The Beginning of Infinity: Explanations That Transform the World (45 page)

It is a rather counter-intuitive fact that if objects are merely identical (in the sense of being exact copies), and obey deterministic laws that
make no distinction between them, then they can never become different; but
fungible
objects, which on the face of it are even more alike, can. This is the first of those weird properties of fungibility that Leibniz never thought of, and which I consider to be at the heart of the phenomena of quantum physics.

Here is another. Suppose that your account contains a hundred dollars and you have instructed your bank to transfer one dollar from this account to the tax authority on a specified date in the future. So the bank’s computer now contains a deterministic rule to that effect. Suppose that you have done this because the dollar already belongs to the tax authority. (Say it had mistakenly sent you a tax refund, and has given you a deadline to repay it.) Since the dollars in the account are fungible, there is no such thing as
which one
belongs to the tax authority and which belong to you. So we now have a situation in which a collection of objects, though fungible, do not all have the same owner! Everyday language struggles to describe this situation: each dollar in the account shares literally all its attributes with the others, yet it is not the case that all of them have the same owner. So, could we say that in this situation they have no owner? That would be misleading, because evidently the tax authority does own one of them and you do own the rest. Could one say that they all have two owners? Perhaps, but only because that is a vague term. Certainly there is no point in saying that one cent of each of the dollars is owned by the tax authority, because that simply runs into the problem that the cents in the account are all fungible too. But, in any case, notice that the problem raised by this ‘diversity within fungibility’ is one of language only. It is a problem of how to describe some aspects of the situation in words. No one finds the situation itself paradoxical: the computer has been instructed to execute definite rules, and there will never be any ambiguity about what will happen as a result.

Diversity within fungibility is a widespread phenomenon in the multiverse, as I shall explain. One big difference from the case of fungible money is that in the latter case we never have to wonder about – or predict – what it would be like to
be
a dollar. That is to say, what it would be like to be fungible, and then to become differentiated. Many applications of quantum theory require us to do exactly that.

But first: I suggested temporarily visualizing our two universes as
being next to each other in space – just as some science-fiction stories refer to doppelgänger universes as being ‘in other dimensions’. But now we have to abandon that image and make them coincide: whatever that ‘extra dimension’ was supposed to denote, it would make them non-fungible.
*
It is not that they coincide
in
anything, such as an external space: they are not in space. An instance of space is part of each of them. That they ‘coincide’ means only that they are not separate in any way.

It 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.

Now our story can begin to have a non-trivial plot. For example, the voltage surge that happens in one of the two universes when the transporter malfunctions could cause some of the neurons in a passenger’s brain to misfire in that universe. As a result, in that universe, that passenger spills a cup of coffee on another passenger. As a result, they have a shared experience which they do not have in the other universe, and this leads to romance – just as in
Sliding Doors
.

The voltage surges need not be ‘malfunctions’ of the transporter. They could be a regular effect of the way it works. We accept much larger unpredictable jolts during others forms of travel such as flying or bronco-riding. Let us imagine that a tiny surge is produced in one of the universes whenever the transporter is operated in both, but that it is too small to be noticeable unless measured with a sensitive voltmeter, or unless it nudges something that happens to be on the brink of changing but would recede from the brink if not nudged.

In principle, a 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. I have excluded that possibility from our story because there are no such variables in real physics. The second, which is at least partly responsible for most everyday unpredictability, is that the factors affecting the phenomenon,
though deterministic, are either unknown or too complex to take account of. (This is especially so when they involve the creation of knowledge, as I discussed in
Chapter 9
.) The third – which had never been imagined before quantum theory – is that two or more initially fungible instances of the observer become different. That is what those transporter-induced jolts bring about, and it makes their outcomes strictly unpredictable despite being described by deterministic laws of physics.

These remarks about unpredictable phenomena could be expressed without ever referring explicitly to fungibility. And indeed that is what multiverse researchers usually do. Nevertheless, as I have said, I believe that fungibility is essential to the explanation of quantum randomness and most other quantum phenomena.

All three of these radically different causes of unpredictability could in principle feel exactly the same to observers. But, in an explicable world, there must be a way of finding out which of them (or which combination of them) is the actual source of any apparent randomness in nature. How could one find out that it is fungibility and parallel universes that are responsible for a given phenomenon?

In fiction, there is always the temptation to introduce inter-universe communication for this purpose, making the universes no longer ‘parallel’. As I have said, that would really make it a single-universe story – but we might try to disguise that fact by saying that such communication is
difficult
. For example, it might be that there is a way of adjusting the transporter in either universe so that it produces a voltage surge in the other. Then one could use it to transmit a message there. But we could imagine that this is very expensive, or dangerous, so that the ship’s regulations limit its use. ‘Personal communication’ with one’s own doppelgänger is especially prohibited. Nevertheless, one crew member illicitly ignores this prohibition during the night watch, and is startled to receive a message ‘
HAVE MARRIED SONAK
.’ We know, but the character does not, that this marriage is a knock-on effect of the coffee-spilling incident which was itself a knock-on effect of the voltage surge in the other universe. Then the transmission ends and no more such messages are received. We know – but again the character does not – that this is because the illicit use of the equipment has been detected in the other universe and stricter safeguards have
been implemented. The story could then explore what might happen when the crew member acts upon that startling message.

How
should
one react to the news that one’s doppelgänger has married? Should one seek out the spouse’s doppelgänger in one’s own universe – whom one has never even met personally, let alone formed a romantic relationship with? Or whom, in the time-honoured tradition of love stories, one finds annoying. It can’t do any harm. Or can it?

Ideas originating in the other universe are at least as fallible as those in ours; and if they are difficult to obtain, that makes error-correction harder. Knowledge-creation depends on error-correction. So perhaps the message would have continued ‘
ALREADY REGRETTING IT
’. Or perhaps Sonak had just turned up in the transporter room in the other universe, making it impossible to send that warning. Or perhaps the couple are happy at the moment, but will shortly have a disastrous break-up resulting in divorce. In all those cases, that inter-universe communication, far from being helpful, could cause a doubling of the number of disastrous marriage decisions made by the two instances of that crew member.

More generally, the news that your doppelgänger seems happy having made a particular decision in the other universe does not imply that you will be happy if you make the ‘corresponding’ decision. Once there are differences between the universes (and without such differences news from the other universe is not news), there is no good reason to expect the outcome of a decision to be unaffected by them. In one universe, you met because of an accidental shared experience; in the other, because you have illegally used the ship’s equipment. Can that affect the happiness of a marriage? Perhaps not, but you can only know that if you have a good explanatory theory of which factors affect the outcomes of marriages and which do not. And if you have such a theory, then perhaps you have no need to be skulking in transporter rooms.

Still more generally, the benefit of inter-universe communication would be, in effect, that it permits new forms of information processing. In the fictional case I have described, since the two universes have been identical until quite recently, communicating with one’s other-universe counterpart achieves the same effect as running a computer simulation of an alternative version of a period of one’s own life, without having to know all the relevant physical variables explicitly. This computation
is infeasible in any other way, and could be helpful in testing explanatory theories of how various factors affect outcomes. Nevertheless, it is no substitute for thinking of those theories in the first place.

Therefore, if such communication is a scarce resource, a more efficient way of using it might be to exchange the theories themselves: if your doppelgänger solves a problem and tells you the solution, then you can see for yourself that it is a good explanation even if you have no way of knowing how your doppelgänger arrived at it.

Another efficient use of inter-universe communication might be to share the work of a lengthy computation. For instance, the story might be that some crew members have been poisoned and will die within hours unless the antidote is administered. To find the antidote requires computer simulations of the effects of many variants of a drug. So the two instances of the ship’s computer can each search half the list of variants, thus running through the full list in half the time. When the cure is found in one universe, its number in the list can be transmitted to the other universe, the result can be checked there, and the crew in both universes are saved. Again, evidence that there is computer power accessible in this way through the transporter would be evidence that there really was a computer out there, performing different calculations from one’s own. Reflecting on the details (about what the doppelgängers breathe and so on) would then let the inhabitants know that the other universe as a whole was a real place with similar structure and complexity to their own. So their world would be explicable.

Since there is no inter-universe communication in real quantum physics, we shall not allow it in our story, and so that specific route to explicability is not open. The history in which our crew members are married and the one in which they still hardly know each other cannot
communicate
with each other or
observe
each other. Nevertheless, as we shall see, there are circumstances in which histories can still
affect
each other in ways that do not amount to communication, and the need to explain those effects provides the main argument that our own multiverse is real.

After the universes in our story begin to differ inside one starship, everything else in the world exists in pairs of identical instances. We must continue to imagine those pairs as being fungible. This is necessary
because the universes are not ‘receptacles’ – there is nothing to them apart from the objects that they contain. If they did have an independent reality, then each of the objects in such a pair would have a property of being in one particular universe and not the other, which would make them non-fungible.

Typically, the region in which the universes are different will then grow. For instance, when the couple decide to marry, they send messages to their home planets announcing this. When the messages arrive, the two instances of each of those planets become different. Previously only the two instances of the starship were different, bur soon, even before anyone broadcasts it intentionally, some of the information will have leaked out. For instance, people in the starship are moving differently in the two universes as a result of the marriage decision, so light bounces off them differently and some of it leaves the starship through portholes, making the two universes slightly different wherever it goes. The same is true of heat radiation (infra-red light), which leaves the starship through every point on the hull. Thus, starting with the voltage happening in only one universe, a
wave of differentiation
between the universes spreads in all directions through space. Since information travelling in either universe cannot exceed the speed of light, nor can the wave of differentiation. And since, at its leading edge, it mostly travels at or near that speed, differences in the head start that some directions have over others will become an ever smaller proportion of the total distance travelled, and so the further the wave travels the more nearly spherical it becomes. So I shall call it a ‘
sphere
of differentiation’.

Even inside the sphere of differentiation, there are comparatively few differences between the universes: the stars still shine, the planets still have the same continents. Even the people who hear of the wedding, and behave differently as a result, retain most of the same data in their brains and other information-storage devices, and they still breathe the same type of air, eat the same types of food, and so on.

However, although it may seem intuitively reasonable that news of the marriage leaves most things unchanged, there is a different commonsense intuition that seems to prove that it must change everything, if only slightly. Consider what happens when the news reaches a planet – say, in the form of pulse of photons from a communication laser.
Even before any human consequences, there is the physical impact of those photons, which one might expect to impart momentum to every atom exposed to the beam – which will be every atom in something like that half of the surface of the planet which is facing the beam. Those atoms would then vibrate a little differently, affecting the atoms below through interatomic forces. As each atom affected others, the effect would spread rapidly through the planet. Soon, every atom in the planet would have been affected – though most of them by unimaginably tiny amounts. Nevertheless, however small such an effect was, it would be enough to break the fungibility between each atom and its other-universe counterpart. Hence it would seem that nothing would be left fungible after the wave of differentiation had passed.