SPACE, it seems, is fair game. For years, physicists discontented with the
paltry three dimensions of space that our senses offer us have been merrily
adding extra ones to their equations. First there were four, then there were
nine. The best bet today appears to be ten dimensions of space, with seven of
them curled up so tightly that we can鈥檛 see them.
Time, on the other hand, has been largely left alone by the theorists. One
time dimension is all you need, they say. Add any more and all hell will break
loose. But in the past couple of years all that has changed. One daring
physicist鈥擟umrun Vafa from Harvard鈥攈as discovered that an extra time
dimension could solve more problems than it creates.
But problems there certainly are. Where is this extra time? Is it just a
mathematical convenience or is it really out there? What will it do to our
notions of past and future, cause and effect? 鈥淲e find ourselves floundering
around when there鈥檚 more than one time,鈥� says theorist Michael Duff of Texas
A&M University. 鈥淚t becomes very confusing.鈥�
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The whole idea that extra dimensions can be useful stems from attempts to
unify the different forces of nature. Back in 1920, mathematicians found that
moving up to five dimensions, instead of the four dimensions of space-time,
helped them to reconcile electromagnetism with gravity. It was like climbing a
hill to look down on a two-dimensional battlefield. Suddenly, they could see how
all the parts of the battle plan fitted together.
In recent years, more dimensions have entered the fray. In 1984 came the
superstring revolution鈥攖he idea that the Universe is made up of
one-dimensional strings vibrating in a background of nine dimensions of space
and one of time. Then in 1995, Edward Witten of the Institute for Advanced Study
at Princeton, New Jersey, and Paul Townsend of the University of Cambridge added
a further space dimension to create M-theory. At a stroke, this last addition
seemed to unify the embarrassing plethora of string theories that physicists had
dreamt up
(鈥淚nto the eleventh dimension鈥�, 快猫短视频, 18 January, p 32).
Yet despite its great promise, M-theory has not ironed out all the
differences between the various string theories, which is where Vafa and his
鈥淔-theory鈥� comes in, upping the ante to 12 dimensions. The remaining problems
began to fall away with an extra dimension, and theorists eagerly welcomed
Vafa鈥檚 equations. But the new dimension was one of time, and the philosophical
implications are rather more troubling.
鈥淢ost theorists would shun the idea of more than one time,鈥� says Duff, who
has himself dabbled with the idea of a 12th time-like dimension. 鈥淚t brings all
sorts of headaches that we would rather do without.鈥� It鈥檚 easy to see why. If
time is one-dimensional, like a straight line, every point on the line is either
before or after every other point. Future and past are well defined. Every set
of events has a unique sequence. But add another dimension and the line becomes
a plane. How do you define future and past now? How do you link events鈥攖he
whole game of physics鈥攚hen the idea of effect following cause has
evaporated?
According to Duff that鈥檚 not the end of it. Time dimensions differ
fundamentally from space dimensions in one important respect: when you insert
time into your equations it tends to come in with a negative rather than a
positive sign. If you start to mess around with extra time dimensions, all sorts
of nasties start to emerge鈥攐bjects that travel faster than light, photons
with negative energy, events where the probabilities of all possible outcomes
don鈥檛 add up to one.
Primitive tools
Admittedly, says Duff, the tools we use to understand the world may be
at fault. Perhaps the existing approaches are too primitive to describe multiple
times. But since these are the only tools around, the best approach seems to be
to treat Vafa鈥檚 extra time dimension as a convenient device rather than a real
physical entity. Exploit the benefits it offers and finesse your way around the
disadvantages.
Indeed, Vafa鈥檚 new time has some suspicious characteristics that could
justify this approach. For instance, while the 11 dimensions of M-theory obey
Einstein鈥檚 relativity principle, which says that the laws of physics should look
the same to all observers, Vafa鈥檚 12 dimensions do not. This is one more reason
for physicists to discount the new dimension鈥檚 physical reality. 鈥淚t鈥檚 by no
means on the same footing as ordinary time,鈥� says Frank Wilczek of the Institute
for Advanced Study. Duff agrees. Though it looks like time in some limited ways,
he says, 鈥渋t鈥檚 not a real, honest-to-goodness extra time dimension.鈥�
Vafa admits that his extra dimension has many of the hallmarks of an abstract
mathematical device rather than a real physical entity. But this may not be the
case for much longer. 鈥淎t this point, it鈥檚 making the formalism look nicer,鈥� he
says. 鈥淲henever that happens in the history of physics, there鈥檚 usually
something behind it.鈥� Take quarks. A few decades ago, quarks were a mathematical
construction鈥攁 way of thinking about the make-up of particles such as
protons. According to the equations, quarks could never exist as single
individuals. They seemed to be theoretical conveniences. Now, says Vafa, most
physicists agree that quarks do exist in the physical world. The same happy fate
could await his mysterious extra time dimension.
But if it鈥檚 really out there, why haven鈥檛 we seen it? One possibility is
that, along with the seven 鈥渕issing鈥� space dimensions, the extra time dimension
is curled up so tightly that it鈥檚 invisible to us. If so, the only way to unwrap
it would be to focus huge amounts of energy into a tiny volume. This would have
remarkable consequences.
鈥淚f the [extra] time dimension could be unleashed, objects would not have the
sensation of moving in time the way that we do,鈥� says Vafa. Think about it. In
space we have choices about how to move, forwards and backwards, up and down,
left and right. For time, our only choice appears to be forward into the
future鈥擧obson鈥檚 choice. But with more than one time dimension, says
Wilczek, it might become possible to manoeuvre sideways in time, or diagonally.
If we saw an undesirable event looming in the 鈥渇uture鈥� we might even be able to
sidestep it.
Perhaps it鈥檚 just as well, then, that the prospects of releasing Vafa鈥檚
hidden dimension are actually rather remote. It is extremely unlikely that an
energy intense enough to activate the missing time exists anywhere in our
Universe鈥攖hough some physicists speculate that it might happen in the
centre of a black hole. But that鈥檚 not the end of the line for real-life
multiple times. After all, according to the latest cosmological theories there
could be plenty of other universes, each of which might have its own unique
combination of space and time dimensions.
What would it be like in a truly multi-time universe? 鈥淚t would really be a
mind-stretcher,鈥� says Wilczek. 鈥淚s it impossible? No I don鈥檛 think so. You can
write down the equations, but I have very little feeling for what the solutions
would be like to live in.鈥�