Shulou(Shulou.com)11/24 Report--

Cosmologists have spent decades trying to understand our universe. As far as we can see, it is not only smooth and flat (not crumpled by gravity or torn apart by dark energy), but also expands at an extremely slow rate. To explain the flatness of the universe, physicists proposed that the universe expanded like a balloon at the beginning of the Big Bang, eliminating any curvature. To explain the slow growth of space after the initial expansion, some people think that our universe is just one of the multiverse.

But now, two physicists have subverted people's traditional view of the universe. Following a series of studies begun by Stephen Hawking and Gary Gibbons in 1977, the two published new calculations showing that the flatness of the universe was to be expected. According to Neil Turok of the University of Edinburgh and Latham Boyle of the circumferential Institute of theoretical Physics in Waterloo, Canada, this is how our universe works, for the same reason that air spreads evenly in a room.

This conclusion is based on a mathematical technique that involves a clock timing in imaginary numbers. As Hawking did in the 1970s, Turok and Boyle used virtual clocks to calculate a quantity called entropy, which seems to correspond to our universe. But the "virtual time technique" is a circuitous way to calculate entropy, and the meaning of this quantity remains to be discussed without a more rigorous method. When physicists are puzzled by the correct interpretation of entropy calculation, many see it as a new guidepost to the basic quantum properties of space and time.

It opens a window for us to see the microstructure of time and space.

Last year, to study the possibility of the universe, Turok and Boyle turned to a technology developed by Richard Feynman in the 1940s.

To capture the probabilistic behavior of particles, Feynman imagines all possible paths of a particle from beginning to end: a straight line, a curve, a loop, and infinity. He devised a way to give each path a number related to its possibility, and then add up all the numbers. This "path integral" technique has become a powerful framework for predicting the most likely performance of any quantum system.

Physicists have discovered a strange connection between path integral and thermodynamics. It is this bridge between quantum theory and thermodynamics (path integral) that makes Turok and Boyle's calculations possible.

Neil Turok thermodynamics uses statistical methods, using only a few numbers to describe a system of many parts, such as the countless air molecules in a room. For example, temperature (essentially the average velocity of air molecules) can roughly reflect the energy of a room. Overall properties such as temperature and pressure describe the "macro state" of the room.

But the macroscopic state is a rough description; air molecules can be arranged in a large number of ways, and they all correspond to the same macroscopic state. Each unique microstructure is called micro-state, and the number of micro-states corresponding to a given macro-state determines its entropy.

Entropy provides physicists with a way to compare the probabilities of different results. the higher the entropy of the macroscopic state, the greater the possibility. For example, air molecules are arranged much more in the whole room than in a corner. As a result, air molecules are expected to disperse and remain dispersed. The self-evident fact that "the possible outcome is possible", expressed in the language of physics, has become the famous second law of thermodynamics: the total entropy of the system tends to increase.

There is no doubt about its resemblance to the path integral: in thermodynamics, all possible configurations of a system are added up. Through the path integral, add up all the paths that the system may take. There is only one fairly obvious difference: thermodynamics studies probability. But in the path integral, the number assigned to each path is plural, which means it involves the imaginary number I. When complex numbers are added together, they can increase or decrease-allowing them to capture the wavy properties of quantum particles, which can be combined or offset.

However, physicists have found that a simple transformation can take you from one field to another. If you set the time to an imaginary number, the second I will enter the path integral, eliminate the first I, and convert the imaginary number into a real probability. By changing the time variable into the reciprocal of temperature, a famous thermodynamic equation is obtained.

In 1977, Hawking brought this sensational discovery, which is the end of a series of theoretical discoveries about space and time.

The entropy of time and space as early as a few decades ago, Einstein's general theory of relativity revealed that space and time together constitute a unified realistic structure (space-time). Gravity is actually the trend of objects moving along the folds of space-time. In extreme cases, spacetime can bend sharply to form an inescapable black hole.

In 1973, Jacob Beckenstein proposed the heresy that black holes are imperfect universes. He reasoned that black holes should absorb entropy from the universe, rather than removing entropy from the universe, thus violating the second law of thermodynamics. But if black holes have entropy, they must also have temperature and must radiate heat.

Stephen Hawking tried to prove Beckenstein wrong and began to make complex calculations about the behavior of quantum particles in the curved space-time of a black hole. To his surprise, in 1974, he found that the black hole was indeed radiating. Another calculation confirms Beckenstein's guess that the entropy of a black hole is equal to 1/4 of the area of its event horizon.

In the years that followed, British physicists Gibbons and Malcolm Perry, and later Gibbons and Hawking, reached the same results in the other direction. They established a path integral that in principle adds up all the different ways in which space-time bends to form a black hole. Next, they made a Wick turn on the black hole, marked the flow of time with imaginary numbers, and carefully observed its shape. They found that in the direction of imaginary time, black holes periodically return to their initial state.

In physics, Wick rotation is a method of using imaginary variables instead of real variables to find solutions to mathematical problems in Minkowski space from the solutions of related problems in Euclidean space. This transformation is also used to find solutions to problems in quantum mechanics and other fields.

If the answers are not entirely consistent with earlier calculations by Beckenstein and Hawking, they may not believe them. Their research has produced a startling concept: the entropy of a black hole means that space-time itself is made up of tiny, rearrangeable fragments, just as air is made up of molecules. Miraculously, even if they don't know what these gravitons are, physicists can calculate their arrangement by observing a black hole in imaginary time.

Calculate all possible universes

Soon, Hawking and Gibenswick turned the simplest universe imaginable-one that contained only the dark energy of space itself. This empty, expanding universe, called "de Sitter" spacetime, has an event horizon. Beyond the event horizon, space expands so fast that no signal can reach the observer at the center of the space. In 1977, Gibbons and Hawking calculated that the entropy of the de Sitter universe, like a black hole, is equal to 1/4 of the area of its event horizon. Once again, space-time seems to have countable microscopic states.

But the entropy of the actual universe is still an open question. Our universe is not empty, it is full of radiant light, galaxies and dark matter. In the youth of the universe, light promotes the rapid expansion of space, and then in the adolescence of the universe, the gravity of matter slows things down. Now dark energy seems to have the upper hand, driving the uncontrolled expansion of the universe.

Over the past year or so, Turok and Boyle have built such a clear solution. First, in January, they noticed that adding radiation to de Sitter space-time did not destroy the simplicity needed for Wick to rotate the universe.

In the summer, they found that the technology could even withstand a mixture of substances. The mathematical model describing the more complex history of expansion still belongs to a set of functions that are easy to deal with, while the world of thermodynamics is still understandable.

Through the expansion history of Wick's rotating universe, they obtained a more general equation of cosmic entropy. For a wide range of macro states of the universe defined by radiation, matter, curvature and dark energy density, the formula can calculate the number of corresponding micro states. Turok and Boyle published their findings online in early October.

Latham Boyle experts affirmed this clear and quantitative result. But from their entropy equation, Boyle and Turok drew an unconventional conclusion about the nature of the universe.

Boyle and Turok believe that this equation makes a census of all the imaginable history of the universe. Just as the entropy of a room calculates all the arrangements of air molecules at a given temperature, they suspect that their entropy calculates all the ways in which atoms in space-time may be disrupted, resulting in a universe with a given overall history, curvature and dark energy density.

Boyle likens the process to exploring a bag of marbles, each representing a different universe. Negative curvature may be green. Those who have a lot of dark energy may be cat winks and so on. Their census shows that the vast majority of marbles have only one color, corresponding to one type of universe: roughly similar to our universe, with no obvious curvature, only a little dark energy. Weirder types of the universe are rare. In other words, the strange common features of our universe may not be surprising at all.

The core of entropy is ignorance. Boyle and Turok gave an equation for calculating the number of universes. They have come to the startling conclusion that universes like ours seem to account for the vast majority of all imaginable universes.

The two men did not try to explain how the quantum theories of gravity and cosmology make some universes universal or rare. Nor can they explain how our universe was formed. In the end, they think that their calculation is more of a clue than a close to a complete cosmological theory.

Their research also reactivates a question that has not been answered since Hawking first turned on space-time entropy: what exactly is the micro-state calculated by this method?

The key here is that we don't know what entropy means, said Henry Maxfield, a physicist who studies the quantum theory of gravity at Stanford University.

The core of entropy is ignorance. For example, for a gas made up of molecules, physicists know the temperature, but not the behavior of each particle; the entropy of the gas reflects the possible number of microscopic configurations.

After decades of theoretical research, physicists have a similar understanding of black holes. Now, many theorists believe that the area of the event horizon describes their ignorance of the matter that falls into the black hole-all the components inside the black hole match its appearance.

Researchers still don't know what the microstate is; these ideas include the configuration of particles called gravitons or strings in string theory.

But when it comes to the entropy of the universe, physicists are not even sure where their ignorance lies.

In April, two theorists tried to build cosmic entropy on a more solid mathematical foundation. University of Maryland physicist Ted Jacobson (Ted Jacobson) is famous for deducing Einstein's theory of gravity from the thermodynamics of black holes. He and his graduate students clearly defined the entropy of de Sitter's universe. They adopted the perspective of a central observer. They added a virtual surface between the central observer and the event horizon, and then shrank the surface until it reached the central observer and disappeared, and got the answer of Gibbons and Hawking that entropy is equal to 1/4 of the area of the event horizon. They concluded that de Sitt entropy calculated all possible micro-states in the event horizon.

Ted Jacobson and his graduate students Boyle and Turok calculated the same entropy as Jacobson calculated the entropy of the empty universe. But in their new calculation of a real universe full of matter and radiation, they get more microscopic states-proportional to volume rather than area. In the face of this obvious conflict, they speculate that different entropy can answer different questions: the smaller de Sitt entropy calculates the micro-state of pure space-time surrounded by the event horizon, while they suspect that the larger entropy calculates all the micro-states of space-time full of matter and energy inside and outside the event horizon.

In the end, to solve the problem that Boyle and Turok are counting, a clearer mathematical definition of the set of microstates is needed.

Cosmologists say expansion and the multiverse are far from extinct. Modern expansion theory, in particular, deals with more than just the smoothness and flatness of the universe. Turok and Boyle's entropy argument has passed an important first test, but it needs other more detailed data to fight inflation more forcefully.

As a measure of ignorance, the mystery rooted in entropy was once a harbinger of unknown physics. In the late 19th century, an accurate understanding of entropy from the perspective of microscopic arrangement helped to confirm the existence of atoms. Now, the hope is that if researchers calculate cosmic entropy in different ways, they will be able to pinpoint the questions they are answering. These numbers will lead them to a similar understanding of how Lego bricks of time and space are piled up to create the universe around us.

Turok said

Our calculations provide a huge extra impetus for those who are trying to establish a microscopic theory of quantum gravity. Because the prospect of this theory is that it will eventually explain the large-scale geometry of the universe.

This article comes from the official account of Wechat: Lao Hu Shuo Science (ID:LaohuSci). Author: I am Lao Hu.

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