Einstein's mistakes

Everyone makes mistakes sometimes. But the mistakes of the great physicists are especially instructive: in three noteworthy cases Einstein seriously failed to assess the importance of his findings or concluded that his valid discovery was incorrect. The ideas he conceived and then plundered later proved to be essential to the development of modern cosmology. The gravitational cooling phenomenon is used to map galaxy clusters; Gravitational waves open a window for us to the first moments of the Big Bang; The cosmological constant may prove to be a determining factor in the evolution of the universe/Lawrence M. Kraus

The article was published with the approval of Scientific American Israel and the Ort Israel network

Although endowed with extraordinary intellectual skills, Einstein repeatedly failed to understand the significance of some of the most important ideas he himself conceived or failed to recognize their importance and far-reaching effects.

Einstein did not recognize the importance of the phenomenon of gravitational relaxation, initially doubted the reality of gravitational waves and failed to predict the expansion of the universe.

Examining the mistakes Einstein made allows us to follow his way of thinking and understand how it developed, and it sheds new light on the history of three of the most fascinating research fields in modern cosmology.

And all human beings, Einstein also made mistakes sometimes, and like many other physicists, he sometimes made his mistakes public. Most of us prefer to forget about those embarrassing incidents where we were tortured along the way. But in Einstein's case even the mistakes are worth noting. They allow us to follow his way of thinking and understand how it developed, and thus deeply understand the transformations in the conception of the universe in science. Einstein's mistakes also reveal the challenges facing those at the forefront of scientific research. When we are at the forefront of human understanding, it is difficult to know if the ideas we put down in writing actually reflect actual phenomena, and if a new revolutionary idea that flashed in our minds will create deep insights or fade away.

Over the years, Einstein, the man who dared to break through and redefine the concepts of space and time, underestimated the value of his discoveries and challenged his own ideas incredibly often. These ideas, which Einstein misjudged, are today the basis of three vibrant and fruitful fields of cosmological research: gravitational repulsion, gravitational waves, and the accelerated expansion of the universe.

Einstein's distorted lenses

In the field of gravitational repulsion, Einstein's critical mistake was that he underestimated the value of one of the most famous results of his thought: the prediction, derived from the theory of general relativity, that the path of a light beam would be bent under the influence of a gravitational field. In December 1936, Einstein published in the journal Science a short article entitled "The lens-like effect of a star on the deflection of the path of light rays in its gravitational field". The article opens with a condescending comment of the kind that can no longer be found in today's academic literature: "Some time ago R. V. Mandel [Czech engineer] visited my home and asked me to publish the results of a small calculation I made at his request. I hereby comply with his wish."

The same "small calculation" examined the possibility of an extreme deviation of the path of light rays under the influence of gravity. From this it was a short way to the conclusion that if there is a body with a sufficiently large mass that stands in the way of light rays that originate in an object located at a great distance behind the blocking body, and the light rays pass close enough to it, the gravitational field of the blocking body will bend the path of the light rays to such a great extent that they They will return and gather [after passing by him]. This will result in the creation of an enlarged image or several images of the distant source, in a manner similar to the bending of light rays as they pass through a lens, hence the name gravitational distortion given to the phenomenon. The dimming phenomenon has become one of the most important means of observation in modern cosmology, as it allows us to learn about the distribution of mass in the universe even when matter is invisible.

However, Einstein did not recognize the importance of the aging phenomenon and did not insist on its far-reaching effects. In fact, in an article he wrote in 1936, Einstein stated that the splitting of the image of the source object into several images caused by the passage of light near a star is expected to be so marginal that it will not actually be possible to measure it. There is no doubt that this statement explains the tone of self-deprecation in the introduction to the article. Technically, Einstein was right, but apparently it did not occur to him that stars are not the only objects that can cause such a bending of light.

The fact that Einstein was not aware of the importance of the phenomenon is even more surprising in view of the enormous impact of the discovery of gravitational repulsion on his reputation as a scientist. The deflection of the path of light rays by an object with mass was one of the basic predictions of general relativity that could be confirmed by observation. A scientific expedition led by the physicist Arthur Eddington in 1919 observed a solar eclipse and determined that light rays originating from the stars are indeed deflected from their orbits when they pass near the sun, just as Einstein predicted. The news of the confirmation of the prediction appeared in the headlines of newspapers around the world, and the dramatic story of a British delegation confirming the work of a German scientist immediately after the end of the First World War also undoubtedly stirred the imagination of many. Ben Lil Einstein became a famous figure in the whole world and won a scientific fame that has not been known since.

And there is another interesting side to the story. It turns out that a few years earlier, in 1911, Einstein made the exact same calculation of the bending of light rays under the influence of gravity. But even then he did not recognize the cosmological importance of the phenomenon. And worse than that, he made an almost fatal mathematical error: he made his calculation based on an early version of the theory of general relativity, which predicted that the amount of deflection of light under the influence of gravity is only half of the true value. A scientific expedition was supposed to examine the deflection of starlight rays as they passed near the sun during a solar eclipse in 1914, but the plan was canceled with the outbreak of the First World War. Fortunately for Einstein, the observation was never made. Had it been conducted, the first prediction of the theory that Einstein then developed in an attempt to explain the phenomenon of gravity would have contradicted the data. How this would have affected his life and the history of science in the years that have passed since then - no one knows.

After the publication of his article in 1936, Einstein wrote a charming letter to the editor of Science in which he again misjudged the importance of the research: "I would like to thank you for your cooperation in publishing this little article, which Mr. Mendel extorted from me. The article doesn't have much value, but it makes the poor guy happy."

What Einstein missed was that stars form galaxies. The brilliant but short-tempered astrophysicist, Fritz Zwicky of the California Institute of Technology, made this very clear in an article he published in the journal Physical Review a few months later. The clumping effect of individual stars can be so weak as to be undetectable, Zwicky wrote, but clumping that forms giant galaxies containing perhaps a hundred billion stars may well be observable.

Zwicky's article, published in 1937 and only one page long, was impressive in its vision. In the article, Zwicky was ahead of his time by proposing three uses for the gravitational cooling phenomenon, almost all the uses that astronomers have actually applied in the decades that have passed since then: putting the theory of general relativity to the test; Using the blur that galaxies create to magnify more distant objects that cannot otherwise be seen; and using Idus to measure the masses of the largest structures in the universe. Zwicky did not foresee a fourth application, which turned out to be just as important: using the eddies that form galaxies to study the geometry and evolution of the universe at its most massive scales.

It is hard to imagine a greater miscalculation of the significance of a physical calculation ever made.

Simulated singularity states pose question marks

Einstein understood at an early stage that general relativity predicts the existence of gravitational waves, that is, fluctuations in space-time, but for a while he retreated from his original and correct claims regarding their existence. Today, the discovery of gravitational waves that originate in the collision between black holes and exploding stars or in the era of cosmic inflation (where the universe underwent a process of accelerated expansion immediately after the big bang) is expected to open a new vast window into the universe.

Einstein first observed the existence of gravitational waves in 1916, shortly after completing the formulation of general relativity. Although the mathematical formulas describing the phenomenon are very complicated, the line of thought that guided Einstein is simple and clear. According to the laws of electromagnetism, the movement of an electric charge back and forth creates a periodic disturbance that manifests itself as an electromagnetic wave, such as a light wave. Similarly, if we move a pebble on the surface of the water in the pond, we will cause water waves to form on the surface of the pond. Einstein proved that every mass warps the space around it, and hence a moving mass will create an analogous periodic disturbance in space. But then Einstein began to doubt the physical reality of such disturbances.

Einstein expressed his doubts in an article he submitted in 1936 to the Physical Review (the same prestigious American journal that published Zwicky's article on gravitational repulsion). The story of the mistake he made and the way he later stood up for his mistake sounds almost like a comedy of errors. Einstein had left Germany and immigrated to the United States three years earlier, and apparently still had not gotten used to the way things were done in the new world. Close to the submission of his article entitled "Do Gravitational Waves Really Exist?" Einstein sent a letter to his colleague Max Born, in which he wrote: "Together with a young partner, I came to the interesting conclusion that gravitational waves do not exist, even though we assumed their existence with certainty in a first linear approximation. This proves to us that the nonlinear field equations of relativity can teach us or, in fact, limit us more than we thought so far."

The article that Einstein submitted to the Physical Review is no longer available, and was never published in the journal. According to standard procedure, the journal's editor sent the paper (written by Einstein with Nathan Rosen, who was then his research assistant at the Institute for Advanced Study at Princeton University in New Jersey) for peer review. A critical appraisal received from an anonymous reviewer was forwarded to Einstein's review for comments. Einstein was astonished to find that his work had been criticized, as this policy was not acceptable in the German journals he used to submit articles for publication in the past.

In response, Einstein wrote an arrogant letter to the editor with the following language: "We (Mr. Rosen and myself) sent you our manuscript for publication and did not authorize you to show it to any experts before its publication. I do not find it appropriate to address the comments, which are wrong anyway, of your anonymous expert. Following this event, I prefer to publish the article in another journal." This was the last time Einstein submitted an article for publication in the Physical Review. It also seems that he did not bother to read the report written by the appreciative reader, the great American cosmologist Howard Percy Robertson, who correctly explained the critical error in Einstein's way of thinking.

Einstein and Rosen tried to write a formula that would describe planar gravitational waves (waves with a planar wave front and a constant wavelength, such as waves created in a pond when a stone is thrown into it from a long distance), but in doing so they encountered a singularity: a point where the values ​​become infinitely large. This illogical result led them to conclude that such waves cannot be real. In fact, Einstein misunderstood the mathematics of the theory he himself had devised. According to general relativity, nature does not depend on how scientists choose to define coordinates in space. Today we understand that many apparently strange results obtained from solving the equations of relativity are false results of using the wrong coordinate system. For example, a black hole is surrounded by an imaginary envelope known as an event horizon, according to the definition of which, everything inside is subject to the influence of the black hole's enormous gravity and cannot break free and escape outside it. When trying to describe the geometry surrounding a black hole, many quantities, including distance and time, appear to become infinite as they cross the event horizon. But these infinite sizes do not agree with the laws of physics. Indeed, in another coordinate system, defined in terms of the movement of light in space, they simply disappear. The same is true for gravitational waves. There is no single coordinate system in which plane gravitational waves can be described without seemingly singular points appearing, but these are not real. If we use two different and overlapping coordinate systems, the singularity points will disappear.

Einstein, who was still convinced of the rightness of his arguments, submitted his article for publication in the journal of the Franklin Institute, but even before the article saw the light of day he was also aware of his mistake and informed the editors of the journal that he found mistakes in it. The final version of the article, which was finally published under the title "On Gravitational Waves", presents a solution to the equations of general relativity using a different coordinate system - a system suitable for describing cylindrical rather than planar gravitational waves in which singular points do not appear, just as Robertson suggested.

How did Einstein finally reach the correct conclusion? According to Leopold Infeld, Einstein's research assistant in a later period, Robertson approached him about his venture and very politely explained to him what the error was in the original paper and what the possible solution was. Infeld passed the explanation on to Einstein. Apparently, Robertson never disclosed that he was the evaluative reader of the paper, and Einstein for his part never mentioned the evaluation report again. In the end, Einstein never published his erroneous heretical claim about the existence of gravitational waves only thanks to the intervention of a particularly alert and thorough evaluator.

Einstein had a little less luck with black holes. The singularity in the event horizon, which does not conform to the laws of physics, was a mystery to him, and since he did not find a solution to it, he assumed that it could not be real. Einstein claimed that the conservation of angular momentum would cause the particles that make up an object to stabilize in orbits with a finite radius, thereby ruling out the possibility of the formation of an event horizon. He never recognized the existence of black holes as physically real objects.

A brilliant mistake?
Einstein's most famous mistake is the change he made in the theory of general relativity to allow the existence of a static, non-expanding universe. This mistake became widely known because, as is said, Einstein himself later admitted that the idea was a "serious mistake". In 1915, when Einstein completed the formulation of the theory of general relativity, it was widely believed that our galaxy, the Milky Way, was surrounded by infinite, static and eternal space. But Einstein understood that according to the theory of general relativity (and also according to Newton's theory), the force of gravity exerted by matter is a universal force of attraction, and this has the effect of ruling out a static solution. According to the theory, gravity was supposed to cause the matter in the universe to collapse in on itself.

In 1917, Einstein published an article entitled "Cosmological considerations in the theory of general relativity", in which he added to the equations of general relativity a constant term that verifies that the universe is static. This "cosmological constant" was supposed to represent a force of repulsion that acts in the opposite direction to the force of gravity throughout the entire universe. Einstein hoped that he would "balance gravity". From a physical point of view, there was no justification for adding this organ. Its sole purpose was to prevent the material from collapsing.

In the ten years that have passed since the addition of the cosmological constant, evidence has begun to accumulate that, after all, the universe is not static. At first Einstein rejected this possibility. The Belgian physicist who was also a Catholic priest, Georges Lemaître, developed a model of an expanding universe, which included a description of a sort of big bang, as early as 1927, two years before Edwin Hubble published his groundbreaking paper documenting the moving away of galaxies from each other. Lemaître told how Einstein scolded him: "Your calculations are correct, but your physics is terrible!"
Einstein later retracted his objection. He visited Hubble at the Mount Wilson Observatory, near Pasadena, California, and watched the sky through his telescope. In 1933, Einstein even praised Lemaître's cosmological theory with these words: "It is the most beautiful and satisfactory explanation of the creation story that I have ever heard."

Einstein understood very well that if the universe is expanding, there is no longer a need for a cosmological constant to ensure the staticity of things. Back in 1919, Einstein wrote that the constant "severely damages the formal beauty of the theory". This matter is also reflected in the oft-quoted anecdote from George Gamow's book, "The Line of My World: An Unofficial Autobiography." And so Gamov recounts: "In a much later period, when I discussed cosmological problems with Einstein, he commented that adding the cosmological constant was the most serious mistake of his life."

In retrospect, Einstein was completely wrong when he thought the cosmological constant was worthless, but adding the constant to the equations was a serious mistake for two reasons: if he had the courage to admit it, he would have recognized the fact that the contradiction between general relativity and the static universe view is actually a prediction of his theory. In the days when no one thought the universe was dynamic on its vast scales, Einstein could have predicted the expansion of the universe rather than reluctantly accepting the idea at a later stage.

But adding the cosmological constant was also a mistake in a deeper sense. To put it simply, the constant could not fulfill its intended role: it could not enable the static universe that Einstein intended. The mistake was partly due to the fact that in this case too, Einstein used a coordinate system that did not fit his calculations. But his perception was also wrong from the point of view of physics. Even if it is possible for a short time to balance the pull of gravity with the repulsion force represented by the cosmological constant, any disturbance, even the smallest, will cause an accelerated expansion or collapse of the universe. With or without a cosmological constant, the universe must be dynamic.

Ultimately, the cosmological constant proved itself and survived over time, unlike the limited astronomical knowledge it inspired. Although the constant was an improvised addition to the equations of general relativity, physicists now understand that when viewed from the perspective of quantum theory, its existence corresponds to the existence of energy that might be found in empty space. In fact, quantum physics requires the existence of such a cosmological constant. Moreover, the energy content of empty space is not just a theoretical concept. In one of the most amazing measurements in recent years, made in 1998, two teams of astronomers discovered that the universe is expanding at an accelerated rate, and that its accelerated expansion is caused by something that appears to act just like the cosmological constant. In this context, it can be said that Einstein erred twice: once when he raised the idea of ​​the cosmological constant for the wrong reasons, and a second time when he dismissed the idea instead of investigating its meanings in depth.

The mistake that Einstein never admitted
Einstein's mistakes were intellectually fruitful, as they all stemmed from revolutionary and controversial ideas about the fundamental laws of physics. The same is also true for the mistake that is generally considered to be the most serious of all his mistakes: his refusal to see quantum mechanics as a fundamental theory of nature.

Although it was Einstein who laid the foundations of quantum mechanics in his explanation of the photoelectric effect (which later earned him the Nobel Prize in Physics), he never completely abandoned the worldview of classical physics. The idea that the location of a particle is a matter of probability or the possibility that a particle can have an instantaneous effect from a great distance on another particle seemed absurd to him, although his views on the questions raised by quantum theory were much more complex than is commonly thought [see the article "Is the universe random?" by George Moser, Scientific American Israel]. Einstein devoted the last decades of his life to an effort to integrate the gravitation and electromagnetic equations into one classical theoretical framework, known as unified field theory.

During his efforts to formulate such a unified theory, Einstein's attention was drawn to a wild hypothesis put forward by the German mathematician Theodor Kaluza in 1921 and developed a few years later by the Swiss physicist Oskar Klein. The two proposed that if the universe has five dimensions, the three known dimensions of space, the dimension of time and a fifth dimension "coiled within itself" and invisible, we can formulate one comprehensive explanation of both gravity and electromagnetic force. What Einstein particularly liked about this theory is that it is completely classical. Klein showed that in the proposed model the apparent quantization of electric charge could be the result of electromagnetism reflecting the geometry of the closed circular form of the fifth dimension.

Einstein's efforts to formulate a unified field theory did not go well, but the ideas he put forward, even if flawed, led to important breakthroughs in this case as well. Kalutza and Klein's idea of ​​extra dimensions, which Einstein adopted and brought up for discussion in the scientific community, was a source of inspiration in the development of the mathematics in higher dimensions used in modern string theory, a popular theory that today tries to integrate general relativity into quantum mechanics. Einstein would have rejected outright the attempt to present general relativity as a theory based on a quantum worldview. But as we have seen, with all his greatness, Einstein was not without mistakes either.

About the writers
Lawrence M. Kraus heads the Origins Project at Arizona State University, serves as a professor in the School of Earth and Space Studies and in the Department of Physics at that university and is a member of the elite club of scholarship-winning academics. Krauss is the author of nine books (including the bestsellers The Physics of Star Trek and A Universe from Nothing) and the producer of the science and logic documentary The Unbelievers.
for further reading

The Origin of Gravitational Lensing: A Postscript to Einstein's 1936 Science Paper. Jürgen Renn, Tilman Sauer and John Stachel in Science, Vol. 275, pages 184–186; January 10, 1997
Einstein versus the Physical Review. Daniel Kennefick in Physics Today, Vol. 58, no. 9, pages 43–48; September 2005
A Cosmic Riddle, Lawrence M. Krauss and Michael S. Turner, Scientific American Israel, December 2004
The Right Way to Go Wrong, David Kaiser and Angela N. H. Krieger, Scientific American Israel, October 2012

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