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Unique, or not unique?

That is the question. The search for a single theory of everything is as old as science itself, and is now the beat of quantum cosmologists. But some basic tenets that inform the quest are being challenged.

Whether 'tis nobler in the mind to suffer The slings and arrows of outrageous fortune, Or to take arms against a sea of troubles, And, by opposing, end them?

Hamlet Act III, Scene i

Hamlet's existential agony has always been, in a variant form, part of the mindset of those researching quantum gravity. In this field, a large faction has deemed itself to be in the outrageously fortunate position of being close to a unique theory of how the Universe is as it is. This theory would not only put descriptions of all forms of matter and their interactions on the same footing, but also reconcile the two seemingly inharmonious pillars of modern physics: general relativity, which describes gravity, and quantum theory. The belief in such an all-encompassing theory has been the driving force for the various models known as string theories, grouped under the umbrella of 'M-theory', that have been developed in the past decades.

But there is an alternative concept. This holds that solutions, rather than models, are unique. Solutions are generally more important for physics than theories: observations are compared with properties that emerge from a theory, not with the construct itself. But finding realistic solutions to theories — solutions that reproduce the features of the Universe that we observe now — has proved much harder and messier than constructing the theories themselves.

That applies even with a modest interpretation of 'realistic', such as merely requiring the solution to undergo the kind of accelerated late expansion that our Universe appears to be going through now. Once such solutions were finally uncovered1, myriads of them turned up in various corners of the string landscape2. Thus, as there is currently no selection criterion by which to choose among this vast range of solutions, it does not seem particularly useful to claim that any one string theory is unique.

Stephen Hawking and Thomas Hertog3, writing in Physical Review D, now propose arms to be taken against this sea of troubles. The arms they propose are admittedly not new, having been developed4 in the 1980s by Hawking, James Hartle and others. Then, too, the motivation was uniqueness of solutions: specifically, if a quantum-cosmological model explains properties of our Universe (of which, by definition, we see only one), then it should also explain why this, and only this, solution emerges. Such a model can be compared with observations, making the whole framework testable and thus predictive.

Hartle and Hawking called their condition for establishing uniqueness4 the no-boundary proposal, because it removed the boundaries of space-time. According to this view, the Universe is a closed surface — rather like a surface of an inflating balloon — and has no beginning in time. Such a closure of space-time is not meaningful in classical general relativity, and thus requires the introduction of aspects of quantum theory. This in turn serves to establish uniqueness: although there are several possible closures, quantum theory can, unlike classical theory, deal with all of them at once as a probabilistic superposition. Alternatives to the Hartle–Hawking proposals include Alexander Vilenkin's proposal that the Universe initially tunnels out of a quantum state where space and time are not defined5, and more recent models based on new formulations of quantum gravity.

In their recent paper3, Hawking and Hertog refresh the no-boundary proposal, adding new insight and giving it a new name: top-down cosmology. Looking at a space-time diagram where time runs in the upward direction, the conventional approach to cosmology is 'bottom-up' (Fig. 1a): one starts with initial conditions in the past and calculates forward to aim at properties seen now. This process usually requires very specific, fine-tuned initial values. The top-down approach (Fig. 1b) avoids this problem by taking the properties of the Universe as it appears now and calculating its history backwards. This process is applied to a quantum superposition of different Universe states, with 'final', rather than initial, conditions being set to select one history in the super-position relevant for our observations. In this way, the non-intuitive quantum superposition is reduced to a classical Universe as we observe it.

Figure 1: Take it from the top.

a, A bottom-up description requires fine-tuned initial values for individual histories to arrive close to a universe as we see it now. b, A top-down formulation avoids that problem by starting with present properties and working backwards. Both viewpoints can be used in classical and quantum physical frameworks, but the top-down interpretation is most strongly motivated by quantum cosmology. The quantum top-down approach picks suitable histories from a quantum superposition of all possible histories that lead to the current Universe. Thus here, the solution, rather than the theory that leads to it, is unique.

Traditional bottom-up cosmologies also suffer from the problem that they break down at points where infinite energies arise in solutions of the equations of general relativity. These points are known as singularities, and our Universe may have experienced one at the Big Bang. Starting from a simple initial state that explains the emergence of the Universe, the chances are that one will run into a singularity before even getting close to the present. On its own, the top-down approach is not free from this problem, as the probability of hitting a singularity when calculating backwards is just as great as when calculating forwards. But when combined with the no-boundary proposal, top-down is safer: this combination has the effect of closing off singularities from classical space-time before the history being traced can approach them. Again, this act of closing off introduces aspects of quantum theory, and leads directly to a quantum description of gravity.

The arguments that Hawking and Hertog present are not complete, as they distinguish only between 'classical bottom-up' and 'quantum top-down'. That mixes up the singularity problem, which is a matter of classical against quantum theory, with the issue of predictivity. This second point amounts to what preconditions, whether initial or final, we may set when evaluating a theory and is the dividing line between bottom-up and top-down theories. Elsewhere in physics, it is clear which approach is better: one predicts final observations from the initial set-up of an experiment. But this option is clearly not available in cosmology, as we have no influence over the initial conditions of the Universe. Hawking and Hertog's suggestion is indeed a radical shift of approach: it is, as befits the description of the evolution of the Universe, much more akin to the holistic methods of 'universal history' (advocated in an early form by Friedrich Schiller in his inaugural lecture at Jena in Germany in 1789)6 than anything familiar from the physical sciences.

A further imprecision is that the authors sometimes use 'top-down' and 'no-boundary' interchangeably, although these are different concepts. That undermines some claims and disregards alternatives: there are, for instance, more general solutions of the singularity problem that do not require a top-down approach; and theories of decoherence7,8,9,10 provide detailed descriptions of the quantum–classical transition as a physical process in which a superposition evolves into a semi-classical history.

Hawking and Hertog present examples3 for final conditions that can be chosen as the starting point for the backwards computation of the Universe's history. Currently, that choice is wide open, and no clear line is drawn between anthropic conditions — conditions that must be so, because otherwise we humans could not be there to observe them — and conditions that arose accidentally during the development of the Universe, but are nonetheless regarded as important for the purposes of the computation. The fewer final conditions there are, the more predictive a theory will be. What is considered an accident or not is often just theoretical pre-judice. Not distinguishing between 'accidental' and other conditions in the determining final set allows one to escape a firm decision, but could undermine the top-down approach by relinquishing deeper explanations. Indeed, without any final conditions whatsoever, we are back to a decoherence approach as most predictive: this approach attempts to describe the emergence of the current state of the Universe through a physical process in which accidents may arise, but do not affect the overall theory.

So will the no-boundary, top-down cosmology really turn the string landscape into a goldmine of physical predictions? Hawking and Hertog's paper is mainly about how to interpret physics from the top-down perspective, with few supporting calculations, so their answer remains uncertain. Clearly, with too much leeway in choosing final conditions (these might include, the authors propose, the number of dimensions in space-time, or the observed features of the standard model of particle physics), physics is in danger of becoming a tautology — a proposition already true by definition. But approached carefully, a top-down viewpoint on cosmology can, at some expense of losing explanatory power, serve well as an interpretational framework to test theories in the string landscape.

Hawking and Hertog's work also represents a welcome attempt to combine pivotal ideas from different approaches to quantum gravity. Such cross-fertilization has rarely happened, but can only improve our overall understanding. That such efforts should continue is indeed, to return to Hamlet, “a consummation devoutly to be wished”.


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