by Adam Frank
With this definition in mind, the Big Bang’s entropy problem can be simply stated: our universe has been evolving for thirteen billion years, so it could not have begun in equilibrium. Somehow, all the matter—energy, space and time—in the universe began in a state of low entropy. That is the only way change and evolution could have occurred. That is the only way we could start with a Big Bang and end up with the wonderfully diverse cosmos of stars, planets and people we find today.
The idea that the Big Bang had low entropy might seem strange at first. It was a hot, chaotic mess, right? How could the empty, cold universe we find today, a universe full of stars, planets and mosquitos, have higher entropy? The answer is gravity. The universe is not a box of atoms; it is an expanding space-time full of gravitational effects.11 By including gravity in calculations, the movement from a smooth primordial soup of particles to the clumpy universe of galaxies we see today can be understood for what it is—an increase in entropy. But you don’t have to work through these details to make the connection between evolution, entropy and equilibrium. If the universe evolved (as it did and still does), then it must have started with lower entropy than it has now.
Once you recognize that point, as mathematical physicist Roger Penrose did in the 1970s, you have a problem. If entropy is equivalent to the number of ways to arrange a system, then the low-entropy beginning suggested by the Big Bang is remarkably unlikely.
If you had a bag filled with a million black marbles and only a few white marbles, you would be pretty surprised to reach into the bag and pull out a white marble. That is the situation facing cosmologists trying to explain the low-entropy Big Bang. “There are, literally, an infinite number of ways to set up the initial universe”, says Sean Carroll, “and pretty much all of them have high entropy.” But these numerous high-entropy universes would begin in equilibrium, making evolution and change impossible.
The probability that our universe began in a low-entropy state is so astonishingly unlikely that it’s almost embarrassing. Without a compelling explanation, physicists have to admit our Big Bang must somehow have been fine-tuned. It began improbably far out of equilibrium and can, therefore, point the arrow of time in one direction. We have encountered fine-tuning before, in the standard model of particle physics. Recall that the twenty or so constants needed in the standard model are amazingly sensitive. If nature had “chosen” even a slightly different value for these numbers, the universe would look so different that life as we know it could never form. The low-entropy Big Bang requires a similar kind of fine-tuning. With so many ways to make a universe begin with high entropy, how did we end up in one that began with low entropy? For physicists, fine-tuning is akin to saying that a miracle occurred—which doesn’t sit well with most scientists. The beauty of science’s approach to the world is its emphasis on plausible and purely physical explanations, even in a field like cosmology. So for Carroll and others the real problem is not just explaining what happened before the Big Bang but also explaining our universe’s unlikely low-entropy origin, which tipped time’s arrow forward.
“Our universe” is the key phrase that Carroll and others lean on for their solution. If our universe is one of many, then a new kind of steady-state model becomes possible in which even the arrow of time is explained. Eternal inflation’s multitude of universes gave Carroll the raw material he needed to create a time-symmetric cosmology. As Carroll explains it:
People immediately asked if eternal inflation could work in both directions. That means there would be no need for a single Big Bang. Pocket universes would always sprout from the uninflated background without beginning or end. The trick needed to make eternal inflation work is to find a generic “starting point”. This would be an easy-to-achieve condition that would occur infinitely many times and allow eternal inflation to flow in both directions.
It’s important to see exactly what Carroll means by time symmetry. In any particular pocket universe, the local arrow of time will simply run from low entropy to high entropy. For someone living in that universe, the past points to the time of low disorder and the future points towards the direction of higher disorder. What Carroll is looking for is time symmetry for an entire multiverse. From a god’s-eye view, the entire web of evolving pocket universes should look the same if the film of its global evolution ran backwards or forward.
In 2004, Carroll and his student Jennifer Chen found exactly that—a version of eternal inflation without any global arrow of time. “All you need”, said Carroll, “is to start with some empty space, a shard of dark energy and some patience.” As counterintuitive as it sounds, detailed calculations show that an empty space-time driven to expansion via dark energy is the one with the highest possible entropy. Empty, flat space-time is, therefore, the condition a generic universe will evolve towards. It is the most generic form of cosmic equilibrium—the one you’d expect to occur for a randomly chosen universe with a randomly chosen starting point. It’s also the perfect generic starting point for Carroll.
A background of dark energy in an empty, flat space-time is also crucial for Carroll and Chen because quantum physics states that any energy field produces random functions. These rapid, quantum spikes in the dark energy can serve as the trigger for the next step in their story. Wait long enough and strong fluctuations can momentarily push some tiny region of the empty background up inflation’s potential energy curve into a false vacuum state. The result is a new region of inflation creating new crops of baby universes from the empty space. Note the term baby universe is used rather than pocket universe. Even if the details of quantum gravity remain unknown, physicists expect that quantum fluctuations can give rise to separate, disconnected domains of space-time. Carroll used this possibility to go further with his multiverse than the usual ideas of eternal inflation. Baby universes literally tear themselves away from the space-time of their parents and, in doing so, begin in a low-entropy state. By the nature of their creation, the baby universes begin with low entropy and can go on to inflate and evolve on their own.
“Some of these baby universes will collapse into black holes and evaporate, taking themselves out of the picture”, says Carroll. “But other universes will expand forever. The ones that expand eventually thin out. They become the new empty space from which more inflation can start.” Since the ever-expanding universes evolve towards the generic empty-space condition, the whole process is renewed again and again.
More important, the direction of time does not matter in the process. “That is the funny part”, says Carroll. “You can evolve the little inflating universes in either direction away from your generic starting point.” When Carroll speaks about different directions in time, he is taking the god’s-eye view, looking at the evolution of different individual baby universes from the point of the multiverse as a whole. “You can do [inflation] going backwards in time from the initial state; the generic evolution is the same. The universe will empty out and eventually begin to spontaneously inflate. So in the super-far past of our universe, before our Big Bang (which is nothing special), we will find other Big Bangs for which the arrow of time is running in the opposite direction.” On the largest scales, the entire cosmos is like a connected foam of baby universes, which are completely symmetric with respect to the multiverse’s time. There is no direction of time for the multiverse as a whole.
There is a compelling vertigo in Carroll and Chen’s solution. Their multiverse always exists and always will exist. It is dynamic and evolving but is, in a statistical sense, always the same. The Big Bang is just our Big Bang and not unique. We define it as our past because that is the direction where entropy was lower. But limits on the entropy of the whole multiverse are never reached because more baby universes can always be created and inflated. New universes flow continually into the multiverse’s past and future. The distinction loses any absolute cosmic meaning. The multiverse stands outside of time because there is no universal flow of its time in any particular direction. The question of “
before” has not just been answered, it has been overwhelmed.
FIGURE 10.4. A steady-state time symmetric multiverse. Beginning from the generic condition of flat space, separate “baby universes” can be created. Each baby universe will have its own thermodynamic arrow of time. The multiverse as a whole, however, need not have a global direction of time.
From Carroll’s perspective, eternal inflation’s multiplication of universes may offer a way around both time’s beginning and its arrow. But for many scientists, eternal inflation of any form has not been a welcome development. The multiplication of universes (all unobserved and perhaps forever unobservable) seems more akin to a Star Trek episode than to serious science. But for others the universe’s radical redefinition of the cosmos not only answers cosmology’s oldest questions but pushes the definition of science in new directions.
OUR MEDIOCRE UNIVERSE: THE ANTHROPIC PRINCIPLE MAKES NEW CONVERTS
Fine-tuning is a real problem for physicists and cosmologists. From the twenty constants needed for the standard model to the Big Bang’s demand for a special, low-entropy initial conditions, the imperative for the universe to be built “just so” (down to many decimal places) for life to form has haunted the project of fundamental physics for decades. The goal of physics had always been to find timeless laws that specify the exact form of nature and its evolution. But the more scientists probed the universe, the more they saw happy accidents picking out special conditions and values of constants. All these accidents appeared in just the right form to create a cosmos where life could grow. It was a dilemma sure to please deity-happy advocates of intelligent design. With fine-tuning, they could claim physics itself provided evidence for a superintelligence turning knobs on his creation, dialing in exactly the right conditions (out of an infinity of possibilities) to make this implausible cosmos. Such an easy way out would be an anathema to the project Thales, the creator of the Greek rational tradition, began 2,500 years ago. For many scientists the multiverse, with its infinity of universes, seemed to provide a clear explanation for the dilemma. But to fully invoke its power, scientists would have to confront the dreaded A-word of cosmology: the Anthropic Principle.12
The Anthropic Principle has been hovering in the background of cosmological thinking for decades.13 In its simplest form, it states that the universe and its laws must take a form consistent with our existence within it. This may seem like a tautology at first—so obvious it’s not worth stating—but over the years, some physicists and cosmologists have been keen to show how the Anthropic Principle could be used to make cosmological predictions. In the 1950s, none other than Fred Hoyle stumbled upon an early example of anthropic reasoning when he predicted that specific nuclear reactions had to exist for carbon (essential to our existence) to be built up within stars. Hoyle’s nuclear physics prediction was confirmed just a few years later in experiments. A more recent “success” of the Anthropic Principle came in 1995 when Nobel Prize–winning physicist Steven Weinberg wondered why the cosmological constant was so much smaller than particle physics calculations would suggest.
Recall that physicists have long known that quantum mechanics predicts that the vacuum is anything but empty space; rather, it is a state seething with virtual particles that pop into and out of existence while never violating the rules of uncertainty. Particle physicists saw that this quantum vacuum could be expressed as an energy permeating all space, exactly like a cosmological constant. But their predictions for the size of the cosmological constant based on vacuum energy was so large that the universe as we know it never could have formed. Somehow, they reasoned, the quantum vacuum fluctuations must cancel each other out. Most researchers thought the cancellation would be complete, leading to a cosmological constant that was exactly zero. Using anthropic reasoning relating the necessity of forming galaxies as a precursor to the formation of life, Weinberg went further and was able to derive an upper value to the cosmological constant. Any value larger than his prediction, Weinberg argued, tore protogalaxies apart before they could fully form. For galaxies and hence life to exist, Weinberg concluded, the constant had to be just so big, but no bigger. The discovery of dark energy in 1999, if interpreted as a cosmological constant, gave a value exactly in the range Weinberg predicted.14
The Anthropic Principle takes many forms. Some forms are so weak as to be useless and exist as a kind of parody of the idea—“the existence of life tells us the universe has to allow life to exist”. Some forms are so strong as to make most materialist scientists balk—“the laws of physics must take a form that makes life a necessary feature of cosmic evolution”. After its introduction in the late 1960s and 1970s, most scientists rejected anthropic thinking, seeing it as so obvious as to be useless or so constrictive as to be an exercise in mysticism. Hoyle’s often-cited success, for example, was dismissed as not being really anthropic. Carbon is just as important for limestone as it is for life, after all. The problem was always seeing how the laws for this one universe could be linked to our existence. But if more than one universe existed, then anthropic reasoning would take on an entirely new meaning.
A multiverse makes anthropic reasoning a question of statistics. Eternal inflation gives us a vast ensemble of universes, each of which will have different physics and distinct constants guiding that physics. With so many possibilities, our appearance in this particular pocket universe with its apparent fine-tuning of constants and initial conditions becomes something less than a mystery. Even if life is exquisitely sensitive to this universe’s constants of nature, the multiverse’s infinite, or nearly infinite, sample of pocket universes means constants favourable to life must have happened somewhere. We, of course, are in one of those universes that won the life lottery. But there are other universes with other physics, and many of those will be sterile. In some of those other universes, dark energy pushed space apart so fast that galaxies never formed and no structure or stars exist. Matter and energy spread out like wisps of wind blowing across an endless void. In other universes, the nuclear physics of carbon and other elements is just different enough to keep stars from cooking heavy elements in their cores. Stars burn, but life and even planets might be barred from existence. There are many possibilities. In a multiverse, some scientists argue, it will be anthropic reasoning that provides a way to sort through them all.
Some researchers have taken this logic further. It has long been a tenet of science that explaining phenomena based on the observer’s perspective was a form of special pleading. Scientists often invoke what they call the Copernican principle to eliminate claims that an observer is in a special time or a special place that led to special results. Using the multiverse and anthropic arguments, some cosmologists argue that we shouldn’t expect to end up in a “special” universe either. That would just be more fine-tuning.
Reach into the multiverse’s bag of pocket universes and choose one at random. On average, you would choose a universe that possessed the average kind of conditions for the multiverse as a whole. The same rule applies for the universe we find ourselves occupying. If the Copernican principle holds, then our universe should be close to the average universe. A scientist should, therefore, be able to use our existence to say something about the actual statistics of pocket universes across the multiverse. We should not expect anything less than to find ourselves in an average, mediocre universe. Depending on how you look at it, this prospect is either humbling or insulting.
There is, however, enormous and contentious debate within the cosmological community over what “statistics across universes” means. Some scientists argue that it’s impossible to define an average universe, while others offer what they claim are working definitions. But below the technical debate lies a deeper issue about the direction and aim of cosmological science in a post–Big Bang era.
MANY UNIVERSES, ONE SCIENCE
For many researchers in the field, eternal inflation is now seen as a natural consequence of inflation. With that step, the radical possibility of a mult
iverse becomes a real possibility. But it remains unclear if, in lieu of observational evidence one way or the other, the costs of accepting the multiverse as a research paradigm outweigh its benefits.
Whatever their personal religious affiliations, many physicists share the vision of a nonreligious God of sorts, and this is reflected in their holy grail—the search for the ultimate description of ultimate reality.15 For many the multiverse, with its implied anthropic logic, is nothing less than an affront to that quest. Following the bright line of reasoning from Pythagoras to Kepler to Newton and onward, the modern enterprise of physics has been a search for a single, unified description of the world. That description, so sparse it could fit on a T-shirt, would unequivocally determine the origin, form and evolution of this one universe. That describes the search for the holy of holies in physics. The effort put into the standard model, the quest for grand unified field theories and the hopes pinned on quantum gravitational theories of everything were all driven by this ancient desire to find this one true description of reality. Once the final equation is determined, everything we see, everything we experience, the whole of cosmic history—be it eternal or springing into time—should stand revealed. Unless, of course, the faithful fear, we retreat to an anthropic logic of the multiverse.
