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

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.


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.