Superstring theory has led to a resurgence of interest in the anthropic principle. This increased interest has also led to a backlash against it by some physicists. In the May 2006 issue of APS News, there was a letter written by A. R. P. Rov of Baton Rouge, where he attempts to discredit the anthropic principle, and in the process, inadvertently proves its truth with the example of the solar system, and the analogy between the solar system and the Universe. The word "universe" with a lower case "u" refers to a hypothetical or model universe. The word "Universe" with a capital "U" refers to the actual real Universe.
First, let me address the issue of randomness. Laplace said that if you had perfect knowledge of the initial conditions, you would be able to predict everything that ever happened in the history of the Universe. Within Newtonian mechanics, this is true. This is not true if you take into account quantum mechanics, which is probabilistic, but obviously Laplace was unaware of quantum mechanics. However, even if you consider only Newtonian mechanics, the premise of Laplace’s thought experiment, which is having perfect knowledge of the initial conditions, can never be achieved or even approximated in practice. This is especially true for chaotic systems with a hypersensitivity to initial conditions. A very small change in initial conditions causes a very large change in the results. So the final results, from a practical point of view, are unpredictable. Let’s say you’re playing pool, and one pool ball hits another. You can predict where the second ball will go. However, let’s say the second pool ball hits another, which then hits another, and so hitting the pool ball causes a chain of events where a dozen pool balls ricochet off each other and the walls a dozen times. In that case, you can never predict the final position of the balls because the tiniest change at any point causes tremendous changes later on in the trajectories of the balls, and you can never have good enough information to be able to predict it.
In the American southwest, there lived the Anasazi, the only Indian tribe in what is now the United States to build large stone structures. Among other things, they practiced ritual cannibalism, but what I’m discussing here is the fact that in the area of Chaco Canyon, they built large monumental temples that were very precisely aligned over long distances with each other and to astronomical phenomena, such as the solstices, equinoxes, phases of the Moon, and to precise points on the horizon where the Sun and Moon would rise and set at various points throughout the year. Building these temples required enormous knowledge and skill at astronomy, mathematics, architecture, and engineering. They also required enormous effort and manpower. Why did they go through all this effort? The reason is because they assumed that all of these astronomical phenomena, such as the solstices, equinoxes, phases of the Moon, and the points on the horizon where the Sun and Moon would rise and set, were of profound cosmological significance. This was also the assumption of European astronomy throughout most of history. When Renaissance astronomers would build an elaborate 3D model of the solar system called an armillary, they thought it represented something of cosmological importance. Laplace was the first person to successfully apply Newtonian mechanics to the solar system, and show that the solar system is stable. However, Laplace’s work did nothing to explain why the solar system had the form that it does, nor would any other theory ever be able to do that.
The reason is because the formation of the solar system was a chaotic system with a hypersensitivity to initial conditions. The tiniest possible change in the details of the formation of the solar system would have dramatically altered the final form that the solar system would take. Obviously, you can never know every detail of the formation of the solar system, and so you could never have a theory that would be able to predict the final form that the solar system would take. In the past, everyone assumed that the characteristics of the solar system, such as the number of planets, number of moons at each planet, the size of each planet, their distance from the Sun, their speed of rotation and revolution, their inclination, the eccentricity of their orbit, the size of the Earth, the size of the Moon, the distance from the Earth to the Moon, the distance from the Earth to the Sun, etc., were all of profound cosmological significance, but we now know that all of those things have zero significance whatsoever, and would all have had different values if the details of the formation of the solar system had been ever so slightly different. We can never have a theory that will be able to predict any of those values because we’ll never know the details of the formation of the solar system with sufficient precision. By now, we’ve discovered dozens of solar systems other than ours, and they all differ significantly from ours. In other words, the details of the solar system are essentially random. It’s not literally random but it’s essentially random in that it’s unpredictable.
Of all the worlds in the solar system, including the nine major planets, hundreds of moons, millions of asteroids and comets, trans-Neptunian objects, Kuiper belt objects, Oort cloud objects, etc., only one currently has large amounts of liquid water on the surface. Europa might have large oceans of liquid water below the surface. Enceladus sprays water into space but it doesn’t stay on the surface. Mars had oceans of liquid water in the past but that was billions of years ago. Titan might have lakes of methane but that’s not water. Earth is the only world in the solar system that currently has large amounts of liquid water on the surface. If you were to randomly choose a world in our solar system, it’s very unlikely it would have liquid water on the surface. Yet, despite that, we happen to be living on the only world in the solar system that currently has large amounts of liquid water on the surface. How do you explain that coincidence? Well, of course, it’s not a coincidence at all. The fact is that even though the details of the solar system might be random, our location within the solar system is not random. Life as we know it requires large amounts of liquid water, as well as access to sunlight, and can only survive with a certain range of temperatures. The world on which we live would have to be one that exists within a certain range of temperatures where water is liquid, and have enough gravity to keep it on the surface. In other words, if there is only one world in the solar system with large amounts of liquid water on the surface, then that would have to be the world that we live on. The world that we live on would have to possess characteristics that would allow life to be possible. That explains why we are on this world. This is called the anthropic principle, and in this example, it is obviously trivially true.
Now if there is some aspect of our planet that has no bearing on the likelihood of life arising and surviving, such as the number of moons, the speed of Earth’s rotation, or the precise location of the magnetic north pole, then that aspect is random. If there is some aspect of our planet that is relevant to the likelihood of life arising and surviving, such as the range of temperatures, then that aspect is not random. Obviously, our planet would have to exist within a certain range of temperatures in order for life to exist. However, what the temperature is within that range of allowed values would be random. It wouldn’t make much difference if the temperature were slightly hotter or slightly colder, but if it were much hotter or much colder, life would not be possible. Therefore, parameters that are not relevant to life are random. Parameters that must lie within a certain range of values in order for life to be possible are not random but must be within that range since otherwise we wouldn’t be here. However, even those parameters are random in regards to where they are within the range of acceptable values. Keep in mind that when I say random, I mean effectively random from our point of view, in the sense that you can never predict it or derive it from underlying principles. True randomness doesn’t exist in Newtonian mechanics, and we’re ignoring quantum mechanics, but effective randomness does exist for chaotic systems, such as the formation of the solar system, in the sense that the parameter can take any value, except for those that exclude the existence of life. Since we’re here, we know those values are excluded.
The main point of this article is that everything that I have said about our solar system might be equally true for the Universe. The details of the Universe might be random, and not derivable from any underlying theory in the same way that the details of our solar system are random and not derivable from any underlying theory. Just as our planet is one of many worlds in our solar system, and the only one with characteristics that allow life, our universe might be one of a very large number of universes, and one of the very few that have characteristics that allow life to be possible. Just as the Anasazi in Chaco Canyon assumed that the details of our solar system were of profound importance, but turned out to be wrong, most late 20th Century physicists assumed that all the details of our universe, such as all the free parameters of the Standard Model, were of profound cosmological significance, and in principle derivable from some fundamental theory, but that also turned out to be wrong. There are many parameters of the Standard Model, so-called “fundamental constants”, the values of which we can’t explain, such as the coupling constants, the particle masses, the entries in the KM-matrix, the neutrino mass matrix, etc., and many physicists hoped it would be possible to derive them from an underlying theory. They tried to come up with a theory that would predict these values. However, it’s quite possible that the origin of our universe was a chaotic system, and these parameters could have taken any value. It’s random what values they ended up taking, and it would not be possible to predict what values they would take. Of course, the parameters would have to take values that would allow life to be possible, since otherwise we wouldn’t be here. If there is a parameter of the Standard Model or characteristic of the universe that has no effect on the ability for life to exist, that parameter could take any value, and is therefore random. If there is a parameter of the Standard Model or characteristic of the universe that would have to lie within a certain range of values in order for life to be possible, that means that in our universe, it would have to be within that range since otherwise we wouldn’t here. Where it lies within that range, would be random.
Let me give an example. In the Standard Model, the terms for the fermion masses come from interaction terms between the fermions and the Higgs particle. During electroweak symmetry breaking, the Higgs field rolls down a Mexican hat potential. It’s like if you put a ball at the top of a hill, and let it roll down. What direction it rolls down will be random. What direction the Higgs field ends up taking is random. Before a lake freezes, the water molecules point in all directions. After it freezes, they align with those nearby and end up pointing in the same direction, but not over the whole lake. In different parts of the lake, it points in different directions. Similarly, in different parts of the Universe, the Higgs field could point in different directions than in our universe. More generally, in superstring theory, there are many scalar fields rolling down potentials in the vast superstring landscape, and it’s random where they all end up within this superstring landscape. In superstring theory, the laws of physics are also determined by the precise topology of space. There are approximately 10500 string vacua, and in inflationary cosmology, each of these would be realized, and each would have different laws of physics. Also, in brane world cosmology, there could be many branes, and each would be a different universe. If there are many universes, and they each have different values of the Standard Model parameters, then there’s nothing particularly significant about the values they take in our universe.
It could be that the Big Bang that formed our universe was a chaotic system with a hypersensitivity to initial conditions, and the laws of physics, fundamental particles, forces, etc., are determined by the details of how various fields rolled down their potentials, which is essentially random, and thus unpredictable. Therefore, you could never come up with a theory that could predict those values, anymore than you could come up with a theory that predicted the characteristics of our solar system. Just because the details of our solar system are random doesn’t mean we live on a random world in our solar system. Just because the values of the Standard Model parameters in any given universe are random, doesn’t mean we live in a random universe. We would have to live in a universe in which they take values that allow life to be possible, since otherwise we wouldn’t be here. If there is a cosmological parameter that has no effect on life, then it could take any value. If there is a parameter that has to lie within a given range of values in order for life to be possible, then in our universe, they must lie within that range of values, but they could take any value within that range. In other words, if it has no effect on life, it’s random. If it does affect life, it must be within the acceptable range of values that allow life, but it’s random where it is within that range.
There are examples where it’s self-evident that the anthropic principle is trivially true, such as the above example where the anthropic principle explains why we are on the only world in our solar system with large amounts of liquid water on the surface. The anthropic principle is in opposition to the Copernican principle which states that we are typical observers located at a typical time and place in the Universe. The anthropic principle states that we are not typical observers because life does not arise under typical circumstances. What that means is that if you find a circumstance where we clearly aren’t typical, the anthropic principle explains why we are at these atypical circumstances by claiming that these atypical circumstances are required for life to exist. For instance, Earth is obviously an atypical world in our solar system in that it has large amounts of liquid water on the surface, and the anthropic principle explains why we are on an atypical world by stating that those unusual circumstances are required for life to exist. This is an example where the Copernican principle is obviously untrue. Yet, there are other times where the Copernican principle is true. Whether the Copernican principle or the anthropic principle is applicable to a given situation depends on whether whatever it is you’re talking about affects the likelihood of life arising and surviving. For instance, the redshift of the galaxies could be explained as either the expansion of the Universe, or as an explosion. We choose the former explanation, since the latter would require that we be located at the center of the Universe, which would violate the Copernican principle. In this case, the anthropic principle isn’t applicable since there’s no reason to think that life would be more likely to arise at the center of the Universe.
Here’s another example where the Copernican principle is untrue. The Earth is located at one astronomical unit, or 1 AU, or 93 million miles, from the Sun. In other words, we are 1 AU from a star. The observable universe is a sphere where the radius is the horizon distance, which is the distance light could have traveled since the Big Bang, which was 13.7 billion years ago. Therefore, the observable universe is a sphere with a radius of 13.7 billion light-years. Now let’s say you took the observable universe, which is a sphere with a radius of 13.7 billion light-years, and divided into smaller spheres, each of which had a radius of 1 AU. What percentage of those smaller spheres would contain a star? Obviously, it’s a tiny percentage. Yet we happen to be located in one of those spheres. How do you explain that coincidence? Of course, it’s not a coincidence at all. It’s very unlikely that a randomly selected point in the observable universe would be as close to a star as we are, but we are not located at a randomly selected point in the observable universe. We would have to be at a place where life could arise. Life is far more likely to arise near a star than in the depths of intergalactic space. This seemingly unlikely coincidence is explained by the anthropic principle. This is another example where the Copernican principle is clearly false. Obviously, we’re not located at typical point in the observable universe.
Not only are we not located at a random point in space, we’re not located at a random point in time. The Universe began in the Big Bang 13.7 billion years ago, but will go on forever, and never recollapse into a Big Crunch. Therefore, there will always be a finite length of time behind you, and an infinite length of time ahead of you. Why are we only 13.7 billion years after the Big Bang, instead of, say, a googolplex years? The answer is because there is only a specific finite window in the history of the Universe in which life is possible. Life can only exist after the first generation of stars die, creating heavy elements, and before the last stars die, after which there are no stars at all. It’s not surprising that we are currently located within that window of time.
In each of these examples, a seemingly unlikely coincidence is explained by saying it is necessary for life. It is possible that this same anthropic principle may explain could be used to explain coincidences in the values of the Standard Model parameters. It may be that our universe is only one of a large number of universes, and our universe is not typical, and has the unusual characteristics that it has in order for us to be here, which ultimately explains why we observe the Standard Model parameters to have the values they do. If they had different values, we wouldn’t be here.
Often in physics, you look for patterns. If you find a pattern, and later discover that the pattern does not hold true throughout, there must be some reason. Often this reveals new interesting physics. Here are the masses and charges of the quarks.
There are three generations of fermions, each containing two quarks, one of which has a charge of -1/3, and the other of which has a charge of 2/3. I listed them alternating between the quark that has a charge of -1/3, and the quark that has a charge of 2/3. Notice something unusual about the masses. As you go down the table, the masses usually increase, with each one heavier than the previous. The exception is the first generation where the quark with a charge of -1/3 is actually heavier than the quark with a charge of 2/3. Also, the mass difference between the first two quarks is much less than the mass difference between any other two quarks. If as a physicist, you were given the above table with the mass of the down quark omitted, and you were asked to guess its value by extrapolating the pattern in the table, you would probably guess that the down quark had a mass of about 1 MeV. Yet this is not the case. The down quark is actually heavier than the up quark. They have masses that would not be expected from looking at the other quarks. Why do they have these unusual masses?
One way to address this question is to ask what would happen if the masses of the up and down quark had different values. Let’s say the mass of the down quark minus the mass of the up quark was equal to v.
(md - mu) = v
Let’s say the v0 is the value of v in our universe. Then let’s see what would happen if v were to take values different than the observed value.
1. v/v0 > 1000
Protons decay into Δ++ (uuu) particles, leaving a universe with only helium-like Δ++ atoms.
2. 1000 > v/v0 > 5
Neutrons decay into protons even inside of nuclei, resulting in a universe with no elements other than hydrogen.
3. 5 > v/v0 > 2
Deuterium is unstable, drastically altering standard stellar neucleosynthesis.
4. 2 > v/v0 > 1.01
There will be orders of magnitude less oxygen produced.
5. 1.01 > v/v0 > 0.99
This is our universe.
6. 0.99 > v/v0 > 0.8
There will be orders of magnitude less carbon produced.
7. 0.8 > v/v0 > 0.5
Diprotons and dineutrinos are bound, resulting in a universe devoid of hydrogen.
8. 0.5 > v/v0
Protons (uud) quickly decay into neutrons (udd) giving a universe with no atoms.
As you can see, if the mass of the up quark and the mass of the down quark had almost any other values than the ones we observe, life as we know it would not be possible. If our universe was the only universe there was, this would be a staggering coincidence. The only way it would not be a coincidence is if our universe was only one of a very large number of universes, and ours was one of the very few in which life was possible. This is very strong evidence that the anthropic principle applies to our entire Universe. The people against the anthropic principle have never put forward their own alternative explanation for what is otherwise a stupendous coincidence.
If the up quark and down quark did not have the masses they do, life would not be possible, and we would not exist. Combine that with the fact that the masses of the up and down quark do not follow the pattern of the other quarks. In the second and third generation, the quark with a charge of 2/3 is heavier than the quark with a charge of -1/3. If the first generation followed the same pattern, we wouldn’t be here. In fact, if they had any other masses then the ones they have, we wouldn’t be here. This would seem to be a staggering coincidence. It’s possible we’re just very lucky, but that’s very unlikely. The best explanation is that it’s not a coincidence. There would be a very large number of universes, and in the vast majority, there is nothing resembling the Standard Model. Of those that do have the Standard Model, the vast majority would have different masses for the up and down quarks. As you saw in the above list, life would not be possible in those universes. Probably, in most universes with the Standard Model, the pattern that you see in the second and third generation would also hold true in the first generation, and life would not be possible. Our universe is a typical. However, it’s not surprising that we’re in an atypical universe because we’re not in a randomly selected universe, since we know that we must be in a universe in which life is possible. This explains why we observe the up and down quark masses that we do.
There are a lot of other values of cosmological parameters where if they had different values, we wouldn’t be here. If the cosmological constant was too large, it would overpower gravitational attraction, and matter would never coalesce into stars and galaxies. Therefore, we’d have to be in a universe with a small cosmological constant. The fact that the cosmological constant is small but nonzero is additional evidence for the anthropic principle. I said before that the anthropic principle is the explanation for why we’re on a world where the temperature range is such that water is liquid. However, if the average surface temperature of the Earth was exactly halfway between freezing, 0° C, and boiling, 100° C, such as if it was exactly 50.000000° C, that would suggest that there was some physical process at work, or that some underlying law of physics determined the temperature. If the cosmological constant was exactly zero, that would imply that there was something making it zero. However, since the cosmological constant is very small but nonzero, that implies that there is nothing making it what it is, and the value we observe is simply one that would allow life.
To apply the anthropic principle to the Universe, you have to assume that there is a very large number or infinite number of universes. Many theories in physics predict exactly that. The observable universe is a sphere where the radius is the horizon distance, and other parts of the universe are casually disconnected from ours, and could be thought of as other universes. Max Tegmark claims that all possibilities are realized in these distant parts of our universe. Inflationary cosmology and chaotic inflation, put forward by Alan Guth and Andrei Linde, assumes that tiny parts of the universe suddenly undergo inflation and become other universes, and this has been going on for an infinite length of time, and would produce an infinite number of universes. Some people think black holes could give rise to baby universes. String theory predicts a vast string landscape of 10500 string vacua. Lenny Susskind predicts that in the context of inflationary cosmology, each of the string vacua would be realized. In brane world cosmology, our universe is actually a brane in higher dimensional space, and there could be a large number of branes, and thus a large number of universes. You could even go back to the Everett Many Worlds Principle in quantum mechanics. So many theories of physics predict many universes, which allows for the anthropic principle to explain the characteristics of our universe.