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.
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
. . . thinking of a plan
To dye one’s whiskers green,
And always use so large a fan
That they could not be seen.
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:
If an object is unentangled, it can be made to undergo interference by something acting on it alone.
(The arrows ‘’ and ‘’ represent the action of the transporter.) Once the object is entangled with the rest of the world in regard to the values X and Y, no operation on the object alone can create interference between those values. Instead, the histories are merely split further, in the usual way:
In entangled objects, further splitting happens instead of interference.
When two or more values of a physical variable have differently affected something in the rest of the world, knock-on effects typically continue indefinitely, as I have described, with a wave of differentiation entangling more and more objects. If the differential effects can all be undone, then interference between those original values becomes possible again; but the laws of quantum mechanics dictate that undoing them requires fine control of all the affected objects, and that rapidly becomes infeasible. The process of its becoming infeasible is known as decoherence. In most situations, decoherence is very rapid, which is why splitting typically predominates over interference, and why interference – though ubiquitous on microscopic scales – is quite hard to demonstrate unambiguously in the laboratory.
Nevertheless, it can be done, and quantum interference phenomena constitute our main evidence of the existence of the multiverse, and of what its laws are. A real-life analogue of the above experiment is standard in quantum optics laboratories. Instead of experimenting on voltmeters (whose many interactions with their environment quickly cause decoherence), one uses individual photons, and the variable being acted upon is not voltage but which of two possible paths the photon is on. Instead of the transporter, one uses a simple device called a semi-silvered mirror (represented by the grey sloping bars in the diagrams below). When a photon strikes such a mirror, it bounces off in half the universes, and passes straight through in the other half, as shown on next page:
Semi-silvered mirror
The attributes of travelling in the X or Y directions behave analogously to the two voltages X and Y in our fictitious multiverse. So passing through the semi-silvered mirror is the analogue of the transformation above. And when the two instances of a single photon, travelling in directions X and Y, strike the second semi-silvered mirror at the same time, they undergo the transformation , which means that both instances emerge in the direction X: the two histories rejoin. To demonstrate this, one can use a set-up known as a ‘Mach–Zehnder interferometer’, which performs those two transformations (splitting and interference) in quick succession:
Mach–Zehnder interferometer
The two ordinary mirrors (the black sloping bars) are merely there to steer the photon from the first to the second semi-silvered mirror.
If a photon is introduced travelling rightwards (X) after the first mirror instead of before as shown, then it appears to emerge randomly, rightwards or downwards, from the last mirror (because then, happens there). The same is true of a photon introduced travelling downwards (Y) after the first mirror. But a photon introduced as shown in the diagram invariably emerges rightwards, never downwards. By doing the experiment repeatedly with and without detectors on the paths, one can verify that only one photon is ever present per history, because only one of those detectors is ever observed to fire during such an experiment. Then, the fact that the intermediate histories X and Y both contribute to the deterministic final outcome X makes it inescapable that both are happening at the intermediate time.
In the real multiverse, there is no need for the transporter or any other special apparatus to cause histories to differentiate and to rejoin. Under the laws of quantum physics, elementary particles are undergoing such processes of their own accord, all the time. Moreover, histories may split into more than two – often into many trillions – each characterized by a slightly different direction of motion or difference in other physical variables of the elementary particle concerned. Also, in general the resulting histories have unequal measures. So let us now dispense with the transporter in the fictional multiverse too.
The rate of growth in the number of distinct histories is quite mind-boggling – even though, thanks to interference, there is now a certain amount of spontaneous rejoining as well. Because of this rejoining, the flow of information in the real multiverse is not divided into strictly autonomous subflows – branching, autonomous histories. Although there is still no communication between histories (in the sense of message-sending), they are intimately affecting each other, because the effect of interference on a history depends on what other histories are present.
Not only is the multiverse no longer perfectly partitioned into histories, individual particles are not perfectly partitioned into instances. For example, consider the following interference phenomenon, where X and Y now represent different values of the position of a single particle:
How instances of a particle lose their identity during interference. Has the instance of the particle at X stayed at X or moved to Y? Has the instance of the particle at Y returned to Y or moved to X?
Because these two groups of instances of the particle, initially at different positions, have gone through a moment of being fungible, there is no such thing as which of them has ended up at which final position. This sort of interference is going on all the time, even for a single particle in a region of otherwise empty space. So there is in general no such thing as the ‘same’ instance of a particle at different times.
Even within the same history, particles in general do not retain their identities over time. For example, during a collision between two atoms, the histories of the event split into something like this
and something like this
So, for each particle individually, the event is rather like a collision with a semi-silvered mirror. Each atom plays the role of the mirror for the other atom. But the multiversal view of both particles looks like this
where at the end of the collision some of the instances of each
atom have become fungible with what was originally a different atom.
For the same reason, there is no such thing as the speed of one instance of the particle at a given location. Speed is defined as distance travelled divided by time taken, but that is not meaningful in situations where there is no such thing as a particular instance of the particle over time. Instead, a collection of fungible instances of a particle in general have several speeds – meaning that in general they will do different things an instant later. (This is another instance of ‘diversity within fungibility’.)
Not only can a fungible collection with the same position have different speeds, a fungible group with the same speed can have different positions. Furthermore, it follows from the laws of quantum physics that, for any fungible collection of instances of a physical object, some of their attributes must be diverse. This is known as the ‘Heisenberg uncertainty principle’, after the physicist Werner Heisenberg, who deduced the earliest version from quantum theory.
Hence, for instance, an individual electron always has a range of different locations and a range of different speeds and directions of motion. As a result, its typical behaviour is to spread out gradually in space. Its quantum-mechanical law of motion resembles the law governing the spread of an ink blot – so if it is initially located in a very small region it spreads out rapidly, and the larger it gets the more slowly it spreads. The entanglement information that it carries ensures that no two instances of it can ever contribute to the same history. (Or, more precisely, at times and places where there are histories, it exists in instances which can never collide.) If a particle’s range of speeds is centred not on zero but on some other value, then the whole of the ‘ink blot’ moves, with its centre obeying approximately the laws of motion in classical physics. In quantum physics this is how motion, in general, works.
The Beginning of Infinity Page 34
