In late 1907, the editor of the Yearbook of Radioactivity and Electronics in Germany invited a "Technical Expert Second Class" from the Swiss Patent Office to write an annual review of relativity.
Albert Einstein, then 28, had just been promoted from "level three technologist" to "level two," and his personal life improved slightly with a corresponding increase in salary. But he was clearly more attentive to writing this review than to his job in the patent office.
Einstein working at the Swiss Patent Office.
Special relativity has been published for more than two years at this time and has gradually been accepted by the physics community. But Einstein was always obsessed with the "narrow sense" of his own theory. The reason for this definite sentence is that she has two obvious flaws. One is that it cannot be harmonized with Isaac Newton's gravitational attraction: the transient "hyperactivity" property of the latter violates the limit of the speed of action of force in relativity; second, the theory applies only to "inertial frames of reference" of uniform motion, and cannot be applied to systems with acceleration.
As Einstein sat in the patent office wrestling with how to summarize these two deficiencies, a spark popped into his head: If a person falls freely in the air, he does not feel gravity — he is in a state of "weightlessness." It's not just the man's own feelings: if he let go of the apple in his hand during the fall, he wouldn't see the apple fall to the ground, as Newton said, but would stay "still" at his hand. (Of course, to the onlookers, Apple is falling to the ground with this man.) ）
Einstein later said it was the "happiest thought" of his life, and deduced from this what he famously called the "elevator hypothetical experiment": a person in a closed elevator had no way of knowing whether his "weightlessness" was due to the elevator crashing or whether the elevator was actually floating in a space where gravity did not exist. Conversely, if the person feels gravity, he can't possibly know if it's because the elevator is parked on the surface of the Earth or if it's accelerating in space without gravity.
Therefore, there is no difference between gravity and acceleration, but the focus is different. Thus, the two flaws of special relativity are actually the same and can be solved at the same time. In special relativity, concepts such as time and distance are no longer absolute, but "relative" to the frame of reference in which they are located. In generalized theory of relativity, gravity—or gravitational force—is no longer absolute, but exists relative to whether the frame of reference in which it is accelerated.
Thus, he added a section to the end of his review of special relativity for the almanac, which became the first signpost towards general relativity.
In the blink of an eye, many years have passed. Albert Einstein had long since bid farewell to the patent office and became an official and increasingly famous physicist. He also gradually had a clear idea of how to generalize the theory of relativity: gravitational phenomena such as the apple falling to the ground, the moon turning around the earth, etc. are actually because the mass of the earth bends the space near it, and the apple and the moon only do inertial motion in the curved space. Moreover, not only "objects" such as apples and moons, but even light without mass will bend with space near mass.
But until 1915, he had been losing many battles in his quest for a complete theory, and he had no point. That summer, Einstein went to the University of Göttingen to give a visiting lecture and interact with the mathematical master there, David Hilbert. Both had intuition that the mathematical form of general relativity was almost within reach and was waiting for the final breakthrough.
After returning to Berlin, Einstein went into a state of near-madness. The First World War had begun, and Germany imposed wartime regulations and limited supplies of necessities. At this time, his wife ran away from home with her two sons, leaving him alone in the apartment, unable to eat a delicious meal. They are constantly fighting in correspondence for money and children. But what worries him even more is the constant correspondence with Hilbert, who is becoming more and more apparent in the correspondence that Hilbert may have preemptively discovered and published the field equations of general relativity.
In order not to lose priority, Einstein arranged a weekly academic lecture at the Prussian Academy of Sciences in November to release his latest progress "first time". At the beginning of the first lecture on November 4, he was still very confused about the direction of the series.
Outside of the lectures, Einstein spent all day writing letters to his wife, Hilbert, and other colleagues and friends, immersed himself in calculus, discovering and correcting errors in his own deductions again and again. Finally, in mid-November, when he tried to derive the perihelion precession problem of Mercury's orbit using a new formula under construction, he obtained a value that was different from Newtonian mechanics and almost ideally consistent with actual observations.
It was the first success of his new theory, solving an old problem that has plagued astronomers and physicists for decades. Einstein, who was no longer so young, was suddenly excited and flustered, and he could not calm down for three consecutive days.
On November 25, Einstein gave the final lecture in his lecture series at the Prussian Academy of Sciences. What remains on the blackboard is an incredibly concise equation, a general relativistic field equation that unifies inertial frames of reference and accelerated motion.
Hilbert also held his own lecture series in Göttingen and released the field equation he discovered on the 20th, five days before Einstein. But he didn't try to fight for the right to invent. He said that everyone in Göttingen knew better than Einstein the mathematics of four-dimensional space-time [as used in general relativity], but only Einstein understood the physics behind it.
Einstein's general relativistic field equation is a seemingly straightforward equation: on the left is the tensor describing the "shape" of four-dimensional space-time, and on the right is the distribution of energy (and mass) and momentum in space-time. The equal sign in the middle connects these two previously unrelated elements. There is no "force" in the equation, but it describes Mercury's orbit around the sun: because the sun's mass causes the space near it to bend, Mercury in this curved space naturally circles around the sun—and more precisely than in Newtonian mechanics.
Murals on the east wall of the Museum Boerhaave in the Netherlands commemorate general relativity. Above is a schematic diagram of the bending of light caused by the sun's gravity. Below is the field equation of general relativity, the third of which is the cosmic constant term introduced by Einstein out of nothing ("Λ" is the cosmological constant).
Later, the American physicist John Wheeler summed up the true meaning of the general relativistic field equation in a concise and concise way: "Space-time tells objects how to move, and objects tell space-time how to bend." ”（“Spacetime tells matter how to move; matter tells spacetime how to curve.” The two complement each other and are one and the same.
After the publication of the theory of general relativity, it was not only convincing in the calculation of the precession of Mercury's orbit, but also because the prediction that the light would bend due to the sun was confirmed by the observations of the British astronomer Arthur Eddington during the total solar eclipse in 1919, which established Einstein's position in the history of science in one fell swoop.
Einstein was overwhelmed and entered another creative peak after a decade earlier when he published a series of epoch-making papers on photoelectric effects, Brownian motion, special relativity, and the equivalence of mass and energy. His vision goes beyond the solar system and into the wider universe: since "objects tell how space-time bends", the shape of the entire universe can be directly deduced by knowing the mass distribution of the stars in the universe.
At the beginning of the 20th century, human beings had only a very simple intuitive understanding of the pattern of the universe. Our solar system has one star: the Sun. Orbiting the Sun at different distances were eight planets, including Mercury and Earth (the controversial "ninth planet," Pluto, had not yet been discovered), and most of the planets had a different number of moons.
Beyond the solar system, we can see the sky full of stars. Although they look overwhelming, they are not very symmetrical: most of the stars seem to be concentrated on a relatively narrow strip, like a river in the sky. This is called the Milky Way in China and the Milky Way in the West. The distribution of stars outside the river is noticeably sparse, and in some parts it is even pitch black, and there seems to be no stars.
With so many stars, astronomers only guess their distance and mass, and actually know nothing.
But Einstein didn't stick to those details.
A widely circulated joke goes that a rancher consulted experts over milk production. After some careful investigation and research, a theoretical physicist figured out how to deal with it. He confidently said to the rancher, "First of all, we must assume that the cow is a standard round ball..."
When confronted with complex problems that are unknown or not fully grasped, simple models that are highly simplified and abstracted to the point where they seem meaningless are the best tricks for theoretical physicists. The results of such research may not be directly applicable, but they can help people understand qualitative traits.
The universe in Einstein's mind—or rather, on computational paper—is such a "spherical cow": assuming that the mass in the universe is perfectly idealized and evenly distributed, nowhere more, nowhere less. Let's take a look at what shape the newly released field equations of general relativity would give to the universe.
This hypothesis, while sounding bizarre, is actually not so outrageous. The solar system appears to be structurally complex, but all of its mass is nearly 99.9 percent concentrated at this point in the Sun. Compared with the Sun, the masses of other planets and moons are completely negligible, which means that they do not exist. Beyond the solar system, Einstein felt that the universe might be much larger than we can see with the naked eye. At that large scale, perhaps the concentration of stars close to us in the Milky Way would also seem insignificant, and the distribution of distant stellar masses is still nearly uniform.
More importantly, of course, is that only such an extremely simplified model can find a solution from the mathematically complex field equations of general relativity. Even so, Einstein spent a year. Because he encountered a rather strange problem.
Suppose that after the mass of the universe is evenly distributed, the shape of the entire universe is determined by one variable: density. Einstein discovered that his universe was not infinitely large, but had a size determined by density. But at the same time, because space and time in the equations of general relativity are closely linked four-dimensional space-time, the size of this universe is not constant, but evolves with time, either smaller and smaller (collapsing), or getting larger and larger (expanding). No matter how much he tossed, he could not find a static universe that did not change with time.
He did not think too much about the possible implications behind this, but decided that such a solution was absurd and inconsistent with physical reality. The general theory of relativity he invented was clearly incomplete, missing a physical property that would stabilize the universe.
After much trial and error, Einstein finally found the flaw: if he added another term to the left of the field equation, he could come up with a static cosmic solution.
This newly added term is also a tensor used to describe the shape of space-time, but with a new constant as a coefficient. Einstein called it the "cosmological constant." Because this new addition is only effective when studying such a large scale as the universe. On "small" scales like the Solar System, this term is negligible because the value of the cosmological constant is too small. In this way, his previous calculations of Mercury's orbital precession, light due to the curvature of the Sun's mass, and so on are not affected.
Einstein's cosmological paper, published in 1917.
In February 1917, he preached this new work at the Prussian Academy of Sciences and published a 10-page paper in the journal Cosmological Considerations in the General Theory of Relativity, formally publishing his model of the universe.
Einstein's difficulties were not new problems posed by general relativity. As early as Newton discovered gravity, he faced the same question: since all masses are attracted to each other, they must gradually approach, and eventually all "collapse" to a point. Therefore, the universe cannot be stable. Newton didn't have a good idea. He argued wishfully that if the universe were infinitely large, no point was the center, and it would not collapse to any one point. Alternatively, in an infinite universe, each mass is simultaneously subject to attraction from all directions, canceling each other out and therefore having no practical utility.
Neither of these arguments holds true because they describe unstable systems that cannot actually exist. Some physicists have been trying to construct different models to try to solve or bypass this problem, but they have not gotten the point. In fact, Einstein's paper also begins with a discussion of this old problem of Newtonian mechanics, pointing out that if a term were artificially introduced into Newton's gravitational field equation, this difficulty could at least be avoided mathematically, but there was no physical reason to do so.
He proposed this possibility in order to pave the way for the introduction of nearly identical terms of "cosmic constant" in the field equations of general relativity. But even so, he could not find a reason to impose this additional item in the theory of relativity.
Einstein himself was frustrated. The introduction of the cosmic constant term is completely artificial, destroying the original natural beauty of the field equations. He could only argue that it was really a last resort to describe the universe in which we lived. Fortunately, the term itself does not break the original symmetry of the equation, and is at least mathematically permissible.
When Einstein's model of the universe was published, what stood out was not the cosmological constant that only physicists would wonder, but the shape of the universe he described: a sphere of a certain size whose radius was determined by the density of mass in the universe. But she's not the ball we're familiar with in our daily lives. Albert Einstein knew that although the size of the universe is limited, it has no boundaries.
The mass in the universe "tells" that space needs to be bent. Because the mass is evenly distributed, all places in the universe have the same curvature. Like a paper strip bent to form a ring end to end, the universe bends into a standard ball—just like a cow in the minds of theoretical physicists.
If we could shoot a beam of light with enough energy in a certain direction in the sky (there was no concept of lasers at that time), this beam of light would return to Earth in the opposite direction in hundreds of millions of years, just as Ferdinand Magellan's fleet triumphantly returned to the port of departure after completing its round-the-world voyage.
Magellan's fleet could only sail on the surface of the earth, and they returned to the same place in a circle around the earth in 3 years, indicating that the earth's surface is a world of limited size and no borders. This is a projection of the two-dimensional world on the surface of the three-dimensional Earth.
Einstein explained that the cosmic sphere in which we live is actually a projection of shapes in a four-dimensional space in the three-dimensional space that humans can perceive. Humans living in three-dimensional space cannot see the true shape of the four-dimensional universe, and can only perceive such a finite and boundless spherical projection.
This bizarre image is not only confusing for the average person. Even physicists and astronomers will be skeptical, calling her the "Einstein universe."
But after thousands of years of looking up at the stars and making countless conjectures and sighs about the stars, Einstein was the first person to construct a model for the entire universe based on the principles of physics. His paper thus marked the birth of modern cosmology.
It's just that how big the universe is, whether it's finite, whether it has boundaries, whether it's static or evolving, or even... Is there really only one universe? In Einstein's day, these questions were not only unanswered, but even unsure. Einstein's "cow" universe and his "cosmological constant" out of nothing is just a starting point that points the way for subsequent generations to examine the universe.
And to go down this path, we also need to really know the universe in which we live.
Source: Cheng Hu's Science Network Blog, Global Science, etc
Editor: Xu Shiheng