The Beginning of Infinity: Explanations That Transform the World

by David Deutsch

science as explanation, in the sense that I am advocating in this

itself still a minority view even among theoretical physicists.

retain the speed-of-light limit on communication, and let the laws of physics be universal and symmetrical

deterministic: nothing random ever happens, which is why the universes have remained alike – so far.

Nor can one bring new information – even random information – into the world: everything that happens is determined by laws of physics from what has gone before. However, one can, of course, bring new knowledge into the world. Knowledge consists of explanations, and none of those conditions prevents the creation of new explanations. All this is true of the real world too.

In real physics, even space is a physical object, capable of warping and affecting matter and being affected by it.

‘configurational’ entities: they are states or configurations of objects, not what we usually think of as physical objects in their own right.

The vacuum, which we perceive as empty at everyday scales and even at atomic scales, is not really emptiness, but a richly structured entity known as a ‘quantum field’.

Elementary particles are higher-energy configurations of this entity: ‘excitations of the vacuum’.

Diversity within fungibility is a widespread phenomenon in the multiverse,

is hard to imagine perfectly identical things coinciding. For instance, as soon as you imagine just one of them, your imagination has already violated their fungibility. But, although imagination may baulk, reason does not.

phenomenon could appear unpredictable to observers for one or more of three reasons. The first is that it is affected by some fundamentally random (indeterministic) variable.

there are no such variables in real physics.

the factors affecting the phenomenon, though deterministic, are either unknown or too c...

especially so when they involve the creation of knowledge, as I dis...

two or more initially fungible instances of the observer...

That is what those transporter-induced jolts bring about, and it makes their outcomes strictly unpredictable despite being descri...

explanations of classical physics, because in classical physics most fundamental quantities (such as energy) are continuously variable. The opposing intuition comes from thinking about the world in terms of information processing, and hence in terms of discrete variables such as the contents of people’s memories.

Quantum theory adjudicates this conflict in favour of the discrete. For a typical physical quantity, there is a smallest possible change that it can undergo in a given situation.

For instance, there is a smallest possible amount of energy that can be transferred from radiation to any particu...

any less than that amount, which is called a ‘qua...

In reality, the typical response of a large physical object to very small influences is that most of its atoms remain strictly unchanged, while, to obey the conservation laws, a few exhibit a discrete, relatively large change of one quantum.

The discreteness of variables raises questions about motion and change. Does it mean that changes happen instantaneously? They do not – which raises the further question: what is the world like halfway through that change?

Also if a few atoms are strongly affected by ...

the rest are unaffected, what determines which are the on...

The effects of a wave of differentiation usually diminish rapidly with distance – simply because physical effects in general do. The sun, from even a hundredth of a light year away, looks like a cold, bright dot in the sky. It barely affects anything. At a thousand light years, nor does a supernova. Even the most violent of quasar jets, when viewed from a neighbouring galaxy, would be little more than an abstract painting in the sky. There is only one known phenomenon which, if it ever occurred, would have effects that did not fall off with distance, and that is the creation of a certain type of knowledge, namely a beginning of infinity.

knowledge can aim itself at a target, travel vast distances having scarcely

any effect, and then utterly transform th...

a voltage surge happens ‘in one universe but not the other’ cannot be deterministic unless the universes are fungible. So, what happens when the transporter is used again, after the universes are no longer fungible?

‘In one universe but not the other’ is no longer a deterministic specification. Also, a surge must not happen if

is remarkable how much subtlety there can be in the apparently straightforward, binary distinction between ‘same’

and different’ – or between ‘affected’ and ‘unaffected’.

There is a way – I think it is the only way – to meet simultaneously the requirements that our fictional laws of physics be universal and deterministic, and forbid faster-than-light and inter-universe communication: more universes.

Thus the outcomes of such experiments are subjectively random (from the perspective of any observer) even though everything that is happening is completely determined objectively.

origin of quantum-mechanical randomness and probability in real physics: it is due to the measure that the theory provides for the multiverse, which is in turn due to what kinds of physical processes the theory allows and forbids.

when a random outcome (in this sense) is about to happen, it is a situation of dive...

the diversity is in the variable ‘what outcome they a...

Every formula purporting to predict the sequence of outcomes will eventually fail: that tests the unpredictability. And in the overwhelming majority of universes (and histories) the surge will happen approximately half the time: that tests the predicted value of the probability.

The number of distinct histories will now increase rapidly. Whenever the transporter is used, it takes only microseconds for the sphere of differentiation to engulf the whole starship, so, if it is typically used ten times per day, the number of distinct histories inside the whole starship will double about ten times a day. Within a month there will be more distinct histories than there are atoms in our visible universe. Most of them will be extremely similar to many others, because in only a small proportion will the precise timing

and magnitude of the voltage surge be just right to precipitate a noticeable, Sliding Doors-type change.

Nevertheless, the number of histories continues to increase exponentially, and soon there are so many variations on events that several significant changes have been caused somewhere in the multiversal diversity of the starship. So the total number of such histories increases exponentially too, even though they...

in an even smaller but still exponentially growing number of histories, uncanny chains of ‘accidents’ and ‘unlikely coincidences’ will have come to dominate events. I put those terms in quotation marks because those events are not in the least accidental. They have all happened inevitably, accordin...

the fact that certain circumstances can explain other events without being in any way involved in causing them is very familiar despite being counter-intuitive.

failing to understand it as part of

a wider phenomenon, most of which they do not observe.

common sense and classical physics contain the parochial error that only one history exists.

This error, built into our language and conceptual framework, makes it sound odd to say that an event can be in one sense extremely unlikely and in another certain to happen.

But there is nothing odd about it...

the histories are nearly autonomous: what happens in each of them depends almost entirely on previous events in that history alone – with transporter-induced voltage surges being the only exceptions.

what exactly is the difference between the instance of you that I can interact with and the ones that are imperceptible to me? The latter are ‘in other universes’