The book “On the Origin of Time”. Stephen Hawking’s Last Theory” by Thomas Hertog, a friend and colleague of Hawking who worked with him during the last 20 years of his life. Based on many conversations with Stephen, the author recalls the scientific development of the great physicist and the development of his ideas. We publish a section of the chapter on how Hawking arrived at his revolutionary hypothesis about the absence of a beginning to the Universe. The crux of Jim and Stephen’s proposal is that the expanding universe has no singularity in the past – the time dimension on its way to the starting point dissolves into a quantum blur. At the bottom of the bowl in Figure 23(b), time has become space. So the question of what might have happened before loses its meaning. “Asking what happened before the Big Bang is like asking what lies south of Antarctica,” Hawking summarizes the meaning of his theory; talking about his quantum cosmology, he called this idea the “no-boundary proposition”.

According to the boundaryless hypothesis, two seemingly contradictory characteristics merge. On the one hand, the past must be finite: time does not extend indefinitely into the past. On the other hand, there is also no beginning – no first moment where time “turns on” in some way. If you were an ant crawling on the surface, looking for the starting point of the Universe, you wouldn’t find it. The cup’s spherical base symbolizes the limits of time in the past but does not mark the moment of creation. In the no-boundary theory, any attempt to determine the true beginning of the Universe fails – the point is lost in quantum uncertainty. From an aesthetic standpoint, there is of course something appealing about the way the no-boundary hypothesis breaks down the mystery of zero time. The bowl at the bottom of space-time looks a lot like a geometric version of Lemaître’s “elementary atom.” According to Hamlet, who said “in a word, lock me up and I will feel like the lord of infinity”, Hawking sees the newly born Universe as the seed of a walnut in his hand.

In July 1983, Jim and Stephen submitted their manuscript, “The Wave Function of the Universe,” for publication in the journal Physical Review. But the fate of the job is difficult. The first reviewer objected to publication on the grounds that the authors had extrapolated clearly incorrectly Feynman’s “synthesis of stories” from quantum theory to the Universe as a whole. Jim and Stephen seek a second opinion. The second reviewer writes that he agrees with the first: the authors’ extrapolation of quantum theory is indeed clearly incorrect. However, he added, the manuscript should be published “because the work is very original.” And that’s what happened. Fifty years after Lemaitre’s 1931 manifesto announcing a quantum approach to the origin of time, Jim and Stephen’s historical discovery transformed his vision into a formal scientific hypothesis.

The universal wave function they introduced sparked a genuine wave of interest in the quantum foundations of cosmological theory; Their work has become a beacon in the search for solutions to “the world’s design conundrum.” Essentially, the no-boundary hypothesis arose from a completely new approach to studying the quantum nature of gravity, which Stephen, along with his first generation of students, developed throughout the 1970s. This so-called Cambridge method is based on the geometric language that Einstein used to describe gravity, but is notable in that it uses curved spatial shapes with four spatial dimensions, no direction of time, instead of time curving according to relativistic space.

In Einstein’s classical theory of relativity, space is space and time is time. More precisely, space and time are combined in a four-dimensional spacetime, which is clearly shown by the diagrams I have presented: from the empty Minkowski spacetime to the black hole geometry of Penrose. But in all these diagrams, space is easy to distinguish from time: the arrow of time is oriented everywhere inside the light cone of the future, while this is not true of the spatial directions . Now Stephen imagined that curved geometries in four spatial dimensions contained the fundamental quantum properties of gravity. Such geometries are called Euclidean geometries, named after the Greek mathematician Euclid, who was the first to systematically study the geometry of spatial dimensions. This is why Stephen’s program is also known as the Euclidean approach to quantum gravity. Geometrically, the conversion of time into space is achieved by rotating the direction of time by 90 degrees. This can be clearly seen in the quantum table, where the “initial” time at the bottom of the bowl begins to “flow” in the horizontal plane, at the same speed as the circularity of space . This “revolution of time in space” is often described as a transition of time into the imaginary region, since mathematically such a rotation corresponds to the multiplication of time by an imaginary number, radical quadratic of negative numbers. Obviously, such an activity devalues ​​the concept of the passage of time. It makes no sense to set the alarm for 7am to catch the morning train. Even a slow process like Brexit happens in real time. “Any subjective conception of time that is tied to consciousness or the ability to measure must end,” Stephen said.

But by bending Einstein’s curved geometries further than anyone had done before and moving from real time to virtual time, he found a surprising new path to the world of quantum gravity. . Take a black hole. Penrose’s famous drawing depicts the shape of a classical black hole existing in real time. The shape of a quantum black hole is completely different in imaginary time. It looks more like a “cigar”. The “forward” motion in virtual time in this black hole shape corresponds to motion in a circle. The tip of the cigar represents the event horizon of a black hole. There is nothing outside, to the left of this point, so unlike a real-time black hole, its Euclidean component has no singularity that would stop the theory from working. Just as the no-boundary proposition replaces the singularity that created the classical Universe with a circular quantum origin, so the Euclidean description of black holes has a smooth, silent geometry that is completely consistent with the laws (quantum law!) of physics. . By studying the Euclidean shapes of black holes, Stephen and his Cambridge team were able to understand the deeper reason why black holes are not completely black: they emit quantum particles, just like objects. normal body at a certain temperature.

Stephen was impressed by the power of Euclidean geometry in describing the quantum properties of gravity. His proposed method of imaginary time became the basis of his efforts to combine the principles of gravity and quantum theory to solve the mysteries of the Big Bang. “We can assume that quantum gravity, and all of physics in general, is effectively defined in terms of virtual time,” he said. “Our interpretation of the Universe in real time is simply a consequence of our perception.” In conventional quantum mechanics, without gravity, rotating the time axis in space is a classic trick that physicists use to perform Feynman summations of particle histories. The point is that adding paths in virtual time simplifies the complex summation procedure. These calculations end up rotating one of the spatial dimensions in real time, then reading the probability results of certain particle actions. But Jim and Steven don’t want to do this reversal in real time. The audacity of the borderless proposal lies in the fact that when it comes to the origins of the universe, turning time into space is not just a clever computer trick but a profound and fundamental idea.

In fact, there was a time in the history of the Universe when there was no time. On the other hand, there is something Einsteinian about the idea of ​​no borders. In 1917, when Einstein laid the foundations of relativistic cosmology, he could not decide what boundary conditions he should impose on the spatial limits of the Universe. He concluded that it would be much easier if space had no borders! Therefore, he came up with the idea of ​​​​the spatial structure of our Universe as a giant three-dimensional hypersphere, like the two-dimensional surface of an ordinary sphere, with neither edges nor boundaries. term. With their boundaryless hypothesis, Stephen and Jim eliminated the problem of boundary conditions at time 0 in the same Einsteinian fashion by hypothesizing that there is no initial boundary there. Note that Stephen developed his geometric approach to quantum gravity precisely when his hands began to tire and he could no longer write the equations. It is possible that this loss led him to try to describe the difficult world of quantum gravity in the language of geometry and topology: he could visualize this language on a tablet and manipulate it. to some extent in the brain. Visualization is truly central to Stephen’s thinking. Working with Stephen means working with shapes and images that represent the physics of mathematical relationships. At the beginning of our collaboration, I got a taste of his way of calculating when he couldn’t write the equation: it was when I visited him one day in the hospital, where he was recovering from an operation. life-saving art. We talked a bit about the ordeal he had just gone through, but Stephen quickly stopped me and asked me to find him a sign somewhere. When I finally found him in a hospital room, he asked me to draw a circle. This circle represents the edge of the disk that would form if one projected the expanding quantum evolution onto the plane. The moment of the birth of the Universe is located in the center of the disk, and the circle itself corresponds to the Universe today. Of course, all this happens in an imaginary time.

Using a Euclidean approach to quantum gravity, Stephen achieved insights that were virtually unattainable otherwise. And the hypothesis of the absence of boundaries is perhaps the most striking example of this depth. But the rotation of time in space on which this understanding is based makes it difficult to imagine exactly what happened at the beginning of the Universe. The rounded, bowl-like shape of the “bottom” of space-time reminds us that we will have to say goodbye to the cherished idea that time always exists and the words “before” and “after.” always makes sense. But that says little about what, if anything, actually happens in the absence of time, or what kind of microscopic quantum fog condenses to create the bowl-shaped geometry. This theory seems to be trying to tell us that it’s better not to ask such difficult questions. Physicists complained that Stephen’s innovative use of Euclidean geometry seemed magical. Often his whole approach is dismissed as a “Cambridge eccentricity”. Why must time behave in such a strange way? Part of the problem is that within the framework of Euclidean ideas one can construct not a full-fledged quantum theory of gravity but a kind of semi-classical alloy of quantum and traditional elements has no clear mathematical basis. The “rules of the game” were quickly invented by Stephen and his students as they dug deeper into the problem. As Harvard theorist Sidney Coleman said after attempting to prove by the Euclidean method that the cosmological constant must be zero: “The Euclidean formula for gravity has no solid foundation or clear rules of application.” clearly; the situation is more reminiscent of wandering around on a swamp off-road vehicle. It seems to me that I managed to overcome these swamps safely, but it is always possible that , without realizing it, I found myself standing upright in a quagmire that was about to swallow me whole. Stephen, however, remained unmoved. “I prefer precision to meticulous precision,” he reflected. He had a strong intuitive belief that Euclidean geometry provided a unique and powerful means of understanding the extreme manifestations of the nature of the Universe – black holes and the Big Bang.

And today, nearly forty years after Stephen’s pioneering work on quantum cosmology, the no-boundary hypothesis continues to generate enormous interest, profound confusion and heated debate – as There are no other possible explanations for the origin of the universe. Clearly hoping for a widespread response, Stephen publicly proposed for the first time that the Universe has no boundaries nor a specific “moment of creation” at a meeting of the Academy of Sciences The Pope at the Vatican in October 1981. The academy’s mission is to help the Vatican. solve scientific problems and enhance mutual understanding between science and religion. To achieve this goal, the Institute invited scientists from around the world to the picturesque Villa Pius IV, located in the beautiful gardens behind St. Peter’s Basilica, to participate in the competition. week-long lecture on “Cosmology and Fundamental Physics”19. But the question of Big Bang turned out to be very sensitive. Right at the beginning of the discussion week, Pope John Paul II told the assembled scientists: “All scientific hypotheses about the origin of the world, such as the hypothesis that the primordial atom arose, out the entire physics of the universe, leave the question.” about the beginning of the universe unfolding. Science alone cannot solve this problem. The answer requires knowledge beyond the realm of physics and astrophysics, into the realm known as metaphysics. And above all, it requires knowledge that comes from divine revelation. » As if responding to this appeal of the Pope, Stephen, in his astonishing lecture “The Boundary Conditions of the Universe”, put forward the bold idea that the Universe may not have had any beginning any.

Юж“There must be something absolutely exceptional associated with the boundary conditions of the Universe—and what could be more exceptional than the condition that there is no boundary?” – he proclaimed, to the great amazement of his listeners. The wave function of the Universe, which follows from this idea in the absence of a boundary, was—and, of course, still remains—a physical law of a fundamentally new type. It is not a law of dynamics, not a boundary condition, but a combination of both, and as such it embodies an entirely new kind of physics. I noted above that classical physics and ordinary quantum particle mechanics alike remain within the orthodox dualistic concept of prediction, which distinguishes between laws and initial conditions. This cannot be said about a cosmology built on the absence of boundaries; it abandons this dichotomy in favor of a more general picture in which initial conditions and dynamics are equal. According to the no-boundary hypothesis, the Universe does not have point A to set initial conditions. In reality, something like this takes a long time to happen. During the 1939 Edinburgh conference, Paul Dirac predicted the end of dualism in physics. “The division [between laws and conditions] is so philosophically unsatisfactory – for it is contrary to all ideas of the unity of nature – that it seems to me to predict with certainty enough the transformation its loss, despite striking changes in our usual ideas. what will this disappearance lead to” Four decades later, the borderless proposal has played precisely this role.

In coming up with their hypothesis, Jim and Stephen achieved what great thinkers, from Kant to Einstein, considered impossible. Bridging the age-old gap between evolution and creation, this theory firmly puts the question of the origin of the Universe within the framework of natural science. She finally had the chance to solve the puzzle of the creation of the world – a particularly exciting opportunity, of course. It seemed to Stephen that he had found a way to solve the problem of singularity and thus had unraveled the great mystery of existence. Unlike Lemaître, he did not refrain from evoking the role of theology in his cosmology. He wrote in A Brief History of Time: “The universe must be completely self-sufficient and subject to no outside influence.” – It cannot be created or destroyed. It just has to be… So where is the place for the Creator? According to Stephen, the no-boundary theory eliminates the need for primordial motions, the first driving force that began the history of the universe, because it demonstrates that the universe could be created “out of nothing.” Of course, the “God of the Voids” invoked by Étienne in A Brief History of Time is not at all the same as Lemaître’s Deus Absconditus, the “Hidden God,” who remained hidden even at the beginning of creation. Let us explain – this is what the first Hawking, a supporter of Einstein’s metaphysical views, said. Like Einstein, the early Hawkings believed that the mathematical laws of physics had a form of existence more important than the physical reality they governed. Einstein could not accept the idea of ​​a Big Bang, largely because it seemed to undermine this ideal. But while Stephen’s singularity theorem seemed to confirm Einstein’s suspicions, the idea of ​​a boundaryless “bowl” replacing the singularity in quantum cosmology would provide clarity. on the question of how the universe began while keeping Einstein’s idealism intact. Of course this is a great achievement.