Many Worlds in One: The Search for Other Universes (14 page)
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Authors: Alex Vilenkin
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Many readers are, no doubt, wondering, Do we really have to believe all this nonsense about our clones? Is there any way to avoid these bizarre conclusions? If you absolutely cannot stand the thought of your double in a distant galaxy being a Republican (or a Democrat, as the case may be), and if you are willing to clutch at any straw to avoid it, let me offer you a couple of straws.
First of all, there is always a chance that the theory of inflation is wrong. The idea of inflation is very compelling, and the observational signs are encouraging,
but inflation is not nearly as well established as, for example, Einstein’s theory of relativity.
but inflation is not nearly as well established as, for example, Einstein’s theory of relativity.
Even if our universe is a product of inflation, it is conceivable that inflation is not eternal. This outcome, however, can be achieved only at the cost of making the theory rather contrived. In order to avoid eternal inflation, the energy landscape of the scalar field needs to be custom-tailored specifically for that purpose.
8
8
Neither of these options appears to be attractive. The theory of inflation is by far the best explanation we have for the big bang. If we accept this theory, and refuse to mutilate it by adding any ad hoc, unnecessary features, then we have no choice but to accept eternal inflation—with all of its consequences, whether we like them or not.
In times of antiquity we, humans, were at the center of the universe. The sky was not far off, and the fates of kingdoms and individuals could be read from the pattern of stars and planets on its velvet vault. Our descent from center stage started with Copernicus, and by the end of the last century it was nearly complete. Not only is the Earth not the center of the solar system, but the Sun itself is an unremarkable star at the outskirts of a rather typical galaxy. And yet, we could still hold on to the idea that there was something distinctly special about our Earth—that it was the only planet with this particular set of life forms, and that our human civilization, with its art, culture, and history, was unique in the entire universe. One might think that that alone was reason enough to treasure our little planet like a precious work of art.
Now, we have been robbed of this last claim to uniqueness. In the worldview that has emerged from eternal inflation, our Earth and our civilization are anything but unique. Instead, countless identical civilizations are scattered in the infinite expanse of the cosmos. With humankind reduced to absolute cosmic insignificance, our descent from the center of the universe is now complete.
9
9
The Cosmological Constant Problem
Few theoretical estimates in the history of physics … have ever been so inaccurate.
—LARRY ABBOTT
T
he most mysterious object ever encountered by physicists is the vacuum. And the most daunting secret of the vacuum is the origin of its energy. I should clarify that I do not mean the high-energy false vacuum of inflationary cosmology. False-vacuum physics is, in fact, relatively well understood. The enigmatic object I am talking about is the ordinary, true vacuum that we now inhabit.
he most mysterious object ever encountered by physicists is the vacuum. And the most daunting secret of the vacuum is the origin of its energy. I should clarify that I do not mean the high-energy false vacuum of inflationary cosmology. False-vacuum physics is, in fact, relatively well understood. The enigmatic object I am talking about is the ordinary, true vacuum that we now inhabit.
Vacuum is what you get when you remove all particles and radiation. For a classical physicist, it is just empty space, and there is not much more to say about it. But in quantum physics, the vacuum is a scene of frenetic activity.
Take, for example, electromagnetic radiation. It consists of photons—little lumps of electromagnetic energy. Suppose you have a box of pure vacuum. You clear the interior of the box and make sure there is not a single photon, or any other particle, left inside. You might think that the electric and magnetic fields in the box should now be strictly equal to zero. But they are not. The quantum vacuum refuses to stay still. Just like the scalar field
during inflation, electric and magnetic fields experience random jerks, or quantum fluctuations.
during inflation, electric and magnetic fields experience random jerks, or quantum fluctuations.
If you try to measure, say, the magnetic field inside the box, the answer you get depends on the size of your measuring device. Suppose you start with a fairly large device, which probes the field on the scale of 1 centimeter. The magnitude of the field will then come out to be a few billionths of a gauss. (To put this in perspective, note that the strength of the magnetic field on the Earth’s surface is about 1 gauss.) One nanosecond
ah
later, the direction of the field will be completely different, while its magnitude will be anywhere between zero and a few billionths of a gauss. To detect these rapid fluctuations of the field, you will have to measure it very quickly. If the measurement takes longer than a nanosecond, you will get the averaged value of the field, which is very close to zero.
ah
later, the direction of the field will be completely different, while its magnitude will be anywhere between zero and a few billionths of a gauss. To detect these rapid fluctuations of the field, you will have to measure it very quickly. If the measurement takes longer than a nanosecond, you will get the averaged value of the field, which is very close to zero.
A 1-millimeter detector would measure a magnetic field that is 100 times stronger and fluctuates 10 times faster. The same pattern holds as you go to still smaller scales: every time you reduce the distance scale by 10, the magnitude of the fluctuations grows by a factor of 100 and their frequency increases tenfold. On the atomic scale, the fluctuating magnetic field is 10 million gauss and changes its direction about 10
17
times per second.
17
times per second.
The reason we are not aware of these huge magnetic fields is that they vary so rapidly from one point to another and from one moment to the next. A compass needle, for example, reacts to the magnetic field averaged over the needle’s length and over the time it takes to turn by a noticeable amount (say, 0.1 second). The effect of quantum fluctuations on such scales is completely negligible.
1
1
All is well until we check the energy of the fluctuations. The energy density in a magnetic field depends only on the field strength, not on its direction. Hence, even though the magnetic field fluctuates back and forth, its energy density does not average to zero. Large, rapidly fluctuating fields on smaller-distance scales give a greater contribution to the energy density. And that’s where we run into a problem. As we include fluctuations on smaller and smaller scales, the energy density grows without bound. Thus, we arrive at the absurd conclusion that the energy density of the vacuum is infinite!
Something clearly went very wrong with our theory. Let us try to see what this could be and how we can avoid this bizarre conclusion.
Something clearly went very wrong with our theory. Let us try to see what this could be and how we can avoid this bizarre conclusion.
The infinity arises when we allow the length scale of the fluctuations to get arbitrarily small. But there may be a limit to how small it can be. At supersmall distances, the geometry of space and time is also subject to large quantum fluctuations. As in the case of electromagnetism, the smaller the distance scale, the larger the fluctuations. Below a certain critical distance, called the
Planck length
, spacetime acquires a chaotic, foamlike structure. The space warps and twists violently, small disconnected space “bubbles” pop out and collapse, and multiple “handles,” or “tunnels,” are being created and instantly destroyed (see
Figure 12.1
). The Planck length is incredibly small: it is one billion-trillion-trillionth of a centimeter. On much larger scales, the space appears to be smooth and the “spacetime foam” is not visible—just as the foamy surface of the ocean appears smooth when viewed from a large distance.
Planck length
, spacetime acquires a chaotic, foamlike structure. The space warps and twists violently, small disconnected space “bubbles” pop out and collapse, and multiple “handles,” or “tunnels,” are being created and instantly destroyed (see
Figure 12.1
). The Planck length is incredibly small: it is one billion-trillion-trillionth of a centimeter. On much larger scales, the space appears to be smooth and the “spacetime foam” is not visible—just as the foamy surface of the ocean appears smooth when viewed from a large distance.
It is possible that the drastic change in the character of spacetime intervenes to suppress the runaway electromagnetic fluctuations. We cannot tell for sure, since the physics of spacetime foam is not well understood. But even in the best-case scenario, there seems to be nothing to restrain the fluctuations on scales greater than the Planck length. An estimate of the energy density of such fluctuations gives an astounding 10
88
tons per cubic centimeter, much higher than in the grand-unified vacuum!
88
tons per cubic centimeter, much higher than in the grand-unified vacuum!
Figure 12.1
.
Spacetime foam.
.
Spacetime foam.
The energy density of the true vacuum is what Einstein called the cosmological constant. If indeed it were so tremendously large, the universe would now be in the state of explosive inflationary expansion. But the observed rate of expansion of the universe puts a bound on the cosmological constant, which is 10
120
(more than a google!) times smaller. We thus have a puzzle on our hands: Why isn’t the vacuum energy density huge? The glaring discrepancy between the predicted and observed values of the cosmological constant is known as the cosmological constant problem. It is one of the most tantalizing and frustrating mysteries that we now face in theoretical particle physics.
120
(more than a google!) times smaller. We thus have a puzzle on our hands: Why isn’t the vacuum energy density huge? The glaring discrepancy between the predicted and observed values of the cosmological constant is known as the cosmological constant problem. It is one of the most tantalizing and frustrating mysteries that we now face in theoretical particle physics.
Apart from electromagnetism, quantum fluctuations of other fields also contribute to the vacuum energy. It turns out that some of these contributions are negative, and there is some hope that positive and negative energy contributions might compensate one another. This possibility has inspired numerous attempts to solve the cosmological constant problem.
All elementary particles can be divided into two types:
bosons
and
fermions
.
ai
Photons, for example, are bosons, and electrons, positrons, and quarks are fermions. Fermi-particles can be pictured as small bundles of fermionic fields, but in contrast to electromagnetism, the magnitudes of such fields are characterized by the Grassmann numbers,
aj
which are very different from ordinary numbers. When you multiply ordinary numbers, the result does not depend on the order of multiplication; for instance, 4 x 6 = 6 x 4 = 24. But for Grassmann numbers the product changes sign if you reverse the order of multiplication:
a
x
b
= –
b
x
a.
The Grassmann character of the fermionic fields is responsible for many distinctive features of Fermi-particles, but what is important for us here is that the vacuum fluctuations of Fermi fields have a negative energy density.
bosons
and
fermions
.
ai
Photons, for example, are bosons, and electrons, positrons, and quarks are fermions. Fermi-particles can be pictured as small bundles of fermionic fields, but in contrast to electromagnetism, the magnitudes of such fields are characterized by the Grassmann numbers,
aj
which are very different from ordinary numbers. When you multiply ordinary numbers, the result does not depend on the order of multiplication; for instance, 4 x 6 = 6 x 4 = 24. But for Grassmann numbers the product changes sign if you reverse the order of multiplication:
a
x
b
= –
b
x
a.
The Grassmann character of the fermionic fields is responsible for many distinctive features of Fermi-particles, but what is important for us here is that the vacuum fluctuations of Fermi fields have a negative energy density.
Could it be that the positive vacuum energy of Bose fields is compensated by the negative energy of Fermi fields? This is possible in principle,
but seems extremely unlikely. The huge positive and negative terms, which depend in complicated ways on particle masses and interactions, have to cancel one another with an accuracy better than one part in a google. What could have caused such a miraculous coincidence?
but seems extremely unlikely. The huge positive and negative terms, which depend in complicated ways on particle masses and interactions, have to cancel one another with an accuracy better than one part in a google. What could have caused such a miraculous coincidence?
Remarkable cancellations do occur in particle physics, but they can usually be traced to some underlying symmetry. Take, for example, electric charge conservation. A high-energy collision can produce myriads of new particles, but you can always be sure that the numbers of positively and negatively charged particles that have been created are exactly equal, so the total charge is unchanged. This property is due to a special symmetry of the equations of elementary particle physics, called
gauge symmetry
.
ak
gauge symmetry
.
ak
It follows from gauge symmetry that electric charge is conserved in all elementary particle interactions. The beauty of symmetry is that details are unimportant. It does not matter what particle masses are or what kinds of interactions they are involved in. Charge conservation follows anyway.
Until very recently, the great majority of physicists believed that something of this sort should be going on in the case of the vacuum energy. There should be some deep symmetry, waiting to be discovered, that enforces the cancellation of different contributions to the cosmological constant.
2
Since the 1970s, numerous attempts have been made to figure out what this symmetry might be—some of them by the best minds in theoretical physics. However, after several decades, there was little to show for all that effort. The cosmological constant problem looked as formidable as ever.
2
Since the 1970s, numerous attempts have been made to figure out what this symmetry might be—some of them by the best minds in theoretical physics. However, after several decades, there was little to show for all that effort. The cosmological constant problem looked as formidable as ever.
“Any coincidence,” said Miss Marple to herself, “is worth noticing. You can throw it away later if it is only a coincidence.”
—AGATHA CHRISTIE,
Nemesis
Nemesis
It came as a total surprise when in the late 1990s two teams of astronomers announced that they had evidence for a nonvanishing cosmological constant. As we discussed in Chapter 9, this discovery was great news for the
theory of inflation. The mass (energy) density of the vacuum provided precisely the amount that was missing to make the universe flat. But it was dreadful news for the particle theory.
theory of inflation. The mass (energy) density of the vacuum provided precisely the amount that was missing to make the universe flat. But it was dreadful news for the particle theory.
The goal of solving the cosmological constant problem with a beautiful symmetry appeared now even more elusive. A symmetry would do a perfect job; it would not leave even a trace of vacuum energy uncompensated. But that was not all. The actual value of the cosmological constant that was obtained from the data looked extremely suspicious—so much so that most particle physicists and cosmologists refused to believe it and hoped that it would somehow go away.
The observed mass density of the vacuum is slightly more than twice the average density of matter. The puzzle is that the two densities are comparable, in the sense that one is not very much greater or smaller than the other. This is surprising, because the matter density and the vacuum density behave very differently with the expansion of the universe. The vacuum density does not change at all (as long as we stay in the same vacuum), while the matter density decreases as the volume grows. If the two densities are more or less the same today, then at the time of last scattering the matter density was a billion times greater than the vacuum density, and at 1 second A.B. it was 10
45
times greater. In the distant future the pattern will be reversed and the density of matter will become much smaller than that of the vacuum. For example, a trillion years from now it will be 10
50
times smaller.
45
times greater. In the distant future the pattern will be reversed and the density of matter will become much smaller than that of the vacuum. For example, a trillion years from now it will be 10
50
times smaller.
Thus, throughout most of the history of the universe the density of matter is strikingly different from that of the vacuum. Why, then, do we happen to live at the very special epoch when the two densities are close to each other? Considering the huge range of variation of the matter density, the coincidence is so extraordinary that it’s very hard to dismiss it as “only a coincidence.”
It looked as if nature were trying to tell us something. But, in her usual manner, she refused to make it easy for us to understand. Why would a fundamental constant of nature, like the cosmological constant, be related to the matter density at the particular epoch when we humans happen to be around? The idea of some connection between these two quantities appeared totally ridiculous. The particle physics community was in disarray.
And then there was a remarkable fact that made the situation even
more peculiar. A nonzero cosmological constant, not far off the observed value, had been theoretically predicted years before the observations were made. But there was a problem with that prediction. It was based on
anthropic selection
—an idea so controversial that most self-respecting physicists avoided it like the plague.
more peculiar. A nonzero cosmological constant, not far off the observed value, had been theoretically predicted years before the observations were made. But there was a problem with that prediction. It was based on
anthropic selection
—an idea so controversial that most self-respecting physicists avoided it like the plague.
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