London
Mark Hadley was at a crossroads. In 1992, after more than ten years in the
electronics industry, he had a keen business sense and a reputation for getting
results. His record of promotion was second to none, and buoyed by success, he
was starting up his own software company. The future was very bright. Yet all
the same, some very peculiar questions were circling relentlessly in Hadley’s
head.
The questions had nothing to do with the prospects for his company. They were
the kind that only universities pay people to think about. What is an electron?
What is a photon? What, exactly, is a particle? “Surprisingly,” says Hadley,
“these are questions that very few physicists ask.”
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Hadley had turned to electronics after leaving university in 1979 with a
degree in physics, but financial success wasn’t everything. Those questions
wouldn’t go away. They kept niggling. And in the end there was nothing for it
but to put off his entrepreneurial plans and return to university.
Astonishingly, in so doing Hadley has found an answer to his questions that is
turning accepted scientific ideas on their heads.
Some of the biggest concepts in physics are locked in two theories: the
quantum theory of the submicroscopic world and the general theory of
relativity—Einstein’s theory of gravity. Of the two, quantum theory is
almost universally considered to be the more fundamental. But Hadley, now at the
University of Warwick, is claiming that quantum theory is actually a consequence
of the theory of gravity.
What is a particle?
It is a remarkable claim, because quantum theory would appear to be
completely incompatible with any “classical” theory such as general relativity.
In the quantum world, atoms and electrons have the strange ability to be in many
places at once. By contrast, in a classical theory such as general relativity,
the trajectory of a body is always distinct and definite. Conjuring quantum
effects out of classical theory seems nothing short of a miracle. Hadley,
however, has managed to pull off this trick with ease using his peculiar new
perspective on the question of what makes a particle.
It’s a question with a history, for it also caught the attention of Albert
Einstein. Because general relativity views gravity as a distortion in the fabric
of space-time, Einstein had hoped that particles could be viewed as localised
kinks in that fabric. Alas, he never found a way to prove it. In the 1960s, John
Wheeler and Charles Misner at Princeton University in New Jersey took up the
challenge and viewed charged particles as “wormholes” through which an electric
field is threaded.
Wormholes are hypothetical tunnels that connect far-flung regions of
space-time. If an electric field enters through one hole and leaves through the
other, then from far away one hole would look like a “source” and the other a
“sink” of electric field, just like charged particles.
But Hadley has taken this approach one step further. Einstein, Wheeler and
Misner all viewed particles as distortions in the topology of space alone. That
is, they considered kinks of only a limited kind. None wanted to mess with
distortions in time because of the havoc this might wreak with “causality”, the
requirement that a cause should always precede an effect. Hadley, however, has
gone the whole hog. Embracing the spirit of general relativity—a theory in
which space and time mingle inextricably—he has postulated that particles
are indeed distortions in the fabric of space-time.
He was already thinking this way in 1992. But at the time his mathematics was
not up to handling such concepts. So in 1993, Hadley left the corporate world
and embarked on a masters degree in mathematics at Warwick. He followed it with
a doctorate. In theory, he had two academic advisers—one in mathematics
and one in physics. “But the mathematician refused to supervise me because he
didn’t have the expertise, while the physicist agreed to supervise me as long as
I realised he might not be able to help,” says Hadley.
The physicist was Gerard Hyland. “To make real advances in science, you
always have to go out on a limb,” he says. “Mark took a big risk by adopting
such a strategy for a PhD.” The essence of Hadley’s idea was that a subatomic
particle is a region of space-time so dramatically warped that it bends back on
itself like a knot. Such a knot necessarily contains a “closed, time-like
curve”—a loop of time. “This is the crucial ingredient which enables
general relativity to reproduce the effects of quantum theory,” says Hadley.
Tunnels through time
A loop of time—a circuit which returns to its starting time just as a
circuit in space returns to its starting place—is essentially a time
machine. That such a thing is permitted to exist is one of the most puzzling
features of general relativity. Crucially, a time loop enables a particle to
interact with other particles not only in its past but in its future, too. “Not
surprisingly, this changes everything,” says Hadley.
Hadley gives the example of a billiard ball rolling across a table. Its
trajectory is fully determined by its initial speed and direction. However, if a
wormhole is placed in its path, things change. Wormholes can act not only as
tunnels through space but as tunnels through time as well, so other trajectories
are suddenly possible. For instance, if a wormhole connects two of the pockets,
then the ball can be deflected by itself, having entered one pocket and emerged
from the other in the past
(see Diagram). And this is not the only
possibility. “Where there was only one outcome, suddenly there are many,” says
Hadley.
The lack of a single outcome leads to the “fuzziness” of the quantum
world—the fact that it is impossible to determine both the exact position
and speed of a particle like an electron. “The properties of a fundamental
particle,” says Hadley, “are determined by measurements that can be made on it
in the future. If those measurements are mutually incompatible, the particle’s
properties will be ill-defined.” This also explains why making a quantum
measurement can affect the outcome—the particle can already “feel” what is
going to happen to it in the future.
According to Hadley, one way to think of classical particles is to imagine a
blind man throwing a ball into a bin. Getting the ball into the bin depends only
on releasing it with the right speed and direction. Once the ball has been
thrown, moving the bin makes no difference to its trajectory. However, imagine
jiggling a rope. The shape of the wave travelling along it depends not only on
what is happening at your end but also on what is happening at the other end.
This is what happens with quantum particles.
Physicists call these “boundary conditions”. “For a classical particle there
is no other end and everything is determined,” says Hadley. “For a quantum
particle, there is another end—another, unknown boundary condition in the
future—and not everything is determined.”
In principle, this could explain why quantum events never occur with
certainty, only with a particular probability. “Probabilities are not
fundamental but exist because some of the boundary conditions are undetermined,”
says Hadley. “It’s like not being able to predict the throw of a dice because of
not knowing the initial conditions perfectly.”
The jiggling rope picture also suggests how each one of two particles created
together and separated at birth can continue to “know” what the other is up
to—a phenomenon called “entanglement”. It’s as if someone is jiggling two
ropes with the same hand. However, since the wave shape depends on what is
happening at the other end of the rope, which may be different for each, they do
not have everything in common. “In the same way the properties of such particles
are correlated but not completely correlated—not enough, for instance, to
be exploited to send a useful signal between them.”
Another way of looking at entanglement is that subatomic particles, by virtue
of the time machines they contain, are not constrained by time. “There is
nothing to stop apparently instantaneous interactions between
particles—even if they are at opposite ends of the Universe,” says Hadley.
Name a quantum phenomenon and Hadley can explain it in terms of a time loop. His
picture can reproduce the fundamental “logic” of quantum theory, from which the
entire theory flows. It is a logic that is strikingly different from that of the
ordinary world.
Now you see it . . .
Suppose you take balls out of a box and discover that when you check the
colour of one it is either blue or red and when you check the size it is either
large or small. You can then safely conclude that you have four types of
ball—small blue, small red, large blue and large red. This follows from
what logicians call the distributive law. Ordinary balls can have properties
such as colour and size at the same time.
There is an equivalent quantum experiment. An electron has a property called
spin, and quantum theory says that an electron’s spin is always either “up” or
“down” in any direction. An electron’s spin is either left or right in the
horizontal direction (corresponding to blue or red), and either up or down in
the vertical (corresponding to large or small).
Experiments bear this out. Attach an electron to an atom and send it between
a pair of magnets, and the atom flies off in one of two directions that reflect
the electron’s spin in relation to the orientation of the magnets
(see Diagram).
In quantum theory, however, the distributive law doesn’t hold, and so you
cannot conclude that you have four types of electron. For unlike colour and size
for ordinary objects, you cannot measure an electron’s spins in the horizontal
and vertical directions at the same time. The boundary conditions—set by
the position of the magnets—are incompatible. Hadley claims that what
makes them incompatible, and what spoils the distributive law, is that their
effects leak back into the past to determine how the electrons behave. This is
why the quantum world has a peculiar logic of its own.
Hadley presented his idea in his PhD thesis, which he defended last year. His
examiner was gravity expert Chris Isham of Imperial College in London. “At the
outset, he said he didn’t believe a single word,” says Hadley. “That really put
me at my ease!” The grilling by Isham lasted four and a half hours and, halfway
through, Hadley admits he was “in despair”. Despite everything, however, Isham
passed Hadley. “A less sympathetic examiner could easily have failed him,” says
Hyland.
The response from other physicists since Hadley got his PhD has been muted.
“Hadley offers a spiffy bit of mathematical trickery to reconcile classical
theory with quantum mechanics,” says Jonas Mureika of the University of Southern
California in Los Angeles. “It is a bold and novel solution to a problem which
has for some time plagued the community. We can only speculate on whether it is
.”
“I’ve always been very sceptical, but it’s growing on me,” says Hyland. “It’s
a highly novel idea which at present cannot be proved wrong or .” Isham is
harsher. “Hadley’s idea is certainly interesting, but it is very speculative,”
he says. “Most importantly, Hadley has nothing half-resembling a proper theory
to give any real substance to his ideas.”
Sticking points
The widespread belief that quantum theory is more fundamental than
gravity—contrary to what Hadley claims—stems from the beginning of
the century when the classical theory of electromagnetism encountered grave
difficulties in dealing with atoms. According to classical theory, electrons
orbiting in atoms should radiate away their energy as light and in a split
second spiral into the nucleus. In other words, classical theory says there
shouldn’t be any atoms. The situation could only be rescued with quantum
theory.
Just as classical electromagnetism met its Waterloo in the atom, classical
general relativity comes to grief in black holes and at the big bang. In both
instances, the theory predicts an infinite density of matter. Up until now, says
Hadley, the standard way out has been heavily influenced by the successes of
quantum theory. “Physicists have sought to find a quantum theory of gravity,”
says Hadley. “But this may be the wrong route.”
Ironically, Hadley believes he is more conservative than those trying to
bring gravity into the quantum fold. “They too require a strange and radical new
theory of time but they expect to find it in an entirely new theory,” he says.
“I’m just using standard general relativity.”
If Hadley is right, there is no such thing as a graviton, the hypothetical
particle that mediates the gravitational force. This is because a gravitational
wave, according to general relativity, is a smooth ripple in space-time, and its
distortion is not severe enough to produce a kink. “It is topologically far too
simple to be associated with a time loop, the recipe for a quantum particle,”
says Hadley.
In principle . . .
Hadley is only too aware that those who make extraordinary claims must
provide extraordinary proof. Working part-time at Warwick as an astronomy
demonstrator, he continues to strengthen his case that general relativity can,
in principle, give rise to quantum theory. The “in principle” is very important.
“To be precise, I am not able to offer an explanation for quantum mechanics,”
says Hadley. “What I have done is to show that, in principle, a gravitational
explanation is possible.”
The Achilles heel of Hadley’s idea is that he cannot yet point to a solution
of general relativity that corresponds to a knot in space-time with the
properties of a subatomic particle. “People have told me to forget looking for a
solution because it’s too difficult,” says Hadley.
Setting aside the difficulty of finding a particle-like solution of general
relativity, Hadley has done what no one else has done—suggest an origin
for quantum theory, and an origin in classical physics to boot. One wonders what
Einstein would have thought. “He would have liked some bits of the theory and
hated others,” says Hadley. “For instance, he believed in causality and would
have been horrified at its violation.” And yet, Hadley takes heart from the fact
that Einstein instinctively opposed other predictions of general relativity such
as the expanding Universe and black holes.
However, the discovery that he was right after all about quantum theory not
being fundamental would surely have brought a smile to Einstein’s face. It would
have been a delicious irony to learn that quantum theory, with which he was so
dissatisfied, was merely a consequence of his own theory. “I think he would have
been absolutely delighted,” says Hadley.
