Recently, Stephen Hawking's main idea - that the universe could have arisen from nothing - has been challenged, and cosmologists have had to choose which side to take. After two years of confrontation, scientists agreed that their differences boil down to different views on how nature works. The friendly debate helped preserve the value of Hawking's idea.
In 1981, many of the world's leading cosmologists gathered at the Pontifical Academy of Sciences, which witnessed the fusion of science and theology, located in an elegant villa in the Vatican Gardens. Stephen Hawking chose August day to present what he would later call his most important idea: the hypothesis that the universe could have arisen out of nothing.
Before Hawking's speech, all stories of cosmological origin, scientific or theological, were objectionable: "What happened before that?" For example, the Big Bang theory - first proposed 50 years before Hawking's lecture by the Belgian physicist and Catholic priest Georges Lemaître, who later served as president of the Vatican Academy of Sciences - says that before the expansion began, the universe was a hot, dense bundle of energy … But where did the original energy come from?
The Big Bang theory had other flaws as well. Physicists understood that the expanding bundle of energy would rather turn into something crumpled and chaotic, rather than into the huge smooth space that modern astronomers observe. In 1980, a year before Hawking's speech, cosmologist Alan Guth realized that the Big Bang's inaccuracies could be corrected with a small addition: an initial, exponential spike in growth known as cosmic inflation that would make the universe huge, smooth, and flat. before gravity could destroy it. Inflation quickly became the leading theory for the origin of our cosmos. And yet the question remained, what were the initial conditions: where did the tiny spot that supposedly swell into our universe, and the potential energy that expanded it from?
The magnificent Hawking found a way to put an end to endless attempts to look even further into the past: he assumed that there was no end or beginning at all. According to the minutes of the conference at the Vatican, the Cambridge physicist, then 39 years old and who could still speak with his own voice, told the audience: “There must be something special in conditions at the edge of the universe, and what could be more special than that. a state in which there is no border?"
Hawking and James Hartle, with whom they often worked together, finally formulated their "no-boundary hypothesis" in their 1983 paper, where they suggested that space is shaped like a shuttlecock. Just as a shuttlecock has a diameter of zero at its lowest point and gradually expands along the way up, the universe, according to the hypothesis of no boundaries, smoothly expands from a point of zero size. Hartle and Hawking came up with a formula describing the entire shuttlecock - the so-called "wave function of the universe" that encompasses the entire past, present and future - making it meaningless to search for the origins of creation, a creator, or any transition from one state to another in the past.
“In accordance with the hypothesis of the absence of boundaries, it makes no sense to ask the question of what happened before the Big Bang, since there is no concept of time that could become a starting point,” Hawking said during another lecture at the Pontifical Academy in 2016, one and a half years before his death. "It's like asking what is south of the South Pole."
The Hartle-Hawking hypothesis radically revised the concept of time. Every moment in the universe became a cross-section of a shuttlecock; while we perceive the universe as expanding and evolving from one moment to the next, time actually consists of correlations between the size of the universe in each section and other properties - especially its entropy, or disorder. Entropy increases from cork to feathers, targeting the emerging arrow of time. However, near the rounded bottom of the shuttle, the correlations are less reliable; time ceases to exist and is replaced by pure space. Hartle, a professor at the University of California at Santa Barbara, now 79, recently commented in a telephone conversation: “There were no birds in the earliest universe; subsequently the birds appeared. There was no time in the early universeand then time appeared."
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The no-boundary hypothesis has fascinated and inspired physicists for nearly forty years. “It's a stunningly beautiful and provocative idea,” said Neil Turok, a cosmologist at the Canadian Perimeter Institute for Theoretical Physics in Waterloo and a former Hawking collaborator. The hypothesis was the first draft of a quantum description of the cosmos - the wave function of the universe. Soon, a whole field of science, quantum cosmology, emerged, and various researchers began to offer alternative ideas for how the universe could come from nothing, analyzed various predictions and ways of testing these theories, and interpreted their philosophical implications. The infinite wave function "was in some ways the simplest explanation for this," Hartle said.
But two years ago, an article by Turok, Job Feldbrugge of the Perimeter Institute and Jean-Luc Lehners of the Max Planck Institute for Gravitational Physics in Germany challenged the Hartle-Hawking hypothesis. This hypothesis, of course, is only viable if a universe that emerges from a dimensionless point, as Hartle and Hawking envisioned, naturally grows into a universe like ours. Hawking and Hartl argued that this is indeed the case: universes without borders are likely to be huge, incredibly smooth, impressively flat and expanding, just like the cosmos itself. “The problem with Stephen and Jim’s approach is that it was ambiguous,” Turok said, “deeply ambiguous.”
In a 2017 article published in Physical Review Letters, Turok and his co-authors approached the Hartle-Hawking no-boundary hypothesis with new mathematical techniques that they believe make his predictions much more specific. than before. “We found it had failed miserably,” Turok said. "In terms of quantum mechanics, the universe simply could not have appeared the way they imagined." The three scientists carefully checked the calculations and baseline data before publishing them, but "unfortunately," Turok said, "it seemed inevitable that the Hartle-Hawking proposal was unsuitable."
Controversy erupted over this article. Other experts vehemently upheld the idea of no borders and refuted the arguments of Turok and his colleagues. "We disagree with his technical arguments," said Thomas Hertog, a physicist at the Catholic University of Leuven in Belgium who worked closely with Hawking for the last 20 years of his life. “But, more importantly, we also disagree with its definition, its concept, its methodology. This is what we would like to argue with in the first place”.
After two years of confrontation, the groups of scientists agreed that their differences boil down to different views of how nature works. A heated, but at the same time, friendly debate helped to preserve the value of the idea that excited Hawking. Even their critics with Hartl of the special formula, and including Turok and Lehner, develop competing quantum cosmological models, trying to avoid the supposed pitfalls of the original, while maintaining the charm of the idea of infinity.
The garden of cosmic delights
Since the 1970s, Hartle and Hawking met frequently, usually when they had long collaborations at Cambridge. Theoretical studies of black holes and mysterious singularities at their centers forced them to turn to the question of the origin of our universe.
In 1915, Albert Einstein discovered that concentrations of matter or energy deform the fabric of spacetime, producing gravity. In the 1960s, Hawking and Oxford University physicist Roger Penrose proved that when spacetime bends sharply enough, for example, inside a black hole or perhaps during the Big Bang, it inevitably collapses, bending infinitely steeply into side of the singularity, where Einstein's equations do not work and a new, quantum theory of gravity is needed. The Penrose-Hawking Singularity Theorems say that space-time cannot arise smoothly, unsharply at one point.
Thus, Hawking and Hartl pondered the possibility that the universe arose as pure space rather than dynamic space-time. And this led them to the idea of the geometry of the shuttlecock. They defined a limitless wave function to describe such a universe using an approach invented by Hawking's idol physicist Richard Feynman. In the 1940s, Feynman developed a scheme for calculating the most likely outcomes of quantum mechanical events. Feynman found that, say, to predict the most likely outcomes of a collision of particles, one could sum up all the possible paths that colliding particles could travel, giving straight paths more importance than meandering. Calculation of this "path integral" gives the wave function: the probability distribution,indicating the various possible states of the particles after collision.
Likewise, Hartle and Hawking presented the wave function of the universe - describing its probable states - as the sum of all possible paths in which it could smoothly expand from a point. They hoped that the sum of all possible "expansion stories", smooth-bottomed universes of all shapes and sizes, would produce a wavefunction that is likely to generate a huge, smooth, flat universe like ours. If the weighted sum of all possible expansion histories is the most likely outcome of some other kind of universe, the no-boundary hypothesis is inconsistent.
The problem is that the integral over all possible expansion histories is too complex to be accurately calculated. There are countless variations in the shapes and sizes of universes, and each of them can prove to be a very confusing story. "Murray Gell-Mann used to ask me," Hartle said of the late Nobel Prize-winning physicist, "if you know the wave function of the universe, why didn't you get rich?" Of course, in order to actually find the wave function using Feynman's method, Hartl and Hawking had to radically simplify the situation, ignoring even the specific particles that inhabit our world (which meant that their formula was very far from predicting stock markets). They believed that the trajectory is integral for all possible toy universes in "mini-superspace",that is, in the aggregate of all universes with a single energy field passing through them: the energy that fueled cosmic inflation. (In the Hartle-Hawking shuttlecock, this initial expansion period corresponds to a rapid increase in diameter at the base of the plug.)
Even minisuperspace is difficult to calculate accurately, but physicists know that there are two possible expansion histories that could be the most likely outcomes of these calculations. These competing forms of the universe correspond to two sides of the current debate.
These two competing theories represent two "classic" stories of the expansion of the universe that could have taken place. After the initial burst of size zero cosmic inflation, these universes are steadily expanding in accordance with Einstein's theory of gravity and spacetime. More complex expansion stories, such as soccerball and caterpillar universes, are largely negated by quantum computing.
One of the two classic solutions resembles our universe. On a larger scale, it is smooth, and energy is randomly scattered throughout it due to quantum fluctuations during inflation. As in the real universe, the density differences between its different regions form a Gaussian curve close to zero. If this possible solution is indeed the most plausible when calculating the wavefunction for minisuperspace, it’s possible to imagine that a much more detailed and accurate version of the infinite wavefunction could serve as a viable cosmological model of the real universe.
Another potentially dominant form of the universe is not at all like the real one. As it expands, the energy that fills it varies more and more sharply, creating huge density gradients from one place to another, and gravity is constantly increasing. Density changes form an inverted Gaussian curve, where differences between regions approach infinity, rather than zero. If this is the dominant term in the infinite wavefunction for minisuperspace, then the Hartle-Hawking proposal may seem wrong.
Two dominant expansion stories force us to choose how the path integral should be performed. If the dominant stories are two locations on a map, megacities in the realm of all possible quantum mechanical universes, the question is what trajectory we should take through these lands. What dominant history of expansion, and there can only be one, should our "integration contour" choose? Researchers have already charted different paths.
In a 2017 article, Turok, Feldbrugge, and Lehner took a path through the garden of possible expansion stories that led them to a second dominant decision. In their opinion, the only sane contour is one that looks at real values (as opposed to imaginary values, which include the square roots of negative numbers) for a variable called "spacing." Basically, the spacing is the height of each possible shuttlecock universe, the distance at which it reaches a certain diameter. Since the deviation has no starting point, it does not fit into our understanding of time. Nevertheless, Turok and his colleagues partly refer in their reasoning to causation, arguing that physical meanings have only real values of the interval. And summation over universes with real values of this variable leads to a solution that is highly unstable and meaningless from the point of view of physics.
“People place a lot of value on Steven's intuition,” Turok said over the phone. “For obvious reasons - I mean, he probably had the best intuition on these matters. But he was not always right."
Imaginary worlds
Jonathan Halliwell, a physicist at Imperial College London, has studied the no-boundary hypothesis since he studied with Hawking in the 1980s. Together with Hartl, they analyzed the question of the contour of integration in 1990. From their point of view, as well as from the point of view of Hertog and, apparently, Hawking, the contour is not fundamental, but rather the mathematical tool that provides the most benefits. Similarly, the trajectory of a planet around the Sun can be represented mathematically as a series of angles, as a series of times, or as any of several other convenient parameters. “You can do this parameter estimation in many ways, but none of them is more physical than the other,” Halliwell said.
He and his colleagues argue that in the case of minisuperspace, only outlines that capture the correct expansion story make sense. Quantum mechanics requires probabilities to add up to 1 or be "normalizable," but the highly unstable universe that Turok's team came to is not. This decision is meaningless, suffers from infinities and does not obey quantum laws - according to the advocates of the no-boundary hypothesis, this clearly indicates the need to go the other way.
It is true that the contours passing through the correct solution sum up the possible universes with the imaginary values of their variables. But apart from Turok and company, few consider this a problem. Imaginary numbers pervade quantum mechanics. Critics of the Hartle-Hawking team cite a misconception of causality by demanding that the "interval" be real. “This is a principle that is not ordained by heaven, and with which we deeply disagree,” says Hertog.
Hertog says that Hawking has rarely mentioned the integral form of the path of the infinite wave function in recent years, in part due to ambiguity in the choice of the contour. He viewed the normalized expansion history, which was recently discovered using the integral path, as a solution to a more fundamental equation of the universe, posed in the 1960s by physicists John Wheeler and Bryce DeWitt. Wheeler and DeWitt, pondering this question while stopping at Raleigh-Durham International Airport, argued that the wave function of the universe, whatever it may be, cannot be time dependent, since there is no external clock by which it could be measure. Therefore, the amount of energy in the universe when you add up the positive and negative contributions of matter and gravity must always remain zero. The unbounded wave function satisfies the Wheeler-DeWitt equation for minisuperspace.
In the last years of Hawking's life, he and his co-workers began to use holography, a new blockbuster approach that views space-time as a hologram, to better understand the wave function as a whole. Hawking sought a holographic description of the universe in the form of a shuttlecock, in which the geometry of the entire past would be projected from the present.
These efforts continue in Hawking's absence. But the Turk sees this shift in emphasis as a change in the rules. According to him, refusing to formulate the path integral, the supporters of the no-boundary model made it poorly defined. In his opinion, what they are studying is no longer the Hartle-Hawking model, although Hartl himself does not agree with this.
Over the past year, Turok and colleagues at the Perimeter Institute Latham Boyle and Kieran Finn have been developing a new cosmological model that has much in common with the boundaryless model. But instead of one shuttlecock, it consists of two hourglass-shaped corks in which time flows in both directions. Although the model is not yet sufficiently developed to predict anything, its beauty lies in the fact that its petals implement CPT symmetry, apparently a fundamental natural mirror that simultaneously reflects matter and antimatter, left and right, as well as forward motion and back in time. One of its disadvantages is that the petals of the mirror image of the universe occur in the singular, in space-time,which requires an understanding of the unknown quantum theory of gravity. Boyle, Finn and Turok are betting on the singularity, but this attempt is speculative.
There is also a resurgence of interest in the "tunneling model", an alternative concept of the origin of the universe from nothing, developed in the 1980s by the independent Russian-American cosmologists Alexander Vilenkin and Andrei Linde. The model, which differs from the infinite wave function mainly by the minus sign, considers the birth of the universe as a quantum mechanical "tunneling" event, similar to when a particle floats behind a barrier in a quantum mechanical experiment.
There are many questions about how the various models relate to anthropic reasoning and the infamous idea of a multiverse. For example, an infinite wave function favors empty universes, while a huge complex universe requires significant amounts of matter and energy. Hawking argued that a huge range of possible universes that fit into the wave function must be realized in some larger multiverse, within which only such complex universes as ours will have inhabitants capable of observing. (Recent controversy revolves around the question of whether these complex habitable universes will be smooth or highly fluctuating.) The advantage of the tunneling model is that it favors universes filled with matter and energy.like ours, there is no need to resort to anthropic reasoning - although universes tunneling into existence may have other problems.
Whatever happens, perhaps some of the essence of the painting, first painted by Hawking at the Pontifical Academy of Sciences 38 years ago, will still remain. Or, perhaps, instead of a non-beginning like the South Pole, the universe has emerged from the singularity, and some completely different kind of wave function is required. In any case, the search will continue. "If we are talking about quantum mechanical theory, what else can be found besides the wave function?" asked Juan Maldacena, a distinguished theoretical physicist at the Institute for Advanced Study in Princeton, New Jersey, who has largely kept aloof from recent controversy. According to Maldacena, who, incidentally, is a member of the Pontifical Academy, the question of the wave function of the universe is "the right question." “Do we find the correct wave function,or how we should imagine the wave function is not so clear anymore."
Natalie Wolchover