have to face”.

Einstein refused to accept that the Jews are chosen to be in a covenant with God. In Deuteronomy 7:6 we find the biblical famous claim that:

“For thou art a holy people unto the LORD thy God: the LORD thy God hath chosen thee to be a special people unto himself, above all people that are upon the face of the earth”.

To this Einstein responded:

“For me, the Jewish religion like all other religions is an incarnation of the most childish superstitions. And the Jewish people to whom I gladly belong and with whose mentality I have a deep affinity have no different quality for me than all other people. As far as my experience goes, they are also no better than other human groups, although they are protected from the worst cancers by a lack of power. Otherwise, I cannot see anything ‘chosen’ about them”.

The Jewish people to whom I gladly belong and with whose mentality I have a deep affinity,… I 100% agree with the above statement of Einstein.

Einstein explained why he opposed to the idea that the Jews are the chosen people:

“In general I find it painful that you [Gutkind] claim a privileged position and try to defend it by two walls of pride, an external one as a man and an internal one as a Jew. As a man you claim, so to speak, a dispensation from causality otherwise accepted, as a Jew the privilege of monotheism. But a limited causality is no longer a causality at all, as our wonderful Spinoza recognized with all incision, probably as the first one. And the animistic interpretations of the religions of nature are in principle not annulled by monopolization. With such walls we can only attain a certain self-deception, but our moral efforts are not furthered by them. On the contrary”.

Einstein opposed to any kind of “walls” and privileged position —“walls of pride”, “the privilege of monotheism”, “monopolization” — because he was a pacifistic internationalist.

The animistic interpretation of nature is seeing a spirit or spiritual force behind every event or attributing souls and spirits to the animals, sea, thunder etc (“mother nature”). In the Bible, God transforms the animistic views of Israel into a biblical view. He teaches them that the other gods are not gods at all (Isaiah 43:10):

“Ye are my witnesses, saith the Lord, and my servant whom I have chosen: that ye may know and believe me, and understand that I am he: before me there was no God formed, neither shall there be after me”.

He condemns the use of magic, witchcraft, and divination. He shows that suffering is not the result of the spirits or the gods but His sovereign act of bringing people back to Himself.

Einstein opposes to monopolization and he argues that religious monopoly cannot annul animistic interpretations of nature.

On the other hand, Einstein believed in Baruch Spinoza’s nature religion: the natural world is an embodiment of divinity.

See translation of God letter to English

Why was Einstein’s God letter sold for almost $3 million? The considerations in the pricing of an autograph or a holograph letter or document (a document which is written entirely in the handwriting of the person whose signature it bears) are basically the following:

The rarity of the autograph letter, the significance of the holograph letter and the market’s fluctuations. Today there is a booming market in Einstein’s letters and documents. Einstein inspires many people and his autograph letters and manuscripts are the world’s auction leaders in top prices. Age of the documents does not play any role. Indeed, when a certain auction house auctions off Einstein’s autographs, they fetch more than a million dollars but an autograph document from the middle ages is hardly worth $2000.

In February 1938, Allan Devoe, an autograph dealer, published the article, “The Scrawls of the Great Go to Market” (Autographically Speaking) in The Rotarian. He discussed the characteristics of the autograph market and why are some letters sold for a high price and others for a low price. Not much has changed since then in the pricing method of autograph documents.

Before I discuss the pricing of autograph documents, I would like to say a few words about evaluating the signatures and autograph letters and documents. There are individuals who fabricate documents. Howard C. Rile explains in his paper, “Identification of Signatures” that a careful scientific examination can reveal much of the fraudulent work. He gives several examples. For instance, two examples: an individual fabricated a wide range of documents supposedly prepared in the 1880s. Careful examination revealed much of his fraudulent work: while he did duplicate the components of the ink used in the time period, he needed to artificially dry the ink. In doing so, he created a pattern on the ink that, when examined microscopically, was found to be different than the ink lines that had dried normally over the years. Another document involving a supposed relationship between president John Kennedy and Marilyn Monroe was found to be bogus because the typewriter used was not commercially available until three years after the date on the documents in question.

Now, let us discuss the pricing of autograph documents and the pricing of Einstein’s documents. The considerations in the pricing of an autograph document are the following:

(1) The rarity of an autograph:

Allan Devoe writes:

“The reader, unaccustomed to the oddities of autograph dealing, may now become a little dizzy at the information that a personal holograph letter written by the late President Warren G. Harding, would have been cheap at $250! … You may readily acquire, if you are so minded, an enormous and most imposing document signed by the great Bonaparte for the price of a couple of tickets to a musical comedy, but it is rarely indeed that a note from the pen of Oscar Wilde can be purchased as cheaply. …

There are reasons for these price paradoxes and traceable causes for the fantastic fluctuations of the market. In part, of course, autograph prices are governed – like the prices in all other businesses – by laws of supply and demand. The catch is in the supply end.

Original documents signed by Napoleon are inexpensive for the simple reason that the Little Corporal was one of the most prolific document signers who ever wielded a quill. Military decrees and state pronunciamentos [political manifestos] flowed from his desk by the ream [500 sheets of papers] and the ton [400 reams, i.e. 200,000 sheets of paper]. …

Every autograph dealer worthy of the name either has in his files or can pick up at the drop of a hat any required quantity of yellowing papers and parchments signed “Bonaparte” or “Nap” (the Emperor used the signatures quite indiscriminately). But he is a lucky dealer indeed who can find for his files a holograph letter by President Harding, and he is an affluent collector who can buy it. Why?

[Harding was] the ex-editor of [The] Marion [Star], Ohio, [and] became addicted to the typewriter early in life. Longhand was an abominable chore to him. Result: Harding handwriting is superlatively rare and the price skyrockets. Every autograph collector who goes in for “sets of Presidents” must, of course, have a “Harding … autograph letter signed” … and he must pay through the nose for it. …”

As to rarity. Einstein penned many handwritten letters. He hardly saved any early letters but later, other people tended to save his, for obvious reasons. Thus, Einstein’s handwriting is not superlatively rare. So why do we pay so much for an Einstein autograph? Because of the significance of the autograph.

(2) Interest or significance of an autograph:

Allan Devoe writes:

“Thus you can buy a George Washington item for as little as $60, and you can also pay $6000 for one. The important question, in considering an autograph letter or document, is whether it reveals the personality of its author, whether it constitutes a new historical sidelight. …”

On March 7, 2018, an Einstein letter written in 1298 on the theory of relativity fetched $100,000 at Jerusalem auction but the Einstein “God letter” fetched $3 million dollars. People seem to be especially interested in Einstein’s religious feelings and his approach to religious issues, which reveal his personality.

A four-page holograph, i.e. a handwritten letter signed “Albert”, which Einstein wrote to his close friend Michele Besso in 1916 on gravitation, brought $125,000. In this letter, Einstein expresses his delight in his work, his relish for a new theory, his sense of elevation when grasping at fundamental truths — which he expresses as “getting closer to God”.

Thus, when Einstein spoke about his general relativity and said he was getting closer to God it was not sold for a million dollars or two because the letter did not have the title “God Letter” and it, therefore, did not explicitly reveal the personality of Einstein.

(3) Different kinds of autograph documents:

Allan Devoe writes:

“The lowest form of autograph is a plain signature; there is hardly any sign of earth (excepting that of one Button Gwinnett, one of the American signers of the Declaration of Independence) which is worth more than a few dollars. The highest form of holograph is a lengthy manuscript of holograph document of historical importance. You can buy a simple signature of Lewis Carroll for almost nothing: the original manuscript of his Alice in Wonderland brought $52,000.”

Sotheby’s is asking $3500 for the photograph below, signed by Albert Einstein and dated 1933. This is the pre-sale estimated value of the photo:


How much this photo will be sold for?…

Two handwritten notes penned by Einstein have been sold at an auction for a combined $1.8 million — hundreds of times their pre-estimated sale value.

Last year, a handwritten in German by Einstein for a Japanese deliveryman was sold at an auction in Jerusalem for $1.56 million. The signed note was written in 1922, shortly after Einstein won the Nobel Prize for Physics, on the stationery of the Imperial Hotel Tokyo. It reads:

“A calm and humble life will bring more happiness than the pursuit of success and the constant restlessness that comes with it”.



The letter had a pre-sale estimated value of $5,000-$8,000.

The second note was sold for $240,000 and is even more succinct:

Where there’s a will, there’s a way.

The auction house had expected to get an estimated $1,000 for the one-line missive:

one line missive

One-line missive

The description of the items:

“In October 1922, Albert Einstein took a trip to Japan to deliver a series of lectures. While traveling from Europe to Japan he was informed by telegram that he will be awarded the Nobel Prize of 1921. Einstein decided to continue his journey according to his original plan, and he was absent from the ceremony in Stockholm in December.

The news of the Nobel Prize winner’s arrival in Japan spread quickly, and when he arrived he found himself being welcomed by thousands of people flocking to see him.

He was impressed but also a little embarrassed by the publicity he received and while he was staying at the Imperial Hotel in Tokyo he tried to record his thoughts and feelings on paper. When a messenger came to his room to give him something, Einstein did not have a tip available, and he decided to make the most of his new exalted status and give the messenger two of his writings. When he gave him the articles he told the messenger to keep them, as their future value may be much higher than a standard tip”.

(4) More age has absolutely nothing to do with the value of an autograph.

Allan Devoe writes:

“Any autograph dealer or collector will … swap with a happy heart your 20th Century [John Calvin] Coolidge holograph for his 14th Century parchment deed. …

They are inexpensive, not because they are unwanted or because they lack historical interest, but simply because the monks and the abbots of medieval times were great hands with the pen. … they have glutted the market”.

Einstein’s autograph “God Letter” brought over three million dollars but a 14th Century Medieval Manuscript worth no more than $500.

Indeed, a rare book buyer has written in 2015:

“So, what is the value of a document like this from the 14th century? Surprisingly, they can be collected for rather modest sums. …

True, this one is perhaps a bit earlier than some of the examples listed above (and dates to the early part of the 14th century). However, at auction it would at most reasonably fall into the $400-500 range and perhaps a bit less as it is missing its original hanging seal.

To me that is rather remarkable: this small and ephemeral document has escaped the ravages of time for 700 years and is only worth approx. $500?”

Einstein’s “God Letter” worth more than a document which “has escaped the ravages of time for 700 years”. This is a result of hero-worship.

(5) Leaders in top prices:

Allan Devoe writes:

“The autograph market, like the stock market, is subject to sudden and obscure maladies, and its price graph now and then swoops and dives in the same catastrophic manner. Twenty years ago there was a booming market here in European material. Autographs of European artists, composers, statesmen, and the like were at a premium; … And then, quite suddenly, European material slumped. Gone was the market for European autographs; in its place came a boom in American. …”

Today leaders in top prices are Hollywood actors’ material, autograph letters and manuscripts of scientists and celebrities.

In 2013 Christie’s sold a copy of Newton’s Principia from 1687 for almost 3 million dollars.

In 2017 Steve Jobs signature on a newspaper was sold for 50,000 dollars.

In 2003 Christie’s auctioned off an autograph music manuscript signed by Mozart and got $318,000 dollars.

Several months ago, Christie’s sold Darwin’s autograph manuscript for 112,500 dollars.

Judy Garland’s Ruby Slippers are worth three million dollars.

The leader in top prices is Leonardo da Vinci. In 1994 Leonardo’s Codex Hammer was sold for $30,802,500.


First appeared on Quora.

אין לתרגם את הפוסט לעברית ללא רשות ואין להשתמש בו בהרצאות

Time Travel into the Past: How can a wormhole be transformed into a time machine?

In 1988, Kip Thorn and his students published a technical article about traversable wormholes (see here). In their article, they conjectured that if the laws of physics were to permit traversable wormholes they would probably also permit such a wormhole to be transformed into a time machine, which violates causality. This would allow for travel into the past. More than 25 years later, Thorn was involved with the movie Interstellar from its inception and he helped the producer Christopher Nolan and others weave science into the film’s fabric. However, according to Thorn, today almost thirty years have gone by and, the preponderance of evidence still suggests that traversable wormholes are an impossibility.

Wormhole creation would be governed by the laws of quantum gravity. A seemingly plausible scenario entails quantum foam (“foamy” topologies of space-time on length-scales of the order of the Planck length 1.3 x 10-33). One can imagine an advanced civilization pulling a wormhole out of the quantum foam, enlarging it to classical size, and threading it with exotic matter to hold it open. Of course, says Thorn, we do not understand the quantum gravity laws that control the foam, the pull, and the stages of enlargement. Moreover, we do not understand exotic matter very well either.

Thorn suggests the following thought experiment. I am paraphrasing here. Suppose both California desert and Dublin are connected by a wormhole. The two mouths of the wormhole are synchronized. Since the California desert and Dublin are not moving with respect to each other, I in the California desert can synchronize my clock with that of my friend in Dublin. Hence clocks remain synchronized inside the throat and between the two mouths regardless of the outside time. While a wormhole is a single unit connected by a throat, its two mouths open onto places that are totally different from each other. The wormhole throat itself is a single reference system. According to special relativity, we can, therefore, synchronize clocks in this reference system.


Mouth in California Desert                             Mouth in Dublin

The images seen through a wormhole’s mouths. Photos by Catherine MacBride and Mark Interrante.

Both mouths look like crystal balls. When I look into my California desert mouth, I see a distorted image of a street in Dublin. That image is brought to me by light that travels through the wormhole from Dublin to California, rather like light traveling through an optical fiber. When you look into your Dublin mouth, you see a distorted image of the trees in the California desert.

In Thorn, Kip, The Science of Interstellar, W. W. Norton & Company, p. 133.

Imagine a situation where the wormhole has been created by an advanced civilization in some future year, say 3000. On January 1, 3000 the wormhole’s two mouths, A and B, are at rest with respect to each other. Subsequently, mouth A remains at rest in Dublin, while mouth B, in California desert, accelerates to near-light speed, then reverses its motion and returns to its original location. Suppose the advanced beings produce this motion by pulling on mouth B gravitationally. I, therefore, take mouth B for a round trip and travel outside the wormhole with mouth B moving at relativistic velocities. Mouth A will not have moved since nothing has been pulling on it. The two mouths A and B of the wormhole are moving with respect to each other, and the wormhole throat now has mouth A at one end and a hole B at the other end. Hence the geometry of the wormhole throat does not change during the whole trip of mouth B so that the length of the wormhole’s throat remains fixed.

Since the two mouths move with respect to each other, time dilation creates a time difference between the clocks next to each mouth. The motion of the mouth is like that of the twins in the standard special-relativistic twin paradox. Outside the wormhole, mouth B ages less than mouth A, but inside the wormhole, the clocks are still synchronized; mouth A and hole B are at rest relative to each other and therefore, both entrances of the wormhole will age equally. If I have traveled with mouth B at close to the speed of light, I might find myself ensconced for many years in the future after returning to my original location in California desert.

I finally return to California desert with mouth B and find I have aged only one day (namely, on the date January 2, 3000, as measured by my own time – my proper time). Suppose that I find myself, on returning to California desert, to have arrived on, say, January 1, 3010 (according to the standard special-relativistic twin paradox). This is the date that appears on the calendar on the wall of an abandoned creepy cabin in the desert. Stepping through mouth B in California desert on January 1, 3010 and emerging out of A in Dublin will take me back in time. I will emerge from A and find that it is January 2, 3000. This is so because it is as seen from Dublin and my clock remains synchronized with the clock in mouth A. Recall that I have aged only one day during the trip (on my subsequent return to California desert, the date was January 2, 3000, as measured by my own time).

Consequently, by traversing the wormhole from mouth B to mouth A, one can travel backward in time, namely one can traverse a closed timelike curve. The same relative aging that occurs in the twin paradox produces, here, closed timelike curves that loop through the wormhole. However, that traveler could never go further back into the past than the year 3000. No traveler can ever go further back in time than the original date of creation of the wormhole.

Fur further reading see my book: General Relativity Conflict and Rivalries: Einstein’s Polemics with Physicists.

How do science fiction writers explain traversable wormholes? In The Strange Days at Blake Holsey High science fiction television program, a group of science students (science club) at a private boarding school have discovered that their science teacher’s office floor has a traversable wormhole that connects major time periods and therefore deposits a traveler back in time to October 4, 1987, April 11, 1977, and October 4, 1879 (when Blake Holsey High and the wormhole were founded). One of the students is getting sucked into the wormhole:






Albert Einstein and the old white boys’ club

Yesterday the Hebrew University in Jerusalem asked on the official Albert Einstein Facebook wall:

“Did you know? Einstein was the first Chairman of the Hebrew University of Jerusalem’s Academic Council and was on the University’s first Board of Governors. Support the University that Einstein loved on July 24th, on the 1st annual Global Giving Day. Every donation counts. Help fulfill Einstein’s legacy today”.


And the university also asked the other day:


How can students answer these questions if they haven’t learned about Einstein’s legacy and theories? Over the past decade, the Hebrew University in Jerusalem has not offered any course on Albert Einstein’s legacy and theories (relativity, unified field theory, etc.).

I am an expert in Einstein studies; the Hebrew University in Jerusalem awarded me two extraordinary doctoral prizes (Bar Hillel and Edelstein) for my thesis on Albert Einstein. I could teach this topic but a decade ago the university abruptly closed my course and there were no other professors that offered the same course on Einstein’s legacy. That field was much a “unicorn”.

It was not until a decade after the university canceled my course that people realized that the program for the history and philosophy of science at the Hebrew University in Jerusalem was actually dependent on Einstein’s legacy.

When history and philosophy both were living under the same roof, historians were mumbling their medieval and early history of science and philosophers were discussing quantum and statistical mechanics. I’ve told them many times that Einstein was the Hebrew University founder and therefore the university has to offer a course on Albert Einstein’s legacy, but people in the program for the history and philosophy of science wouldn’t listen. You can lead a horse to water but you can’t make it drink…

If we try to bring out the circumstances that were going on in the program for history and philosophy of science then when we look beneath the surface the program was dominated by the good ole boys club. The program was about to flourish but then came the 2018 closing or redefinition of the program (you can call it whatever you want) in terms of two or so courses in the department of philosophy at the Hebrew University in Jerusalem; and the realization that more than a decade of great legacy is falling apart. And now, unfortunately, it’s a lame duck, almost a dead duck.


Total Eclipse of the Sun and Deflection of light Rays

According to Einstein’s prediction, that is to say the deflection (bending) of light rays in the gravitational field of the Sun: those stars closest to the limb of the Sun during the eclipse are found to be displaced slightly by amounts that are inversely proportional to the distance of the stellar image from the Sun. The light from a star close to the limb of the Sun is bent inward, toward the Sun, as it passes through the Sun’s gravitational field. The image of the star appears to observers on the Earth to be shifted outward and away from the Sun.

The Universe and Dr. Einstein by Barnett (with forward by Einstein)


In 1915 Einstein calculated the angle between the actual path of the starlight, the true position of the star, and the apparent path of the ray of light, the star seen during the eclipse. He obtained a result: 1.7” (seconds of arc).

However, in 1911 and 1913 he derived a different result, actually he had obtained half of this result: 0.84” (seconds of arc).


Einstein’s letter to George Ellery Hale which illustrates starlight being deflected by the gravity of the Sun. Oct. 14, 1913. The Huntington Library, Art Collections, and Botanical Gardens. Here

During a total eclipse of the Sun, it is possible to take pictures of the field of stars surrounding the darkened location of the Sun, because during its occultation, the light emanating from the Sun does not interfere with visibility of fainter objects.

In the eclipse expedition of 1919 Sir Arthur Stanley Eddington and Charles Rundle Davidson went to find whether they could verify Einstein’s prediction of the deflection of starlight in the gravitational field of the Sun. Eddington and his assistant went to the island of Principe off the coast of Africa while Davidson and his assistant went to Sobral in North Brazil. In presenting their observations to the Royal Society of London in November 1919, the conclusion was that they verified Einstein’s prediction of deflection at the Sun’s limb to very good accuracy.


Sir Arthur Stanley Eddington. Source (internet, unknown). If anyone knows the source please leave a comment.

The pictures taken during the solar eclipse are compared with pictures of the same region of the heavens taken at night. An astronomer compares his photographs taken during a total eclipse of the Sun with check plates, that is to say with comparison plates of the same stars (the eclipse field) when the Sun has moved away.

In 1919 Eddington examined the check field of stars that was photographed at Oxford Observatory. It was nearly the same as that of the total eclipse field of stars, which was photographed at the small island belonging to Portugal, Principe, at the same altitude as in Oxford in order to ensure that any systematic error, due to imperfections of the telescopes or other causes, might affect both sets of plates equally. There were differences in scale though between the compared photographs. Eddington determined these differences of scale between Oxford and Principe. The primary purpose of the comparison was to check the possibility of systematic errors arising from the different conditions of observation at Oxford and Principe.

After comparing the Oxford and Principe check plates, Eddington concluded that the Oxford photographs show none of the displacements which are exhibited by the photographs of the eclipse field taken under precisely similar instrument conditions. Eddington inferred that the displacements in the latter case could only be attributed to presence of the eclipsed Sun in the field and not to systematic errors.

Eddington’s four values of deflection in Principe were: 1.94, 1.44, 1.55 and 1.67 seconds of arc. He calculated the mean of these to be: 1.65” (seconds of arc). He added corrections due to experimental errors and due to the fact that the four determinations involved only two eclipse plates. The final Principe result was: 1.61±0.30 seconds of arc. Eddington calculated the final Sobral result: 1.98±0.12 seconds of arc and concluded: “They evidently agree with Einstein’s predicted value 1.75 seconds of arc.



Photos taken at the Science Museum, London. Eddington’s original negative photo.

Final confirmation of Einstein’s prediction of the deflection of light near the Sun came from William Wallace Campbell and his assistant Robert J. Trumpler at the eclipse of September 22, 1922 in Australia. Campbell and Trumpler also compared the eclipsed plates with the photographs of the same stars taken at Tahiti four months before the eclipse. The observations with the first camera led to a stellar deflection of 1.82±0.15 seconds of arc for the light deflection at the Sun’s limb. The combined observations from the two instruments used by Campbell and Trumpler gave the value of 1.75±0.9 seconds of arc for the deflection at the Sun’s limb, which is in excellent agreement with the value predicted by Einstein’s theory.


For more photos see here.

For more information on the history of eclipse expeditions and Einstein’s general theory of relativity see my books:

General Relativity Conflict and Rivalries: Einstein’s Polemics with Physicists


Einstein’s Pathway to the Special Theory of Relativity (2nd Edition)






My new paper on Einstein and general relativity

didMy new paper on Einstein and the general theory of relativity:


My new book: Einstein’s Pathway to the Special Theory of Relativity (2nd Edition)


My new book Einstein’s Pathway to the Special Theory of Relativity (2nd Edition) is coming out in August 2017.

My new book is a comprehensive monograph on Albert Einstein’s Odyssey to Special and General Relativity.

It is the second edition of my first book, Einstein’s Pathway to the Special Theory of Relativity:


The book brings together the most recent studies regarding the discovery of Special Relativity between 1895 and 1905 and pertaining to the genesis of General Relativity between 1905 and 1918.

The book encompasses an in-depth historiographical analysis of Einstein’s theory of relativity and Einstein’s own derivations and philosophical perspectives of Einstein’s work.

The first chapter provides a narrative of Einstein’s early life until 1914 without resorting to hagiography.

The second chapter discusses Fin de siècle physics.

The third chapter deals with Einstein’s path to the Special Theory of Relativity and Henri Poincaré’s Dynamics of the Electron.

The fourth chapter focuses on the genesis of the General Theory of Relativity from 1905 until approximately 1922.

The fifth chapter centralizes on Einstein’s methodology and creativity, and on Poincaré’s philosophy.

The final chapter analyzes the sources.

The book is 660 pages long, a comprehensive study of Einstein’s discovery of special and general relativity and of Einstein’s cosmology.

I drew the cover of the book.

Einstein loved sailing and he owned a sailboat, which he called Tümmler (porpoise).


The cover of my new book Einstein’s Pathway to the Special Theory of Relativity (2nd Edition) shows Einstein, the young patent clerk wearing the patent office suit, the young man and the sea.