This article is an authorized excerpt from The Nature of the BBC Universe (Jiangsu Phoenix Science and Technology Press, 2022).
Author | John Gribbin
Translated by | Zhou Yuheng
In 1917, Einstein attempted to use his general theory of relativity to describe the universe from a mathematical perspective. He wanted to paint the simplest model possible, in which matter is completely evenly distributed in space. At the same time, he also wanted the model to be static, neither expanding nor contracting, in keeping with the fact that the Milky Way was neither expanding nor contracting (at that time humans thought that the Milky Way was the entire universe). The only way to make a model meet these conditions is to include in the equations the so-called "cosmological constant", which is represented by the Greek letter Λ. Einstein's equations do not specify the value of this constant—according to the equation, it can be zero or any positive or negative value. Depends on the specific value of the cosmological constant: it may either play an "anti-gravitational" role, supporting matter against gravitational attraction inward, or as an addition to gravity, promoting the aggregation of matter. Einstein chose a value for the constant that would keep the model static, which in a sense canceled out the gravitational pull. The last sentence of his first paper on cosmology, published in 1917, reads: "This constant is necessary only to make the quasi-static distribution of matter possible, as required by the smaller velocities of stars." ”
When Hubble and Hermason discovered that the universe was expanding, Einstein said the introduction of the cosmological constant was the biggest mistake of his academic career. Other researchers, however, place greater emphasis on the value of the cosmological constant.
Einstein's general theory of relativity laid the foundation for human understanding of the universe
Search space model
Einstein was always looking for a single solution to the equations of general relativity, a unique model of the real universe. However, general relativistic equations in fact provide a large number of different models. The first to realize this was Alexander Friedman, who was also the first to make inflation an intrinsic feature of the cosmological model. He explored these cosmological models mathematically.
In 1922, Friedman published his interpretation of the cosmological equations in general relativity. According to his understanding, these equations do not exist as unique solutions as Einstein had hoped, but correspond to a series of models that describe different possible ways of evolution in space-time, namely different models of the universe. At that time, there was no way for humans to discern which of these models matched the universe in which we lived. Importantly, all of Friedman's models of the universe experience expansion at some stage of evolution.
In these different variations of the same theme, some models of the universe expand forever, while others contract again after expanding for a period of time. Some models of the universe expand faster, while others are slower. There are even some models of the universe that were very large when they were born, shrinking to a certain density over time, and then began to expand. For all of these models of the universe, however, at least at some stages of evolution, the universe expands in such a way that no matter which point in the universe it is, it sees other points receding, moving away from itself, and the apparent regressive velocity of one point is proportional to the distance between that point and the observer—exactly the same as Hubble and Hermason's discoveries toward the end of the 1920s.
Hubble is operating the hook telescope's control device
A universal model of the universe
Einstein was never satisfied with the coexistence of multiple models, and he continued to search for a unique model that could describe the real universe. In the early 1930s, shortly after Hubble's law was discovered, Einstein and the Dutch astronomer Willem de Sitter co-proposed the Einstein-Desitor model of the universe, the simplest of the many variations allowed by the equations of general relativity. In this model, the universe happens to be straight (the only exception that Einstein could have imagined at the time), and Λ = 0. It becomes a benchmark model that can be compared with other models.
However, the Einstein-Dessitt model of the universe has an embarrassing feature that both Einstein and Desit try not to mention. In this model, there is a unique correspondence between the current rate of expansion of the universe and its age — obviously, the faster the universe expands now, the less time it takes to reach its current size, but we also need to take into account the slowdown in the expansion of the universe after the Big Bang. Assuming that the Einstein-Desit model of the universe does indeed accurately describe the universe, then using the constant values in Hubble's law (redshift-distance relationship) discovered by Hubble himself, the calculated age of the universe is only 1.2 billion years, much smaller than the age of the Earth, which was widely known in the 1930s.
Obviously, something went wrong. We now know that early measurements of the Hubble constant were much larger than they really were, and that the true age of the universe was about 14 billion years. But in the 1930s (and decades thereafter), there was another way out of this predicament, and George Lemaite also loved it. If the value of Λ is chosen just right, then the equations of general relativity can describe the following model of the universe: the universe was born in an extremely dense state, and after a period of expansion, it remained stable like a bird circling in place, neither expanding nor contracting, remaining in this state for an indeterminate period of time, and then began to expand again. If our universe were moving in this way, and we were in the second stage of expansion, the age of the universe might be much greater than the age calculated using measurements of the current redshift-distance relationship. In the 1930s, the type of model chosen to describe the universe seemed purely based on personal preference.
Take the cosmological constant seriously
Choosing different cosmological constants can solve any problems encountered in cosmological research, including the age of the universe. Mathematicians are happy to explore these possibilities, but astronomers want to abandon the concept of the cosmological constant because it would seem too arbitrary to use as a correction coefficient that adjusts to the needs of observation. However, when observations of the real universe become precise enough to exclude many of the more crazy cosmological assumptions, it becomes clear that even given the newly arrived estimates of hubble's constant and the correspondingly extended age of the universe, the Einstein-Desseter model of the universe is still lacking. In the 1990s, the cosmological constant was finally no longer left out in the cold, and it wasn't so much that astronomers hoped for it that they had no choice. The English writer Arthur Conan Doyle once famously said in the words of Sherlock Holmes: "After eliminating all the impossible, the rest, even if it seems impossible, must be the truth." ”
A supernova moving at high speed
By the end of the 1990s, the concept of inflation (see page 129 for details) had been embraced by many scholars, supported by data from cosmic background detectors and other measurements of cosmic microwave background radiation. The universe must be straight. At the same time, however, studies of the way galaxies move have been unable to produce conclusive evidence that the mass of matter in the universe exceeds 30% of the mass needed to straighten the universe. In the mid-to-late 1990s, one approach to breaking through the bottleneck of research became more and more important: the concept of the cosmological constant.
Place a spring in the space
In fact, the cosmological constant can have two diametrically opposed effects on the universe. Let's start with the first impact. If the value of Λ is chosen properly, then it can make space-time "elastic" and produce some kind of anti-gravitational effect, that is, some kind of cosmic repulsion. It corresponds to the energy of a vacuum, just as gravity corresponds to the energy of matter.
Let's discuss the second effect of the cosmological constant on the universe. According to the mass-energy equation, there is an equivalence relationship between mass and energy, and mass is related to gravity, so that energy related to the cosmological constant can also exert a gravitational effect. If the value of Λ is chosen properly, the energy present in the universe related to the aforementioned cosmic repulsion could reach about 70% of the mass (mass energy) needed to straighten the universe, while at the same time ensuring that the expansion of the universe is affected only insignificantly, an effect that is so small that it is almost impossible to detect today.
By adding about 70% given by the cosmological constant to about 30% in the form of matter, we get the mass energy that happens to make the universe straight. Theorists explored the possibilities allowed by the model and found the simplest explanation that the mass that exists in the form of dark matter in the universe is indeed only about 30% of the mass energy corresponding to the critical density and that inflation has indeed occurred. This theory is still not as concise as many people expect, and it still seems far-fetched, but like all outstanding theories, it can be tested with further observations of the real universe.
The story of a supernova
The role that supernovae play in this story is standard candlelight, through which we can measure distant distances in the universe. Type I supernovae don't have exactly the same brightness, but by the way they gradually darken after peaking, we can infer their highest absolute luminosity. Astronomers can first observe type I supernovae in known nearby galaxies, and when the presence of type I supernovae is also detected in extremely distant galaxies, the distance of this supernova in the extremely distant galaxy is calculated by comparing its apparent brightness with the apparent brightness of the nearby supernova. The difficulty with this approach to ranging lies in the search for supernovae in very distant galaxies, and it wasn't until 1998 that the technology was developed enough to accomplish the task. At that time, two scientific research teams used the latest technology to conduct independent research on the same phenomenon. Luckily, they got the same answer.
One of the two international teams used the Keck telescope in Hawaii and the other at the Mount Stromlo Observatory and the Siding Spring Observatory in Australia. They measured the brightness of dozens of Type I supernovae in extremely distant galaxies and compared the inferred distances to the redshifts of those galaxies. After applying the Hubble constant calculated from nearby galaxies to extremely distant galaxies, they found that the apparent receding velocity of extremely distant galaxies was slightly smaller than previously expected.
This means that the expansion of the universe is accelerating, not decelerating. The point is that for nearby galaxies, we observe their state not long ago; for distant galaxies, we observe their state in the distant past, because the light they emit takes a long time to reach us. Neighboring galaxies are moving away from each other faster than distant galaxies, suggesting that the universe is expanding at a faster and faster rate.
On its own, the findings are enough to attract attention. What's even more striking, however, is that the magnitude of the cosmic repulsion needed to match the observations can also provide about 70 percent of the mass energy needed to straighten the universe.
Two giant telescopes at the Keck Observatory on Mount Mauna kea in Hawaii, USA. Both telescopes each have an objective lens with a diameter of 10 meters
Finally confirmed
After these findings, there remains the uncertain question of whether the universe is indeed completely straight, as predicted by inflationary theory. Once again, newly developed technologies provide a way to test prophecies. Radiation propagating in space is affected by the curvature of space, and the farther it travels, the greater the impact. Cosmic microwave background radiation travels through space longer than any other radiation that humans can detect. So in principle, a map of the precise variation between this radiation from different parts of the sky could reveal the curvature of space from the beginning of the Big Bang 's "fireball" to our location spanning 14 billion light-years of space.
At the end of the 1990s, the fluctuations in the cosmic microwave background radiation detected by instruments carrying hot air balloons into the sky were 1/35 of the smallest fluctuations that cosmic background detectors could detect. The results of two hot air balloon missions published in 2000 showed that the universe was straight, with an error of less than 10 percent — meaning the Ω was between 0.9 and 1.1. Given that there is clear evidence that only about 30 percent of the mass energy needed to straighten the universe exists in the form of matter, this means that about 70 percent of that mass energy must be in energy form — consistent with the results of studies of supernovae. Humans thus gained strong evidence that cosmological constants are true, whether Einstein is willing to accept it or not.
Ripples in the cosmic ocean
The close fit of all the components of inflationary theory—the total amount of matter in the universe, the acceleration required by the Supernova Institute, and the cosmic flatness revealed by measuring the cosmic microwave background radiation—makes inflation the undisputed best cosmological theory of the early 21st century. It offers a way to solve the final puzzle: Why isn't the universe completely homogeneous, but has a large enough degree of irregularity to make human existence possible?
Quantum fluctuations
Where does the energy of the vacuum come from? According to quantum physics, a true "vacuum" does not exist because a true "vacuum" requires an energy value of zero, and one of the most famous laws of quantum physics, the Heisenberg uncertainty principle, states that nothing can have an exact value—not only can we measure things precisely, but absolute precision does not exist at all in the universe. From this point of view, in any tiny space, there is a balance between time and energy. Particles called "virtual particle pairs" can (in fact must) appear out of thin air from nothing, provided they annihilate each other for a definite period of time. The specific time limit is determined by the mass of the virtual particle pair - the greater the mass of the virtual particle pair, the shorter the time it can exist, but the measurements show that this time is always much shorter than 1 second. The existence of these particles is as if the universe is "not paying attention", and once the universe has time to "discover" their existence, they will disappear into the void again.
The uncertainty principle proposed by the German physicist Werner Heisenberg may be the key to understanding the birth of the universe
As a result of this phenomenon, space becomes a boiling bubble made of virtual particles, and space acquires energy and structure. It is this energy that provides outward cosmic repulsion, and the mass associated with this energy accomplishes the task of leveling the universe.
It is no coincidence that the sum of the various forms of mass energy in the universe makes the universe straight (Ω equal to 1). Inflation pushes the universe towards a straighter, so there is only so much mass energy available for conversion, in the form of baryons, hot dark matter, cold dark matter, and dark energy, respectively. It is as if water is poured from a 1-liter container into a variety of bottles and cans, and no matter what proportion of water is distributed to different containers, the total amount of water is always equal to 1 liter.
Although quantum fluctuations are usually fleeting, they should have engraved their mark on the universe.
The problem of scale
Quantum fluctuations occur not only in very short periods of time, but also on very small distance scales, because perturbations in the vacuum involved in this phenomenon do not have time to propagate farther distances before being forced to disappear. Quantum fluctuations have occurred long before the very beginning of the universe, after the first Planck time, before inflation began. When inflation began to dominate the entire observable universe that followed, all the mass energy of the observable universe was trapped in a single particle of diameter
Centimeters of tiny "seeds" inside. This length is 100 million times the length of Planck, but still only one trillionth of the diameter of the proton. Even such an unimaginably small "seed" is large enough to accommodate quantum fluctuations, which involve energy fields (like electromagnetic fields) rather than particles. In summary, the structure of the vacuum is constantly changing, but this structure always conforms to a specific statistical pattern.
Subsequently, inflation occurred, and everything in the cosmic "seed" was torn apart and spread widely. In the process, all the quantum fluctuations in the vacuum that were taking place inside the seed at the moment when the inflation began were "frozen" in the rapidly expanding "seed" structure and greatly stretched as space expanded. During inflation, the universe is in fact expanding at a faster rate than the speed of light (this is entirely permitted by Einstein's equations, because only motion in space-time cannot exceed the speed of light), and the pattern of last-minute quantum fluctuations is permanently engraved in the "steaming hot gas" emerging from the "cosmic fireball".
There is a statistical pattern called "scale invariance" because, statistically speaking, quantum fluctuations look the same at all scales: if a portion of the entire picture is taken and magnified, the local picture, although not exactly consistent with the original image, has the same statistical appearance as the original image in terms of the arrangement of hot and cold points. The ripples detected by the Cosmic Background Detector and subsequent similar satellites in the cosmic microwave background radiation have exactly the same scale invariance, except that in this case the pattern is presented in a range of hundreds of millions of light-years, rather than confined to a sphere with a diameter equal to only one trillionth of the diameter of a proton. We humans are also part of this pattern — life is also part of the structure of the quantum ups and downs that occurred shortly after the birth of time engraved in the universe.
Each smaller component of a fractal pattern can reproduce the entire pattern when enlarged
Book information
Author: [English] by John Gribbin
Publisher: Jiangsu Phoenix Science and Technology Press
Publication Date: 2022-2-1
"The Nature of the BBC Universe: Why the Night Sky is Black" is a popular science work focusing on the frontiers of the universe: from the fate of the stars to the ultimate fate of the universe, from the search for extraterrestrial life to the exploration of another universe, widely involving wormholes, relativity, inflation theory, quantum mechanics, multiverse and other theories, science sorts out the process of human cognition and exploration of the universe, and gives answers to the essential issues of the universe.
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