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.
I arrived at the notion of Platonia (or,
as I originally called it, the relative configuration space of the
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
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.
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
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.
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:
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
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).
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
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.
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".
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.
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.
'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
time is reduced to change.
This rich configuration space has enough structure, enough things
happening, so that you can order them in time.
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'
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.
Boltzmann: only the probable is
Here, it is not the boring random states that are highly probable,
it is the coherent, structured ones. Why?
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
The second issue is how the paths are formed, and distinguished.
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.
By a time capsule, I mean any fixed
pattern that creates or encodes the appearance of motion, change or
These time capsules have a (memory of) history encoded in them, and
are the high probability points.
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.
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
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.
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.
We now are down to two [concepts]: a
static but well-behaved wave function and the configuration space
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
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
Asymmetric Platonia is defined by configurations; the probability of
those configurations are "funnelled" by the laws of physics.
What are these laws?
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
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.
consciousness and understanding are
always tied to a short time span, which was called the specious
present by the philosopher and psychologist William James
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.
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
... 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:
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
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 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.
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.
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
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
There appears to be more to
the universe than its relative configurations.
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:
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
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
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.
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
any quantum state can
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
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.
that happens as time passes is that the patterns of mist change. The
mists come and go, changing constantly over a landscape that itself
All solutions of the
time-dependent equation can be found by adding stationary solutions
with different frequencies. Each stationary solution
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:
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
On accepting a many-worlds view:
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.
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!
... 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
QM waves goodbye to reductionism:
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.
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
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
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.
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?)
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:
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
there will be a corresponding cloud of
points that record the same history up to that point in different
... In any section
[cloud of points] all tell essentially
the same story but in different ways, though some may tell it with
The only reference to evolution:
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:
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.)
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