杏吧原创

THIS is a story about God鈥攁bout His Intentions, and His Limitations.
But it is not about religion. When Sandu Popescu talks about God, he is not
referring to a deity, and there is no thought of spiritual transcendence in what
he says. 鈥淕od does not play dice,鈥� Albert Einstein once said, expressing
contempt for the notion that randomness might be an inherent part of whatever
spirit, urge or process is behind our Universe. Now Popescu, a physicist at the
University of Cambridge, wants to turn Einstein鈥檚 phrase on its head, and to ask
some questions that probe even deeper.

Nearly a century after we first glimpsed the quantum nature of our world, the
details of quantum events remain utterly unpredictable. So we may as well admit
it: from atomic transitions to nuclear decays, the world really does seem to be
random. God really does play dice. What Popescu wants to know is鈥攚hy? Why
is the Universe quantum mechanical? What鈥檚 the point?

Physicists usually ask 鈥渉ow鈥� questions. How do photons and electrons pull off
the quantum trick of being in many places at once? How does measuring them
mysteriously cause them to make up their minds? By transforming 鈥渉ow鈥� into
鈥渨hy鈥�, Popescu aims to sidestep this impenetrable forest of quantum weirdness.
He鈥檚 more interested in the cosmic plan behind it. 鈥淲hy does God play dice?鈥� he
asks. 鈥淲hat does He get out of it?鈥� Or, in more down-to-earth terms, why is the
world as it is and not otherwise?

It鈥檚 an audacious question. Yet he and other physicists have some clues and
leads鈥攁nd perhaps even the embryo of an answer. The randomness in the
quantum world, they suspect, has a purpose. If they are right, the effect of
quantum uncertainty is not to build chaos and disorder into our world. Quite the
opposite. God uses it to ensure that all of the Universe鈥檚 far-flung regions
remain a coherent part of His overall plan.

That paradoxical conclusion follows from studies of one of the weirdest of
all quantum happenings, a phenomenon known as 鈥渜uantum entanglement鈥�.
Entanglement is an unnerving kind of link that can develop between two or more
photons, electrons or atoms, even if they inhabit distant parts of the Universe.
Consider, for example, a pion, a subatomic particle which can decay into an
electron and its antiparticle, a positron. When this happens, the particles fly
off in opposite directions. But according to quantum theory, no matter how far
apart the particles get, they remain mysteriously connected.

Up and down

One of the oddities of quantum particles is that their properties only take
on definite values when measured. The electron and positron, for instance, are
both effectively spinning. Either particle鈥檚 spin is equally likely to be
clockwise (known as 鈥渦p鈥�) or anticlockwise (鈥渄own鈥�)鈥攂ut you won鈥檛 know
which unless you measure it. Until that measurement is made the particle is in a
weird indefinite state, a 鈥渟uperposition鈥� of both spins. What is definite,
however, is that in an entangled state, the spins of the two particles are
intimately linked. Since the original pion had no spin, the positron and
electron must always spin in opposite senses so that their net spin remains
zero. If you find the electron鈥檚 spin to be 鈥渦p鈥�, you鈥檒l find the positron鈥檚 to
be 鈥渄own鈥�, and vice versa.

So it is as if the two entangled particles, no matter how far they are apart,
are not really separate at all. Measure one, and as its spin becomes definite
this triggers the other to respond. Its indeterminate spin also becomes
definite, in the opposite direction to that of its partner. What is astonishing
and disturbing is that this response happens instantaneously鈥� even if the
particles are separated by huge distances.

Consequently, quantum theory requires action at a distance. What happens in
one part of the Universe can have instantaneous 鈥渘onlocal鈥� consequences in other
parts, no matter how far away they might be. And this poses a problem, because
instantaneous action at a distance is a punch in the nose for Einstein. His
theory of relativity鈥攖he cornerstone of physics 鈥攃laims that our
Universe has an absolute speed limit. Nothing, according to Einstein, can travel
faster than light.

So you might wonder鈥攄o we really need to swallow this nonlocal quantum
weirdness? Perhaps there is a better theory that accounts for these
entanglements without action at a distance?

Think of this: if someone separated a pair of your shoes by a great distance
and then weighed one, they would immediately have a good estimate of the weight
of the other. There鈥檚 no mystery here. Nothing nonlocal. Shoes have weight. And
if they come from a pair, their weights are correlated from the outset. Could
something similar be true for entangled particle pairs? Despite what quantum
theory says, perhaps the particles do have definite spins, arranged oppositely
at all times, and measurements merely reflect this pre-existing situation.

This is an obvious possibility. It might even be true. The trouble is, it
doesn鈥檛 cushion the blow for relativity. In 1964, physicist John Bell of CERN,
the European Laboratory for Particle Physics, examined this line of argument in
detail and proved a famous theorem which fellow physicist Henry Stapp of the
Lawrence Berkeley Laboratory in California calls 鈥渢he greatest discovery of all
science鈥�. Bell first supposed that quantum theory doesn鈥檛 say all there is to
say about quantum particles. He then proved that if any more complete
theory鈥攁ny theory imaginable鈥攚ere to give predictions in agreement
with quantum theory, it would necessarily still contain the same kind of
nonlocal influences as ordinary quantum theory. 鈥淲hat Bell gave us,鈥� says
philosopher David Albert of Columbia University in New York, 鈥渋s a proof that
there is a genuine nonlocality in the workings of nature, however we attempt to
describe it, period.鈥� Every conceivable story about entangled states has to be
nonlocal. There is no escape. Unless, of course, entangled states don鈥檛 really
exist, and quantum theory is wrong.

Farewell, isolation

But we can be pretty sure it isn鈥檛 wrong because there are experiments to
prove it. In 1981, Alain Aspect of the University of Paris at Orsay showed using
pairs of photons that entanglement works just as quantum theory says it does.
Other researchers have since improved on Aspect鈥檚 results. Last year, Nicolas
Gisin and his colleagues at the University of Geneva used photon pairs that
travelled inside fibre-optic cables to separate cities in Switzerland to show
that entanglement can persist even for particles separated by 30 kilometres.
Distance is irrelevant. Despite what a few diehards say (See 鈥淪ceptics鈥�),
it looks as if entanglement and nonlocality are real.

What鈥檚 more, entanglement does not only apply to pairs of particles. At
Cambridge, mathematician Noah Linden has been working with Popescu to understand
entanglement between larger numbers of particles. They have found that in the
typical quantum state occupied by any group of particles the links between the
particles are mostly of a nonlocal character. Quantum theory isn鈥檛 just a tiny
bit nonlocal. It鈥檚 overwhelmingly nonlocal. Nonlocality is the rule for our
Universe.

That is an unsettling conclusion. Nonlocality cuts into the idea of the
separateness of things, and threatens to ruin the very notion of isolation. To
isolate an object we ordinarily move it a long way away from everything else, or
build impenetrable walls around it. But the link of entanglement knows no
boundaries. It isn鈥檛 a cord running through space, but lives somehow outside
space. It goes through walls, and pays no attention to distance.

Does this mean the idea of separateness is doomed? And if faster-than-light
connections are possible, is relativity鈥攄espite its huge
successes鈥攄oomed too?

Uncontrollable outcomes

This is where God鈥檚 dice-playing comes in. Popescu believes that the
randomness at the heart of quantum mechanics is God鈥檚 safeguard against such
grotesque consequences. It ensures what physicist Abner Shimony of Boston
University calls the 鈥減eaceful coexistence鈥� of quantum theory and relativity.
Sure, the outcome, up or down, at one end of an entangled link instantaneously
alters what happens at the other end. But the outcomes themselves are completely
uncontrollable. No matter which particle you measure, you find the results up or
down randomly, in equal measure. So you can鈥檛 control the outcome at the other
end. You can鈥檛 use the link to send any kind of message.

And whatever tricks you try, this block on sending information
instantaneously seems to remain unbreachable. Suppose you chose two separate
axes, say A and B, on which to measure the spin of your particles. If you
measured the spin of one particle on axis A, then its partner鈥檚 spin on axis A
would immediately be defined.

Likewise for spins on axis B. The fact that you can鈥檛 control whether the
spin is up or down would no longer matter. As long as you had some kind of
device to tell you on which axis the spin had been defined you would have a way
of sending a binary code: ABBABBAB, for example, would convey the same
information as the conventional digital byte 01101101.

But it turns out that any conceivable detector capable of doing this is also
prohibited by the mathematics of quantum theory. An experimenter at the other
end can鈥檛 possibly learn from individual outcomes, from the statistics of the
outcomes, or from anything else, what was the sequence of your measurements.
Quantum randomness prevents it.

So a stream of entangled particles is something like a combination of the
most perfect telephone link and the most useless handsets you could ever
imagine. The link can carry influences instantaneously across the Universe. But
the handsets at either end have the property that when you talk into them, they
randomise your speech. 鈥淗ello, it鈥檚 me鈥� you say, and into the line goes 鈥淣bsl
Cvdibobo鈥�. You can send a message faster than light, all right. You just can鈥檛
extract any meaning from it when it arrives. Whatever goes from one particle to
the other, as Asher Peres of Technion, Israel Institute of Technology in Haifa
puts it, is 鈥渋nformation without information鈥�.

According to Popescu, this answers the 鈥渨hy鈥� question. For despite the raw
nonlocality in the links of entanglement, randomness ensures that quantum theory
doesn鈥檛 transgress the letter of Einstein鈥檚 law. At the core of Einstein鈥檚
theory is the 鈥渘o-signalling鈥� criterion: you cannot send energy or information
from one place to another faster than light. This protects the chain of cause
and effect, and ensures that effects never happen before their causes. In a
deterministic world, any action at a distance would violate no-signalling. But
quantum theory allows what Shimony calls 鈥減assion-at-a-distance鈥�, a weaker
linking up of distant things which stops just short of upsetting the principle
of causality.

So the picture of God鈥檚 world is this: through relativity, He ensures a
degree of separateness and individuality for distant pieces of His Universe.
Through quantum entanglement, he maintains links between distant regions, and
keeps the whole Universe coherently connected. It鈥檚 the randomness that makes it
possible for God to tie distant parts of the Universe together more tightly than
He otherwise could, while ensuring that cause and effect stay distinct. This is
what He gets by playing dice.

鈥淚t is wondrous鈥�, says Popescu, 鈥渢hat quantum mechanics combines nonlocality
and causality鈥�. But he hopes to wring from his questions a bit more insight than
that. In playing dice, does God have no other choice but to use quantum rules?
鈥淚s quantum mechanics the only theory that can reconcile nonlocality with
relativity?鈥� asks Popescu. If so, this might explain not only why the Universe
contains randomness, but why it enters the world in quantum mechanical
clothing.

In the early 1990s, Gisin explored the question of whether quantum theory
could be modified in any way and still be consistent with what we know
experimentally about the world. He found that fiddling with the edifice is an
extraordinarily sensitive business. 鈥淚f you try to alter the theory very
slightly by adding some nonlinearity to the Schrodinger equation,鈥� he says,
鈥渢hen quantum nonlocality immediately becomes malignant: it can be used for
faster-than-light signalling.鈥� But what if you alter it wildly? Is there any
theory whatsoever besides the quantum theory in which nonlocality and causality
can coexist?

To find out, Popescu and his colleague Daniel Rohrlich of Tel Aviv University
in Israel have been playing some odd intellectual games. Their idea is to probe
the realm of possible theories, and to consider alternative theories that go
beyond quantum theory.

This isn鈥檛 so much an exercise in physics as in mathematics. It鈥檚 not hard to
dream up nonlocal theories. You can make up any number of them at will just by
inventing forces that act at a distance between particles. However, most of
these theories violate relativity by allowing faster-than-light signalling. It鈥檚
also not hard to invent theories that respect no-signalling. Any theory with
strictly local causes, for example, will do it. But the interesting theories are
those that achieve both nonlocality and no-signalling at once. Are there many
theories like that? Or is quantum theory the only one?

Simple and fundamental

Popescu and Rohrlich haven鈥檛 had to go far to find an answer: quantum theory,
they think, is not the only nonlocal theory with no-signalling. Their proof
comes in the form of a model world they have constructed, in which particles can
be entangled even more strongly than they are in the quantum world. This
super-entanglement leads to 鈥渟upercorrelations鈥� between spin measurements. And
yet the physics still doesn鈥檛 violate no-signalling. So this hypothetical world
provides a proof of principle: there are other inhabitants of the weird
theoretical terrain where nonlocality and causality can coexist.

This doesn鈥檛 mean that quantum theory is about to be ousted by one of these
alternatives: in our world, quantum theory unquestionably rules. But the mere
existence of these theories means that the need to have both nonlocality and
causality is not enough to tie God鈥檚 hands and fix the laws of physics. There
has to be something else.

鈥淥ur models raise a question,鈥� says Popescu. 鈥淲hat is the minimal set of
principles鈥攏onlocality plus no-signalling plus something else, simple and
fundamental, from which we could derive quantum mechanics?鈥� Is there something
we don鈥檛 yet know about, some other principle as deep and pervasive as both
causality and nonlocality?

So while we may know why God plays dice, we don鈥檛 yet know why he throws them
as he does. Why quantum mechanical dice? What else constrains His hands? More
bold questions for Popescu and his colleagues to get their teeth into.

Does the world really allow weird 鈥渘onlocal鈥� connections between very distant
objects? Some physicists refuse to believe it. 鈥淭here are two kinds of
physicists still believing in locality,鈥� says Nicolas Gisin of the University of
Geneva. 鈥淪ome who simply cannot believe in nonlocality, and others searching for
logical loopholes in the experiments.鈥� And there is at least one loophole.

True, there are famous experiments which seem to prove that quantum particles
can communicate instantaneously over large distances. But the particle detectors
that do the measuring are still not very good. They detect only a small fraction
of the particles that fly through them. So to draw conclusions, physicists have
to assume that the detected particles are a good sample. In 1970, physicist
Philip Pearle of Hamilton College in Clinton, New York, showed that in all these
experiments, entanglement might seem to be occurring not because it is real, but
because of sampling errors. Pearle pointed out the loophole merely as a logical
possibility, not as a serious issue. But a few physicists are clinging to it and
hoping that further experiments will disprove nonlocality.

Emilio Santos of the University of Cantabria in Santander, Spain, is one of
them. 鈥淓xperiments such as these,鈥� he says, 鈥渃annot discriminate between quantum
mechanics and theories based on local influences.鈥� He bases this claim on models
that he and others have developed in which certain properties of the particles
not currently known to physicists鈥攃alled 鈥渉idden
variables鈥濃�攄etermine not only what the spins of particles are when they
are detected, but also whether they are detected at all. If these hidden
variables conspire in just the right way, then such models lead to results that
make it seem as if nonlocality is real.

On strict logic, these models can鈥檛 be ruled out. But most physicists don鈥檛
give them much weight. 鈥淭hese models are ad hoc,鈥� says Gisin. 鈥淚t would be
amazing if these hidden variables were found to exist.鈥� Asher Peres of Technion,
Israel Institute of Technology in Haifa, puts it more bluntly: 鈥淧eople who
dislike quantum theory will never be convinced. They will find all kinds of
reasons not to believe in experimental evidence.鈥�