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What Banged, How It Banged, and What Caused It to Bang
In the context of inflationary cosmology, it is fair to say that the universe is the ultimate free lunch.
—ALAN GUTH
O
n a Wednesday afternoon, in the winter of 1980, I was sitting in a fully packed Harvard auditorium, listening to the most fascinating talk I had heard in many years. The speaker was Alan Guth, a young physicist from Stanford, and the topic was a new theory for the origin of the universe. I had not met Guth before, but I had heard of his spectacular rise from obscurity to stardom. Only a month before, he belonged to the nomadic tribe of postdocs—young researchers traveling from one temporary contract to another, in the hope of distinguishing themselves and landing a permanent job at some university. Things were looking bleak for Guth: at age thirty-two he was getting a bit old for the youthful tribe, and the contract offers were beginning to dry out. But then he was blessed with a happy thought that changed everything.
n a Wednesday afternoon, in the winter of 1980, I was sitting in a fully packed Harvard auditorium, listening to the most fascinating talk I had heard in many years. The speaker was Alan Guth, a young physicist from Stanford, and the topic was a new theory for the origin of the universe. I had not met Guth before, but I had heard of his spectacular rise from obscurity to stardom. Only a month before, he belonged to the nomadic tribe of postdocs—young researchers traveling from one temporary contract to another, in the hope of distinguishing themselves and landing a permanent job at some university. Things were looking bleak for Guth: at age thirty-two he was getting a bit old for the youthful tribe, and the contract offers were beginning to dry out. But then he was blessed with a happy thought that changed everything.
Guth turned out to be a short, bouncy fellow, full of boyish enthusiasm, apparently untarnished by his long wanderings as a postdoc. From the outset, he made it clear that he was not trying to overthrow the big bang
theory. There was no need to. The evidence for the big bang was very persuasive, and the theory was in good shape.
theory. There was no need to. The evidence for the big bang was very persuasive, and the theory was in good shape.
The most convincing evidence is the expansion of the universe, discovered by Edwin Hubble in 1929. Hubble found that distant galaxies are moving away from us at very high speeds. If the motion of the galaxies is traced backward in time, they all merge together at some moment in the past, pointing to an explosive beginning of the universe.
Another major piece of evidence in favor of the big bang is the
cosmic background radiation
. Space is filled with microwaves of about the same frequency as we use in microwave ovens. The intensity of this radiation dwindles as the universe expands; hence what we now observe is the faint afterglow of the hot primeval fireball.
cosmic background radiation
. Space is filled with microwaves of about the same frequency as we use in microwave ovens. The intensity of this radiation dwindles as the universe expands; hence what we now observe is the faint afterglow of the hot primeval fireball.
Cosmologists used the big bang theory to study how the fireball expanded and cooled, how atomic nuclei formed, and how the grand spirals of galaxies emerged from featureless gas clouds. The results of these studies were in excellent agreement with astronomical observations, so there was little doubt that the theory was on the right track. What it described, however, was only the aftermath of the big bang; the theory said nothing about the bang itself. In Guth’s own words, it did not say “what ‘banged,’ how it ‘banged,’ or what caused it to ‘bang.’”
1
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To compound the mystery, on closer examination the big bang appeared to be a very peculiar kind of explosion. Just imagine a pin balancing on its point. Nudge it slightly in any direction and it will fall. So it is with the big bang. A large universe sprinkled with galaxies, like the one we see around us, is produced only if the power of the primordial blast is fine-tuned with an incredible precision. A tiny deviation from the required power results in a cosmological disaster, such as the fireball collapsing under its own weight or the universe being nearly empty.
The big bang cosmology simply postulated that the fireball had the required properties. The prevailing attitude among physicists was that physics can describe how the universe evolved from a given initial state, but it is beyond physics to explain why the universe happened to start in that particular configuration. Asking questions about the initial state was regarded as “philosophy,” which, coming from a physicist, translates as a waste of time. This attitude, however, did not make the big bang any less enigmatic.
Now Guth was telling us that the veil of mystery surrounding the big
bang could be lifted. His new theory would uncover the nature of the bang and explain why the initial fireball was so contrived. The seminar room fell suddenly silent. Everybody was intrigued.
bang could be lifted. His new theory would uncover the nature of the bang and explain why the initial fireball was so contrived. The seminar room fell suddenly silent. Everybody was intrigued.
The explanation the new theory gave for the big bang was remarkably simple: the universe was blown up by repulsive gravity! The leading role in this theory is played by a hypothetical, superdense material with some highly unusual properties. Its most important characteristic is that it produces a strong repulsive gravitational force. Guth assumed that there was some amount of this material in the early universe. He did not need much: a tiny chunk would be sufficient.
The internal gravitational repulsion would cause the chunk to expand very rapidly. If it were made of normal matter, its density would be diluted as it expanded, but this antigravity stuff behaves completely differently: the second key feature of the strange material is that its density always remains the same, so its total mass is proportional to the volume it occupies. As the chunk grows in size, it also grows in mass, so its repulsive gravity becomes stronger and it expands even faster. A brief period of such accelerated expansion, which Guth called
inflation
, can enlarge a minuscule initial chunk to enormous dimensions, far exceeding the size of the presently observable universe.
inflation
, can enlarge a minuscule initial chunk to enormous dimensions, far exceeding the size of the presently observable universe.
Figure 1.1
. A chunk of gravitationally repulsive material.
. A chunk of gravitationally repulsive material.
The dramatic increase in mass during inflation may at first appear to contradict one of the most fundamental laws of physics, the law of energy conservation. By Einstein’s famous relation, E = mc
2
, energy is proportional to mass. (Here,
E
is energy,
m
is mass, and
c
is the speed of light.) So
the energy of the inflating chunk must also have grown by a colossal factor, while energy conservation requires that it should remain constant. The paradox disappears if one remembers to include the contribution to the energy due to gravity. It has long been known that gravitational energy is always negative. This fact did not appear very important, but now it suddenly acquired a cosmic significance. As the positive energy of matter grows, it is balanced by the growing negative gravitational energy. The total energy remains constant, as demanded by the conservation law.
2
, energy is proportional to mass. (Here,
E
is energy,
m
is mass, and
c
is the speed of light.) So
the energy of the inflating chunk must also have grown by a colossal factor, while energy conservation requires that it should remain constant. The paradox disappears if one remembers to include the contribution to the energy due to gravity. It has long been known that gravitational energy is always negative. This fact did not appear very important, but now it suddenly acquired a cosmic significance. As the positive energy of matter grows, it is balanced by the growing negative gravitational energy. The total energy remains constant, as demanded by the conservation law.
In order to provide an ending for the period of inflation, Guth required that the repulsive gravity stuff should be unstable. As it decays, its energy is released to produce a hot fireball of elementary particles. The fireball then continues to expand by inertia, but now it consists of normal matter, its gravity is attractive, and the expansion gradually slows down. The decay of the antigravity material marks the end of inflation and plays the role of the big bang in this theory.
The beauty of the idea was that in a single shot inflation explained why the universe is so big, why it is expanding, and why it was so hot at the beginning. A huge expanding universe was produced from almost nothing. All that was needed was a microscopic chunk of repulsive gravity material. Guth admitted he did not know where the initial chunk came from, but that detail could be worked out later. “It’s often said that you cannot get something for nothing,” he said, “but the universe may be the ultimate free lunch.”
All this assumes, of course, that the repulsive gravity stuff really existed. There was no shortage of it in science fiction novels, where it had been used in all sorts of flying machines, from combat vehicles to antigravity shoes. But could professional physicists seriously consider the possibility that gravity might be repulsive?
They sure could. And the first to do that was none other than Albert Einstein.
The Rise and Fall of Repulsive Gravity
“We have conquered gravity!” the Professor shouted, and crashed to the floor.
—J. WILLIAMS and R. ABRASHKIN,
Danny Dunn and the Anti-Gravity Paint
Danny Dunn and the Anti-Gravity Paint
E
instein created two theories of stunning beauty that forever changed our concepts of space, time, and gravitation. The first of the two, called the special theory of relativity, was published in 1905, when Einstein was twenty-six and by most standards could be regarded a failure. His fierce independence and his casual class attendance did not make him popular among the professors at Zurich Polytechnic, where he got his diploma. When the time came to apply for jobs, all his fellow graduates were appointed assistants at the Polytechnic, while Einstein failed to get any academic position. He thought himself lucky to have a job as a clerk at the patent office in Berne, which he got with the help of a former classmate. On the positive side, the patent office work was not without some interest and left plenty of time for Einstein’s research and other intellectual pursuits. He spent evenings with friends, smoking a pipe, reading Spinoza and Plato, and discussing his ideas about physics. He also played string quintets in the unlikely company of a lawyer, a bookbinder, a schoolteacher, and a prison
guard. None of them suspected that their second violin had something profound to say about the nature of space and time.
instein created two theories of stunning beauty that forever changed our concepts of space, time, and gravitation. The first of the two, called the special theory of relativity, was published in 1905, when Einstein was twenty-six and by most standards could be regarded a failure. His fierce independence and his casual class attendance did not make him popular among the professors at Zurich Polytechnic, where he got his diploma. When the time came to apply for jobs, all his fellow graduates were appointed assistants at the Polytechnic, while Einstein failed to get any academic position. He thought himself lucky to have a job as a clerk at the patent office in Berne, which he got with the help of a former classmate. On the positive side, the patent office work was not without some interest and left plenty of time for Einstein’s research and other intellectual pursuits. He spent evenings with friends, smoking a pipe, reading Spinoza and Plato, and discussing his ideas about physics. He also played string quintets in the unlikely company of a lawyer, a bookbinder, a schoolteacher, and a prison
guard. None of them suspected that their second violin had something profound to say about the nature of space and time.
Einstein completed the special theory of relativity in less than six weeks of frenzied work. The theory shows that space and time intervals do not by themselves have absolute meaning, but rather depend on the state of motion of the observer who measures them. If two observers move relative to one another, then each of them will find that the other’s clock ticks more slowly than his own. Simultaneity is also relative. Events that are simultaneous for one observer will generally occur at different times for the other. We do not notice these effects in our everyday life because they are completely negligible at ordinary velocities. But if the speed of the two observers relative to each other is close to the speed of light, the discrepancies between their measurements can be very large. There is one thing, though, that all observers will agree upon: light always travels at the same speed, approximately 300,000 kilometers per second.
The speed of light is the absolute speed limit in the universe. As you apply a force to a physical object, the object accelerates. Its velocity grows, and if you keep up the force, the velocity of the object will eventually approach the speed of light. Einstein showed that it would take increasingly large amounts of energy to get closer and closer to the speed of light, so the limit can never be reached.
Perhaps the best-known consequence of special relativity is the equivalence of energy and mass, expressed in Einstein’s formula E = mc
2
. If you heat an object, its thermal (heat) energy grows, so it should weigh more. This may give you the idea to take a cold shower before you step on the scale. But this trick is likely to decrease your weight by no more than a few billionths of a pound. In conventional units, like meters and seconds, the conversion factor
c
2
between energy and mass is very large, and it takes a huge amount of energy to noticeably change the mass of a macroscopic body. Physicists often use another system of units, where
c
= 1, so that energy is simply equal to mass and can be measured in kilograms.
a
I will mostly follow this tradition and make no distinction between energy and mass.
2
. If you heat an object, its thermal (heat) energy grows, so it should weigh more. This may give you the idea to take a cold shower before you step on the scale. But this trick is likely to decrease your weight by no more than a few billionths of a pound. In conventional units, like meters and seconds, the conversion factor
c
2
between energy and mass is very large, and it takes a huge amount of energy to noticeably change the mass of a macroscopic body. Physicists often use another system of units, where
c
= 1, so that energy is simply equal to mass and can be measured in kilograms.
a
I will mostly follow this tradition and make no distinction between energy and mass.
The word “special” in “special relativity” refers to the fact that this theory applies only in special circumstances when the effects of gravity are
unimportant. This limitation is removed in Einstein’s second theory, the general theory of relativity, which is essentially a theory of gravitation.
unimportant. This limitation is removed in Einstein’s second theory, the general theory of relativity, which is essentially a theory of gravitation.
The general theory of relativity grew out of a simple observation, that the motion of objects under the action of gravity is independent of their mass, shape, or any other properties, as long as all nongravitational forces can be neglected. This was first recognized by Galileo, who forcefully argued the point in his famous
Dialogues
. The accepted view at the time, that of Aristotle, was that heavier objects fall faster. Indeed, a watermelon does fall faster than a feather, but Galileo realized that the difference was due only to air resistance. Legend has it that Galileo dropped rocks of different weight from the Leaning Tower of Pisa, to make sure that they landed at the same time. We do know that he experimented with marbles rolling down an inclined plane and found that the motion was independent of the mass. He also offered a theoretical proof that Aristotle could not be right. Suppose, says Galileo, that a heavy rock falls faster than a light rock. Imagine then tying them together with a very light string. How will this affect the fall of the heavy rock? On the one hand, the slower-moving light rock should make the fall of the heavy rock somewhat slower than it was before. On the other hand, viewed together, the two rocks now constitute one object that is more massive than the heavy rock was initially, and thus the two rocks together should fall faster. This contradiction demonstrates that Aristotle’s theory is inconsistent.
Dialogues
. The accepted view at the time, that of Aristotle, was that heavier objects fall faster. Indeed, a watermelon does fall faster than a feather, but Galileo realized that the difference was due only to air resistance. Legend has it that Galileo dropped rocks of different weight from the Leaning Tower of Pisa, to make sure that they landed at the same time. We do know that he experimented with marbles rolling down an inclined plane and found that the motion was independent of the mass. He also offered a theoretical proof that Aristotle could not be right. Suppose, says Galileo, that a heavy rock falls faster than a light rock. Imagine then tying them together with a very light string. How will this affect the fall of the heavy rock? On the one hand, the slower-moving light rock should make the fall of the heavy rock somewhat slower than it was before. On the other hand, viewed together, the two rocks now constitute one object that is more massive than the heavy rock was initially, and thus the two rocks together should fall faster. This contradiction demonstrates that Aristotle’s theory is inconsistent.
Einstein was pondering this peculiar kind of motion, which is completely independent of what is moving. It reminded him of inertial motion: in the absence of forces, an object moves along a straight line at a constant speed, regardless of what it is made of. In effect, the motion of the object in space and time is the property of space and time themselves.
Here Einstein made use of the ideas of his former mathematics professor, Hermann Minkowski. As a student, Einstein did not think much of Minkowski’s lectures, while Minkowski remembered Einstein as a “lazy dog” and did not expect him to do anything worthwhile. To Minkowski’s credit, he changed his mind quickly after reading Einstein’s 1905 paper.
Minkowski realized that the mathematics of special relativity becomes simpler and more elegant if space and time are not regarded as separate, but
are united in a single entity called
spacetime
. A point in spacetime is an
event
. It can be specified by four numbers: three for its spatial location and one for its time. Hence, spacetime has four dimensions. If you had all of spacetime in front of you, then you would know all the past, present, and future of the universe. The history of each particle is represented by a line in spacetime, which gives the position of the particle at every moment of time. This line is called the
world line
of the particle. (George Gamow, one of the founders of the big bang cosmology, called his autobiography
My World Line
.)
are united in a single entity called
spacetime
. A point in spacetime is an
event
. It can be specified by four numbers: three for its spatial location and one for its time. Hence, spacetime has four dimensions. If you had all of spacetime in front of you, then you would know all the past, present, and future of the universe. The history of each particle is represented by a line in spacetime, which gives the position of the particle at every moment of time. This line is called the
world line
of the particle. (George Gamow, one of the founders of the big bang cosmology, called his autobiography
My World Line
.)
The uniform motion of particles in the absence of gravity is represented by straight lines in spacetime. But gravity makes particles deviate from this simple motion, so their world lines are no longer straight. This led Einstein to a truly astonishing hypothesis: even deviant particles with curved world lines might still be following the straightest possible paths in spacetime, but the spacetime itself must be curved around massive bodies. Gravity, then, is nothing but the curvature of spacetime!
The distortion of spacetime geometry by a massive body can be illustrated by a heavy object resting on a horizontally stretched rubber sheet (see
Figure 2.1
). The rubber surface is warped near the object, just as spacetime is warped near a gravitating body. If you try playing billiards on this rubber sheet, you will discover that the billiard balls are deflected on the curved surface, especially when they pass near the heavy mass. This analogy is not perfect—it illustrates only the warping of space, not that of spacetime—but it does capture the essence of the idea.
Figure 2.1
). The rubber surface is warped near the object, just as spacetime is warped near a gravitating body. If you try playing billiards on this rubber sheet, you will discover that the billiard balls are deflected on the curved surface, especially when they pass near the heavy mass. This analogy is not perfect—it illustrates only the warping of space, not that of spacetime—but it does capture the essence of the idea.
Figure 2.1
. A massive body causes space to curve.
. A massive body causes space to curve.
It took Einstein more than three years of truly heroic effort to express these ideas in mathematical terms. The equations of the new theory, which he called the general theory of relativity, relate the geometry of spacetime to the matter content of the universe. In the regime of slow motion and not-too-strong gravitational fields, the theory reproduced Newton’s law, with the force of gravity being inversely proportional to the square of the distance. There was also a small correction to this law, which was utterly negligible for planetary motion, except in the case of Mercury, the planet closest to the Sun. The effect of the correction was to cause a slow precession, or advance, of Mercury’s orbit. Astronomical observations did in fact show a tiny precession, which remained unexplained in Newton’s theory, but was in perfect agreement with Einstein’s calculation. At this point Einstein was certain that the theory was correct. “I was beside myself with ecstasy for days,” he wrote to his friend Paul Ehrenfest.
1
1
Figure 2.2
. Einstein’s equations.
. Einstein’s equations.
Perhaps the most remarkable thing about the general theory of relativity is how little factual input it required. The essential fact that Einstein placed at the foundation of the theory—that the motion of objects under the action of gravity is independent of their mass—was known already to Galileo. With this minimal input, he created a theory that reproduced Newton’s law in the appropriate limit and explained a deviation from this law. If you think about it, Newton’s law is in some sense arbitrary. It states that the gravitational force between two bodies is inversely proportional to the second
power of their distance, but it does not say why. It could equally well be the fourth power or the 2.03rd power. In contrast, Einstein’s theory allows no freedom. The picture of gravity as curvature of spacetime inevitably leads to Einstein’s equations, and the equations yield the inverse square law. In this sense the general theory of relativity not only describes gravity, it
explains
gravity. So compelling was the logic of the theory and so beautiful its mathematical structure that Einstein felt it simply had to be right. In a letter to a senior colleague, Arnold Sommerfeld, he wrote, “Of the general theory of relativity you will be convinced, once you have studied it. Therefore I am not going to defend it with a single word.”
2
power of their distance, but it does not say why. It could equally well be the fourth power or the 2.03rd power. In contrast, Einstein’s theory allows no freedom. The picture of gravity as curvature of spacetime inevitably leads to Einstein’s equations, and the equations yield the inverse square law. In this sense the general theory of relativity not only describes gravity, it
explains
gravity. So compelling was the logic of the theory and so beautiful its mathematical structure that Einstein felt it simply had to be right. In a letter to a senior colleague, Arnold Sommerfeld, he wrote, “Of the general theory of relativity you will be convinced, once you have studied it. Therefore I am not going to defend it with a single word.”
2
With his general theory of relativity now complete, Einstein wasted no time in applying it to the entire universe. He was not interested in trivial details, such as the position of this star or that planet. Rather, he wanted to find a solution of his equations that would describe, in broad brushstrokes, the structure of the universe as a whole.
Little was known at the time about the distribution of matter in the universe, so Einstein had to make some guesses. He made the simplest assumption that, on average, matter is uniformly spread throughout the cosmos. There are, of course, local deviations from uniformity, with the density of stars being a little higher in this place and a little lower in that. What Einstein assumed was that if matter is smoothed over large enough distance scales, then, to a good approximation, the universe can be described as perfectly homogeneous. This assumption implies that our location in space is not in any way special: all places in the universe are more or less the same. Einstein also assumed that the universe is on average
isotropic
, which means that from any point it looks more or less the same in all directions.
isotropic
, which means that from any point it looks more or less the same in all directions.
Finally, Einstein assumed that the average properties of the universe do not change with time. In other words, the universe is static. Although Einstein had little observational evidence to support this assumption, the picture of an eternal, unchanging universe seemed very compelling.
Having specified the kind of universe he was looking for, Einstein could now try to find a solution of his equations that would describe a universe with the desired properties. It did not take him long, however, to discover
that his theory admitted no such solutions. The reason was very simple: masses distributed throughout the universe refused to stay at rest and “wanted” instead to collapse onto one another, because of their gravitational attraction. Einstein was deeply puzzled and perplexed by this situation. After a year of struggle, he decided that the equations of general relativity had to be modified to allow for the existence of a static world.
that his theory admitted no such solutions. The reason was very simple: masses distributed throughout the universe refused to stay at rest and “wanted” instead to collapse onto one another, because of their gravitational attraction. Einstein was deeply puzzled and perplexed by this situation. After a year of struggle, he decided that the equations of general relativity had to be modified to allow for the existence of a static world.
Einstein realized that it was possible to add an extra term to his equations without violating the physical principles of the theory. The effect of the new term was to endow empty space, or vacuum, with nonzero energy and tension. Each cubic centimeter of empty space has a fixed amount of energy (and therefore mass). Einstein called this constant energy density of the vacuum the
cosmological constant
.
b
The mathematics of Einstein’s equations dictates that the tension of the vacuum is exactly equal to its energy density and is therefore determined by the same constant. The vacuum tension is like the tension in a stretched rubber band that would cause the band to shrink if you let it go. Tension is opposite to pressure, which causes things to expand—as when a balloon expands under the pressure of compressed air. Thus, tension acts as negative pressure.
cosmological constant
.
b
The mathematics of Einstein’s equations dictates that the tension of the vacuum is exactly equal to its energy density and is therefore determined by the same constant. The vacuum tension is like the tension in a stretched rubber band that would cause the band to shrink if you let it go. Tension is opposite to pressure, which causes things to expand—as when a balloon expands under the pressure of compressed air. Thus, tension acts as negative pressure.
If the vacuum has energy and tension, how come they seem to have no effect on us? Why don’t we see empty space shrink because of its tension? The reason is that it is not so easy to notice
constant
energy and tension. If you increase the pressure inside a balloon, it will expand. But if you also increase the air pressure outside the balloon by the same amount, then there will be no effect. Similarly, if negative-pressure vacuum fills the entire universe, its overall effect is nil. The energy of the vacuum is elusive because it is impossible to extract this energy. You cannot burn the vacuum; you cannot use it to run a car or a hair dryer. Its energy is set by the cosmological constant and cannot be reduced. Thus, the energy and tension of the vacuum are undetectable—except for their gravitational effect.
constant
energy and tension. If you increase the pressure inside a balloon, it will expand. But if you also increase the air pressure outside the balloon by the same amount, then there will be no effect. Similarly, if negative-pressure vacuum fills the entire universe, its overall effect is nil. The energy of the vacuum is elusive because it is impossible to extract this energy. You cannot burn the vacuum; you cannot use it to run a car or a hair dryer. Its energy is set by the cosmological constant and cannot be reduced. Thus, the energy and tension of the vacuum are undetectable—except for their gravitational effect.
The gravity of the vacuum turned out to hold a big surprise. According to general relativity, pressure and tension contribute to the gravitational force of massive bodies. If you compress an object, its gravity is enhanced, and if you stretch it, gravity is reduced. This effect is normally very small,
but if you could keep stretching the object without breaking it, you could in principle reduce gravity to the point of completely neutralizing it, or even making it repulsive. This is precisely what happens in the case of the vacuum. The repulsive gravity of vacuum tension is more than sufficient to overcome the attractive pull of its mass, so the net result is gravitational repulsion.
but if you could keep stretching the object without breaking it, you could in principle reduce gravity to the point of completely neutralizing it, or even making it repulsive. This is precisely what happens in the case of the vacuum. The repulsive gravity of vacuum tension is more than sufficient to overcome the attractive pull of its mass, so the net result is gravitational repulsion.
This property was exactly what Einstein needed to solve his problem. He could now adjust the value of the cosmological constant so that the attractive gravitational force of matter is balanced by the repulsive gravity of the vacuum. The result is a static universe. He found from his equations that the balance is achieved when the cosmological constant is half the energy density of matter.
A striking consequence of the modified equations was that the space of a static universe must be curved, so that it closes in upon itself like the surface of a sphere. A spaceship moving straight ahead in such a closed universe would eventually come back to its starting point. This closed space is called a three-dimensional sphere. Its volume is finite, although it has no boundary.
Einstein described his closed-universe model in a paper published in 1917. He admitted that he had no observational evidence for a nonzero cosmological constant. His only reason for introducing it was to save the static picture of the world. More than a decade later, when the expansion of the universe was discovered, Einstein regretted he had ever proposed the idea and called it the greatest blunder of his life.
3
After this unsuccessful debut, repulsive gravity disappeared from mainstream physics research for nearly half a century—but only to return later with a vengeance.
3
After this unsuccessful debut, repulsive gravity disappeared from mainstream physics research for nearly half a century—but only to return later with a vengeance.
BOOK: Many Worlds in One: The Search for Other Universes
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