Short works

Books : reviews

Julian B. Barbour.
The End of Time: the next revolution in our understanding of the universe.
Phoenix. 1999

rating : 2.5 : great stuff
review : 11 August 2010

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.

p68. I arrived at the notion of Platonia (or, as I originally called it, the relative configuration space of the universe). … we orient ourselves in real life by objects we actually see, not by invisible space ... There is also the fortunate fact that we live on the nearly rigid Earth. We can orient ourselves by means of just a few objects fixed on its surface, say church spires when hiking in the English countryside. Always there, the Earth provides a natural background. Motion seems to take place in a framework. …
     The fact is that we live in a very special location. Only the tiniest fraction of matter in the solar system, let alone the universe, is in solid form. Imagine that we lived in an environment much more typical of the universe - in space. To simplify things, let there be only a finite number of objects, all in motion relative to one another. At any instant there are certain distances between these other objects and us. There is nothing else. In these circumstances, what would be the natural way to answer what is always a fundamental question: where are we? We have no other means of saying where we are except in terms of our distances to other objects. What is more, it would be artificial to choose just a few of them to locate ourselves. Why these rather than those? It would be much more natural to specify our distances to all objects. They define our position. This conclusion is very natural once we become aware that nothing is fixed. Everything moves relative to everything else.

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.

p69. In Newton's game, individual objects play in absolute space. In Mach's game, there is only one player - the universe. It does not move in absolute space, it moves from one configuration to another. The totality of these places is its relative configuration space: Platonia. As the universe moves, it therefore traces out a path in Platonia. ...
     … We must not think of the history of the universe in terms of some walker on a path who can move along it at different speeds. The history of the universe is 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.

p2. Richard Feynman once quipped, 'Time is what happens when nothing else does.' My conclusion ... was the exact opposite: time is nothing but 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:

pp96-7. it is water, not time, that flows. Speed is not distance divided by time but distance divided by some real change elsewhere in the world. … Galileo measured the water carefully and made sure that it escaped steadily from the tank ... But the innocent word 'steadily' itself presupposes a measure of time. Where does that come from? ... No sooner do we present some measure that is supposed to be uniform than we are challenged to prove that it is uniform.
     … time will become a distance through which things have moved.
     Merely describing the clocks shows that speed is not distance divided by time, but distance divided by some other real change, most conveniently another distance.

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).

pp106-8. To make [the solar system] into a clock, they assumed that Newton's laws governed it. … However, the astronomers had no direct access to any measure of time. Instead, they had to assume the existence of a time measure for which the laws were true.
     Ephemeris time may be called the unique simplifier. … When we hold the configurations apart in time and put a duration between them, this something we put there is a kind of imagined space, a fourth dimension. The spacing is chosen so that the happenings of the world unfold in accordance with simple laws (Newton's or Einstein's). ...
     ... The universe is its own clock.
     ... some motions are distinguished from others for timekeeping. They are those that march in step with the cosmic clock

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.

p180. Poincare's idea that duration is defined so as to make the laws of nature take the simplest form possible

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".

p16 Physicists are using too many concepts. They assume that there are many things, and that these things move in a great invisible framework of space and time.
     A radical alternative put forward by Newton's rival Leibniz provides my central idea. The world is to be understood, not in the dualistic terms of atoms (things of one kind) that move in the framework and container of space and time (another quite different kind of thing), but in terms of more fundamental entities that fuse space and matter into the single notion of a possible arrangement, or configuration, of the entire universe. Such configurations, which can be fabulously richly structured, are the ultimate things. There are infinitely many of them; they are all different instances of a common principle of construction; and they are all, in my view, the different instants of time. … I shall call them Nows. The world is made of Nows.
     Space and time in their previous role as the stage of the world are redundant. There is no container. The world does not contain things, it is things.

p70. 'The history of the universe is a continuous curve in its relative configuration space.' ... Instants of time and positions of the objects within the universe are all subsumed into the single notion of place in Platonia. If the place is different, the time is different. If the place is the same, time has not changed. … time is reduced to change.

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

p20. Time is inferred from things

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.

p266. Boltzmann: only the probable is experienced

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

p321. The configurations at which Ψ collects strongly must be special -- in some sense they must resonate with all the other configurations that are competing for wave function.

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

p109. Any continuous curve through Platonia is ... a path. A natural question is whether some paths are distinguished compared with others.

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

p30. By a time capsule, I mean any fixed pattern that creates or encodes the appearance of motion, change or history.

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

p283. [with quantum mechanics] all configurations are allowed, but some are more probable than others. By its very nature, quantum mechanics selects special configurations - those that are the most probable. This opens up the possibility that records, which are special configurations by virtue of their structure, are somehow selected by quantum mechanics. ... quantum mechanics could create a powerful impression of history by direct selection of special configurations that happen to be time capsules and therefore appear to be records of history. There will be a sense in which the history is there, but the time capsule, which appears to be its record, will be the more fundamental concept.

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.

p274. I feel sure that the mystery of our deep sense and awareness of history can be unravelled from the timeless mists of Platonia through the latent histories that Hamilton showed can be there.

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

pp282-3. Even if history is a unique succession of instants, modelled by a path in configuration space, it can be studied only through records, since historians are not present in the past. This aspect of history is not captured at all by a path. All the solutions of a Newtonian system correspond to unique paths, but they very seldom resemble the one history we do experience, in which records of earlier instants are contained in the present instant. This simply does not happen in general in Newtonian physics, which has no inbuilt mechanism to ensure that records are created. It is a story of innumerable histories but virtually no records of them.
     … Up to now the priority has been to achieve successions of states and to assume that records will somehow form. But nothing in the mechanisms that create successions ensures that records of them will be created. Now a record is a configuration with a special structure. Quantum mechanics, by its very construction, makes statements about configurations: some are more probable than others. …. In contrast, there is no way that quantum mechanics can be naturally made to make statements about histories. It is just not that kind of theory.

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.

p300. As Bell says, 'We have no access to the past. We have only our "memories" and "records". But these memories and records are in fact present phenomena.' Our only evidence for the past is through present records. If we have them, the actual existence of the past is immaterial. It will make no difference to what we know. Hence 'there is no need whatever to link successive configurations of the world into a continuous trajectory'.
     … Sentient beings within them will possess memories and records that convince them they are the product of history. But this will be an illusion.

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.

p308. We now are down to two [concepts]: a static but well-behaved wave function and the configuration space… Platonia....
      … the wave function of the universe, playing the great game in timelessness, seeks and finds time capsules. What all-pervasive influence can put such a rooted bias into the game? ….
     My conjecture is this. The Wheeler-DeWitt equation of our universe concentrates any of its well-behaved solutions on time capsules. ... The inherent asymmetry of the configuration space will always 'funnel' the wave function onto time capsules. I could fill up pages with hand-waving arguments for why this should be so, but they would baffle the non-specialist and offend the specialist.

(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?

p254. Now, my suggestion is this. There are no laws of nature, just one law of the universe. .... Just one, all-embracing static equation. … Its solutions (which may be one or many) must merely be well behaved … It is an equation that creates structure as a first principle …. This is because it attaches a ranking - a greater or lesser probability - to each conceivable static configuration of the universe.

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.

p28. consciousness and understanding are always tied to a short time span, which was called the specious present by the philosopher and psychologist William James …. It has a duration of up to about three seconds.
     The key element in Boltzmann's idea is comparison of structures. There needs to be qualitative change in the brain patterns along a segment of the 'line of time'. If the brain pattern in each instant is likened to a card, then the patterns become a pack of cards, and our conscious experience of time flow arises (somehow) from the change of pattern across the pack. Though we may not understand the mechanism, the effect does have a cause.

pp266-7. when we think we see motion at some instant, the underlying reality is that our brain at that instant contains data corresponding to several different positions of the object perceived to be in motion. My brain contains, at any one instant, several 'snapshots' at once. The brain, through the way in which it presents data to consciousness, somehow 'plays the movie' for me.
     ... This brain configuration, with its simultaneous coding of several snapshots, nevertheless belongs to just one point in Platonia.
     ... a time capsule ... is so highly structured 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:

p251. … why is it supposed that the universe was created in the past rather than newly created in every instant that is experienced? No two instants are identical. The things we find in one are not exactly the same as the things we find in another. What, then, is the justification for saying that something was created in the past and that its existence has continued into the present?

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.

p333. I do also feel that novelty is a genuine element of quantum mechanics, especially in the many-worlds form, not present in classical mechanics. ... I see no fundamental line of time and causal evolution along which we march as robots; each experienced Now is new and distinct. I think that the many-worlds hypothesis is the scientific counterpart of the thrill of artistic creation …. It is something essentially new for which there is no adequate explanation in any supposed past from which we have tumbled via a computer algorithm. There is no explanation of any one triangle [configuration] in terms of any others, and the same is true of all Nows.

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.

pp323-4. The history of science shows that physicists have tended to be wrong when they have not believed counter-intuitive results of good theories.

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.

pp90-2. Energy is the most basic quantity in physics. It comes in two forms: kinetic energy measures the amount of motion in a system, while potential energy is determined by its instantaneous configuration. … in an isolated system the sum of the two remains constant. ...
     Energy, like the whole of mechanics, has a curious hybrid nature. Absolute space and time are needed to calculate kinetic but not potential energy. Each body of mass m and speed v in a system contributes a kinetic energy ½mv2. The speed is measured in absolute space, which is why it is needed to calculate kinetic energy. By contrast, the potential energy of a system depends only on its relative configuration. …
      … There appears to be more to the universe than its relative configurations.

p109. two snapshots of a dynamical system are nearly but not quite sufficient to predict its entire history. We need to know not only two snapshots, but also their separation in time and their relative orientation in absolute space. These are exactly the things that determine the energy and angular momentum of any system

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:

pp118-9. the unique Machian history with a given direction through a point is identical to one of the many Newtonian histories through the point with the same direction. It is, in fact, the Newtonian history for which the energy and angular momentum are both exactly zero. The small fraction of Newtonian solutions with this property are all the solutions of a simpler timeless and frameless theory.
     This brought to light an unexpected reconciliation between the positions of Newton and Leibniz in their debate about absolute and relative motion. Both were right! The point is that in a universe which, like ours, contains many bodies, there can be innumerable subsystems that are effectively isolated from one another. This is true of the solar system within the Galaxy, and also for many of the galaxies scattered through the universe. Each subsystem, considered by itself, can have non-zero energy and angular momentum. However, if the universe is finite, the individual energies and angular momenta of its subsystems can add up to zero. In a universe governed by Newton's laws this would be an implausible fluke. But if the universe is governed by the Machian law, it must be the case.

p120. When this distinguished simplifier is used as 'time', it turns out that each object in the universe moves in the Machian framework described above exactly as Newton's laws prescribe. Newton's laws and his framework both arise from a single law of the universe that does not presuppose them.

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

p167. if general relativity is to be cast into a dynamical form, then the 'thing that changes' is not, as people had instinctively assumed, the four-dimensional distances within space-time, but the distances within three-dimensional spaces nested in space-time.

pp226-7. any quantum state can … be regarded as made up of other states - branches in an Everett-type 'many-worlds' picture. The difficulty is that this representation is not unique. There are many different ways in which one and the same state, formed from the same two 'observer' and 'object' systems, can be represented as being made up of other states. We can, for example, use position states, but we can equally well use momentum states.
     … Depending on the representation, different sets of parallel worlds are obtained: 'position histories' in the one case, 'momentum histories' in the other. One quantum evolution yields not only many histories but also many families of different kinds of history.
     … Because the wave functions of composite systems can be represented in so many ways, the application of Everett's ideas to different kinds of representation suggests that one and the same wave function contains not only many histories, but also many different kinds of history. It leads to a 'many-many-worlds' interpretation.

p229-30. Forget any idea about the particles themselves moving. The space Q of possible configurations, or structures, is given once and for all: it is a timeless configuration space. The instantaneous position of the system is one point of its Q. Evolution in classical Newtonian mechanics is like a bright spot moving, as time passes, over the landscape of Q. I have argued that this is the wrong way to think about time. There is neither a passing time nor a moving spot, just a timeless path through the landscape, the track taken by the moving spot in the fiction in which there is time.
     In quantum mechanics with time, which we are considering now, there is no track at all. Instead, Q is covered by the mists I have been using to illustrate the notion of wave functions and the probabilities associated with them. …. All that happens as time passes is that the patterns of mist change. The mists come and go, changing constantly over a landscape that itself never changes.
     … All solutions of the time-dependent equation can be found by adding stationary solutions with different frequencies. Each stationary solution … has a constant … distribution of its
[probability]. ... All true change in quantum mechanics comes from interference between stationary states with different energies. In a system described by a stationary state, no change takes place.

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

p299. … led Bell to his analysis of the formation of alpha-particle tracks, which have the obvious interpretation that they are records of alpha-particle motion. He showed that 'record formation' is a characteristic quantum property. At least under cloud-chamber conditions, the wave function concentrates itself at configuration points that can be called records.

On accepting a many-worlds view:

p324. Our past is just another world. …. If you accept that you experienced this morning, that commits you to other worlds. All the instants we have experienced are other worlds, for they are not the one we are in now. Can we then deny the existence of worlds on which Ψ collects just as strongly as on our remembered experiences?

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.

p111. in his main philosophical work, the Monadology, Leibniz makes the ... claim that the actual world is distinguished from other possible worlds by possessing 'as much variety as possible, but with the greatest order possible'.

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

p186. ... relativity is completely comprehensible. The mismatch between the relativistic world and its non-relativistic appearance to us is entirely explained by the speed of light. In contrast, the mere smallness of Planck's constant does not fully explain the classical appearance of the quantum world. There is a mystery. It is, I believe, intimately tied with the nature of time.

QM waves goodbye to reductionism:

p193. Most accounts of quantum mechanics concentrate on the simplest situations-- the behaviour of a single particle. That is already very surprising. But the really mysterious properties come to light only in composite systems of several particles, whose behaviour can become bafflingly correlated.
     ... The answer to question of how such things can happen in space and time is that they do not. They neither happen nor are they to be found in space and time.

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.

p210. Contrary to the impression given in many books, quantum mechanics is not about particles in space: it is about systems being in configurations ... That is something quite different from individual probabilities for individual particles being at different points of ordinary space. Each 'point' is a whole configuration - a 'universe'. The arena formed by the 'points' is unimaginably large. And classical physics puts the system at just one point in the arena. The wave function, in contrast, is in principle everywhere.

p220. Despite the sophistication of all his work, in both relativity and quantum mechanics, Einstein retained a naive atomistic philosophy. There are space and time, and distinct autonomous things moving in them. …
     … we first accept that distinct identifiable particles can exist. Imagine three of them. There are two possible realities. In the Machian view, the properties of the system are exhausted by the masses of the particles and their separations, but the separations are mutual properties. Apart from the masses, the particles have no attributes that are exclusively their own. They - in the form of a triangle - are a single thing. In the Newtonian view, the particles exist in absolute space and time. These external elements lend the particles attributes - position, momentum, angular momentum - denied in the Machian view. The particles become three things. Absolute space and time are an essential part of atomism.

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.

p240. As far as I am aware, Leibnizian ideas offer the only genuine alternative to Cartesian-Newtonian materialism which is capable of expression in mathematical form. What especially attracts me to them is the importance, indeed primary status, given to structure and distinguishing attributes, and the insistence that the world does not consist of infinitely many essentially identical things - atoms moving in space - but is in reality a collection of infinitely many things, each constructed according to a common principle yet all different from one another. Space and time emerge from the way in which these ultimate entities mirror each other. I feel sure that this idea has the potential to turn physics inside out - to make the interestingly structured appear probable rather than improbable. Before he became a poet, T. S. Eliot studied philosophy. He remarked, 'In Leibniz there are possibilities.'

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?)

pp320-1. Sitting in the midst of things, we feel ourselves carried forward on the mighty arrow of time. But it is an arrow that does not move. It is simply an arrow that points from the simple to the complex, from less to more, most fundamentally of all from nothing to something.

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

pp304-5. By no means all details need represent history. ... Think again of the number of atoms in a pea. A tiny fraction of them can easily record the pea's history up to its current present. The huge numbers we confront in physics explain why we may have wrong ideas of what history actually is. We may have jumped to a conclusion too quickly.
     … a fraction of a pea's atoms may well seem to record a history of its large-scale features. This does not mean that all its atoms had a unique history. Without change in the pea's large-scale structure, the same large-scale history could be coded in innumerable different ways by only a tiny fraction of its atoms. ... The different points in the cloud simply code the same history in different ways. What is more, for each point along the large-scale history … there will be a corresponding cloud of points that record the same history up to that point in different ways.
     ... In any section … the
[cloud of points] all tell essentially the same story but in different ways, though some may tell it with small variations.

The only reference to evolution:

p325. We are the answers to the question of what can be maximally sensitive to the totality of what is possible. That is quite Darwinian. Species, ultimately genes, exist only if they fit in an environment. Platonia is the ultimate environment.

On looking for a process-based ontology:

p329. In principle, there is no reason why we should not attempt to put our very direct sense of change directly into the foundations of physics. There is a long tradition, going back at least to Hamilton, that seeks to make process the most basic thing in the world. Roughly, the idea is that physics should be built up using verbs, not nouns. In 1929 the English philosopher Alfred North Whitehead published an unreadable - in my experience - book called Process and Reality in which he advocated process. It all sounds very exciting, but I just do not think it can be done ...

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

p330. Would it not be a wonderful reconciliation of opposites if the static wave function were to settle spontaneously on time capsules that are redolent of both flux (evidence of history) and stasis (evidence that things endured through it)?

Julian B. Barbour.
The Discovery of Dynamics.
OUP. 2001

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