The Beginning of Infinity: Explanations That Transform the World (47 page)

We are now seeing the interior of the spaceship as an overwhelmingly complex jumble of superposed objects. Most locations on board are packed with people, some of them on very unusual errands, and all unable to perceive each other. The spaceship itself is on many slightly different courses, due to slightly different behaviours of the crew. Of course we are ‘seeing’ this only in our mind’s eye. Our fictional laws of physics ensure that no observer in the multiverse itself would see anything like that. Consequently, on closer inspection (in our mind’s eye), we also see that there is great order and regularity in that apparent chaos. For instance, although there is a flurry of human figures in the Captain’s chair, we see that most of them are the Captain; and although there is a flurry of human figures in the Navigator’s chair, we see that few of them are the Captain. Regularities of that kind are ultimately due to the fact that all the universes, despite their differences, obey the same laws of physics (including their initial conditions).

We also see that any particular instance of the Captain only ever interacts with one instance of the Navigator, and one instance of the First Officer; and those instances of the Navigator and First Officer are precisely the ones that interact with each other. These regularities are due to the fact that 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. In the story so far, this autonomy of the histories is rather a trivial fact, since we began by making the
universes
autonomous. But it is going to be worth becoming even more pedantic for a moment: 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’ – but, remember, universes consist only of the objects in them, so that amounts only to saying I can see
the ones that I can see. The upshot is that our laws of physics must also say that every object carries within it information about which instances of it could interact with which instances of other objects (except when the instances are fungible, when there is no such thing as ‘which’). Quantum theory describes such information. It is known as
entanglement
information.
*

So far in the story we have set up a vast, complex world which looks very unfamiliar in our mind’s eye, but to the overwhelming majority of the inhabitants looks almost exactly like the single universe of our everyday experience and of classical physics, plus some apparently random jiggling whenever the transporter operates. A tiny minority of the histories have been significantly affected by very ‘unlikely’ events, but even in those the information
flow
– what affects what – is still very tame and familiar. For instance, a version of the ship’s log that contains records of bizarre coincidences will be perceptible to people who remember those coincidences, but not to other instances of those people.

Thus the information in the fictional multiverse flows along a branching tree, whose branches – histories – have different thicknesses (measures) and never rejoin once they have separated. Each behaves exactly as if the others did not exist. If that were the whole story, that multiverse’s imaginary laws of physics would still be fatally flawed as explanations in the same way that they have been all along: there would be no difference between their predictions and those of much more straightforward laws saying that there is only one universe – one history – in which the transporter
randomly
introduces a change in the objects that it teleports. Under those laws, instead of branching into two autonomous histories on such occasions, the single history randomly does or does not undergo such a change. Thus the entire stupendously complicated multiverse that we have imagined – with its multiplicity of entities including people walking through each other and its bizarre occurrences and its entanglement information – would collapse into nothing, like the galaxy in
Chapter 2
that became an emulsion flaw. The multiverse explanation of the same events would be a bad
explanation, and so the world would be inexplicable to the inhabitants if it were true.

It may seem that, by imposing all those conditions on information flow, we have gone to a lot of trouble to achieve that very attribute – to hide, from the inhabitants, the Byzantine intricacies of their world. In the words of Lewis Carroll’s White Knight in
Through the Looking Glass
, it is as if we were

Now it is time to start removing the fan.

In quantum physics, information flow in the multiverse is not as tame as in that branching tree of histories I have described. That is because of one further quantum phenomenon: under certain circumstances, the laws of motion allow histories to rejoin (becoming fungible again). This is the time-reverse of the splitting (differentiation of history into two or more histories) that I have already described, so a natural way to implement it in our fictional multiverse is for the transporter to be capable of undoing its own history-splitting.

If we represent the original splitting like this

where
X
is the normal voltage and
Y
is the anomalous one introduced by the transporter, then the rejoining of histories can be represented as

In an interference phenomenon, differentiated histories rejoin.

This phenomenon is known as
interference
: the presence of the
Y-
history
interferes
with what the transporter usually does to an
X
-history. Instead, the
X
and
Y
histories merge. This is rather like the doppelgängers merging with their originals in some phantom-zone stories, except that here we do not need to repeal the principle of the conservation of mass or any other conservation law: the total measure of all the histories remains constant.

Interference is the phenomenon that can provide the inhabitants of the multiverse with evidence of the existence of multiple histories in their world without allowing the histories to communicate. For example, suppose that they run the transporter twice in quick succession (I shall explain in a moment what ‘quick’ means):

An interference experiment

If they did this repeatedly (with, say, different copies of the transporter on each occasion), they could soon infer that the intermediate result
could not
be just randomly
X
or
Y
, because if it were then the final outcome would sometimes be
Y
(because of
), while in fact it is always
X
. Thus the inhabitants would no longer be able to explain away what they see by assuming that only one, randomly chosen, value of the voltage is real at the intermediate stage.

Although such an experiment would provide evidence that multiple histories not only exist but affect each other strongly (in the sense that they behave differently according to whether the other is present or absent), it does not involve inter-history
communication
(sending a message of one’s choice to the other history).

In our story, just as we did not allow splitting to happen in a way that would allow communication faster than light, so we must ensure the same for interference. The simplest way is to require that the rejoining take place only if no wave of differentiation has happened. That is to say, the transporter can undo the voltage surge only if this has not yet caused any differential effects on anything else. When a
wave of differentiation, set off by two different values
X
and
Y
of some variable, has left an object, the object is
entangled
with all the differentially affected objects.

Entanglement

So our rule, in short, is that interference can happen only in objects that are unentangled with the rest of the world. This is why, in the interference experiment, the two applications of the transporter have to be ‘in quick succession’. (Alternatively, the object in question has to be sufficiently well isolated for its voltages not to affect its surroundings.) So we can represent a generic interference experiment symbolically as follows: