The Fabric of Reality David Deutch

particular snapshot, as spacetime physics does. Instead, it determines what
proportion of all snapshots in the multiverse will have a given property. For
this reason, we inhabitants of the multi-verse can sometimes make only
probabilistic predictions of our own experience, even though what will
happen in the multiverse is completely determined. Suppose, for example,
that we toss a coin. A typical prediction of quantum theory might be that 
if, in
a certain number of snapshots, a coin has been set spinning in a certain
manner and clocks show a certain reading, 
then there will also exist half that
number of universes in which the clocks show a higher reading and the coin
has fallen with ‘heads’ upwards, and another half in which the clocks show
the higher reading and the coin has fallen with ‘tails’ upwards.
Figure 11.7 shows the small region of the multiverse in which these events
happen. Even in that small region there are a lot of snapshots to illustrate, so
we can spare only one point of the diagram for each snapshot. The
snapshots we are looking at all contain clocks of some standard type, and
the diagram is arranged so that all the snapshots with a particular clock
reading appear in a vertical column, and the clock readings increase from
left to right. As we scan along any vertical line in the diagram, not all the
snapshots we pass through are different. We pass through groups of
identical ones, as indicated by the shading. The snapshots in which clocks
show the earliest reading are at the left edge of the diagram. We see that in
all those snapshots, which are identical, the coin is spinning. At the right
edge of the diagram, we see that in half the snapshots in which clocks show
the latest reading the coin has fallen with ‘heads’ upwards, and in the other
half it has fallen with ‘tails’ upwards. In universes with intermediate clock
readings, three types of universe are present, in proportions that vary with
the clock reading.
If you were present in the illustrated region of the multiverse, all copies of
you would have seen the coin spinning at first. Later, half the copies of you
would see ‘heads’ come up, and the other half would see ‘tails’. At some
intermediate stage you would have seen the coin in a state in which it is still
in motion, but from which it is predictable which face it will show when it

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eventually settles down. This differentiation of identical copies of an observer
into slightly different versions is responsible for the subjectively probabilistic
character of quantum predictions. For if you asked, initially, what result you
were destined to see for the coin toss, the answer would be that that is
strictly unpredictable, for half the copies of you that are asking that question
would see ‘heads’ and the other half would see ‘tails’. There is no such thing
as ‘which half would see ‘heads’, any more than there is an answer to the
question ‘which one am I?’. For practical purposes you could regard this as a
probabilistic prediction that the coin has a 50 per cent chance of coming up
‘heads’, and a 50 per cent chance of coming up ‘tails’.
FIGURE 11.7 
A region of the multiverse containing a spinning coin. Each
point in the diagram represents one snapshot.
The determinism of quantum theory, just like that of classical physics, works
both forwards and backwards in time. From the state of the combined
collection of ‘heads’ and ‘tails’ snapshots at the later time in Figure 11.7, the
‘spinning’ state at an earlier time is completely determined, and vice versa.
Nevertheless, from the point of view of any observer, information is lost in
the coin-tossing process. For whereas the initial, ‘spinning’ state of the coin
may be experienced by an observer, the final combined ‘heads’ and ‘tails’
state does not correspond to any possible experience of the observer.
Therefore an observer at the earlier time may observe the coin and predict
its future state, and the consequent subjective probabilities. But none of the
later copies of the observer can possibly observe the information necessary
to retrodict the ‘spinning’ state, for that information is by then distributed
across two different types of universe, and that makes retrodiction from the
final state of the coin impossible. For example, if all we know is that the coin
is showing ‘heads’, the state a few seconds earlier might have been the
state I called ‘spinning’, or the coin might have been spinning in the opposite
direction, or it might have been showing ‘heads’ all the time. There is no
possibility of retrodiction here, even probabilistic retrodiction. The earlier
state of the coin is simply not determined by the later state of the ‘heads’

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snapshots, but only by the joint state of the ‘heads’ and the ‘tails’ snapshots.
Any horizontal line across Figure 11.7 passes through a sequence of
snapshots with increasing clock readings. We might be tempted to think of
such a line — such as the one shown in Figure 11.8 — as a spacetime, and
of the whole diagram as a stack of spacetimes, one for each such line. We
can read off from Figure 11.8 what happens in the ‘spacetime’ defined by the
horizontal line. For a period, it contains a spinning coin. Then, for a further
period, it contains the coin moving in a way that will predictably result in
‘heads’. But later, in contradiction to that, it contains the coin moving in a
way that will predictably result in ‘tails’, and eventually it does show ‘tails’.
But this is merely a deficiency of the diagram, as I pointed out in Chapter 9
(see Figure 9.4, p. 212). In this case the laws of quantum mechanics predict
that no observer who remembers seeing the coin in the ‘predictably heads’
state can see it in the ‘tails’ state: that is the justification for calling that state
‘predictably heads’ in the first place. Therefore no observer in the multiverse
would recognize events as they occur in the ‘spacetime’ defined by the line.
All this goes to confirm that we cannot glue the snapshots together in an
arbitrary fashion, but only in a way that reflects the relationships between
them that are determined by the laws of physics. The snapshots along the
line in Figure 11.8 are not sufficiently interrelated to justify their being
grouped together in a single universe. Admittedly they appear in order of
increasing clock readings which, in 
spacetime, would be ‘time stamps’ which
would be sufficient for the spacetime to be reassembled. But in the
multiverse there are far too many snapshots for clock readings alone to
locate a snapshot relative to the others. To do that, we need to consider the
intricate detail of which snapshots determine which others.
FIGURE 11.8 
A sequence of snapshots with increasing clock readings is not
necessarily a spacetime.
In spacetime physics, any snapshot is determined by any other. As I have
said, in the multiverse that is in general not so. Typically, the state of one
group of identical snapshots (such as the ones in which the coin is
‘spinning’) determines the state of an equal number of differing snapshots
(such as the ‘heads’ and ‘tails’ ones). Because of the time-reversibility
property of the laws of quantum physics, the overall, multi-valued state of the
latter 
group also determines the state of the former. However, in some
regions of the multiverse, and in some places in space, the snapshots of
some physical objects do fall, for a period, into chains, each of whose
members determines all the others to a good approximation. Successive
snapshots of the solar system would be the standard example. In such

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regions, classical physical laws are a good approximation to the quantum
ones. In those regions and places, the multiverse does indeed look as in
Figure 11.6, a collection of spacetimes, and at that level of approximation
the quantum concept of time reduces to the classical one. One can
distinguish approximately between ‘different times’ and ‘different universes’,
and time is approximately a sequence of moments. But that approximation
always breaks down if one examines the snapshots in more detail, or looks
far forwards or backwards in time, or far afield in the multiverse.
All experimental results currently available to us are compatible with the
approximation that time is a sequence of moments. We do not expect that
approximation to break down in any foreseeable terrestrial experiment, but
theory tells us that it must break down badly in certain types of physical
process. The first is the beginning of the universe, the Big Bang. According
to classical physics, time began at a moment when space was infinitely
dense and occupied only a single point, and before that there were no
moments. According to quantum physics (as best we can tell), the snapshots
very near the Big Bang are not in any particular order. The sequential
property of time does not begin at the Big Bang, but at some later time. In
the nature of things, it does not make sense to ask how much later. But we
can say that the earliest moments which are, to a good approximation,
sequential occur roughly when classical physics would extrapolate that the
Big Bang had happened 10 –43 seconds (the 
Planck time) earlier.
A second and similar sort of breakdown of the sequence of time is thought to
occur in the interiors of black holes, and at the final recollapse of the
universe (the ‘Big Crunch’), if there is one. In both cases matter is
compressed to infinite density according to classical physics, just as at the
Big Bang, and the resulting gravitational forces tear the fabric of spacetime
apart.
By the way, if you have ever wondered what happened before the Big Bang,
or what will happen after the Big Crunch, you can stop wondering now. Why
is it hard to accept that there are no moments before the Big Bang or after
the Big Crunch, so that nothing happens, or exists, there? Because it is hard
to imagine time coming to a halt, or starting up. But then, time does not have
to come to a halt or start up, for it does not move at all. The multiverse does
not ‘come into existence’ or ‘cease to exist’; those terms presuppose the flow
of time. It is only imagining the flow of time that makes us wonder what
happened ‘before’ or ‘after’ the whole of reality.
Thirdly, it is thought that on a sub-microscopic scale quantum effects again
warp and tear the fabric of spacetime, and that closed loops of time — in
effect, tiny time machines — exist on that scale. As we shall see in the next
chapter, this sort of breakdown of the sequence of time is also physically
possible on a large scale, and it is an open question whether it occurs near
such objects as rotating black holes.
Thus, although we cannot yet detect any of these effects, our best theories
already tell us that spacetime physics is never an exact description of reality.
However good an approximation it is, time in reality must be fundamentally
different from the linear sequence which common sense supposes.
Nevertheless, everything in the multiverse is determined just as rigidly as in
classical spacetime. Remove one snapshot, and the remaining ones
determine it exactly. Remove 
most snapshots, and the few remaining ones

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may still determine everything that was removed, just as they do in
spacetime. The difference is only that, unlike spacetime, the multiverse does
not consist of the mutually determining layers I have called super-snapshots,
which could serve as ‘moments’ of the multiverse. It is a complex, multi-
dimensional jigsaw puzzle.
In this jigsaw-puzzle multiverse, which neither consists of a sequence of
moments nor permits a flow of time, the common-sense concept of cause
and effect makes perfect sense. The problem that we found with causation
in spacetime was that it is a property of 
variants of the causes and effects,
as well as of the causes and effects themselves. Since those variants
existed only in our imagination, and not in spacetime, we ran up against the
physical meaning-lessness of drawing substantive conclusions from the
imagined properties of non-existent (‘counter-factual’) physical processes.
But in the multiverse variants do exist, in different proportions, and they obey
definite, deterministic laws. Given these laws, it is an objective fact which
events make a difference to the occurrence of which other events. Suppose
that there is a group of snapshots, not necessarily identical, but all sharing
the property X. Suppose that, given the existence of this group, the laws of
physics determine that there exists another group of snapshots with property
Y. One of the conditions for X to be a cause of Y has then been met. The
other condition has to do with variants. Consider the variants of the first
group that do not have the property X. If, from the existence of these, the
existence of some of the Y snapshots is still determined, then X was not a
cause of Y: for Y would have happened even without X. But if, from the
group of non-X variants, only the existence of non-Y variants is determined,
then X was a cause of Y.
There is nothing in this definition of cause and effect that logically requires
causes to precede their effects, and it could be that in very exotic situations,
such as very close to the Big Bang or inside black holes, they do not. In
everyday experience, however, causes always precede their effects, and this
is because — at least in our vicinity in the multiverse — the number of
distinct types of snapshot tends to increase rapidly with time, and hardly ever
decreases. This property is related to the second law of thermodynamics,
which states that ordered energy, such as chemical or gravitational potential
energy, may be converted entirely into disordered energy, i.e. heat, but
never vice versa. Heat is microscopically random motion. In multiverse
terms, this means many microscopically different states of motion in different
universes. For example, in successive snapshots of the coin at ordinary
magnifications, it seems that the setting-down process converts a group of
identical ‘predictably heads’ snapshots into a group of identical ‘heads’
snapshots. But during that process the energy of the coin’s motion is
converted into heat, so at magnifications large enough to see individual
molecules the latter group of snapshots are not identical at all. They all
agree that the coin is in the ‘heads’ position, but they show its molecules,
and those of the surrounding air and of the surface on which it lands, in
many different configurations. Admittedly, the initial ‘predictably heads’
snapshots are not microscopically identical either, because some heat is
present there too, but the production of heat in the process means that these
snapshots are very much less diverse than the later ones. So each
homogeneous group of ‘predictably heads’ snapshots determines the

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existence of — and therefore causes — vast numbers of microscopically
different ‘heads’ snapshots. But no single ‘heads’ snapshot by itself
determines the existence of any ‘predictably heads’ snapshots, and so is not
a cause of them.
The conversion, relative to any observer, of possibilities into actualities — of
an open future into a fixed past — also makes sense in this framework.
Consider the coin-tossing example again. Before the coin toss, the future is
open from the point of view of an observer, in the sense that it is still
possible that either outcome, ‘heads’ or ‘tails’, will be observed by that
observer. From that observer’s point of view both outcomes are possibilities,
even though objectively they are both actualities. After the coin has settled,
the copies of the observer have differentiated into two groups. Each
observer has observed, and remembers, only one outcome of the coin toss.
Thus the outcome, once it is in the past of any observer, has become single-
valued and actual for every copy of the observer, even though from the
multiverse point of view it is just as two-valued as ever.
Let me sum up the elements of the quantum concept of time. Time is not a
sequence of moments, nor does it flow. Yet our intuitions about the
properties of time are broadly true. Certain events are indeed causes and
effects of one another. Relative to an observer, the future is indeed open
and the past fixed, and possibilities do indeed become actualities. The
reason why our traditional theories of time are nonsense is that they try to
express these true intuitions within the framework of a false classical
physics. In quantum physics they make sense, because time was a quantum
concept all along. We exist in multiple versions, in universes called
‘moments’. Each version of us is not directly aware of the others, but has
evidence of their existence because physical laws link the contents of
different universes. It is tempting to suppose that the moment of which we
are aware is the only real one, or is at least a little more real than the others.
But that is just solipsism. All moments are physically real. The whole of the
multiverse is physically real. Nothing else is.
TERMINOLOGY
flow of time The supposed motion of the present moment in the future
direction, or the supposed motion of our consciousness from one moment to
another. (This is nonsense!)
spacetime Space and time, considered together as a static four-dimensional
entity.
spacetime physics Theories, such as relativity, in which reality is considered
to be a spacetime. Because reality is a multiverse, such theories can at best
be approximations.
free will The capacity to affect future events in any one of several possible
ways, and to choose which shall occur.
counter-factual conditional A conditional statement whose premise is false
(such as ‘Faraday had died in 1830, 
then X would have happened’).
snapshot (terminology for this chapter only) A universe at a particular time.

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SUMMARY
Time does not flow. Other times are just special cases of other universes.
Time travel may or may not be feasible. But we already have reasonably
good theoretical understanding of what it would be like if it were, an
understanding that involves all four strands.

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