The Fabric of Reality David Deutch

particular moment cannot become the present, or cease to be the present,
for these would be changes. Therefore the present cannot, objectively, be a
single moment.
The reason why we cling to these two incompatible concepts — the moving
present and the sequence of unchanging moments — is that we need them
both, or rather, that we think we do. We continually invoke both of them in
everyday life, albeit never quite in the same breath. When we are 
describing
events, saying when things happen, we think in terms of a sequence of
unchanging moments; when we are 
explaining events as causes and effects
of each other, we think in terms of the moving present.
For example, in saying that Faraday discovered electromagnetic induction ‘in
1831’ we are assigning that event to a certain range of moments. That is, we
are specifying on which set of snapshots, in the long sheaf of snapshots of
world history, that discovery is to be found. No flow of time is involved when
we say 
when something happened, any more than a ‘flow of distance’ is
involved if we say 
where it happened. But as soon as we say why something
happened, we invoke the flow of time. If we say that we owe our electric
motors and dynamos in part to Faraday, and that the repercussions of his

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discovery are being felt to this day, we have in mind a picture of the
repercussions beginning in 1831 and sweeping consecutively through all the
moments of the rest of the nineteenth century, and then reaching the
twentieth century and causing things like power stations to come into
existence there. If we are not careful, we think of the twentieth century as
initially ‘not yet affected’ by the momentous event of 1831, and then being
‘changed’ by the repercussions as they sweep past on their way to the
twenty-first century and beyond. But usually we are careful, and we avoid
that incoherent thought by never using the two parts of the common-sense
theory of time simultaneously. Only when we think about time itself do we do
that, and then we marvel at the mystery of it all! Perhaps ‘paradox’ is a better
word than mystery, for we have here a blatant conflict between two
apparently self-evident ideas. They cannot both be true. We shall see that
neither is true.
Our theories of physics are, unlike common sense, coherent, and they first
achieved this by dropping the idea of the flow of time. Admittedly, physicists
talk about the flow of time just as everyone else does. For example, in his
book 
Principia, in which he set out the principles of Newtonian mechanics
and gravitation, Newton wrote:
Absolute, true, and mathematical time, of itself, and from its own nature,
flows equably without relation to anything external.
But Newton wisely makes no attempt to translate his assertion that time
flows into mathematical form, or to derive any conclusion from it. None of
Newton’s physical theories refers to the flow of time, nor has any subsequent
physical theory referred to, or been compatible with, the flow of time.
So why did Newton think it necessary to say that time ‘flows equably’? There
is nothing wrong with ‘equably’: one can interpret that as meaning that
measurements of time are the same for observers at different positions and
in different states of motion. That is a substantive assertion (which, since
Einstein, we know to be inaccurate). But it could easily have been stated as I
have just stated it, without saying that time flows. I think that Newton was
deliberately using the familiar language of time without intending its literal
meaning, just as he might have spoken informally of the Sun ‘rising’. He
needed to convey to the reader embarking on this revolutionary work that
there was nothing new or sophisticated in the Newtonian concept of time.
The 
Principia assigns to many words, such as ‘force’ and ‘mass’, precise
technical meanings which are somewhat different from their common-sense
ones. But the numbers referred to as ‘times’ are simply the times of common
sense, which we find on clocks and calendars, and the concept of time in the
Principia is the common-sense one.
Only, it does not flow. In Newtonian physics, time and motion appear much
as in Figure 11.3. One minor difference is that I have been drawing
successive moments separated from one another, but in all pre-quantum
physics that is an approximation because time is a continuum. We must
imagine infinitely many, infinitely thin snapshots interpolating continuously
between the ones I have drawn. If each snapshot represents everything
throughout the whole of space that physically exists at a particular moment,
then we can think of the snapshots as being glued together at their faces to
form a single, unchangeable block containing everything that happens in

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space and time (Figure 11.4) — that is, the whole of physical reality. An
inevitable shortcoming of this sort of diagram is that the snapshots of space
at each moment are shown as being two-dimensional, whereas in reality
they are three-dimensional. Each one of them is space at a particular
moment. Thus we are treating time as a fourth dimension, analogous to the
three dimensions of space in classical geometry. Space and time,
considered together like this as a four-dimensional entity, are called
spacetime.
FIGURE 11.4 
Spacetime, considered as successive moments.
In Newtonian physics this four-dimensional geometrical interpretation of time
was optional, but under Einstein’s theory of relativity it became an
indispensable part of the theory. That is because, according to relativity,
observers moving at different velocities do not agree about which events are
simultaneous. That is, they do not agree about which events should appear
on the same snapshot. So they each perceive spacetime as being sliced up
in a different way into ‘moments’. Nevertheless, if they each stacked their
snapshots in the manner of Figure 11.4, the spacetimes they constructed
would be identical. Therefore, according to relativity, the ‘moments’ shown in
Figure 11.4 are not objective features of spacetime: they are only one
observer’s way of perceiving simultaneity. Another observer would draw the
‘now’ slices at a different angle. So the objective reality behind Figure 11.4,
namely the spacetime and its physical contents, could be shown as in Figure
11.5.
Spacetime is sometimes referred to as the ‘block universe’, because within it
the whole of physical reality — past, present and future — is laid out once
and for all, frozen in a single four-dimensional block. Relative to spacetime,
nothing ever moves. What we call ‘moments’ are certain slices through
spacetime, and when the contents of such slices are different from one
another, we call it change or motion through space.

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FIGURE 11.5 
Spacetime view of a moving object.
As I have said, we think of the flow of time in connection with causes and
effects. We think of causes as preceding their effects; we imagine the
moving present arriving at causes before it arrives at their effects, and we
imagine the effects flowing forwards with the present moment.
Philosophically, the most important cause-and-effect processes are our
conscious decisions and the consequent actions. The common-sense view
is that we have 
free will: that we are sometimes in a position to affect future
events (such as the motion of our own bodies) in any one of several possible
ways, and to choose which shall occur; whereas, in contrast, we are never in
a position to affect the past at all. (I shall discuss free will in Chapter 13.) The
past is fixed; the future is open. To many philosophers, the flow of time is the
process in which the open future becomes, moment by moment, the fixed
past. Others say that the alternative events at each moment in the future are
possibilities, and the flow of time is the process by which, moment by
moment, one of these possibilities becomes 
actual (so that, according to
those people, the future does not exist at all until the flow of time hits it and
turns it into the past). But if the future really is open (and it is!), then that can
have nothing to do with the flow of time, for there is no flow of time. In
spacetime physics (which is, effectively, all pre-quantum physics, starting
with Newton) the future is not open. It is 
there, with definite, fixed contents,
just like the past and present. If a particular moment in spacetime were
‘open’ (in any sense) it would necessarily remain open when it became the
present and the past, for moments cannot change.
Subjectively, the future of a given observer may be said to be ‘open from
that observer’s point of view’ because one cannot measure or observe one’s
own future. But openness in that subjective sense does not allow choices. If
you have a ticket for last week’s lottery, but have not yet found out whether
you have won, the outcome is still open from your point of view, even though
objectively it is fixed. But, subjectively or objectively, you cannot change it.
No causes which have not already affected it can do so any longer. The
common-sense theory of free will says that last week, while you still had a
choice whether to buy a ticket or not, the future was still objectively open,
and you really could have chosen any of two or more options. But that is
incompatible with spacetime. So according to spacetime physics, the
openness of the future is an illusion, and therefore causation and free will
can be no more than illusions as well. We need, and cling to, the belief that
the future can be affected by present events, and especially by our choices;

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but perhaps that is just our way of coping with the fact that we do not know
the future. In reality, we make no choices. Even as we think we are
considering a choice, its outcome is already there, on the appropriate slice of
spacetime, unchangeable like everything else in spacetime, and impervious
to our deliberations. It seems that those deliberations themselves are
unchangeable and already in existence at their allotted moments before we
ever know of them.
To be an ‘effect’ of some cause means to be affected by that cause — to be
changed by it. Thus when spacetime physics denies the reality of the flow of
time, it logically cannot accommodate the common-sense notions of cause
and effect either. For in the block universe nothing is changeable: one part of
spacetime can no more change another than one part of a fixed 
three-
dimensional object can change another.
It so happens that all fundamental theories in the era of spacetime physics
had the property that given everything that happens before a given moment,
the laws of physics determine what happens at all subsequent moments.
The property of snapshots being determined by other snapshots is called
determinism. In Newtonian physics, for instance, if at any moment one
knows the positions and velocities of all the masses in an isolated system,
such as the solar system, one can in principle calculate 
(predict) where
those masses will be at all times thereafter. One can also in principle
calculate 
(retrodict) where those masses were at all previous times.
The laws of physics that determine one snapshot from another are the ‘glue’
that holds the snapshots together as a spacetime. Let us imagine ourselves,
magically and impossibly, outside spacetime (and therefore in an external
time of our own, independent of that within spacetime). Let us slice
spacetime into snapshots of space at each moment as perceived by a