The Fabric of Reality: Towards a Theory of Everything (Penguin Science)

by David Deutsch

Experiments are designed and performed only to resolve controversies.

Now my arguments are exhausted. Intellectually, I am convinced. Yet I must confess that I still feel what I can only describe as an ‘emotional doubt’.

We Popperians

it is not merely the predictions of biology that reduce, in principle, to those of physics: it is, on the face of it, also the explanations.

this appearance is misleading. It is simply not true that life is insignificant in its physical effects, nor is it theoretically derivative.

any theory of the structure of the universe in all but its earliest stages must take a position on what life will or will not be doing by then.

Quantum computation, which is now in its early infancy, is a distinct further step in this progression. It will be the first technology that allows useful tasks to be performed in collaboration between parallel universes.

In quantum mechanics, small deviations from a specified initial state tend to cause only small deviations from the predicted final state.

a photon and its other-universe counterparts all start from the same point on a glowing filament, but then move in trillions of different directions. When we later make a measurement of what has happened, we too become differentiated as each copy of us sees what has happened in our particular universe. If the object in question is the Earth’s atmosphere, then a hurricane may have occurred in 30 per cent of universes, say, and not in the remaining 70 per cent. Subjectively we perceive this as a single, unpredictable or ‘random’ outcome, though from the multiverse point of view all the outcomes have actually happened. This parallel-universe multiplicity is the real reason for the unpredictability of the weather.

Our inability to measure the initial conditions accurately is completely irrelevant. Even if we knew the initial conditions perfectly, the multiplicity, and therefore the unpredictability of the motion, would remain.

The flapping of butterflies’ wings does not, in reality, cause hurricanes because the classical phenomenon of chaos depends on perfect determinism, which does not hold in any single universe.

In 1985 I proved that under quantum physics there is a universal quantum computer.

The classical theory of computation, which was the unchallenged foundation of computing for half a century, is now obsolete except, like the rest of classical physics, as an approximation scheme. The theory of computation is now the quantum theory of computation.

the multiverse is not a discrete set of universes but a continuum, and that not all the universes are different.

Another way in which quantum physics is implicit in classical computation is that all practical implementations of Turing-type computers rely on such things as solid matter or magnetized materials, which could not exist in the absence of quantum-mechanical effects.

Building a universal quantum computer is well beyond present technology.

This is called decoherence. I must add that this problem is often presented the wrong way round: we are told that ‘quantum interference is a very delicate process, and must be shielded from all outside influences’. This is wrong. Outside influences could cause minor imperfections, but it is the effect of the quantum computation on the outside world that causes decoherence.

many mathematical tasks have now been discovered which could be efficiently performed by quantum computation where all known classical methods are intractable. The most spectacular of these is the task of factorizing large numbers. The method, known as Shor’s algorithm, was discovered in 1994

Grover’s algorithm for searching long lists very rapidly.)

It is likely, therefore, that a quantum factorization engine will be built long before the full range of quantum computations is technologically feasible. This is a prospect of great significance for cryptography (the science of securely communicating and authenticating information).

When a quantum factorization engine is factorizing a 250-digit number, the number of interfering universes will be of the order of 10500

I said that the algorithm requires only a few thousand arithmetic operations. I meant, of course, a few thousand operations in each universe that contributes to the answer. All those computations are performed in parallel, in different universes, and share their results through interference.

To those who still cling to a single-universe world-view, I issue this challenge: explain how Shor’s algorithm works.

When Shor’s algorithm has factorized a number, using 10500 or so times the computational resources that can be seen to be present, where was the number factorized?

What quantum computers tell us about connections between the laws of physics, universality, and apparently unrelated strands of explanation of the fabric of reality, we can discover – and are already discovering – by studying them theoretically.

The next chapter is likely to provoke many mathematicians. This can’t be helped. Mathematics is not what they think it is.

the idea that mathematics yields certainties is a myth too.

The angles of a real triangle really do not necessarily add up to 180°: the true total depends on the gravitational field within the triangle.

in 1976, Kenneth Appel and Wolfgang Haken used a computer to prove the famous ‘four-colour conjecture’ (that using only four different colours, any map drawn in a plane can be coloured so that no two adjacent regions have the same colour). The program required hundreds of hours of computer time, which meant that the steps of the proof, if written down, could not have been read, let alone recognized as self-evident, by a human being in many lifetimes. ‘Should we take the computer’s word for it that the four-colour conjecture is proved?’, the sceptics wondered – though it had never occurred to them to catalogue all the firings of all the neurons in their own brains when they accepted a relatively ‘simple’ proof.

confusion between the methods of mathematics and its subject-matter.

the reliability of our knowledge of mathematics remains subsidiary to our knowledge of physical reality.

So mathematical intuition is a species of physical intuition.

mathematical knowledge is inherently derivative, depending entirely on our knowledge of physics.

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 logically cannot accommodate the common-sense notions of cause and effect either.

one part of spacetime can no more change another than one part of a fixed three-dimensional object can change another.

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.

In the multiverse, snapshots do not have ‘time stamps’. There is no such thing as which snapshot from another universe happens ‘at the same moment’ as a particular snapshot in our universe, for that would again imply that there is an overarching framework of time, outside the multiverse, relative to which events within the multiverse happen. There is no such framework.

it makes no sense to ask how many snapshots, numerically, have such-and-such a property, but only what proportion of the infinite total have that property.

To assume that it is physically meaningful to ask which of the identical copies is me, is to assume that there is some frame of reference outside the multiverse, relative to which the answer could be given

the multiverse does not exist in an external space any more than it exists in an external time: it contains all the space and time there is.

Quantum theory does not in general determine what will happen in a 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 multiverse can sometimes make only probabilistic predictions of our own experience, even though what will happen i...

The multiverse does not ‘come into existence’ or ‘cease to exist’; those terms presuppose the flow of time.

Time does not flow. Other times are just special cases of other universes.

Why should we expect every visitor we receive from the future to hail from the particular future snapshots in which we shall eventually find ourselves? We really should not expect this. Asking to be allowed to interact with the past environment means asking to change it, which means by definition asking to be in a different snapshot of it from the one we remember.

A time traveller would return to the same snapshot (or, what is perhaps the same thing, to an identical snapshot) only in the extremely contrived case I discussed above, where no effective interaction takes place between the copies who meet, and the time traveller manages to make all the parallel histories identical.

It is not meaningful to ask which copy of me would have which experience: so long as we are identical, there is no such thing as ‘which’ of us. Parallel universes do not have hidden serial numbers: they are distinguished only by what happens in them.

Does being able to travel to the past of other universes, but not our own, really amount to time travel? Is it just inter-universe travel that makes sense, rather than time travel? No. The processes I have been describing really are time travel.