by Brian Greene
Here’s where theoretical prejudice came to the fore. Assume for the moment that the cosmological constant is not just small. Assume it’s zero. Zero is a favorite number of theoreticians because there’s a tried and true way for it to emerge from calculations: symmetry. For example, imagine that Archie has enrolled in a continuing education course and for homework has to add together the sixty-third power of each of the first ten positive numbers, 163 + 263 + 363 + 463 + 563 + 663 + 763 + 863 + 963 + 1063, and then add the result to the sum of the sixty-third power of each of the first ten negative numbers, (–1)63 + (–2)63 + (–3)63 + (–4)63 + (–5)63 + (–6)63 + (–7)63 + (–8)63 + (–9)63 + (–10)63. What’s the final tally? As he laboriously calculates, getting ever-more frustrated, multiplying and then adding together numbers with more than five dozen digits, Edith chimes in: “Use symmetry, Archie.” “Huh?” What she means is that each term in the first collection has a symmetric balancing term in the second: 163 and (–1)63 sum to 0 (a negative raised to an odd power remains negative); 263 and (–2)63 sum to 0, and so on. The symmetry between the expressions results in a total cancellation, as if they were children of equal weight balancing on opposite sides of a seesaw. Needing no calculations at all, Edith shows that the answer is 0.
Many physicists believed—or, I should really say, hoped—that a similar total cancellation due to an as yet unidentified symmetry in the laws of physics would rescue the calculation of the energy contained in quantum jitters. Physicists surmised that the huge energies from quantum jitters would cancel against some as yet unidentified huge balancing contributions, once the physics was sufficiently well understood. This was about the only strategy physicists could come up with for tamping down the unruly results of the rough calculations. And that’s why many theorists concluded that the cosmological constant had to be zero.
Supersymmetry provides a concrete example of how this could play out. Recall from Chapter 4 (Table 4.1) that supersymmetry entails a pairing of species of particles, and hence species of fields: electrons are paired with species of particles called supersymmetric electrons, or selectrons for short; quarks with squarks; neutrinos with sneutrinos, and so on. All of these “sparticle” species are currently hypothetical, but experiments in the next few years at the Large Hadron Collider may change that. In any event, an intriguing fact came to light when theoreticians examined mathematically the quantum jitters associated with each of the paired fields. For every jitter of the first field, there’s a corresponding jitter of its partner that has the same size but opposite sign, much as in Archie’s math homework. And just as in that example, when we add together all such contributions pair by pair, they cancel out, yielding a final result of zero.12
The catch, and it’s a big one, is that the total cancellation occurs only if both members of a pair have not only the same electric and nuclear charges (which they do), but also the same mass. Experimental data have ruled this out. Even if nature makes use of supersymmetry, the data show that it can’t be realized in its most potent form. The as yet unknown particles (selectrons, squarks, sneutrinos, and so on) must be much heavier than their known counterparts—only this can explain why they haven’t been seen in accelerator experiments. When the different particle masses are accounted for, the symmetry is disturbed, the balancing is unbalanced, and the cancellations are imperfect; the result is once again huge.
Over the years, many analogous proposals were put forward, invoking a range of additional symmetry principles and cancellation mechanisms, but none achieved the goal of establishing theoretically that the cosmological constant should vanish. Even so, most researchers took this merely as a sign of our incomplete understanding of physics, not as a clue that belief in a vanishing cosmological constant was misguided.
One physicist who challenged the orthodoxy was the Nobel laureate Steven Weinberg.* In a paper published in 1987, more than a decade before the revolutionary supernova measurements, Weinberg suggested an alternative theoretical scheme that yielded a decidedly different outcome: a cosmological constant that is small but not zero. Weinberg’s calculations were based on one of the most polarizing concepts to have gripped the physics community in decades—a principle some revere and others vilify, a principle some call profound and others call silly. Its official, if misleading, name is the anthropic principle.
Cosmological Anthropics
Nicolaus Copernicus’ heliocentric model of the solar system is acknowledged as the first convincing scientific demonstration that we humans are not the focal point of the cosmos. Modern discoveries have reinforced the lesson with a vengeance. We now realize that Copernicus’ result is but one of a series of nested demotions overthrowing long-held assumptions regarding humanity’s special status: we’re not located at the center of the solar system, we’re not located at the center of the galaxy, we’re not located at the center of the universe, we’re not even made of the dark ingredients constituting the vast majority of the universe’s mass. Such cosmic downgrading, from headliner to extra, exemplifies what scientists now call the Copernican principle: in the grand scheme of things, everything we know points toward human beings not occupying a privileged position.
Nearly five hundred years after Copernicus’ work, at a commemorative conference in Kraków, one presentation in particular—given by the Australian physicist Brandon Carter—provided a tantalizing twist to the Copernican principle. Carter expounded his belief that an overadherence to the Copernican perspective might, in certain circumstances, divert researchers from significant opportunities for making progress. Yes, Carter agreed, we humans are not central to the cosmic order. Yet, he continued, aligning with similar insights articulated by scientists such as Alfred Russel Wallace, Abraham Zelmanov, and Robert Dicke, there is one arena in which we do play an absolutely indispensable role: our own observations. However far we have been demoted by Copernicus and his legacy, we top the bill when credits are conferred for the gathering and analyzing of the data that mold our beliefs. Because of this unavoidable position, we must take account of what statisticians call selection bias.
It’s a simple and widely applicable idea. If you are investigating trout populations but only canvass the Sahara Desert, your data will be biased by your focusing on an environment particularly inhospitable to your subject. If you are studying the general public’s interest in opera, but send your survey solely to the database collected by the journal Can’t Live Without Opera, your results won’t be accurate because the respondents are not representative of the population as a whole. If you are interviewing a group of refugees who have endured astoundingly harsh conditions during their trek to safety, you might conclude that they are among the hardiest ethnicities on the planet. Yet, when you learn the devastating fact that you are speaking with less than 1 percent of those who started out, you realize that such a deduction is biased because only the phenomenally strong survived the journey.
Addressing these biases is vital for getting meaningful results and for avoiding the futile search to explain conclusions based on unrepresentative data. Why are trout extinct? What’s the cause of the public’s surging interest in opera? Why is it that a particular ethnicity is so astoundingly resilient? Biased observations can launch you on meaningless quests to explain things that a broader, more representative view renders moot.
In most cases, these types of biases are easily identified and corrected. But there’s a related variety of bias that’s more subtle, one so basic it can easily be overlooked. It’s the kind in which limitations on when and where we are able to live can have a profound impact on what we are able to see. If we fail to take proper account of the impact such intrinsic limitations have on our observations, then, as in the examples above, we can draw wildly erroneous conclusions, including some that may impel us on fruitless journeys to explain meaningless MacGuffins.
For instance, imagine that you’re intent on understanding (as was the great scientist Johannes Kepler) why the earth is 93 million miles from the sun. You want to fi
nd, deep within the laws of physics, something that will explain this observational fact. For years you struggle mightily but are unable to synthesize a convincing explanation. Should you keep trying? Well, if you reflect on your efforts, taking account of selection bias, you will soon realize that you’re on a wild goose chase.
The laws of gravity, Newton’s as well as Einstein’s, allow a planet to orbit a star at any distance. If you were to grab hold of the earth, move it to some arbitrary distance from the sun, and then set it in motion again at the right velocity (a velocity easy to work out with basic physics), it would happily go into orbit. The only thing special about being 93 million miles from the sun is that it yields a temperature range on earth conducive to our being here. If earth were much closer or much farther away from the sun, the temperature would be much hotter or colder, eliminating an essential ingredient for our form of life: liquid water. This reveals the inbuilt bias. The very fact that we measure the distance from our planet to the sun mandates that the result we find must be within the limited range compatible with our own existence. Otherwise, we wouldn’t be here to contemplate the earth’s distance from the sun.
If earth were the only planet in the solar system, or the only planet in the universe, you still might feel compelled to carry your investigations further. Yes, you might say, I understand that my own existence is tied to the earth’s distance from the sun, yet this only heightens my urge to explain why the earth happens to be situated at such a cozy, life-compatible position. Is it just a lucky coincidence? Is there a deeper explanation?
But the earth is not the only planet in the universe, let alone in the solar system. There are many others. And this fact casts such questions in a very different light. To see what I mean, imagine that you mistakenly think a particular shop carries only a single shoe size, and so are gleefully surprised when the salesman brings you a pair that fits perfectly. “Of all possible shoe sizes,” you reflect, “it’s amazing that the single one they carry is mine. Is that just a lucky coincidence? Is there a deeper explanation?” But when you learn that the shop actually carries a wide range of sizes, the questions evaporate. A universe with many planets, situated at a range of distances from their host stars, provides a similar situation. Just as it’s no big surprise that among all the shoes in the shop there’s at least one pair that fits, so it’s no big surprise that among all the planets in all the solar systems in all the galaxies there’s at least one at the right distance from its host star to yield a climate conducive to our form of life. And it’s on one of those planets, of course, that we live. We simply couldn’t evolve or survive on the others.
So there is no fundamental reason why the earth is 93 million miles from the sun. A planet’s orbital distance from its host star is due to the vagaries of historical happenstance, the innumerable detailed features of the swirling gas cloud from which a particular solar system coalesced; it’s a contingent fact that’s unavailable for fundamental explanation. Indeed, these astrophysical processes have produced planets throughout the cosmos, orbiting their respective suns at a vast assortment of distances. We find ourselves on one such planet situated 93 million miles from our sun because that’s a planet on which our form of life could evolve. Failure to take account of this selection bias would lead one to search for a deeper answer. But that’s a fool’s errand.
Carter’s paper emphasized the importance of paying heed to such bias, an accounting he called the anthropic principle (an unfortunate name, because the idea would apply equally well to any form of intelligent life that makes and analyzes observations, not just to humans). No one took exception to this element of Carter’s argument. The controversial part was his suggestion that the anthropic principle might cast its net not just over things in the universe, like planetary distances, but over the universe itself.
What would that mean?
Imagine you’re puzzling over some fundamental feature of the universe, say the mass of an electron, .00054 (expressed as a fraction of the proton’s mass), or the strength of the electromagnetic force, .0073 (expressed by its coupling constant), or, of primary interest to us here, the value of the cosmological constant, 1.38 × 10–123 (expressed in Planck units). Your intention is to explain why these constants have the particular values they do. You try and try but come up emptyhanded. Take a step back, Carter says. Maybe you’re failing for the same reason you’d fail to explain the earth-sun distance: there is no fundamental explanation. Just as there are many planets at many distances and we necessarily inhabit one whose orbit yields hospitable conditions, maybe there are many universes with many different values for the “constants” and we necessarily inhabit the one in which the values are conducive to our existence.
In this way of thinking, to ask why the constants have their particular values is to ask the wrong kind of question. There is no law dictating their values; their values can and do vary across the multiverse. Our intrinsic selection bias ensures that we find ourselves in that part of the multiverse in which the constants have the values with which we’re familiar simply because we’re unable to exist in the parts of the multiverse where the values are different.
Note that the reasoning would fall flat if our universe were unique because you could still ask the “lucky coincidence” or “deeper explanation” questions. Much as a potent explanation for why the shop has your shoe size requires that the shelves be stocked with many different sizes, and much as a potent explanation for why there’s a planet situated at a bio-friendly distance from its host star requires planets orbiting their stars at many different distances, so a potent explanation of nature’s constants requires a vast assortment of universes endowed with many different values for those constants. Only in this setting—a multiverse, and a robust one at that—does anthropic reasoning have the capacity to make the mysterious mundane.*
Clearly, then, the degree to which you are swayed by the anthropic approach depends on the degree to which you are convinced of its three essential assumptions: (1) our universe is part of a multiverse; (2) from universe to universe in the multiverse, the constants take on a broad range of possible values; and (3) for most variations of the constants away from the values we measure, life as we know it would fail to take hold.
In the 1970s, when Carter put forward these ideas, the notion of parallel universes was anathema to many physicists. Certainly, there’s still ample reason to be skeptical. But we’ve seen in the previous chapters that although the case for any particular version of the multiverse is surely tentative, there’s reason for giving this new view of reality serious consideration, Assumption 1. Many scientists now are. Regarding Assumption 2, we’ve also seen that, for example, in the Inflationary and Brane Multiverses, we would indeed expect physical features, such as the constants of nature, to vary from universe to universe. Later in this chapter we’ll look at this point more closely.
But what about Assumption 3, concerning life and the constants?
Life, Galaxies, and Nature’s Numbers
For many of nature’s constants, even modest variations would render life as we know it impossible. Make the gravitational constant stronger, and stars burn up too quickly for life on nearby planets to evolve. Make it weaker and galaxies don’t hold together. Make the electromagnetic force stronger, and hydrogen atoms repel each other too strongly to fuse and supply power to stars.13 But what about the cosmological constant? Does life’s existence depend on its value? This is the issue Steven Weinberg took up in his 1987 paper.
Because the formation of life is a complex process about which our understanding is in its earliest stages, Weinberg recognized that it was hopeless to determine how one or another value of the cosmological constant directly impacts the myriad steps that breathe life into matter. But rather than give up, Weinberg introduced a clever proxy for the formation of life: the formation of galaxies. Without galaxies, he reasoned, the formation of stars and planets would be thoroughly compromised, with a devastating impact on the chance that life might em
erge. This approach was not only eminently reasonable but also useful: it shifted the focus to determining the impact that cosmological constants of various sizes would have on galaxy formation, and that was a problem Weinberg could solve.
The essential physics is elementary. While precise details of galaxy formation are an active area of research, the broad-brush process involves a kind of astrophysical snowball effect. A clump of matter forms here or there, and by virtue of being more dense than its surroundings, it exerts a greater gravitational pull on nearby matter and thus grows larger still. The cycle continues feeding on itself to ultimately produce a swirling mass of gas and dust, from which stars and planets coalesce. Weinberg’s realization was that a cosmological constant with a value large enough would disrupt the clumping process. The repulsive gravity it would generate, if sufficiently strong, would thwart galactic formation by making the initial clumps—which were small and fragile—stream apart before they had time to become robust by attracting surrounding matter.