author : Julian B. Barbour

This is a deeply fascinating book about the physics of time. The underlying argument is that the universe is timeless, and this point is argued through a Machian and Leibnizian view of physics, incorporating General Relativity and Quantum Mechanics until it builds up a persuasive picture. Even if you don't believe the conclusion (and I'm not convinced I do, but am having difficulty articulating why), there's lots of fascinating material along the way.

In (brutal and probably misleading) summary: relative configuration space contains all possible instants of time, where the high probability instants have a complex structure that encodes (an illusion of) a coherent history. Let's unpack that. (Warning: this is a long review/summary: probably too long to make the ideas digestible, yet probably not long enough to make them comprehensible: read the book!)

We start off with a Leibnizian philosophy: unlike with Newton, there is no absolute space, but rather things are defined in relation to one another. The simple example Barbour uses is "triangle space". In a Newtonian view, to define a triangle one gives the three sets of coordinates, one for each vertex, relative to some absolute space. In a Leibnizian view, one gives the distances between the vertices. This suffices to define the triangle, but not its orientation in space. But in the Leibnizian view, there is no "orientation in space", because there is no separate "external" space to orient in, there is no space other than what the triangle itself defines.

The next point to to understand is configuration space (or state space as it is often called). This is not the usual physical space we are used to, containing a single configuration of all the things within it, but the space of all possible configurations. In Barbour's running example, this is the space of all possible triangles. But Barbour uses a Leibnizian, relative, configuration space (which he dubs "Platonia"), rather than the more conventional Newtonian configuration space.

Conventionally, in classical mechanics, history can be defined as being traced out by a "spot of light" moving along a path in such a space. Barbour brings in ideas from Mach's view of mechanics, needed to move from an absolute space to a relative space view, which leads to a different interpretation of the path.

There is still a possibility of an absolute time giving the movement along the path. But Barbour takes a Leibnizian, relative, view of time itself. There is no absolute time, but only differences, or change.

In order to support this conclusion, he describes how time is measured: always in terms of some kind of change. He describes Galileo using water clocks and rolling balls to measure time:

Ultimately, time gets measured by the Earth's rotation, then more accurately by the workings of the Solar System (ephemeris time), then by the universe itself (bringing us back to Mach's view).

I first came across this idea in the form of the aphorism "Time is defined so that motion looks simple"; here, Barbour identifies the source.

This idea of a unique or distinguished simplifier is a recurring, and necessary, theme here. I am fascinated by why it should exist. Why should it be possible to define time so that motion looks simple? Why should it be the same time that makes motion in our daily lives (not all of which is governed by gravity), and the motion of the planets, look simple? That is, why is the time we "experience" so closely correlated with ephemeris time? Could there be other simplifiers describing other "simple" laws?

Barbour then identifies the individual configurations in Platonia as "instants of time".

This rich configuration space has enough structure, enough things happening, so that you can order them in time.

Once we have the idea as instants of time being points in configuration space, we need to know: (1) why some points (like now) are experienced in preference to others (never seen events, like giant pink unicorns line-dancing on the surface of the sun, for example); (2) how historical paths are formed (why we have a memory of a coherent past, rather than remembering things like those giant pink unicorns, even if we are not experiencing them now); and (3) how we perceive motion, the actual flow of history. After all, there are points in Platonia with those unicorns dancing, and there are points with "you" remembering those unicorns. Yet there is no motion, so how do they dance?

Barbour spends a lot of time discussing the first two, and a little time on the third. For me, each gets a little less convincing.

For the first, the preferential experience of coherent points, he uses probability. To help explain this, let's move away from physical configuration space, into a more abstract one: Borges' Library of Babel, with every possible book (of a certain format). This space is truly Vast, with most of the books being gibberish (random sequences of characters), and many being similar to existing books but differing by typos, or with people renamed, or roses having a different colour, or whatever. Very very few are coherent books. If you wander in Borges' Library, picking books at random, you will almost never find a proper book. Similarly, in Barbour's Platonia, very very few points are coherent points, yet these are the ones experienced. How? Think of a bigger version of the library of Babel (!), one with many copies of each volume, but with Vastly more copies of the "proper" books, so Vastly more that as you wander at random, if you pull down a book, it is likely to be a proper book. Barbour uses a quantum mechanical probability density "mist" to pick out the coherent points in Platonia. (One thing he doesn't emphasis is the Vastness of Platonia, and the Vast difference in mist density needed. Also, is it possible to have regions of zero probability? If so, do these points "really" exist in Platonia, or not?)

Boltzmann used this idea to explain why high entropy (random) states are preferentially observed: there are so many more of them.

Here, it is not the boring random states that are highly probable, it is the coherent, structured ones. Why?

The second issue is how the paths are formed, and distinguished.

For this, Barbour introduces time capsules, configurations in Platonia with a particular structure.

These time capsules have a (memory of) history encoded in them, and are the high probability points.

There is a lot of interesting discussion about why these time capsules are selected, and why they can be linked into coherent histories (beyond the "resonance" remark quoted earlier). This has a relationship to the semiclassical Principle of Least Action. This principle identifies special paths in absolute space (absolute, because it is given in terms of kinetic energy); Barbour identifies analogous kinds of "shortest paths" between events in Platonia.

However, there is also the point that recognition of a history requires information, records of that history, to be present in the Now.

This remark about Newtonian physics demonstrates that it is somehow an "impoverished" view of physics, looking only at simple, small systems. It is insufficiently complex, has an insufficiently rich configuration space, to construct or contain historical records. But when we look at full real world -- the universe of Leibniz and Mach -- we see a much richer structure, one that can hold records, one that can record time. History, a coherent past, requires complexity.

The physicist Bell produced similar reasoning.

However, Bell stopped, rejecting this view as absurd, and accusing it of "radical solipsism". Barbour takes it further.

Despite these discussions, however, it eventually comes down to a conjecture that the probabilities pick out coherent time capsules, not crystals, or chaos, or nonsense.

(Barbour notes that being "well behaved" is a very strong, but plausible, constraint on the laws of physics, negating the need for initial and boundary conditions.) It is not completely clear to me where this asymmetry comes from. It might be related to there being more configurations of lots of things than a few things. However, the only example Barbour gives in depth is that of the configuration space of triangles, which reduces to a point at the zero-sized triangle. However, there aren't more large triangles than small triangles -- they are just larger, but their edges live in the world of real numbers (in his example), and there are just as many tiny real numbers as enormous ones. He doesn't give an example of where the number of things defining the configuration space changes (which would imply that the dimensionality of the space changes) -- unless you count "degenerate" triangles where one edge is of zero length.

Asymmetric Platonia is defined by configurations; the probability of those configurations are "funnelled" by the laws of physics. What are these laws?

Why this one law? Why does this law pick out time capsules? Why is time one-dimensional? Are there other, weird but equally coherent, paths through Platonia that could be picked out by other laws of physics? (Shades of Gell-Mann's "goblin worlds", perhaps? or of William James' "other minds"?)

The third feature that needs to be explained is the experience of motion in this timeless universe of Platonia. Barbour has this as an actual experience, not a general property of the world. The reason given is that our brains hold a memory of a few seconds of the path, and that memory is "somehow" experienced as motion, that it "creates the impression" of motion.

I confess that here I experience a particular form of motion: hand-waving -- but Barbour does say that this part is less well developed than the rest. However, it seems to me to be a crucial part of the argument -- motion seems to be qualitatively different from a series of configurations. On the other (waving) hand, it is true that we can experience a sufficiently rapidly displayed sequence of still images as motion.

Are these sequence of snapshots any different from the records of histories in configurations? If not, why do we not experience those records as motion? If they are different, in what way, and why are they correlated with those records, so that my experience of motion Now seamlessly joins to my record of previously experienced motion? (And, of course, other low-probability points in Platonia have these sequences of snapshots jumbled, or missing.)

So there we have it: relative configuration space (Platonia) contains all possible instants of time, where the high probability instants have a complex structure that encodes (an illusion of) a coherent history. I hope I've not mangled Barbour's explanations too much in my summary: read the book for yourself to find out more.

I have some quibbles. I'm not entirely sure Barbour is taking account of the true mind-boggling Vastness, and richness, of Platonia.

For one thing, although there is emphasis on experiencing instants, implying a life form doing the experiencing, there is very little on the Vast richness and diversity of evolved life. Okay, all points exist in Platonia, including points that look like life evolved. But why are these high probability points, unless the life forms really evolved (through time)? Why is evolution a distinguished history?

This is a specific instance of a more general problem. Platonia seems to be even bigger than the staggeringly enormous set of universes in Everett's Many Worlds description. There we have all possible worlds; here we seem to have all the many more impossible ones, too. As a computer scientist, I just find this space Too Big. How is it constructed? This question was raised most sharply for me in the following:

Ignoring the obvious "why experienced"?, I found myself answering the question with: Because of parsimony, because of optimisation, maybe? Each instant is different, but related to "earlier" ones on the relevant path. Computationally, and physically, it is often simply easier to create something from a slightly different precursor, than to create it from scratch. And if we are allowed to create things incrementally, then we can create them lazily, only as needed. Even more parsimonious. (But I'm not sure how it all then relates to the idea of probability densities.) Barbour does not think this creation is algorithmic.

I'm perfectly happy if it's not algorithmic. (It could still be incremental.) And if it isn't, I want to exploit that non-algorithmic novelty generation as the basis of a more powerful computer!

There's much more (some of which I discuss separately below, to keep this review moderately coherent!). There is masses of excellent material here -- read the book, and think about it for yourself. I swear my brain imploded more than once while thinking about some of these concepts, but I now have a much clearer idea of Leibnizian relativity, Mach's principle, and timeless aspects of QM and GR. Well worth the effort, and the implosions.

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Some more quotations that are important, but don't fit into the flow of the above review (ie, these are high probability instants in Platonia that aren't part of the preceding history :-)

In particular, there are lots of great discussions about classical dynamics and Mach's principle, about General Relativity, and Quantum Mechanics, as Barbour gradually builds his argument, explaining things in simple physics, adding in consequences of looking at the entire cosmos, then adding the more recent, more sophisticated ideas, until he reaches his fully GR-QM-Platonia.

There are problem with using a state space in Newtonian mechanics: there multiple solutions (paths consistent with the laws of motion) through any point (corresponding to different kinetic energies) -- which is why these problems are typically considered in phase space (which includes velocities as well), to separate these solutions. But considering the universe as a whole, rather than considering a subsystem of it, removes this problem:

But the world doesn't follow Newton's laws -- it follows GR and QM.

Bell was involved in the early development of some of these ideas, here that of records:

On accepting a many-worlds view:

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Additionally, there are some parts that relate to complexity science, and why reductionism doesn't hold. Platonia is all possibly configurations of the entire universe, and its interesting properties and structure are a consequence of that wholeness, that don't necessarily hold for isolated parts.

So, Leibniz invented "edge of chaos" (or maximum statistical complexity) nearly 300 years ago!

QM waves goodbye to reductionism:

If we focus on configuration space, rather than physical space, there is no such thing as "individual particles" -- it's all one configuration -- this directly accounts for the relationships between "things" that are key in complexity science.

Newtonian absolute space and time are essential for atomism, for thinking in terms of individual particles, and hence for reductionism. Reductionism requires a Newtonian philosophy; complexity science seems to require a Leibnizian philosophy.

If these ideas are correct, it invalidates the idea of physics always looking only at simple, reducible, isolated systems. Barbour has time and history as an emergent property of complexity, of sufficiently rich configurations of the entire universe. (Is this the reason for all those problems with the arrow of time in simple systems? they are too simple for the arrow's direction to be able to emerge?)

On coarse-grained and fine-grained histories, maybe helping to reduce the scale of Platonia:

The only reference to evolution:

On looking for a process-based ontology:

(Googling on Process and Reality subsequently, it seems that Barbour's experience is not unique here.)

Originally published as Absolute or Relative Motion? Volume 1, The Discovery of Dynamics. CUP, 1989