Review of “The Singular Universe and the Reality of Time” by Roberto Mangabeira Unger and Lee Smolin
The Singular Universe is effectively two separate books held together by some common ideas. Roberto Mangabeira Unger is a philosopher, social and legal theorist and politician who helped to bring about democracy in Brazil and has twice been appointed as its Minister of Strategic Affairs (in 2007 and 2015). According to Wikipedia (current entry), “his work begins from the premise that no natural social, political or economic arrangements underlie individual or social activity.” A similar spirit informs his approach to cosmology. Lee Smolin is of course well known as one of the creators of loop quantum gravity and as the author of several popular-science books. For brevity, I shall refer to the authors as RMU and LS. The book is over 500 pages in length. The first part, by RMU, is more than twice the length of LS’s and could have been shortened without loss of essential content. There is a final 20-page section detailing differences of view, which are substantial in some cases because RMU advocates a much greater break with the conventional approach to science than LS.
The two authors are agreed that a new ‘historical’ approach to cosmology is needed. For RMU, the mere fact that the universe has been shown to have a history is enough to indicate that the methods hitherto used to study the universe must be radically modified. LS argues for a new approach because of our failures to understand the history and properties of the universe as so far discovered. He points out that, despite all their advances, high-energy physics and cosmology face a severe under-determination crisis. That is, what fixes the 30 odd dimensionless parameters of the standard model of particle physics, and how can one explain the many apparent fine-tunings for life and the very small values of some dimensionless parameters in the two domains? Both authors criticize anthropic resolutions of this crisis within the context of the multiverse. LS points out their failure to make falsifiable predictions.
As regards the individual contributions, RMU’s central thesis is that the science of the last 100 years, above all cosmology, has made a discovery of the utmost significance: the universe has a history. Few will argue with that. Indeed, for me it is a triumph of the kind of science, firmly based on the use of mathematics to describe precise observation, that Galileo inaugurated and an encouragement to continue it. Not so for RMU, for whom it is the reason to argue for a quite different kind of science. He seeks to invert the widely accepted ‘hierarchy’ of scientific disciplines in which, on account of their rigour and precision, mathematics and physics, stand at the top and provide the framework in which chemistry, the life sciences, social sciences and history follow in descending order. Precisely because the universe has a history, the methods of historical research must take precedence over mathematics and timeless laws in an attempt to understand that history. In cosmology, timeless laws of physics are to give way to regularities which evolve coevally with the phenomena that they describe, as happens in the life sciences and in political structures in states. Cosmology is to become an historical science guided by certain key principles (basically shared by LS).
The most fundamental of these is “the inclusive reality of time”. This can actually be summarized as three principles: everything that happens in the universe can be arranged along a unique timeline that extends indefinitely far into the past and into the (unknown) future. Despite the time-reversal symmetry of the known laws of nature, this timeline carries an arrow that points inexorably from the past to the future. This is not primarily because of the second law of thermodynamics but because the very laws that govern change themselves change unidirectionally (RMU frequently asserts that “change changes”). Finally, there is, despite the evidence from special and general relativity, a notion of universal simultaneity. This last is either postulated or justified by the reformulation of general relativity as shape dynamics , in which relativity of simultaneity is ‘swapped’ for relativity of local spatial scale. For both authors, these three properties express ‘the reality of time’ and explain the subtitle of the book. The epithet ‘singular’ applied to the universe has two main significances: radical dismissal of all ideas to do with the multiverse as an explanation for the observed properties of the universe; and the need to find a new way to describe the evolution of a unique object.
In line with their distrust of timeless laws, both authors have a sceptical attitude to mathematics. RMU evinces at times an almost visceral dislike of it (even calling mathematics at one point a “poisoned chalice”). He repeatedly claims it robs nature and the universe “of both time and phenomenal particularity”. The theft of time mainly comes down to the fact that in timeless mathematical syllogisms, the premises and conclusions are simultaneous. This means that the unfolding of a dynamical history is already contained in the law and the initial conditions, so that nothing truly new ever happens. The explanatory power of dynamical laws to model evolving phenomena does not appear to impress RMU; he believes the evolution of the universe is as unpredictable as Darwinian evolution or, more drastically, the history of political states. As regards the loss of phenomenal particularity, I did not find an explanation of what it means. I thought it might be related to the philosophical mystery of primary qualities, but whereas LS does discuss that at some length, RMU does not. If RMU means that cardinality fails to distinguish three apples from three oranges, he does not say so. Even if he does, in this digital age in which my biometric data enable me to pass through UK passport control in a few seconds, it seems to me that mathematics (ably assisted by physics) does a rather good job of capturing phenonemal particularity.
The main contention of both authors is that the universe and its history, which are both unique, cannot be described scientifically within the framework of the Newtonian paradigm of standard science, in which timeless laws of nature and given initial conditions are used to describe phenomena that unfold in subsystems of the universe. Two main problems with this approach are identified. First, in accordance with Mach’s principle, the framework in which local laws of nature are formulated must be expected to be determined by the universe at large, which will be governed, if at all, by a law or laws of a different kind. At the very least, RMU is sure it will not be a timeless law with contingent evolution determined by specification of initial conditions. Second, whatever the law in accordance with which the universe evolves, one cannot assume that its form and any constants that it involves remain unchanged. As it happens, my own work on Mach’s conjecture — that the local inertial frames of reference are determined by the universe at large — played a role in the thinking of both authors, so I am certainly sympathetic to the relational aspect of the book. However, I am not persuaded that it necessarily means one should abandon fully the Newtonian paradigm.
A simple point-particle model can be used to explain why. The laws of standard Newtonian systems, defined relative to an inertial frame of reference, are invariant under the Galilean group of transformations, with the consequence that their energy, momentum and angular momentum are conserved, having values that are determined by initial conditions. Machian considerations lead one to conclude that the dynamics of an ‘island’ universe of point particles should be invariant under a much larger group: the Leibniz group.  This is in fact a gauge group, which means that the dynamics are subject to constraints — the angular momentum of the universe must vanish, which is a prediction that does not follow from Newtonian dynamics. Moreover, the only natural way to ensure that Newton’s absolute time plays no role is to require the total energy of the universe to vanish. By Galilean invariance, the total momentum of the universe can always be set to zero. However, this vanishing of all the standard mechanical conserved quantities for the universe as a whole allows subsystems of the universe to have nonvanishing values of these same quantities in a frame of reference that is determined by the universe. What is more, the structure of the point-particle model is repeated in a much more sophisticated manner in shape dynamics, which is essentially a relational reformulation of general relativity in the case of a spatially closed universe.
What this means is that the basic form of the Newtonian paradigm is retained: one simply swaps Newtonian absolute kinematics for relational kinematics and a variational principle invariant under a finite-parameter Lie group (Noether’s Theorem Part I) for one, for a principle invariant under a Lie group that depends on arbitrary functions (Noether’s Theorem Part II): the law of the universe is a timeless gauge law. Thus, I think the relational requirement in no way leads one to abandon the idea that the universe is governed by a timeless law that admits many different solutions. Indeed, the Noether-II law of the universe explains why the Newtonian paradigm holds in Noether-I form for subsystems of the universe.
The attempts, mainly by LS, to resolve the second problem mentioned earlier (the under-determination problem in high-energy physics and cosmology) do seem to me to have a more secure rationale and might lead to real progress. In particular, the ‘Darwinian’ idea which LS first put forward a couple of decades ago in his The Life of the Cosmos — namely that whenever a black hole is formed it gives rise to a new universe in which the values of the constants of nature have undergone ‘mutations’ — is the only plausible non-anthropic proposal I know that might give a genuine testable explanation of why the observed values of the dimensionless constants of nature do have their observed values. The point is that through evolution universes whose constants favour copious production of black holes will come to predominate. I suspect that readers will find LS’s other specific suggestions, some of which aim to dissolve the distinction between the current state of a system and the law which governs it, to be either a bit contrived or too radical a break with the well-tested methods of physics to be likely to be successful. However, it is clear that we do face severe problems, or at least major puzzles, in our attempts to understand the universe we find around us, so unconventional approaches should not be dismissed out of hand.
In contrast to LS’s specific proposals, RMU presents only general arguments. These rely heavily on causal connections and reflect his historical approach. He supposes that the universe has passed through an indefinite number of ages in which on occasion “causal connections have been stressed but never broken'”. Specifically, this is supposed to have happened at the dawn of our present epoch, when temperatures and densities were high but not infinite and, RMU conjectures, regularities and the phenomena they describe evolved coevally. Perhaps the most striking feature of RMU’s contribution is his blurring of the distinction between laws of nature and regularities. As generalized by Einstein, Galileo’s discovery that all bodies fall with the same acceleration holds, so far as we know, universally; in contrast, rules of, say, parliamentary procedure, which have evolved historically, differ from parliament to parliament. I am not persuaded that this difference can be washed away. RMU argues that it can and that the stability of the currently observed laws of nature is due to the fact that we live in an atypical ‘cooled down’ epoch of the universe. Moreover, one significant thing that neither author mentions is that most physical laws take the form that certain combinations of empirically measured quantities are zero — this is the content of an equation. It is not clear to me that historical or political regularities could ever be cast in this form.
I am also worried by the reliance of both authors on a strong form of causality, in accordance with which, as RMU asserts, “the cause always precedes the effect”. I see two reasons to have doubts about this. First, it is often very difficult to identify genuine causal relations. Second, there is the problem of the time-reversal symmetry of the known laws of nature. A dynamical explanation of the second law of thermodynamics, which is certainly not impossible , would severely undermine the whole basis of RMU’s arguments. Another difficulty in the book is what the authors call the ‘metalaw problem’. This arises from the attempt, especially by RMU, to argue for a universe in which all laws arise contingently and coevally with the described phenomena, as certainly can be argued to be the case in political history. This raises the question of whether anything, some metalaw, determines what has happened and what will happen in the universe. I do not think either author makes any real progress on resolving this conundrum.
However, humans and their unpredictable history are part of this remarkable universe in which we find ourselves. Potentially of even greater significance, as RMU points out, humans do seem to be gaining an increasing measure of control over the universe. Who knows what future intelligences will bring about? There is certainly a case for a book of this kind that challenges head-on the most basic assumptions of the way the universe works.
 See for example Flavio Mercati’s A Shape Dynamics Tutorial, arXiv:1409.0105
 J Barbour and B Bartotti, Proc. R. Soc. (London) A 382, 295 (1982).
 LS is well aware of this and discusses the preprint “A gravitational origin of the arrows of time,” arXiv:1310.5167 by T Koslowski, F Mercati and myself, part of which subsequently appeared as “Identification of a gravitational arrow of time,” Phys. Rev. Letters 113, 181101 (2014). Writing at a time before our subsequent “Entropy and the typicality of universe,” arXiv:1507.06498v2 (which I think does strengthen our approach), he doubted whether this work could lead to a full, purely dynamical explanation of the second law.
The Singular Universe and the Reality of Time
by Roberto Mangabeira Unger and Lee Smolin
Cambridge University Press
566 pages | Hardback
Published: January 2015
Also available as: eBook
This work is licensed under a Creative Commons Attribution 3.0 Unported License.