Great Throughts Treasury

This site is dedicated to the memory of Dr. Alan William Smolowe who gave birth to the creation of this database.

Sean Carroll

American Physicist, Theoretical Cosmologist, Senior Research Associate in the Department of Physics at the California Institute of Technology, and Author

""Beginning" cosmologies typically attempt to replace the Big Bang singularity of classical general relativity with some sort of quantum-mechanical event, and often go by the name "quantum cosmology." These models imagine that space-time is a classical approximation to some sort of quantum-mechanical structure. (Even if we don't have a complete theory of quantum gravity, the hope is that the basic features of quantum mechanics and general relativity are sufficiently robust that the details aren't important for this particular question.) In particular, time may be just an approximate notion, useful in some regimes but not others. Near the Big Bang is an obvious candidate for an era in which time loses its conventional meaning. The important ingredient is then a "boundary condition" that describes the state of the universe at the moment when time is first an intelligible concept. The most famous example is the "no-boundary proposal" of Hartle and Hawking, which constructs the state of the universe by integrating over all possible Euclidean geometries with no other boundaries. By "Euclidean" we mean geometries in which all four dimensions are spatial, in contrast to the "Lorentzian" geometry of space-time with its distinction between time-like and space-like directions. One occasionally speaks of "imaginary time," a phrase that has probably not increased the total amount of understanding in the universe. A provocative way of characterizing these beginning cosmologies is to say that "the universe was created from nothing." Much debate has gone into deciding what this claim is supposed to mean. Unfortunately, it is a fairly misleading natural-language translation of a concept that is not completely well-defined even at the technical level. Terms that are imprecisely defined include "universe," "created," "from," and "nothing." (We can argue about "was.")"

"?Time? is the most used noun in the English language, yet it remains a mystery. We?ve just completed an amazingly intense and rewarding multidisciplinary conference on the nature of time, and my brain is swimming with ideas and new questions. Rather than trying a summary (the talks will be online soon), here?s my stab at a top ten list partly inspired by our discussions: the things everyone should know about time."

"A full understanding of what happens in our everyday lives needs to take into account what happened at the Big Bang. And not only is that intrinsically interesting and just kind of cool to think about, but it's also a mystery that is not given much attention by working scientists; it's a little bit underappreciated."

"A lifespan is a billion heartbeats. Complex organisms die. Sad though it is in individual cases, it?s a necessary part of the bigger picture; life pushes out the old to make way for the new. Remarkably, there exist simple scaling laws relating animal metabolism to body mass. Larger animals live longer; but they also metabolize slower, as manifested in slower heart rates. These effects cancel out, so that animals from shrews to blue whales have lifespans with just about equal number of heartbeats ? about one and a half billion, if you simply must be precise. In that very real sense, all animal species experience ?the same amount of time.? At least, until we master #9 and become immortal."

"At heart, science is the quest for awesome - the literal awe that you feel when you understand something profound for the first time. It's a feeling we are all born with, although it often gets lost as we grow up and more mundane concerns take over our lives."

"A multiverse that arises due to the natural dynamical consequences of a relatively simple set of physical laws should not be discounted because there are a lot of universes out there. Multiverse theories certainly pose formidable problems, especially when it comes to making predictions and comparing them with data; for that reason, most scientists would doubtless prefer a theory that directly predicted the parameters we observe in nature over a multiverse ensemble in which our local environment was explained anthropically. But most scientists (for similar reasons) would prefer a theory that was completely free of appeals to supernatural agents."

"Aging can be reversed. We all grow old, part of the general trend toward growing disorder. But it?s only the universe as a whole that must increase in entropy, not every individual piece of it. (Otherwise it would be impossible to build a refrigerator.) Reversing the arrow of time for living organisms is a technological challenge, not a physical impossibility. And we?re making progress on a few fronts: stem cells, yeast, and even (with caveats) mice and human muscle tissue. As one biologist told me: ?You and I won?t live forever. But as for our grandkids, I?m not placing any bets.?"

"An elegant mechanism emerges: a broken symmetry, hidden from our view by a field pervading space."

"Cosmology studies the universe on the largest scales, and over large scales the most important force of nature is gravity. Our modern understanding of gravity is the theory of general relativity, proposed by Einstein in 1915. The key insight in this theory is the idea that space and time can be curved and have a dynamical life of their own, changing in response to matter and energy. As early as 1917, Einstein applied his new theory to cosmology, taking as an assumption something we still believe is true: that on the largest scales, matter in the universe (or at least our observable part of it) is uniform through space. He also assumed, consistent with the apparent implication of observations at the time, that the universe was static. To his surprise, Einstein found that general relativity implied that any uniform universe would necessarily be non-static ? either expanding or contracting. In response he suggested modifying his theory by adding a new parameter called the "cosmological constant," which acted to push against the tendency of matter to contract together. With that modification, Einstein was able to find a static (but unstable) solution if the cosmological constant were chosen precisely to balance against the attraction of matter on large scales."

"An example of fine-tuning well beyond anthropic constraints is the initial state of the universe, often characterized in terms of its extremely low entropy. Roughly speaking, the large number of particles in the universe were arranged in an extraordinarily smooth configuration, which is highly unstable and unlikely given the enormous gravitational forces acting on such densely-packed matter. While vacuum energy is tuned to one part in 10120, the entropy of the early universe is tuned to one part in ten to the power of 10120, a preposterous number. The entropy didn't need to be nearly that low in order for life to come into existence. One way of thinking about this is to note that we certainly don't need a hundred billion other galaxies in the universe in order for life to arise here on Earth; our single galaxy would have been fine, or for that matter a single solar system."

"Christopher Savage have calculated that in reasonable models, we expect about ten dark-matter particles to interact with the atoms in a typical human body every year. The effects of every individual interaction are pretty negligible, so don?t worry about getting a dark matter stomachache."

"Edwin Hubble and Milton Humason announced in 1929 that the universe is expanding: distant galaxies are receding from us at speeds that are proportional to their distance. It had only been in 1924 that Hubble had established that the spiral nebulae, which many thought were clouds within our own galaxy, were separate galaxies in their own right, demonstrating the true vastness of the universe. The collection of stars we live in, the Milky Way galaxy, contains something over 100 billion stars, and there are over 100 billion such galaxies within the observable universe."

"Complexity comes and goes. Other than creationists, most people have no trouble appreciating the difference between ?orderly? (low entropy) and ?complex.? Entropy increases, but complexity is ephemeral; it increases and decreases in complex ways, unsurprisingly enough. Part of the ?job? of complex structures is to increase entropy, e.g. in the origin of life. But we?re far from having a complete understanding of this crucial phenomenon. (Talks by Mike Russell, Richard Lenski, Raissa D?Souza.)"

"Consciousness depends on manipulating time. Many cognitive abilities are important for consciousness, and we don?t yet have a complete picture. But it?s clear that the ability to manipulate time and possibility is a crucial feature. In contrast to aquatic life, land-based animals, whose vision-based sensory field extends for hundreds of meters, have time to contemplate a variety of actions and pick the best one. The origin of grammar allowed us to talk about such hypothetical futures with each other. Consciousness wouldn?t be possible without the ability to imagine other times"

"Disorder increases as time passes. At the heart of every difference between the past and future ? memory, aging, causality, free will ? is the fact that the universe is evolving from order to disorder. Entropy is increasing, as we physicists say. There are more ways to be disorderly (high entropy) than orderly (low entropy), so the increase of entropy seems natural. But to explain the lower entropy of past times we need to go all the way back to the Big Bang. We still haven?t answered the hard questions: why was entropy low near the Big Bang, and how does increasing entropy account for memory and causality and all the rest?"

"Einstein's paper on the photoelectric effect was the work for which he ultimately won the Nobel Prize. It was published in 1905, and Einstein has another paper in the very same journal where it appeared - his other paper was the one that formulated the special theory of relativity. That's what it was like to be Einstein in 1905; you publish a groundbreaking paper that helps lay the foundation of quantum mechanics, and for which you later win the Nobel Prize, but it's only the second most important paper that you publish in that issue of the journal."

"Everyone experiences time differently. This is true at the level of both physics and biology. Within physics, we used to have Sir Isaac Newton?s view of time, which was universal and shared by everyone. But then Einstein came along and explained that how much time elapses for a person depends on how they travel through space (especially near the speed of light) as well as the gravitational field (especially if it?s near a black hole). From a biological or psychological perspective, the time measured by atomic clocks isn?t as important as the time measured by our internal rhythms and the accumulation of memories. That happens differently depending on who we are and what we are experiencing; there?s a real sense in which time moves more quickly when we?re older."

"Generally, not nearly enough credence is given to option #1 in this list. We know very little about the conditions under which complexity, and intelligent life in particular, can possibly form. If, for example, we were handed the Standard Model of particle physics but had no actual knowledge of the real world, it would be very difficult to derive the periodic table of the elements, much less the atoms and molecules on which Earth-based life depends. Life may be very fragile, but for all we know it may be ubiquitous (in parameter space); we have a great deal of trouble even defining "life" or for that matter "complexity," not to mention "intelligence." At the least, the tentative nature of our current understanding of these issues should make us reluctant to draw grand conclusions about the nature of reality from the fact that our universe allows for the existence of life. Nevertheless, for the sake of playing along, let's imagine that intelligent life only arises under a very restrictive set of circumstances. Following Swinburne, we can cast the remaining choices in terms of Bayesian probability. The basic idea is simple: we assign some prior probability ? before we take into account what we actually know about the universe ? to each of the three remaining scenarios. Then we multiply that prior probability by the probability that intelligent life would arise in that particular model. The result is proportional to the probability that the model is correct, given that intelligent life exists. Thus, for option #2 (a single universe, no supernatural intervention), we might put the prior probability at a relatively high value by virtue of its simplicity, but the probability of life arising (we are imagining) is extremely small, so much so that this model could be considered unlikely in comparison with the other two. We are left with option #3, a "multiverse" with different conditions in different regions (traditionally called "universes" even if they are spatially connected), and #4, a single universe with parameters chosen by God to allow for the eventual appearance of life. In either case we can make a plausible argument that the probability of life arising is considerable. All of the heavy lifting, therefore, comes down to our prior probabilities ? our judgments about how a priori likely such a cosmological scenario is. Sadly, prior probabilities are notoriously contentious objects."

"If anything, the much-more-than-anthropic tuning that characterizes the entropy of the universe is a bigger problem for the God hypothesis than for the multiverse. If the point of arranging the universe was to set the stage for the eventual evolution of intelligent life, why all the grandiose excess represented by the needlessly low entropy at early times and the universe's hundred billion galaxies? We might wonder whether those other galaxies are spandrels ? not necessary for life here on Earth, but nevertheless a side effect of the general Big Bang picture, which is the most straightforward way to make the Earth and its biosphere. This turns out not to be true; quantitatively, it's easy to show that almost all possible histories of the universe that involve Earth as we know it don't have any other galaxies at all. It's unclear why God would do so much more fine-tuning of the state of the universe than seems to have been necessary."

"From one second back to about 10-43 seconds, we expect the kinds of physics we understand ? general relativity and quantum field theory ? to be applicable, even if the details are unclear. That is, we think we can successfully model the world in terms of fields that obey the rules of quantum mechanics, evolving within a curved space-time obeying the laws of general relativity. The value 10-43 seconds is the "Planck time," before which we expect space-time itself to be subject to quantum behavior. Currently we don't have a reliable theory that describes gravity in quantum-mechanical terms; the search for a theory of "quantum gravity" is one of the foremost goals of modern physics. The leading candidate for such a synthesis, string theory, has been the subject of an enormous amount of attention in recent decades. Unfortunately, despite a number of intriguing theoretical discoveries, string theory has neither made direct contact with experiments, nor provided an unambiguous answer to what happened at the Big Bang."

"If our local, observable universe is embedded in a larger structure, a multiverse, then there's other places in this larger structure that have denizens in them that call their local environs the universe. And conditions in those other places could be very different. Or they could be pretty similar to what we have here."

"If the universe is expanding now, it was smaller in the past. (More properly, galaxies were closer together and the universe was more dense; it's possible that space is actually infinite in extent.) Using the rules provided by general relativity, and some assumptions about the types of matter and energy that pervade the universe, we can play the movie backwards in time to reconstruct the past history of our universe. Eventually ? about 13.7 billion years ago, according to our best current estimates ? we reach a moment of infinite density and space-time curvature. This singularity is known as the "Big Bang." Confusingly, the phrase "Big Bang model" refers to the entire history of the expanding universe that began in a hot, dense state, whose broad outlines are established beyond reasonable doubt. In contrast, the "Big Bang event" is not really an event at all, but a placeholder for our lack of complete understanding."

"I don't want to give advice to people about their religious beliefs, but I do think that it's not smart to bet against the power of science to figure out the natural world. It used to be, a thousand years ago, that if you wanted to explain why the moon moved through the sky, you needed to invoke God."

"I'm a big believer that science is part of a larger cultural thing. Science is not all by itself."

"If you find an egg in your refrigerator, you're not surprised. You don't say, 'Wow, that's a low-entropy configuration. That's unusual,' because you know that the egg is not alone in the universe. It came out of a chicken, which is part of a farm, which is part of the biosphere, etc., etc. But with the universe, we don't have that appeal to make."

"I'm trying to understand how time works. And that's a huge question that has lots of different aspects to it."

"I'm trying to understand cosmology, why the Big Bang had the properties it did. And it's interesting to think that connects directly to our kitchens and how we can make eggs, how we can remember one direction of time, why causes precede effects, why we are born young and grow older. It's all because of entropy increasing."

"In contrast to the arbitrarily complicated evolution of a (nonintegrable) classical system, all a quantum state ever does is move in circles."

"In many religious traditions, one of the standard roles of the deity has been to create the universe. The first line of the Bible, Genesis 1:1, is a plain statement of this role.[1] Much has happened, both in our scientific understanding of the universe and in the development of theology, since that line was first written. It's worth examining what those developments imply for the relationship between God and cosmology. In some ways of thinking about God, there's no relationship at all; a conception of divinity that is sufficiently ineffable and transcendent may be completely separate from the workings of the physical world. For the purposes of this essay, however, we will limit ourselves to versions of God that play some role in explaining the world we see. In addition to the role of creator, God may also be invoked as that which sustains the world and allows it to exist, or more practically as an explanation for some of the specific contingent properties of the universe we observe. Each of these possibilities necessarily leads to an engagement with science. Modern cosmology attempts to come up with the most powerful and economical possible understanding of the universe that is consistent with observational data. It's certainly conceivable that the methods of science could lead us to a self-contained picture of the universe that doesn't involve God in any way. If so, would we be correct to conclude that cosmology has undermined the reasons for believing in God, or at least a certain kind of reason? This is not an open-and-shut question. We are not faced with a matter of judging the merits of a mature and compelling scientific theory, since we don't yet have such a theory. Rather, we are trying to predict the future: will there ever be a time when a conventional scientific model provides a complete understanding of the origin of the universe? Or, alternatively, do we already know enough to conclude that God definitely helps us explain the universe we see, in ways that a non-theistic approach can never hope to match?"

"It?s only because the data force us into corners that we are inspired to create the highly counterintuitive structures that form the basis for modern physics."

"Is time real? ?In one sense, it?s a silly question. The reality of something is only an interesting issue if its a well-defined concept whose actual existence is in question, like Bigfoot or supersymmetry. For concepts like time, which are unambiguously part of a useful vocabulary we have for describing the world, talking about reality is just a bit of harmless gassing. They may be emergent or fundamental, but they?re definitely there."

"In recent years, a different aspect of our universe has been seized upon by natural theologians as evidence for God's handiwork ? the purported fine-tuning of the physical and cosmological parameters that specify our particular universe among all possible ones. These parameters are to be found in the laws of physics ? the mass of the electron, the value of the vacuum energy ? as well as in the history of the universe ? the amount of dark matter, the smoothness of the initial state. There's no question that the universe around us would look very different if some of these parameters were changed. The controversial claims are two: that intelligent life can only exist for a very small range of parameters, in which our universe just happens to find itself; and that the best explanation for this happy circumstance is that God arranged it that way."

"Most modern cosmologists are convinced that conventional scientific progress will ultimately result in a self-contained understanding of the origin and evolution of the universe, without the need to invoke God or any other supernatural involvement. This conviction necessarily falls short of a proof, but it is backed up by good reasons. While we don't have the final answers, I will attempt to explain the rationale behind the belief that science will ultimately understand the universe without involving God in any way."

"One implication of these data is that only about 4% of the total energy of the current universe is in the form of "ordinary matter" ? the atoms and molecules consisting of protons, neutrons, and electrons, as well as photons and neutrinos and all the other known elementary particles. Another 23% of the universe is "dark matter" ? a completely new kind of particle, as yet undiscovered here on Earth. In addition to constraints from nucleosynthesis and the CMB, strong evidence for dark matter comes from the dynamics of galaxies, clusters of galaxies, and large-scale structure in the universe."

"Nothing in the fact that there is a first moment of time, in other words, necessitates that an external something is required to bring the universe about at that moment. As Hawking put it in a celebrated passage: So long as the universe had a beginning, we could suppose it had a creator. But if the universe is really self-contained, having no boundary or edge, it would have neither beginning nor end, it would simply be. What place, then, for a creator?"

"One sometimes hears the claim that the Big Bang was the beginning of both time and space; that to ask about space-time "before the Big Bang" is like asking about land "north of the North Pole." This may turn out to be true, but it is not an established understanding. The singularity at the Big Bang doesn't indicate a beginning to the universe, only an end to our theoretical comprehension. It may be that this moment does indeed correspond to a beginning, and a complete theory of quantum gravity will eventually explain how the universe started at approximately this time. But it is equally plausible that what we think of as the Big Bang is merely a phase in the history of the universe, which stretches long before that time ? perhaps infinitely far in the past. The present state of the art is simply insufficient to decide between these alternatives; to do so, we will need to formulate and test a working theory of quantum gravity."

"Our actual universe evolves to empty space."

"Part of the sting was taken away when the American Physical Society awarded its 2010 Sakurai Prize in theoretical physics to Hagen, Englert, Guralnik, Higgs, Brout, and Kibble?in that order, which seems to have been chosen specifically to make it impossible for anyone to complain. (Anderson might have reasonably complained.)"

"Scientifically speaking, the existence of God is an untenable hypothesis. It?s not well-defined, it?s completely unnecessary to fit the data, and it adds unhelpful layers of complexity without any corresponding increase in understanding. Again, this is not an a priori result; the God hypothesis could have fit the data better than the alternatives, and indeed there are still respected religious people who argue that it does. Those people are just wrong, in precisely analogous ways to how people who cling to the Steady State theory are wrong. Fifty years ago, the Steady State model was a reasonable hypothesis; likewise, a couple of millennia ago God was a reasonable hypothesis. But our understanding (and our data) has improved greatly since then, and these are no longer viable models. The same kind of reasoning would hold for belief in miracles, various creation stories, and so on."

"One increasingly hears rumors of a reconciliation between science and religion. In major news magazines as well as at academic conferences, the claim is made that that belief in the success of science in describing the workings of the world is no longer thought to be in conflict with faith in God. I would like to argue against this trend, in favor of a more old-fashioned point of view that is still more characteristic of most scientists, who tend to disbelieve in any religious component to the workings of the universe."

"Science and religion both make claims about the fundamental workings of the universe. Although these claims are not a priori incompatible (we could imagine being brought to religious belief through scientific investigation), I will argue that in practice they diverge. If we believe that the methods of science can be used to discriminate between fundamental pictures of reality, we are led to a strictly materialist conception of the universe. While the details of modern cosmology are not a necessary part of this argument, they provide interesting clues as to how an ultimate picture may be constructed."

"That might be true, even with the hyperbole, if what one was postulating were simply "a trillion trillion other universes." But that is a mischaracterization of what is involved. What one postulates are not universes, but laws of physics. Given inflation and the string theory landscape (or other equivalent dynamical mechanisms), a multiverse happens, whether you like it or not. This is an important point that bears emphasizing. All else being equal, a simpler scientific theory is preferred over a more complicated one. But how do we judge simplicity? It certainly doesn't mean "the sets involved in the mathematical description of the theory contain the smallest possible number of elements." In the Newtonian clockwork universe, every cubic centimeter contains an infinite number of points, and space contains an infinite number of cubic centimeters, all of which persist for an infinite number of separate moments each second, over an infinite number of seconds. Nobody ever claimed that all these infinities were a strike against the theory. Indeed, in an open universe described by general relativity, space extends infinitely far, and lasts infinitely long into the future; again, these features are not typically seen as fatal flaws. It is only when space extends without limit and conditions change from place to place, representing separate "universes," that people grow uncomfortable. In quantum mechanics, any particular system is potentially described by an infinite number of distinct wave functions; again, it is only when different branches of such a wave function are labeled as "universes" that one starts to hear objections, even if the mathematical description of the wave function itself hasn't grown any more complicated."

"That doesn't mean that we can't possibly explain the low entropy of our early universe by invoking the multiverse; it just means that the explanation must rely on detailed dynamical properties of the multiverse, rather than simply the requirement that life can exist. What we would need to show is that, in the context of the particular multiverse scenario under consideration, when life arises at all it typically does so in the aftermath of an extremely low-entropy event like our Big Bang. This is a challenge, but not obviously an insuperable one, and researchers are actively tackling this question."

"The fact that you can remember yesterday but not tomorrow is because of entropy. The fact that you're always born young and then you grow older, and not the other way around like Benjamin Button - it's all because of entropy. So I think that entropy is underappreciated as something that has a crucial role in how we go through life."

"The clearest example of apparent fine-tuning is the vacuum energy. As discussed above, vacuum energy is the leading candidate for the dark energy causing distant galaxies to accelerate; but even if the vacuum energy is exactly zero and the dark energy is something else, we can safely say that the value of the vacuum energy is not greater than that of the dark energy, about 10-8 ergs per cubic centimeter. Using techniques from quantum field theory, we can do a rough calculation of what we would expect the vacuum energy to be, if we hadn't already measured it. The answer is quite a bit larger: about 10112 ergs per cubic centimeter. The fact that the actual value of the vacuum energy is at least 120 orders of magnitude smaller than its natural value is a fine-tuning by anyone's estimation? In the face of these apparent fine-tunings, we have several possible options: (1) Life is extremely robust, and would be likely to arise even if the parameters were very different, whether or not we understand what form it would take. (2) There is only one universe, with randomly-chosen parameters, and we just got lucky that they are among the rare values that allow for the existence of life. (3) In different regions of the universe the parameters take on different values, and we are fooled by a selection effect: life will only arise in those regions compatible with the existence of life. (4) The parameters are not chosen randomly, but designed that way by a deity."

"The idea is simple, if we may boil it down to the essence: some things happen for ?reasons,? and some don?t, and you don?t get to demand that this or that thing must have a reason. Some things just are. Claims to the contrary are merely assertions, and we are as free to ignore them as you are to assert them."

"The important point is that we can easily imagine self-contained descriptions of the universe that have an earliest moment of time. There is no logical or metaphysical obstacle to completing the conventional temporal history of the universe by including an atemporal boundary condition at the beginning. Together with the successful post-Big-Bang cosmological model already in our possession, that would constitute a consistent and self-contained description of the history of the universe."

"The inability of established physics to describe the Big Bang event makes it tempting to consider the possibility that God has a crucial role to play at this unique moment in the history of the universe. If we were able to construct a complete and compelling naturalistic account, the necessity of appealing to God would be diminished. A number of avenues toward this goal are being explored. They can be divided into two types: "beginning" cosmologies, in which there is a first moment of time, and "eternal" cosmologies, where time stretches to the past without limit."

"The favored method of those who would claim that science and religion are compatible ? really, the only method available ? is to twist the definition of either ?science? or ?religion? well out of the form in which most people would recognize it. Often both. Of course, it?s very difficult to agree on a single definition of ?religion? (and not that much easier for ?science?), so deciding when a particular definition has been twisted beyond usefulness is a tricky business. But these are human endeavors, and it makes sense to look at the actual practices and beliefs of people who define themselves as religious. And when we do, we find religion making all sorts of claims about the natural world, including those mentioned above ? Jesus died and was resurrected, etc. Seriously, there are billions of people who actually believe things like this; I?m not making it up. Religions have always made claims about the natural world, from how it was created to the importance of supernatural interventions in it. And these claims are often very important to the religions who make them; ask Galileo or Giordano Bruno if you don?t believe me. But the progress of science over the last few centuries has increasingly shown these claims to be straightforwardly incorrect. We know more about the natural world now than we did two millennia ago, and we know enough to say that people don?t come back from the dead. In response, one strategy to assert the compatibility between science and religion has been to take a carving knife to the conventional understanding of ?religion,? attempting to remove from its purview all of its claims about the natural world."

"The issue of whether or not there actually is a beginning to time remains open. Even though classical general relativity predicts a singularity at the Big Bang, it's completely possible that a fully operational theory of quantum gravity will replace the singularity by a transitional stage in an eternal universe. A variety of approaches along these lines are being pursued by physicists: bouncing cosmologies in which a single Big Crunch evolves directly into our observed Big Bang, cyclic cosmologies in which there are an infinite number of epochs separated by Big Bangs, and baby-universe scenarios in which our Big Bang arises spontaneously out of quantum fluctuations in an otherwise quiet space-time. There is no way to decide between beginning and eternal cosmologies on the basis of pure thought; both possibilities are being actively pursued by working cosmologists, and a definitive judgment will have to wait until one or the other approach develops into a mature scientific theory that makes contact with observations."