Book Review

Richard Arthur

The Reality of Time Flow

Cham, Switzerland: Springer, 2019, 279 pp.

ISBN 9783030159467

Reviewed by Jo Edwards
University College London

A key aspect of consciousness is that it is in the present. I am con­scious now. Einstein claimed now does not exist in physics. So, what is ‘the present’? Does time really exist? This book is not primarily about consciousness, but for those interested in what basic physics and metaphysics can contribute to our understanding of consciousness, I would rate it as the most informative and interesting volume to appear for a while. Arthur combines a meticulous analysis with feet-on-the-ground common sense and, above all, is courteous to both his readers and his sources. He writes clearly and with a light touch.

Arthur’s message is that we need not worry; our sense that, even if metaphorically, time flows, or passes, or has a direction, with us in a present somewhere along the way, is based on something real. We should not be brow-beaten by high-profile physicists or philosophers who claim that time is dead or the same both ways. Careful analysis of such claims reveals surprisingly little substance and, maybe, incoherence.

There is also an important original idea in the book, which the author and Steven Savitt (2015) have been developing for some time: that the present is a real part of physics that is best defined by some­thing called a causal diamond. In contrast to many popular science books we are not assaulted with this as if the solution to everything. It is presented tentatively, with ifs and buts, as something germinating. The book is about why such an idea might be sown in fertile soil. I think it has significant promise.

After a succinct introduction outlining the ground covered, the first three substantive chapters set the historical perspective for arguments for the illusory nature of time, first in broad philosophical/meta­physical terms and then in terms of ‘classical’ physics. For instance, it has been said that time cannot flow because you would need another time to judge how fast. It has also been claimed that there can be no ‘next’ event in a continuous time with infinitesimal parts so time cannot move on. In essence, Arthur shows that these objections use false analogies, rather in the way Eddington claimed that a table in modern physics is mostly ‘empty space’. (If anything, physics now says space is never empty.) The treatment of Zeno’s paradoxes is illuminating. His puzzle of the arrow is neither, on the one hand, just a joke, nor a serious obstacle to time passage, but a useful warning about how not to apply abstract mathematics to reality.

Arthur’s deflation of arguments against the reality of time flow is systematic and not without humour. A sacred cow has been the argu­ment that, because equations in physics are mathematically reversible in time, time has no direction. Arthur points out that this argument is empty. He uses the nice example of PalinnilaP, an imaginary language in which words are the same backwards. This does not in the least imply that sentences have no syntactic direction. I had always thought that the reversibility argument seemed a bit slick, but not stopped to think why. All equations in physics are about predicting what is likely to happen next under controlled conditions. The fact that an isolated process can be matched by a mirror-image process tells us nothing about causal sequence. The future is dependent on how everything is now, not just the linear progression of one process.

This links to the role of entropy. The second law of thermodynamics is often invoked as the reason for the apparent asymmetry of time. But, as I think Arthur implies, it makes more sense to say that the asymmetrical role of time is the reason for the second law. Curiously, perhaps the most obvious proof of time asymmetry is memory — of which there is never any of the future — yet memory depends on order persisting, not decreasing.

Following these historical arguments, Chapters 5 and 6 move to special relativity (SR). The central issue here is that in SR there is no such thing as simultaneity. You can measure the time taken to get from one event in space-time to another but there is no fact of the matter whether two events are ‘at the same time’. This destroys the idea that the present moment is the same across the universe and that we can take a ‘time slice’ and call it the present. Time passes or flows locally, not en bloc. Arthur shows that, despite the absence of time slices having been used to deny the possibility of time flow, if the passage from one present to the next, or the ‘becoming’ of a present, is local, there is no problem.

As part of the analysis of time in SR the concept of a present as a causal diamond is introduced. The motivation is that if the present is a point in time, of infinitesimal extent, we hit two problems. Firstly, since it takes time for any process to occur there seems to be no room in an infinitesimal point to support a rich ‘compresence’ to explain the sorts of patterns we experience as present. If becoming is at a point there is no room for any patterns ‘now’. The other problem comes from Zeno, who claimed that if we treat movement as a series of states, each of infinitesimal duration, movement is never achieved. Movement is not a series of states but the process of becoming that links them.

The alternative account of the present is that it is a finite domain of space-time, within which there is ‘compresence’. Process can occur; richness is available. Whether or not this idea can solve all problems without raising new difficulties may be up for debate, and Arthur does not shy away from that, but a finite present looks more promising than a vanishing point. The idea of a causal diamond comes from a suggestion made by Alexandrov — that a domain of causation could be defined in terms of everything in the light cone spreading out from one point in space-time and also in the light cone narrowing down on to a subsequent point. The domain is a bottom to bottom cone pair with diamond profile. Any process going from one cone apex to the next is allowed by SR to interact with any event in the causal diamond. The idea is that this domain forms the present for that process.

There are a number of questions that arise in relation to applying the concept of a causal diamond to a present as normally understood. Perhaps the most important question is what sort of event hosts the sort of present we experience. Arthur allows a fairly open interpreta­tion of this. Savitt (2015) has suggested that a causal diamond might explain the temporal range of a ‘specious present’ that can accommo­date a tune. As a biologist I think we may need to distinguish here between the domain of events represented in experience and the domain of an event doing the internal representing. The latter seems more likely to be where the richness of the experience is delimited and also where the sort of two-way relation conceived by Alexandrov might apply. The represented content is the brain’s selection of data from various times past, with no obvious limit.

Chapter 7 covers the bewildering complexity of arguments about the history of the universe that have arisen in the context of general relativity (GR), including the unsubstantiated speculation that space-time might curve back on itself. I found this section quite taxing but was left with a sense of satisfaction that Arthur had covered the issues in a cogent and systematic way. The conclusion is, again, that despite claims by physicists that GR makes passage of time impossible, their case looks weak. If the passage of time is a local matter, then worrying about the universe being a sort of Ouroborus of time slices devouring themselves is unnecessary. Moreover, Arthur argues, the principle of local passage of time, or local becoming, is implicit in the foundations of GR.

Chapter 8 is on quantum theory (QT) and time. It notes the idea of probable events turning into actual events being consistent with a concept of local becoming. It considers the claim of nonlocality in entanglement perhaps making local becoming difficult, but points out that there is no violation of SR. It then considers quantum gravity and the possible quantization of space-time. Arthur finds these dependent on speculative assumptions about the existence of a ‘universal wave function’ and concludes that the idea of local becoming remains viable.

To my mind, this chapter tends to underplay the support that quan­tum theory gives to the idea of local becoming. In Bohr’s original view, an actual event emerges from a range of possibilities. Although the dynamic laws in quantum theory still look continuous, the departure from classical theory is that the dynamic units are discrete happenings that arise in a way that is clearly asymmetrical. The probability of occurrence of a mode of excitation of a field is pre­dicted by the initial conditions, not the final conditions. Arthur covers this well enough, but I am a little surprised he does not capitalize on it more.

It has been claimed that the equations in QT are still time-reversible and it is here that I think that Arthur’s point about palindromic words not making sentences work backwards is so powerful. The equations of QT have often been taken as describing the progression of some dynamic unit called a ‘wave function’. Yet this interpretation is counter to Bohr’s original conception and disproven by the result of the experiments used to test Bell’s theorem. A dynamic unit in QT, a mode of excitation, does not exist at all except in its entirety; nothing ‘progresses’ along the way. The equations might superficially look like that but they are just a set of look-up tables for the likelihood of any particular mode of excitation, defined by final conditions, occurring. To say that the equations are time-reversible is a bit like saying that the symmetric pattern of a bus timetable across the day means that buses can drive backwards. It is a totally non sequitur argument.

The quantum domain seems to provide an ideal setting for the development of Savitt’s and Arthur’s idea that the present is a causal diamond. The domain of possible world lines connecting initial and final conditions in an event at the QT level would be a causal diamond that would seem to provide an ideal basis for a local ‘present’ from the point of view of that event. Since in contemporary quantum field theory this domain is a distributed field relation (which can be large), rich compresence is no problem.

The bottom line, as Arthur says, is that local becoming must be in some sense real. It has been argued that the universe is just a space-time block and that our sense of time is a trick played by the brain. An interesting aspect of the way brains represent events is that time is likely to be represented using spatial relations, not temporal ones. Neurons use time to synchronize signals both for computation and for selecting salient material for attention. That only leaves the spatial relations between signals to encode both time and space. However, I see this as no argument for denying that time involves real sequence. Why should brains have evolved to encode a sense of time flow if it was unreal and irrelevant to survival? The fact that we have a strong sense of time flow is a good reason to believe it has real dynamic con­sequences. What encoding in space might explain, however, is why time is so notoriously hard to pin down or describe other than with spatial metaphors.

In conclusion, The Reality of Time Flow is a rich resource for any­one interested in the way we relate to the world. It is an impressive piece of scholarship and also a good read.


Savitt, S. (2015) I love diamonds, Studies in History and Philosophy of Modern Physics, 50, pp. 19–24.

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