What would happen if the lumpiness were larger than 10–5? A factor of one hundred larger, and the universe would be full of violent, ravenous monsters that would swallow and digest galaxies before they were even finished forming. Don’t worry; I haven’t lost my mind. The “mega-monsters” are huge black holes. Remember that gravity is the agent that works on the regions with slight excess mass density and pulls them together to form galaxies. But if the overdensities were too strong, gravity would work too quickly. The gravitational collapse of these regions would go right past the galaxy stage and evolve into black holes. All matter would quickly be gobbled up and destroyed at the infinitely violent central singularity of the black hole. Even density contrasts a factor of ten stronger could endanger life by creating too many collisions between celestial objects in the solar system.
A lumpiness of about 10–5 is essential for life to get a start. But is it easy to arrange for this amount of density contrast? The answer is most decidedly no! The various parameters governing the inflating universe must be chosen with great care in order to get the desired result. More of Hoyle’s monkeying?
There is a lot more. The laws of particle physics include the requirement that every particle has an antiparticle. How then did the universe get to have such a large preponderance of matter over antimatter? Here is what we think happened:
When the universe was very young and hot, it was filled with plasma that contained almost exactly equal amounts of matter and antimatter. The imbalance was extremely small. For every 100,000,000 antiprotons, there were 100,000,001 protons. Then, as the universe cooled, particles and antiparticles combined in pairs and annihilated into photons. One hundred million antiprotons found 100,000,000 partners and, together, they committed suicide, leaving 200,000,000 photons and just 1 leftover proton. These leftovers are the stuff we are made of. Today, if you take a cubic meter of intergalactic space, it will contain about 1 proton and 200,000,000 photons. Without the slight initial imbalance, I would not be here to tell you (who would not be here to read) these things.
Another essential requirement for life is that gravity be extremely weak. In ordinary life gravity hardly seems weak. Indeed, as we age, the daily prospect of fighting gravity gets more and more daunting. I can still hear my grandmother saying, “Oy vey, I feel like a thousand pounds.” But I don’t ever recall hearing her complain about electric forces or nuclear forces. Nonetheless, if you compare the electric force between the nucleus and an atomic electron with the gravitational force, you would find the electric force is about 1041 times larger. Where did such a huge ratio come from? Physicists have some ideas, but the truth is that we really don’t know the origin of this humongous discrepancy between electricity and gravity despite the fact that it is so central to our existence.7 But we can ask what would have happened if gravity had been a little stronger than it is. The answer again is that we would not be here to talk about it. The increased pressure due to stronger gravity would cause stars to burn much too fast—so fast that life would have no chance to evolve. Even worse, black holes would have consumed everything, dooming life long before it began. The large gravitational pull might even have aborted the Hubble expansion and caused a big crunch very shortly after the Big Bang.
Just how seriously should we take this collection of lucky coincidences? Do they really make a strong case for some kind of Anthropic Principle? My own feeling is that they are very impressive, but not so impressive that they would have pushed me past the tipping point to embrace an anthropic explanation. None of these accidental pieces of good luck, with the exception of the remarkable weakness of gravity, involves extraordinarily high-precision (precision to many decimal places) fine-tuning. And even the feebleness of gravity has a possible explanation involving the magic of supersymmetry. Taken together, these coincidences do seem like an unlikely bunch of accidents; but accidents, after all, do happen.
However, the smallness of the cosmological constant is another matter. To make the first 119 decimal places of the vacuum energy zero is most certainly no accident. But it was not just that the cosmological constant was very small. Had it been even smaller than it is, had it continued to be zero to the current level of accuracy, one could have gone on believing that some unknown mathematical principle would make it exactly zero. The event that hit us like the proverbial ton of bricks was the fact that in the 120th place the answer was not zero. No missing mathematical magic is going to explain that.
But even the cosmological constant would not have been enough to tip the balance for me. For me the tipping point came with the discovery of the huge Landscape that String Theory appears to be forcing on us.
When Do Anthropic Explanations Make Sense?
Suppose that you and I were partners in the business of creating life-friendly universes. Your job is to think of all the necessary ingredients and to create a design. My job is just to search the Landscape for a location that satisfies your requirements. You would come up with a design. Then I would go off and search the Landscape. If the Landscape had only a handful of valleys, I almost certainly would not find what you were looking for. I would tell you that you are on a fool’s errand because the thing you’re looking for is incredibly improbable.
But if you knew a bit about String Theory, you might question my judgment: “Are you sure you looked everywhere: at every nook and cranny, in every valley? There are 10500 of them, you know. Surely with that number, it must be possible to find what we are looking for. Oh, and don’t bother looking at the average valleys. Look for exceptional ones.”
This suggests a second criterion for an acceptable anthropic explanation. The number of mathematically consistent possibilities must be so large that even very unlikely requirements will be met in at least a few valleys.
This second requirement has real force only in the context of a precise theory of the Landscape. To give an example, the codmologists could point to Newton’s theory of gravity and argue that the equations permit circular planetary orbits at any distance from a star. The very distant orbits have frozen planets, where water and even methane freeze to ice. The orbits lying close to the star have hot planets, where water instantly boils. But somewhere in between a point must exist where the temperature is right for liquid H2O. The theory has so many solutions that among them there must be some that are just right.
Strictly speaking a planet cannot orbit at any distance. Solar systems are a lot like atoms, the sun and planets replacing the atomic nucleus and the electrons. As Niels Bohr first understood, electrons can orbit only in definite quantized orbits. The same reasoning applies to planets. But fortunately, the possible orbits are so numerous and densely spaced that for practical purposes any distance is possible.
It was not enough for the codmologists to know that the requirements for life are mathematically consistent. They also needed a universe that is so big and diverse that it actually does contain almost everything that can exist. The known universe has 1011 galaxies, each with 1011 planets, for a grand total of 1022 opportunities to satisfy the special requirement for liquid water. With that many planets there is near certainty that many will be habitable.
Following, then, are the requirements:
To explain proposition X anthropically, we should first of all have reason to believe that not-X would be fatal to the existence of our kind of life. In the case of the cosmological constant, this is exactly what Weinberg found.
Even if X seems wildly unlikely, a rich enough Landscape with enough valleys may make up for it. This is where the properties of String Theory are beginning to have impact. At a few universities in the United States and Europe, the exploration of the Landscape has begun. As we will see, all signs point to an unimaginable diversity of valleys: perhaps more than 10500 of them.
And last but certainly not least, the cosmology implied by the theory should naturally lead to a supermegaverse, so large that all the regions of the Landscape will be represented in at least one pocket universe. Once again, String Theory, w
hen combined with the idea of Inflation, fills the bill. But that’s for later chapters.
The Anthropic Principle is the bête noire of theoretical physics. Many physicists express an almost violent reaction to it. The reason is not hard to imagine. It threatens their paradigm, the paradigm that says that everything about nature can be explained by mathematics alone. Are their arguments justified? Do they even make sense?
Let’s look at some of the objections from the viewpoint of the big-brained fish. The objection that the Anthropic Principle is religion, not science, is clearly off the mark. In the view of Andrei and Alexander, there is no need for the hand of God to fine-tune the world for the benefit of her children. If anything, most of the world is a very inhospitable place, far more deadly than the fyshicists ever imagined. In fact the Ickthropic Principle, in the form proposed by Andrei and Alexander, completely removes the mysterious from the fyshicists’ mystery.
A more relevant objection is that physics loses its predictive power. To a large extent that is true if what we want to predict is the temperature of our planet, the amount of sunlight it receives, the precise length of the yearly cycle, the height of the tides, the amount of salt in the ocean, and other environmental facts. But to reject the ickthropic explanation of some of the parameters of the environment on the basis that predictivity would be lost is clearly irrational. Requiring complete predictivity has an emotional basis that has nothing to do with hard facts of planetary science.
The complaint that the big-brained fish are giving up the traditional quest for scientific explanation is also expressing a psychological disappointment but obviously has no scientific merit. At some point fyshicists’ hopes turn into dogmatic religion.
Of all the criticisms of the Anthropic Principle that I have heard, only one strikes me as serious science. It was leveled by two of my close friends, Tom Banks and Mike Dine, who don’t like my ideas.8 Here’s how it goes:
Suppose that there is a fine-tuning in nature that has no anthropic value. I’ll give you an example. The earth and the moon are the same apparent size in the sky. In fact the disk of the moon is so close in size to the disk of the sun that during a solar eclipse the moon blocks out the disk of the sun almost exactly. That is very lucky for solar astronomers: it allows them to make observations that they could not otherwise make. For example, they can study the corona of the sun during the eclipse. They can also measure the precise amount that light rays are bent by the gravity of the sun. But this unusually precise fine-tuning has no particular value for making life possible on the earth. Moreover, it is likely that the majority of habitable planets don’t have moons that match their suns so precisely. The probability of selecting a planet with such solar-lunar fine-tuning if we arbitrarily selected a random habitable planet is very small. So unless we believe in unlikely coincidences, the explanation for our world must be something other than random choice subject only to the anthropic constraint.
The moon-sun coincidence is not really much of a problem. The precision with which the moon matches the sun is not phenomenal. The difference is about 1 percent. One-percent coincidences happen about 1 percent of the time. It is nothing more than a lucky accident. But what if the moon and sun matched to one part in a trillion trillion trillion? That seems so unlikely that it would require an explanation. Something in addition to the Anthropic Principle would have to be at work. It might cast doubt on the idea that the unexplainable specialness of the universe has anything to do with the success of life.
There is at least one very unusual feature of the Laws of Physics that seems very finely tuned with no anthropic explanation in sight. It has to do with the proton, but let’s first review the properties of its almost identical twin, the neutron. The neutron is an example of an unstable particle. Neutrons, not bound inside a nucleus, will last only about twelve minutes before disappearing. Of course the neutron has mass, or equivalently energy, which cannot just disappear. Energy is a quantity that physicists say is conserved. That means the total amount of it can never change. Electric charge is another exactly conserved quantity. When the neutron disappears, something with the same total energy and charge must replace it. In fact the neutron decays into a proton, an electron, and an antineutrino. The initial and final energy and electric charge are the same.
Why does the neutron decay? If it didn’t, the real question would be, why doesn’t it decay? As Murray Gell-Mann once quoted T. H. White, “Everything which is not forbidden is compulsory.” Gell-Mann was expressing a fact about quantum mechanics: quantum fluctuations—the quantum jitters—will eventually make anything happen unless some special law of nature expressly forbids it.
What about protons—can they decay, and if so, what do they become? One simple possibility is that the proton disintegrates into a photon and a positron. The photon has no charge, and the proton and positron have exactly the same charge. It ought to be possible for protons to disintegrate into photons and positrons. No principle of physics prevents it. Most physicists expect that given enough time, the proton will decay.
But if the proton can decay, it means that all atomic nuclei can disintegrate. We know that atomic nuclei of atoms like hydrogen are very stable. The lifetime of a proton must be many times the age of the universe.
There must be a reason why the proton lives so long. Can that reason be anthropic? Certainly our existence places limitations on the lifetime of the proton. It obviously cannot be too small. Let’s suppose the proton lives one million years. Then I would not have to worry very much about my protons disappearing during my life. But since the universe is about ten billion years old, if the proton lived only a million years, they all would have disappeared long before I was born. So the anthropic requirement for the proton lifetime is a lot longer than a human lifetime. The proton must last at least fourteen billion years.
Anthropically, the lifetime of the proton may have to be a good deal longer than the age of the universe. To see why, let’s suppose that the proton lifetime were twenty billion years. The decay of an unstable particle is an unpredictable event that can happen any time. When we say that the proton lifetime is twenty billion years, we mean that, statistically, the average proton will last that long. Some will decay in one year, and some in forty billion years.
Your body has about 1028 protons. If the proton lifetime were twenty billion years, about 1018 of those protons would decay every year.9 This is a negligible fraction of your protons, so you don’t have to worry about disappearing. But each proton that decays in your body shoots out energetic particles: photons and positrons and pions. These particles moving through your body have the same effects as exposure to radioactivity: cell damage and cancer. If 1018 protons decay in your body, they will kill you. So the anthropic constraints on proton decay may be stronger than what you naively think. As far as we know, a lifetime of a million times the age of the universe—1016 years—is long enough not to jeopardize life. On anthropic grounds we can rule out all valleys of the Landscape where the average proton lifetime is less than this.
But we know that the proton lives vastly longer than 1016 years. In a tank of water with roughly 1033 protons, we would expect to see one proton decay each year if the lifetime were 1033 years. Physicists, hoping to witness a few protons decaying, have constructed huge underground chambers filled with water and photoelectric detectors. Sophisticated modern detectors can detect the light from just a single decay. But so far, no cigar; not a single proton has ever been seen to disintegrate. Evidently the lifetime of the proton is even longer than 1033 years, but the reason is unknown.
To compound the problem, we also don’t know any reason why the String Theory Landscape should not have valleys in which the Laws of Physics are life-friendly but where protons live for only 1016 or 1017 years. Potentially the number of such valleys could vastly outweigh those with much greater lifetimes.
This is a serious concern but probably not a showstopper. Unfortunately we don’t have nearly enough information about the Landscap
e to know what percentage of its habitable valleys have such very long proton lifetimes. But there is some reason for optimism. The Standard Model with no modification does not permit the proton to decay at all! This has nothing to do with the Anthropic Principle; it is simply a mathematical property of the Standard Model that the proton cannot disintegrate. If the typical habitable environment requires something fairly similar to the Standard Model, then proton stability may go along for the ride.
But we know that the Standard Model is not the full story. It does not contain gravity. Even though the Standard Model may be a very good description of ordinary physics, it nonetheless must break down. This could happen many ways. Theories called Grand Unified Theories (GUTs) are, despite their awful name, very attractive. The simplest generalization of the Standard Model to a GUT brings the proton lifetime to just around 1033 or 1034 years.
Other extensions of the Standard Model are not so safe. One of them, based on supersymmetry, can lead to significantly shorter proton lifetimes unless it is appropriately adjusted. We need more information before we can draw far-reaching conclusions. Fortunately, particle physics experiments in the near future may bear on the validity of the Standard Model and also on the reasons for the unusual stability of the proton. Stay tuned for a few years.