The Beginning of Infinity: Explanations That Transform the World (46 page)

These two opposite intuitions reflect the ancient dichotomy between the discrete and the continuous. The above argument – that everything in the sphere of differentiation must become different – depends on the reality of
extremely small physical changes
– changes that would be many orders of magnitude too small to be measurable. The existence of such changes follows inexorably from the 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 particular atom. The atom cannot absorb any less than that amount, which is called a ‘quantum’ of energy. Since this was the first distinctive feature of quantum physics to be discovered, it gave its name to the field. Let us incorporate it into our fictional physics as well.

Hence it is not the case that all the atoms on the surface of the planet are changed by the arrival of the radio message. 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 some influence, and the rest are unaffected, what determines which are the ones to be affected? The answer has to do with fungibility, as the reader may guess, and as I shall explain below.

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. Indeed, knowledge can aim itself at a target, travel vast distances having scarcely any effect, and then utterly transform the destination.

In our story, too, if we wanted the transporter malfunction to have a significant physical effect at astronomical distances, it would have to be via knowledge. All those torrents of photons streaming out of the starship and carrying, intentionally or unintentionally, information about a wedding will have a noticeable effect on the distant planet only if someone there cares about the possibility of such information enough to set up scientific instruments that could detect it.

Now, as I have explained, our imaginary laws of physics which say that 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? Imagine a second starship, of the same type as the first and far away. What happens if the second starship runs its transporter immediately after the first one did?

One logically possible answer would be that
nothing
happens – in other words, the laws of physics would say that, once the two universes are different, all transporters just work normally and never produce a voltage surge again. However, that would also provide a way of communicating faster than light, albeit unreliably and only once. You set up a voltmeter in the transporter room and run the transporter. If the voltage surges, you know that the other starship, however far away,
has not yet run its transporter (because, if it had, that would have put a permanent end to such surges everywhere). The laws governing the real multiverse do not allow information to flow in that way. If we want our fictional laws of physics to be universal from the inhabitants’ point of view, the second transporter must do exactly what the first one did. It must cause a voltage surge in one universe and not in the other.

But in that case something must determine
which
universe the second surge will happen in. ‘In one universe but not the other’ is no longer a deterministic specification. Also, a surge must not happen if the transporter is run
only
in the other universe. That would constitute inter-universe communication. It must depend on both instances of the transporter being run simultaneously. Even that could allow some inter-universe communication, as follows. In the universe where a surge has once happened, run the transporter at a prearranged time and observe the voltmeter. If no surge happens, then the transporter in the other universe is switched off. So we are at an impasse. It is remarkable how much subtlety there can be in the apparently straightforward, binary distinction between ‘same’ and different’ – or between ‘affected’ and ‘unaffected’. In the real quantum theory, too, the prohibitions on inter-universe communication and faster-than-light communication are closely connected.

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
. Imagine an uncountably infinite number of them, initially all fungible. The transporter causes previously fungible ones to become different, as before; but now the relevant law of physics says, ‘The voltage surges in
half the universes
in which the transporter is used.’ So, if the two starships both run their transporters, then, after the two spheres of differentiation have overlapped, there will be universes of four different kinds: those in which a surge happened only in the first starship, only in the second, in neither, and in both. In other words, in the overlap region there are four different histories, each taking place in one quarter of the universes.

Our fictional theory has not provided enough structure in its multiverse to give a meaning to ‘half the universes’, but the real quantum
theory does. As I explained in
Chapter 8
, the method that a theory provides for giving a meaning to proportions and averages for infinite sets is called a
measure
. A familiar example is that classical physics assigns
lengths
to infinite sets of points arranged in a line. Let us suppose that our theory provides a measure for universes.

Now we are allowed storylines such as the following. In the universes in which the couple married, they spend their honeymoon on a human-colonized planet that the starship is visiting. As they are teleporting back up, the voltage surge in
half
those universes causes someone’s electronic notepad to play a voice message suggesting that one of the newlyweds has already been unfaithful. This sets off a chain of events that ends in divorce. So now our original collection of fungible universes contains three different histories: in one, comprising
half
the original set of universes, the couple in question are still single; in the second, comprising a
quarter
of the original set, they are married; and in the third, comprising the remaining quarter, they are divorced.

Thus the three histories do not occupy equal proportions of the multiverse. There are twice as many universes in which the couple never married as there are universes in which they divorced.

Now suppose that scientists on the starship know about the multiverse and understand the physics of the transporter. (Though note that we have not yet given them a way of discovering those things.) Then they know that, when they run the transporter, an infinite number of fungible instances of themselves, all sharing the same history, are doing so at the same time. They know that a voltage surge will occur in half the universes in that history, which means that it will split into two histories of equal measure. Hence they know that, if they use a voltmeter capable of detecting the surge, half of the instances of themselves are going to find that it has recorded one, and the other half are not. But they also know that it is meaningless to ask (not merely impossible to know)
which
event they will experience. Consequently they can make two closely related predictions. One is that, despite the perfect determinism of everything that is happening,
nothing
can reliably predict for them whether the voltmeter will detect a surge.

The other prediction is simply that the voltmeter will record a surge with probability one-half. 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. This is also the 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.

Notice that when a random outcome (in this sense) is about to happen, it is a situation of diversity within fungibility: the diversity is in the variable ‘what outcome they are
going
to see’. The logic of the situation is the same as in cases like that of the bank account I discussed above, except that this time the fungible entities are people. They are fungible, yet half of them are going to see the surge and the other half not.

In practice they could test this prediction by doing the experiment many times. 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. Only a tiny proportion of the instances of the observers will see anything different.

Our story continues. In one of the histories, the newspapers on the astronauts’ home planets report the engagement. They fill many column-inches with reports about the accident that brought the astronauts together and so on. In the other history, where there is no astronaut-engagement news, one newspaper fills the same space on the page with a short story. It happens to be about a romance on a starship. Some of the sentences in that story are identical to sentences in the news items in the other history. The same words, printed in the same column in the same newspaper, are fungible between the two histories; but they are fiction in one history and fact in the other. So here the fact/fiction attribute has diversity within fungibility.

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 continue to constitute only a small proportion of all histories that are present.

Soon after that, 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, according to deterministic laws of physics. All of them were caused by the transporter.

Here is another situation where, if we are not careful, common sense makes false assumptions about the physical world, and can make descriptions of situations sound paradoxical even though the situations themselves are quite straightforward. Dawkins gives an example in his book
Unweaving the Rainbow
, analysing the claim that a television psychic was making accurate predictions:

There are about 100,000 five-minute periods in a year. The probability that any given watch, say mine, will stop in a designated five-minute period is about 1 in 100,000. Low odds, but there are 10 million people watching the [television psychic’s] show. If only half of them are wearing watches, we could expect about 25 of those watches to stop in any given minute. If only a quarter of these ring in to the studio, that is 6 calls, more than enough to dumbfound a naive audience. Especially when you add in the calls from people whose watches stopped the day before, people whose watches didn’t stop but whose grandfather clocks did, people who died of heart attacks and their bereaved relatives phoned in to say that their ‘ticker’ gave out, and so on.

As this example shows, 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. The ‘naive’ audience’s mistake is a form of parochialism: they observe a phenomenon – people phoning in because their watches stopped – but they are failing to understand
it as part of a wider phenomenon, most of which they do not observe. Though the unobserved parts of that wider phenomenon have in no way affected what we, the viewers, observe, they are essential to its explanation. Similarly, 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 in reality.