The Fabric of Reality David Deutch

particular observer within spacetime, then shuffle the snapshots and glue
them together again in a new order. Could we tell, from the outside, that this
is not the real spacetime? Almost certainly. For one thing, in the shuffled
spacetime physical processes would not be continuous. Objects would
instantaneously cease to exist at one point and reappear at another.
Second, and more important, the laws of physics would no longer hold. At
least, the real laws of physics would no longer hold. There would exist a
different set of laws that took the shuffling into account, explicitly or implicitly,
and correctly described the shuffled spacetime.
So to us, the difference between the shuffled spacetime and the real one
would be gross. But what about the inhabitants? Could they tell the
difference? We are getting dangerously close to nonsense here — the
familiar nonsense of the common-sense theory of time. But bear with me
and we shall skirt around the nonsense. 
Of course the inhabitants could not
tell the difference. If they could, they would. They would, for instance,
comment on the existence of discontinuities in their world, and publish
scientific papers about them — that is, if they could survive in the shuffled
spacetime at all. But from our magical vantage-point we can see that they do
survive, and so do their scientific papers. We can read those papers, and
see that they still contain only observations of the original spacetime. All
records within the spacetime of physical events, including those in the
memories and perceptions of conscious observers, are identical to those in
the original spacetime. We have only shuffled the snapshots, not changed

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them internally, so the inhabitants still perceive them in the original order.
Thus in terms of real physics — physics as perceived by the spacetime’s
inhabitants — all this slicing up and re-gluing of spacetime is meaningless.
Not only the shuffled spacetime, but even the collection of unglued-together
snapshots, is physically identical to the original spacetime. We picture all the
snapshots glued together in the right order because this represents the
relationships between them that are determined by the laws of physics. A
picture of them glued together in a different order would represent the same
physical events — the same history — but would somewhat misrepresent
the relationships between those events. So the snapshots have an 
intrinsic
order, defined by their contents and by the real laws of physics. Any one of
the snapshots, together with the laws of physics, not only determines what
all the others are, it determines their order, and it determines its own place in
the sequence. In other words, each snapshot has a ‘time stamp’ encoded in
its physical contents.
That is how it must be if the concept of time is to be freed of the error of
invoking an overarching framework of time that is external to physical reality.
The time stamp of a snapshot is the reading on some natural clock that
exists within that universe. In some snapshots — the ones containing human
civilization, for example — there are actual clocks. In others there are
physical variables — such as the chemical composition of the Sun, or of all
the matter in space — which can be considered as clocks because they take
definite, distinct values on different snapshots, at least over a certain region
of spacetime. We can standardize and calibrate them to agree with one
another where they overlap.
We can reconstitute the spacetime by using the intrinsic order determined by
the laws of physics. We start with any of the snapshots. Then we calculate
what the immediately preceding and following snapshots should look like,
and we locate those snapshots from the remaining collection and glue them
on either side of the original snapshot. Repeating the process builds up the
whole spacetime. These calculations are too complex to perform in real life,
but they are legitimate in a thought experiment in which we imagine
ourselves to be detached from the real, physical world. (Also, strictly
speaking, in pre-quantum physics there would be a continuous infinity of
snapshots, so the process just described would have to be replaced by a
limiting process in which the spacetime is assembled in an infinite number of
steps; but the principle is the same.)
The predictability of one event from another does not imply that those events
are cause and effect. For example, the theory of electrodynamics says that
all electrons carry the same charge. Therefore, using that theory we can —
and frequently do — predict the outcome of a measurement on one electron
from the outcome of a measurement on another. But neither outcome was
caused by the other. In fact, as far as we know, the value of the charge on
an electron was not caused by any physical process. Perhaps it is ‘caused’
by the laws of physics themselves (though the laws of physics as we
currently know them do not predict the charge on the electron; they merely
say that all electrons have the same charge). But in any case, here is an
example of events (outcomes of measurements on electrons) that are
predictable from one another, but make no causal contribution to one
another.

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Here is another example. If we observe where one piece of a fully
assembled jigsaw puzzle is, and we know the shapes of all the pieces, and
that they are interlocked in the proper way, we can predict where all the
other pieces are. But that does not mean that the other pieces were 
caused
to be where they are by the piece we observed being where it is. Whether
such causation is involved depends on how the jigsaw puzzle as a whole got
there. If the piece we observed was laid down first, then it was indeed
among the causes of the other pieces being where they are. If any other
piece was laid down first, then the position of the piece we observed was an
effect of that, not a cause. But if the puzzle was created by a single stroke of
a jigsaw-puzzle-shaped cutter, and has never been disassembled, then
none of the positions of the pieces are causes or effects of each other. They
were not assembled in any order, but were created simultaneously, in
positions such that the rules of the puzzle were already obeyed, which made
those positions mutually predictable. Nevertheless, none of them caused the
others.
The determinism of physical laws about events in spacetime is like the
predictability of a correctly interlocking jigsaw puzzle. The laws of physics
determine what happens at one moment from what happens at another, just
as the rules of the jigsaw puzzle determine the positions of some pieces
from those of others. But, just as with the jigsaw puzzle, whether the events
at different moments 
cause one another or not depends on how the
moments got there. We cannot tell by looking at a jigsaw puzzle whether it
got there by being laid down one piece at a time. But with spacetime we
know that it does not make sense for one moment to be ‘laid down’ after
another, for that would be the flow of time. Therefore we know that even
though some events can be predicted from others no event in spacetime
caused another. Let me stress again that this is all according to pre-quantum
physics, in which everything that happens, happens in spacetime. What we
are seeing is that spacetime is incompatible with the existence of cause and
effect. It is not that people are mistaken when they say that certain physical
events are causes and effects of one another, it is just that that intuition is
incompatible with the laws of spacetime physics. But that is all right, because
spacetime physics is false.
I said in Chapter 8 that two conditions must hold for an entity to be a cause
of its own replication: first, that the entity is in fact replicated; and second,
that most variants of it, in the same situation, would not be replicated. This
definition embodies the idea that a cause is something that makes a
difference to its effects, and it also works for causation in general. For X to
be a cause of Y, two conditions must hold: first, that X and Y both happen;
and second, that Y would not have happened if X had been otherwise. For
example, sunlight was a cause of life on Earth because both sunlight and life
actually occurred on Earth, and because life would not have evolved in the
absence of sunlight.
Thus, reasoning about causes and effects is inevitably also about variants of
the causes and effects. One is always saying what 
would have happened if,
other things being equal, such and such an event had been different. A
historian might make the judgement that ‘
if Faraday had died in 1830, then
technology would have been delayed for twenty years’. The meaning of this
judgement seems perfectly clear and, since in fact Faraday did not die in

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1830 but discovered electromagnetic induction in 1831, it seems quite
plausible too. It is equivalent to saying that the technological progress which
did happen was in part caused by Faraday’s discovery, and therefore also
by his survival. But what does it mean, in the context of spacetime physics,
to reason about the future of non-existent events? If there is no such event
in spacetime as Faraday’s death in 1830, then there is also no such thing as
its aftermath. Certainly we can 
imagine a spacetime that contains such an
event; but then, since we are only imagining it, we can also imagine that it
contains any aftermath we like. We can imagine, for example, that Faraday’s
death was followed by an 
acceleration of technological progress. We might
try to get around this ambiguity by imagining only spacetimes in which,
though the event in question is different from that in actual spacetime, the
laws of physics are the same. It is not clear what justifies restricting our
imagination in this way, but in any case, if the laws of physics are the same
then the event in question 
could not have been different, because the laws
determine it unambiguously from the previous history. So the previous
history would have to be imagined as being different as well. How different?
The effect of our imagined variation in history depends critically on what we
take ‘other things being equal’ to mean. And that is irreducibly ambiguous,
for there are infinitely many ways of imagining a state of affairs prior to 1830
which would have led to Faraday’s death in that year. Some of those would
undoubtedly have led to faster technological progress, and some to slower.
Which of them are we referring to in the ‘
if…then …’ statement? Which
counts as ‘other things being equal’? Try as we may, we shall not succeed in
resolving this ambiguity within spacetime physics. There is no avoiding the
fact that in spacetime exactly one thing happens in reality, and everything
else is fantasy.
We are forced to conclude that, in spacetime physics, conditional statements
whose premise is false (‘if Faraday had died in 1830 …’) have no meaning.
Logicians call such statements 
counter-factual conditionals, and their status
is a traditional paradox. We all know what such statements mean, yet as
soon as we try to state their meaning clearly it seems to evaporate. The
source of this paradox is not in logic or linguistics, it is in physics — in the
false physics of spacetime. Physical reality is not a spacetime. It is a much
bigger and more diverse entity, the 
multiverse. To a first approximation the
multiverse is like a very large number of co-existing and slightly interacting
spacetimes. If spacetime is like a stack of snapshots, each snapshot being
the whole of space at one moment, then the multiverse is like a vast
collection of such stacks. Even this (as we shall see) slightly inaccurate
picture of the multiverse can already accommodate causes and effects. For
in the multiverse there are almost certainly some universes in which Faraday
died in 1830, and it is a matter of fact (not observable fact, but objective fact
none the less) whether technological progress in those universes was or was
not delayed relative to our own. There is nothing arbitrary about which
variants of our universe the counter-factual ‘if Faraday had died in 1830…’
refers to: it refers to 
the variants which really occur somewhere in the
multiverse. That is what resolves the ambiguity. Appealing to imaginary
universes does not work, because we can imagine any universes we like, in
any proportions we like. But in the multiverse, universes are present in
definite proportions, so it is meaningful to say that certain types of event are
‘very rare’ or ‘very common’ in the multiverse, and that some events follow

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others ‘in most cases’. Most logically possible universes are not present at
all — for example, there are no universes in which the charge on an electron
is different from that in our universe, or in which the laws of quantum physics
do not hold. The laws of physics that are implicitly referred to in the counter-
factual are the laws that are actually obeyed in other universes, namely the
laws of quantum theory. Therefore the 
‘if… then’ statement can
unambiguously be taken to mean ‘in most universes in which Faraday died
in 1830, technological progress was delayed relative to our own’. In general
we may say that an event X causes an event Y in our universe if both X and
Y occur in our universe, but in most variants of our universe in which X does
not happen, Y does not happen either.
If the multiverse were literally a collection of spacetimes, the quantum
concept of time would be the same as the classical one. As Figure 11.6
shows, time would still be a sequence of moments. The only difference
would be that at a particular moment in the multiverse, many universes
would exist instead of one. Physical reality at a particular moment would be,
in effect, a ‘super-snapshot’ consisting of snapshots of many different
versions of the whole of space. The whole of reality for the whole of time
would be the stack of all the super-snapshots, just as classically it was a
stack of snapshots of space. Because of quantum interference, each
snapshot would no longer be determined entirely by previous snapshots of
the same spacetime (though it would approximately, because classical
physics is often a good approximation to quantum physics). But the super-
snapshots beginning with a particular moment would be entirely and exactly
determined by the previous super-snapshots. This complete determinism
would not give rise to complete predictability, even in principle, because
making a prediction would require a knowledge of what had happened in all
the universes, and each copy of us can directly perceive only one universe.
Nevertheless, as far as the concept of time is concerned, the picture would
be just like a spacetime with a sequence of moments related by deterministic
laws, only with more happening at each moment, but most of it hidden from
any one copy of any observer.
FIGURE 11.6 
If the multiverse were a collection of interacting spacetimes,
time would still be a sequence of moments.
However, that is not quite how the multiverse is. A workable quantum theory
of time — which would also be the quantum theory of gravity — has been a
tantalizing and unattained goal of theoretical physics for some decades now.

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But we know enough about it to know that, though the laws of quantum
physics are perfectly deterministic at the multiverse level, they do not