physics, it’s not easy to un-invent a concept. The cosmological constant is the same as the idea of vacuum energy, the energy of empty space itself. The question is not “Is vacuum energy a valid concept?”—it’s “What value should we expect the vacuum energy to have?”
Modern quantum mechanics implies that the vacuum is not a boring place; it’s alive with virtual particles . A crucial consequence of quantum mechanics is Werner Heisenberg’s uncertainty principle: It’s impossible to pin down the observable features of any system into one unique state with perfect precision, and that includes the state of empty space. So if we were to look closely enough at empty space, we would see particles flashing into and out of existence, representing quantum fluctuations of the vacuum itself. These virtual particles are not especially mysterious or hypothetical—they are definitely there, and they have measurable effects in particle physics that have been observed many times over.
Virtual particles carry energy, and that energy contributes to the cosmological constant. We can add up the effects of all such particles to obtain an estimate for how large the cosmological constant should be. But it wouldn’t be right to include the effects of particles with arbitrarily high energies. We don’t believe that our conventional understanding of particle physics is adequate for very high-energy events—at some point, we have to take account of the effects of quantum gravity, the marriage of general relativity with quantum mechanics, which remains an incomplete theory at the moment.
So instead of appealing to the correct theory of quantum gravity, which we still don’t have, we can simply examine the contributions to the vacuum energy of virtual particles at energies below where quantum gravity becomes important. That’s the Planck energy , named after German physicist Max Planck, one of the pioneers of quantum theory, and it turns out to be about 2 billion joules (a conventional unit of energy). 49 We can add up the contributions to the vacuum energy from virtual particles with energies ranging from zero up to the Planck energy, and then cross our fingers and compare with what we actually observe.
The result is a complete fiasco. Our simple estimate of what the vacuum energy should be comes out to about 10 105 joules per cubic centimeter. That’s a lot of vacuum energy. What we actually observe is about 10 -15 joules per cubic centimeter. So our estimate is larger than the experimental value by a factor of 10 120 —a 1 followed by 120 zeroes. Not something we can attribute to experimental error. This has been called the biggest disagreement between theoretical expectation and experimental reality in all of science. For comparison, the total number of particles in the observable universe is only about 10 88 ; the number of grains of sand on all the Earth’s beaches is only about 10 20 .
The fact that the vacuum energy is so much smaller than it should be is a serious problem: the “cosmological constant problem.” But there is also another problem: the “coincidence problem.” Remember that vacuum energy maintains a constant density (amount of energy per cubic centimeter) as the universe expands, while the density of matter dilutes away. Today, they aren’t all that different: Matter makes up about 25 percent of the energy of the universe, while vacuum energy makes up the other 75 percent. But they are changing appreciably with respect to each other, as the matter density dilutes away with the expansion and the vacuum energy does not. At the time of recombination, for example, the energy density in matter was a billion times larger than that in vacuum energy. So the fact that they are somewhat comparable today, uniquely in the history of the universe, seems like a remarkable coincidence indeed. Nobody knows why.
These are serious problems with our theoretical understanding of vacuum energy. But if we put aside our
Modern quantum mechanics implies that the vacuum is not a boring place; it’s alive with virtual particles . A crucial consequence of quantum mechanics is Werner Heisenberg’s uncertainty principle: It’s impossible to pin down the observable features of any system into one unique state with perfect precision, and that includes the state of empty space. So if we were to look closely enough at empty space, we would see particles flashing into and out of existence, representing quantum fluctuations of the vacuum itself. These virtual particles are not especially mysterious or hypothetical—they are definitely there, and they have measurable effects in particle physics that have been observed many times over.
Virtual particles carry energy, and that energy contributes to the cosmological constant. We can add up the effects of all such particles to obtain an estimate for how large the cosmological constant should be. But it wouldn’t be right to include the effects of particles with arbitrarily high energies. We don’t believe that our conventional understanding of particle physics is adequate for very high-energy events—at some point, we have to take account of the effects of quantum gravity, the marriage of general relativity with quantum mechanics, which remains an incomplete theory at the moment.
So instead of appealing to the correct theory of quantum gravity, which we still don’t have, we can simply examine the contributions to the vacuum energy of virtual particles at energies below where quantum gravity becomes important. That’s the Planck energy , named after German physicist Max Planck, one of the pioneers of quantum theory, and it turns out to be about 2 billion joules (a conventional unit of energy). 49 We can add up the contributions to the vacuum energy from virtual particles with energies ranging from zero up to the Planck energy, and then cross our fingers and compare with what we actually observe.
The result is a complete fiasco. Our simple estimate of what the vacuum energy should be comes out to about 10 105 joules per cubic centimeter. That’s a lot of vacuum energy. What we actually observe is about 10 -15 joules per cubic centimeter. So our estimate is larger than the experimental value by a factor of 10 120 —a 1 followed by 120 zeroes. Not something we can attribute to experimental error. This has been called the biggest disagreement between theoretical expectation and experimental reality in all of science. For comparison, the total number of particles in the observable universe is only about 10 88 ; the number of grains of sand on all the Earth’s beaches is only about 10 20 .
The fact that the vacuum energy is so much smaller than it should be is a serious problem: the “cosmological constant problem.” But there is also another problem: the “coincidence problem.” Remember that vacuum energy maintains a constant density (amount of energy per cubic centimeter) as the universe expands, while the density of matter dilutes away. Today, they aren’t all that different: Matter makes up about 25 percent of the energy of the universe, while vacuum energy makes up the other 75 percent. But they are changing appreciably with respect to each other, as the matter density dilutes away with the expansion and the vacuum energy does not. At the time of recombination, for example, the energy density in matter was a billion times larger than that in vacuum energy. So the fact that they are somewhat comparable today, uniquely in the history of the universe, seems like a remarkable coincidence indeed. Nobody knows why.
These are serious problems with our theoretical understanding of vacuum energy. But if we put aside our
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