Three decades ago, talk of other universes was not seen by most physicists to be part of science. Most research in theoretical physics and cosmology concerned observable features in our universe and most papers and seminars referred to experimental results. However, since then there has been a gradual shift, during which it first became acceptable to work on theories that described not only our universe, but other possible universes, universes with less or more dimensions, or universes with different kinds of particles and forces. In the last few years, we have moved further away from theories of our one universe, as these other worlds went from being logically possible to hypothetically actual. It is now common to hear about the multiverse — a quantum cosmology that takes for granted that the visible universe that we see around us is just one of a vast or infinite number of universes.
The multiverse assumption often comes hand in hand with a metaphysical assumption regarding the nature of time. It has been argued by many experts in quantum cosmology that time is not a fundamental concept, but an approximate and emergent one. If this is correct, then we experience time in a timeless universe for reasons similar to why we, who live in a quantum universe, experience one that obeys classical physics: we are composed of very large numbers of fundamental particles and emergent statistical regularities determine much of what we experience.
Furthermore, the combination of the multiverse assumption and the timeless assumption effectively gives us a static meta-universe. Even if our own universe evolves in time, at a deeper level it is part of a timeless, eternal, ensemble of universes.
There are good reasons for these conclusions, and like many others in the field of quantum cosmology I have explored them. However, in the last few years I have come to believe that these conclusions are profoundly mistaken. In collaboration with the Brazilian philosopher Roberto Mangabeira Unger, we have been trying to understand the source of the problems and develop an alternative notion of time and law on the cosmological scale. Our reasons for doing so are based partly on concerns about whether these theories are testable by doable observations, partly on the current results of attempts to realize the timeless approach and partly on philosophical considerations.
The problem with the timeless multiverse
In a timeless world in which our universe is just one of many equally real universes, the laws of physics must be very different from those that most physicists can ever have conceived. This is because the laws of physics are no longer determinable by what we observe in our own universe, for they must apply to all of the vast ensemble of universes. A fundamental law then no longer proscribes what happens in our universe; instead it gives probability distributions for properties of the ensemble of universes.
To understand why, it is helpful to distinguish between the notion of a fundamental law and an effective law. A fundamental law is posited to hold “meta-universally” from first principles and must be unique. String theory, for instance, is an attempt at discovering such fundamental laws of nature. Effective laws, at the other extreme, govern experiments at scales that we observe directly within one universe, down to the small scales probed by the Large Hadron Collider and up to the scales probed by observations of the cosmic microwave background. We can only observe the effective laws, but we hope that it should be possible to derive them from fundamental laws — otherwise the latter has no connection with what we observe. The question is whether that indirect connection provides enough ground for experimentally testing the fundamental laws so that they are relevant for our scientific understanding of the world.
Unfortunately, it appears that if string theory, or a similar theory, is true, then the fundamental theory does not in fact predict what the effective laws of nature are. Instead, it gives rise to a vast landscape of possible effective laws — a concept I introduced in my book Life of the Cosmos (the word landscape was meant to be evocative of fitness landscapes in biology). We then must have hypotheses for how the single effective laws that describe our universe are chosen from the vast list of possibilities allowed by the fundamental theory. This is one of the major motivations for speculation about multiverses.
Several ideas have been suggested for how to select the effective laws that apply to our universe from the larger set of possibilities. One possibility, which has been much studied, is that the ensemble of universes is populated by laws by an effectively random process. An example is eternal inflation. In this scenario the process that produces the ensemble occurs at energy scales so high that they swamp any processes we have experimental access to. The result is that a universe like ours, populated by structures that depend on physics at much lower energy scales, is very atypical in the ensemble of universes. One then has to depend on the anthropic principle to pick out the very few universes hospitable to life, which are very rare in the actual ensemble. Not surprisingly, given that the characteristics of the ensemble can be postulated at will and are not subject to experimental tests, the result is that we cannot make precise and unambiguous predictions about anything observable in our own universe.
An alternative approach, which does lead to at least a few falsifiable predictions, is cosmological natural selection, which I introduced in 1992. This is based on a cosmological scenario that is constructed to be analogous to population biology. Universes are born from “bounces” deep inside black holes, which replace their singularities, where time had been hypothesized to end, with new expanding universes. This leads to a prediction that a typical universe is one where the parameters are tuned to maximize the production of black holes. There is in fact evidence that this is true of the laws that govern our universe. Most importantly, in this theory our universe is supposed to be typical of the ensemble, which leads to several genuinely testable predictions, all of which have held up since they were first published, such as the prediction that the upper mass limit of stable neutron stars is about 1.6 solar masses.
The contrast between these two kinds of multiverse theories leads to a question: why is the theory based on natural selection predictive — but not the one based on random production of universes? This helps us understand why the reality of time is necessary to explain how the laws of physics are chosen.
It is apparent that a scenario in which a population of universes evolves, rather than just being a random timeless distribution, requires a notion of time that is real at a level above individual universes. But to understand why the timeless picture fails, we have to go deeper to the foundations of quantum theory. For example, without time, and without the assumption that what exists is the single universe that we observe, it is hard to make sense of statements about probability relevant to what we observe in our universe. Since quantum mechanics is a probabilistic theory, we then run into trouble by trying to extend it to a realm where probability appears to make no sense. A number of authors have attempted to address this question, by proposing ad hoc measures for deducing predictions from ensembles of multiverses. At least up to the present time, none of these appears to be justified by anything other than the need to reproduce what we observe.
A related issue is the recovery of classical space and time, which general relativity describes, as part of an effective theory. These must be emergent aspects of a fundamental quantum theory, much like the classical notions of a particle being at a definite place and travelling on definite trajectories is emergent from quantum mechanics. This is non-trivial because the notions of quantum space—time, which arise in quantum theories of gravity, are very different.
So far, approaches to quantum gravity that assume that both space and time are emergent fail to reproduce the space—time that we know. On the other hand, two approaches that assume that time is fundamental and non-emergent succeed, at least to some extent, in describing how space—time may emerge. The most developed of these is causal dynamical triangulations, which has impressive results indicating the emergence of classical space—time. A more recent attempt, quantum graphity, also has preliminary indications for the emergence of space given the existence of time. Furthermore, fundamental time is also needed to make sense of probability and describe the evolution of effective laws, which ties to the earlier issue.
These results were the first evidence that led me to consider the idea that there might have to be a fundamental global notion of time in any fully consistent approach to quantum gravity that can recover general relativity in the approximation in which the universe is large. This hypothesis is strengthened by recent results in unimodular gravity, which several authors have argued solves the long-standing problem of the cosmological constant — something that is necessary for a large classical space—time to emerge. What is remarkable, as pointed out by the physicists Rafael Sorkin of the Perimeter Institute for Theoretical Physics, William Unruh of the University of British Columbia, Vancouver, and others, is that this approach describes evolution in a global time related to the space—time volume of the past.
What is a cosmological law?
To understand the difference between the two paradigms of emergent time versus fundamental time we need to appreciate how much of our usual notion of physical law has evolved historically from our experience of laboratory observations. In the laboratory we do not, by definition, study the whole universe. We study a small subsystem of the universe that, to some reasonable approximation, can be regarded as isolated (apart from the measuring instruments that we use to observe it). When we do this, we explore the possibility that we can prepare that closed system over and over again, at different times and in different places, with the same elements and different configurations. We abstract physical laws from what is common in a large set of experiments, and study what becomes different when the initial conditions are different. This allows us to make a clean distinction between laws and initial conditions. The laws are held to be invariant, at least over scales of time and space larger than the scales pertaining to our experiments.
This situation is almost the same for most astronomical observations. We cannot prepare stars and galaxies in any state that we want, but we can observe vast numbers of them and we can treat them as approximately isolated. Hence, in astronomy we also have a justification for distinguishing between laws and initial conditions.
The separation of scientific explanation into law and initial conditions leads to one of the most universal and powerful notions in physics — the notion of configuration space. This is the space of all possible configurations, or states, of the system. In classical and quantum physics we assume that this space exists a priori and outside of time, and that it can be studied independently of the laws of motion. These laws then specify the rules for how the point that describes the initial conditions in configuration space evolves in time. We call this the Newtonian schema for explanation.
The Newtonian schema is the basis for the claim that time is not fundamental in cosmology. From this point of view, time is seen merely as a parameter on a trajectory in configuration space, and not as an intrinsic part of the physical law. The present moment, the time we experience, has no place in this description. The philosopher who does not believe in the flow of time points to the trajectory in the configuration space and says that the only thing that is real is that the whole history of the universe exists timelessly — what in general relativity is called the “block universe” picture. Many physicists and philosophers have fallen for the temptation of believing in the “block universe” picture. To them, our experience of the flow of time is just an illusion.
This argument is faulty for two reasons. First, it does not prove that time is not fundamental. When we observe motion, we record a series of measurements of a system’s position. These can be graphed on the configuration space, resulting in a curve that represents the record of the motion. This graph is timeless, because it is a representation of a record of a past motion, which is, of course, no longer changing. The correspondence is between a mathematical object, which is static, and a series of records of observations, which is also static. The fact that we can make this correspondence between a mathematical object and a record of past motion does not imply that the actual motion that the observations sampled is timeless. Nor does it imply that behind the real evolution in time of the real world there exists a complete correspondence to a timeless mathematical object. To posit this further relation is a pure metaphysical fantasy, which is not implied by anything in the science (see “The fourth principle: mathematics and Platonism” below).
New principles
The second failure of the argument for time not being fundamental is that it is far from clear that the Newtonian schema applies on the scale of the universe as a whole. Almost all work in classical and quantum cosmology assumes that it does. But given the difficulties that these subjects encounter, I think it more likely that the answer is no.
One reason for suspecting that the Newtonian schema does not apply to cosmology is that the experimental context that gives meaning to the separation of causes into laws and initial conditions is completely missing. There is no possibility of preparing the universe in different initial configurations, and there is no way to determine by observation the full initial conditions. Any observer, within the universe, can only see a fraction of any initial-value surface. Thus, the notion of initial conditions is simply not realizable in cosmology. If there is just one universe, there is no reason for a separation into laws and initial conditions, as we want a law to explain just the one history of the one universe.
The same is true for the configuration space of the cosmos. The universe happens once, so what is the meaning of all the states that exist in state space but are never realized in the history of the universe? The notion of the “quantum state of the universe” is a fiction, divorced from anything that could be prepared or measured in practice. These considerations suggest that the notions of configuration space and state space correspond to measurements and preparations that can be operationally realized only in the case of a small subsystem of the universe. These concepts — or at least their operational basis — fail us when we try to extend them to the whole universe.
The issue of time also looks different from this perspective. Time in the Newtonian schema is a parameter used to label points on a trajectory describing the system evolving in configuration space. When the system is small and isolated, this time parameter refers to the reading of a clock on the wall of the observer’s laboratory, which is not a property of the system. When we try to apply this notion to the universe as a whole, the time parameter must disappear. Some have attempted to argue that this means that time itself does not exist at a cosmological scale, but that is the wrong conclusion. What disappears is not time, but the clock outside of the system — which would be an absurd object since the system is the whole universe.
Indeed, it may be that sticking to the Newtonian schema, when it has no operational significance, leads us to take the multiverse scenario seriously. If our scientific methodology only makes sense when applied to subsystems of a vaster universe, then it is tempting to react to the problems that arise when we try to extend it uncritically to that whole universe by positing that our universe is in fact a subsystem of an even vaster multiverse. We get to do physics as we have been trained to, but this is a trap because to do this we must employ structures that have no operational significance. Better, in our view, to regard the Newtonian schema as inapplicable to cosmology, and to look for another notion of law that can make sense when applied to our entire, but single, universe.
But once we state that the distinction between laws and initial conditions has no counterpart in the cosmological context, this renders moot several puzzles that the extension of the Newtonian paradigm to cosmology has brought about. What is the initial quantum state of the universe? How do we interpret it? How do we define probabilities in quantum cosmology? How do we do physics when time has disappeared?
The physical law in a single, time-bound universe
By discarding the Newtonian schema for cosmology and dispensing with the notion of the multiverse, we also no longer have any reason to suspect that time is an illusion. This led Unger and me to consider the implications of a natural philosophy based on a different set of principles.
1. There is only one universe. There are no others, nor is there anything isomorphic to it.
This logically implies that there are no other universes, nor copies of our universe, whether within or without. The first is impossible as no subsystem can model precisely the larger system it is a part of, while the second is impossible because the one universe is by definition all there is. This principle also rules out the notion of a mathematical object isomorphic in every respect to the history of the entire universe, a notion that is more metaphysical than scientific.
2. All that is real is real in a moment, which is a succession of moments. Anything that is true is true of the present moment.
This says that not only is time real, but also that everything else that is real is situated in time. Nothing exists timelessly.
3. Everything that is real in a moment is a process of change leading to the next or future moments. Anything that is true is then a feature of a process in this process causing or implying future moments.
The third principle incorporates the notion that time is an aspect of causal relations. A reason for asserting it is that anything that just existed in a moment, without causing or implying an aspect of the state at a future moment, would be gone in the next moment. Things that persist must be thought of as processes leading to newly changed processes. An atom in a moment is a process leading to a different or a changed atom in the next moment.
This alternative metaphysical framework has implications for the nature of physical law. Since nothing is true or real outside of time, there is no possibility of speaking of eternal laws. Laws are regularities that we discover hold for very long stretches of time, but there is no reason for laws to be true timelessly — indeed, there is no way to make sense of that notion. This opens the door to the possibility that laws evolve in time, which is an idea that has been on the table ever since the great American logician Charles Sanders Peirce wrote in 1891 that “To suppose universal laws of nature capable of being apprehended by the mind and yet having no reason for their special forms, but standing inexplicable and irrational, is hardly a justifiable position. Uniformities are precisely the sort of facts that need to be accounted for. Law is par excellence the thing that wants a reason. Now the only possible way of accounting for the laws of nature, and for uniformity in general, is to suppose them results of evolution.”
From this point of view, the notion of transcending our time-bound experiences in order to discover truths that hold timelessly is an unrealizable fantasy. When science succeeds, we do nothing of the sort; what we physicists really do is discover laws that hold in the universe we experience within time. This, I would claim, should be enough; anything beyond that is more a religious urge for transcendence than science.
So, what is physics without a clean separation into laws and initial conditions, and hence, without the notion that there is a space of configurations that exists timelessly? We do not know the full answer to this, but we have a few observations.
First, by discarding the Newtonian schema for cosmology we have much less reason to consider our universe one of many other actual universes. Indeed, we may also be able to dispense with the notion of a vast number of other possible universes, that somehow are never realized. We can imagine instead a notion of law that applies only to the single universe that really exists. We also no longer have any reason to suspect that time is an illusion because, as outlined above, the main arguments from physics for time being emergent and not fundamental come from the misapplication of the Newtonian schema to the universe as a whole.
As we attempt to realize those principles, we seek a notion of law that cannot be applied to an imagined universe within a multiverse, and which cannot be imagined to hang around timelessly waiting for a universe to begin that it can then govern. Given that the universe only happens once, we must try to imagine a new kind of law that applies only that one time. Such a law need not — and should not — have any sense in which it exists outside of time. Nor could it be conceived of as apart from the universe it describes. It might indeed be a law that evolves in time; that is, a law where the distinction between a one-time narration of the history of the one universe and the statement of principles governing that history weakens.
If the timeless multiverse paradigm now ascendant is correct, then we are approaching the end of a process that will eliminate the reality of time and replace it with a shadowy kind of “existence” within an eternal frozen world consisting of vast numbers of possibilities. If, on the other hand, the principles that Unger and I propose are closer to the truth, then we are at the beginning of a new adventure in science where we have to reconceive the notion of law to apply to a single universe that happens just once. In either case we will end up conceiving our universe in very different and less familiar terms than before.
But did we really imagine that completing the revolution started by Einstein would be possible without having to discard some of our comfortable beliefs in favour of disturbing and almost inconceivable new ideas? At this level we do science not for ourselves, but for the future generations that will live comfortably in conceptual worlds that we can at best only point roughly towards. Press)
At a Glance: Against the timeless multiverse
• Many cosmologists today believe that we live in a timeless multiverse — a universe where ours is just one of an ensemble of universes, and where time does not exist • The timeless multiverse, however, presents a lot of problems. Our laws of physics are no longer determinable from experiment and it is unclear what the connection is between fundamental and effective laws • Furthermore, theories that do not posit time to be a fundamental property fail to reproduce the space—time that we are familiar with • Many of these puzzles can be avoided if we adopt a different set of principles that postulates that there is only one universe and that time is a fundamental property of nature. This scenario also opens the way to the possibility that the laws of physics evolve in time.
The fourth principle: mathematics and Platonism
Believers in eternal truth often point to mathematics as a model of a realm with timeless truths. What is called the Platonic view of mathematics holds that mathematical objects (the things that the theorems of mathematics are about, such as numbers, spheres, planes, curves and so on) exist in a separate timeless realm of reality. Mathematicians explore this realm with their minds and discover truths that exist outside of time, in the same way that we discover the laws of physics by experiment. But mathematics is not only self-consistent, it also plays a central role in formulating laws of fundamental physics, which the physics Nobel laureate Eugene Wigner once referred to as the “unreasonable success of mathematics in physics”.
One way to explain this success within the dominant metaphysical paradigm of the timeless multiverse is to suppose that physical reality is mathematical, i.e. we are creatures within the timeless Platonic realm. The cosmologist Max Tegmark calls this the mathematical universe hypothesis. A slightly less provocative approach is to posit that since the laws of physics can be represented mathematically, not only is their essential truth outside of time, but there is in the Platonic realm a mathematical object, a solution to the equations of the final theory, that is “isomorphic” in every respect to the history of the universe. That is, any truth about the universe can be mapped into a theorem about the corresponding mathematical object.
If nothing exists or is true outside of time, then this is all wrong. However, if mathematics is not the description of a different timeless realm of reality, what is it? What are the theorems of mathematics about if numbers, formulas and curves do not exist outside of our world? This leads Unger and me to a new view on mathematics that can be summarized in a fourth principle.
4. Mathematics is derived from experience as a generalization of observed regularities when time and particularity are removed.
Consider a game, for example chess. It was invented at a particular time, before which there is no reason to speak of any truths of chess. But once the game was invented, a long list of facts became demonstrable. These are provable from the rules, and can rightly be called the theorems of chess. These facts are objective, in that any two minds that reason logically from the same rules will reach the same conclusions about whether a conjectured theorem is true or not.
Now a Platonist would say that chess always existed timelessly in an infinite space of mathematically describable games. We do not achieve anything by believing that, except an emotion of doing something elevated. Moreover, it is clear that a lot is lost; for example, we have to explain how it is that we finite beings embedded in time can gain knowledge about this timeless realm. We find it much simpler to think that at the moment the game was invented a large set of facts become objectively demonstrable, as a consequence of the invention of the game. We have no need to think of them as eternally existing truths, which are suddenly discoverable, instead we can say they are objective facts that are evoked into existence by the invention of the game of chess. Our view is that the bulk of mathematics can be treated the same way, even if the subjects of mathematics such as numbers and geometry are inspired by our most fundamental observations of nature. Mathematics is no less objective, useful or true for being evoked by and dependent on discoveries of living minds in the process of exploring the single, time-bound universe.
More about: Against the timeless multiverse
R Bousso, B Freivogel and I-S Yang 2008 Boltzmann babies in the proper time measure Phys. Rev. D 77 103514
R Loll 2008 The emergence of spacetime or quantum gravity on your desktop Class. Quantum Grav. 25 114006
F Markopoulou 2008 Space does not exist, so time can
www.fqxi.org/community/essay/winners/2008.1
L Smolin 2000 The present moment in quantum cosmology: challenges to the arguments for the elimination of time
Time and the Instant (ed) R Durie (Manchester, Clinamen Press)
L Smolin 2006 The status of cosmological natural selection arXiv:hep-th/0612185
R M Unger 2007 The Self Awakened: Pragmatism Unbound (Harvard University
