Authors: Stephen Baxter
N
ebogipfel continued his experiments with the billiards table. Repeatedly the ball would encounter that peculiar clattering I had observed about the middle of the table, and several times I thought I saw billiard balls – more
copies
of our original – appearing from nowhere and interfering with the trajectory of our ball. Sometimes the ball emerged from these collisions and continued along the path it might have followed regardless of the clattering-about; sometimes, though, it was knocked onto quite a different path, and – once or twice – we observed the type of incident I described earlier, in which a
stationary
ball was knocked out of its place, without my, or Nebogipfel’s, intervention.
This all made for an entertaining game – and clearly something fishy was going on – but for the life of me
I
could not see it, despite that hint of Plattnerite glow about the pockets. My only observation was that the slower the ball travelled, the more likely it was to be diverted from its path.
The Morlock, though, grew gradually more excited about all this. He would immerse himself in the hide of the patient Constructor, delving once more into the Information Sea, and emerge with some new fragment of knowledge he’d fished up – he mumbled to himself in that obscure, liquid dialect of his kind – and then he would hurry straight to
the billiards table, there to test his new understanding.
At last, he seemed ready to share his hypotheses with me; and he summoned me from my steam bath. I dried myself on my shirt and hurried after him to the Billiards Room; his small, narrow feet pattered on the hard floor as he half-ran back to the table. He was as excited as I could remember seeing him.
‘I think I understand what this table is for,’ he said, breathless.
‘Yes?’
‘It is – how can I express it? – it is only a demonstration, little more than a toy – but it is a
Multiplicity Generator
. Do you see?’
I held up my hands. ‘I fear I don’t see a thing.’
‘You are familiar enough with the idea of the Multiplicity of Histories, by now …’
‘I
should
be; it’s the basis of your explanation of the divergent Histories we have visited.’
At every moment, in every event (I summarized), History bifurcates. A butterfly’s shadow may fall
here
or
there
; the assassin’s bullet may graze and pass on without harm,
or
lodge itself fatally in the heart of a King … To each possible outcome of each event, there corresponds a fresh version of History. ‘And all of these Histories are
real
,’ I said, ‘and – if I understand it right – they lie side by side with each other, in some Fourth Dimension, like the pages of a book.’
‘Very well. And you see, also, that the action of a Time Machine – including your first prototype – is to cause
wider
bifurcations, to generate new Histories … some of them impossible
without
the Machine’s intervention – like this one!’ He waved his hands about. ‘Without your machine, which started off the whole series of events, humans could never have been transported back to the Palaeocene. We should not now be sitting on top of fifty million years of intelligent modification of the cosmos.’
‘I see all that,’ I said, my patience wearing. ‘But what has it to do with this table?’
‘Look.’ He set the single ball rolling across the table. ‘Here is our ball. We must imagine
many
Histories – a sheaf of them – fanning out around the ball at every moment. The most
likely
History, of course, is the one containing the classical trajectory – meaning a straightforward roll of the ball across the table. But other Histories – neighbouring, but some widely divergent – exist in parallel. It is even possible, though very unlikely, that in one of those Histories the thermal agitation of the ball’s molecules will combine, and cause it to leap up in the air and hit you in the eye.’
‘Very well.’
‘Now –’ he ran his finger around the rim of the nearest pocket. ‘This green inlay is a clue.’
‘It is Plattnerite.’
‘Yes. The pockets act as miniature Time Machines – limited in scope and size, but quite effective. And, as we have seen from our own experience, when Time Machines operate – when objects travel into future or past to meet themselves – the chain of cause and effect can be disrupted, and Histories grow like weeds …’
He reminded me of the odd incident we had witnessed with the stationary ball. ‘That was, perhaps, the clearest example of what I am describing. The ball sat at rest on the table –
our
ball, we will call it. Then a
copy
of our ball emerged from a pocket, and knocked our ball aside. Our ball travelled to the cushion, rebounded, and fell into the pocket, leaving the
copy
at rest on the table, in the precise position of the original.
‘Then,’ Nebogipfel said slowly, ‘our ball travelled
back
through time – do you see? – and emerged from the pocket in the past …’
‘And proceeded to knock
itself
out of the way, and took its
own
place.’ I stared at the innocent-looking table. ‘Confound it, Nebogipfel – I see it now! It
was
the same ball after all. It was resting quite happily on the table – but, because of the bizarre possibilities of time travel, it was able to loop through time and knock itself aside!’
‘You have it,’ the Morlock said.
‘But what made the ball start moving in the first place? Neither of us gave it a shove towards the pocket.’
‘A “shove” was not necessary,’ Nebogipfel said. ‘In the presence of Time Machines – and this is the point of the demonstration, really – you must abandon your old ideas of causality. Things are not so simple! The collision with the copy was just one possibility for the ball, which the table demonstrated for us. Do you see? In the presence of a Time Machine, causality is so damaged that even a stationary ball is surrounded by an infinite number of such bizarre possibilities. Your questions about “how it started” are without meaning, you see: it is a closed causal loop – there was
no
First Cause.’
‘Maybe so,’ I said, ‘but look here: I still have an uneasy feeling about all this. Let’s go back to the two balls on the table again – or rather, the one
real
ball and its copy. Suddenly, there is twice as much material present as there was before! Where has it all come from?’
He eyed me. ‘You are worried about the violation of Conservation Laws – the appearance, or disappearance, of Mass.’
‘Exactly.’
‘I did not notice any such concern when you dived into time in search of your younger self. For that was just as much – more! – of a violation of any Conservation Principle.’
‘Nevertheless,’ I said, refusing to be goaded, ‘the objection is valid – isn’t it?’
‘In a sense,’ he said. ‘But only in a narrow, single-History sort of way.
‘The Universal Constructors have been studying these paradoxes of time travel for centuries now,’ he said. ‘Or rather,
apparent
paradoxes. And they have formulated a type of Conservation Law which works in the higher Dimension of the Multiplicity of Histories.
‘Start with an object – like yourself. If, at any given moment, you
add
in a copy of yourself which may be
absent
because you have travelled away into past or future – and then
subtract
any copies
doubly present
because one of you has travelled to the past – then you will find that the sum, overall, stays constant – there is “really” only one of you – no matter how many times you travel up and down through time. So there
is
Conservation, of a sort – even though, at any moment in any given History, it may
seem
that Conservation Laws are broken, because there are suddenly two of you, or none of you.’
I saw it, on thinking it through. ‘There is only a paradox if you restrict your thinking to a single History,’ I observed. ‘The paradox disappears, if you think in terms of Multiplicity.’
‘Exactly. Just as problems of causality are resolved, within the greater frame of the Multiplicity.
‘It is the power of this table, you see,’ he told me, ‘that it is able to demonstrate these extraordinary possibilities to us … It is able to use Time Machine technology to show us the possibility – no, the
existence
– of Multiple, divergent Histories at the macroscopic level. Indeed, it can pick out particular Histories of interest: it has a very subtle design.’
He told me more of the Constructors’ Laws of the Multiplicity.
‘One can imagine situations,’ he said, ‘in which the Multiplicity of Histories is
zero, one, or many
. It is
zero
if that History is impossible – if it is not self consistent. A Multiplicity of
one
is the situation imagined by your earlier philosophers – of Newton’s generation, perhaps – in which a single course of events unfolds out of each point in time, consistent and immovable.’
I understood him to be describing my own original – and naive! – view of History, as a sort of immense Room, more or less fixed, through which my Time Machine would let me wander at will.
‘A “dangerous” path for an object – like you, or our billiard ball – is one which can reach a Time Machine,’ he said.
‘Well, that’s clear enough,’ I said. ‘It’s been obvious that I’ve been splitting off new Histories right, left and centre since the moment the Time Machine was first switched on. Dangerous indeed!’
‘Yes. And as the machine, and its successors, delve ever deeper into the past, so the Multiplicity generated tends towards
infinity
, and the divergence of the new copies of History grows wider.’
‘But,’ I said, a little frustrated, ‘coming back to the matter at hand – what is the purpose of this table? Is it just a trick? – Why have the Constructors given it to us? What are they trying to tell us?’
‘I do not know,’ he said. ‘Not yet. It is difficult … The Information Sea is wide, and there are many factions among the Constructors. Information is not offered freely to me – do you understand? – I have to pick up what I can, make the best understanding of it, and so build up an interpretation that way … I think there is a faction of them who have some scheme – an immense Project – whose outlines I can barely make out.’
‘What is the nature of this Project?’
Nebogipfel said for answer, ‘Look: we know that there are many – perhaps an infinite number – of Histories emerging from each event. Imagine yourself, in two such neighbouring Histories, separated by – let us say – the details of the rebound of your billiard ball. Now: could those two copies of you communicate with each other?’
I thought about that. ‘We have discussed this before. I don’t see how. A Time Machine would take me up and down a single History branch. If I’d gone back to change the rebound of the ball, then I would expect to travel forward and observe a difference, because, it seems, if the Machine causes a bifurcation, it then tends to follow the newly-generated History. No,’ I said confidently. ‘The two versions of me could not communicate.’
‘Not even if I allow you any conceivable machine, or measuring device?’
‘No. There would be two copies of any such device – each as disconnected from its twin as I was.’
‘Very well. That is a reasonable, and defensible, position. It is based on an implicit assumption that twin Histories, after their split, do not affect each other in any way. Technically speaking, you are assuming that Quantum-Mechanical Operators are linear …
But
,’ and now that note of excitement returned to his voice, ‘it turns out there
may
be a way to talk to the other History –
if
, on some fundamental level, the universe and its twin do remain entangled. If there is the smallest amount of Nonlinearity in the Quantum Operators – almost too small to detect –’
‘Then such communication would be possible?’
‘
I have seen it done
… in the Sea, I mean … the Constructors have managed it, but only on the smallest of experimental scales.’
Nebogipfel described to me what he called an ‘Everett phonograph’ – ‘after the twentieth-century
scientist, of
your
History, who first dreamed up the idea. Of course the Constructors have another label – but it is not easily rendered into English.’
The Nonlinearities of which Nebogipfel spoke worked at the most subtle of levels.
‘You must imagine that you perform a measurement – perhaps of the spin of an atom.’ He described a ‘Nonlinear’ interaction between an atom’s spin and its magnetic field. ‘The universe splits in two, of course, depending on the experiment’s outcome. Then,
after
the experiment, you allow the atom to pass through your Nonlinear field. This is the anomalous Quantum Operator I mentioned. Then – it turns out – you can arrange affairs so that your action in one History depends on a decision taken in the
second
History …’
He went into a great deal of detail about this, involving the technicalities of what he called a ‘Stern-Gerlach device’, but I let this wash past me; my concern was to grasp the central point.
‘So,’ I interrupted him, ‘is it possible? Are you telling me that the Constructors have invented such inter-History communication devices? Is our table one such?’ I began to feel excitement at the thought. All this chatter of billiard balls and spinning atoms was all very well; but if I could talk, by some Everett phonograph, to my selves in other Histories – perhaps to my home in Richmond in 1891…