The mother of all theories

Einstein’s geometric theory of gravity (general relativity) and
quantum mechanics have been the two greatest achievements of twentieth century physics, towering above everything else that
we have learnt about our physical world and beyond, both before
and since. Between them, they have cornered the market as far as
describing the most fundamental aspects of reality itself goes. The
problem, as I mentioned in the last chapter, is that they are just not
compatible with each other. They rely on very different types of
mathematics and have completely separate rules and underlying
principles. General relativity breaks down at singularities and
closed time loops, while quantum mechanics fails to describe the
force of gravity within its framework. So how close are we to
a theory of quantum gravity; a ‘theory of everything’ that will
contain within its mathematical structure the rules and principles
of both relativity and quantum mechanics? Well, as we see out
the twentieth century and begin the twenty first, it may be that we
already have such a theory in our grasp.
Einstein completed his general theory of relativity in 1915,
and then played a relatively (no pun intended) minor role in the
subsequent development of the quantum theory which occupied
most of the other leading physicists in the world over the next
ten years. But once the ideas and underlying mathematics had
been sorted out what else was there to do? Someone of Einstein’s
genius would not have been content with dotting the ‘i’s and
crossing the ‘t’s. So for the last thirty years of his life he
searched, unsuccessfully, for what is called a unified field theory;
a theory that would combine general relativity not with quantum
mechanics but with the theory of light (or electromagnetism, to be
more precise). Einstein tried a number of approaches but never
quite cracked it. It is said that papers with his unfinished theory
were found on his desk after he died.
The most mathematically elegant, but at the same time most
puzzling, of the candidates for a unified theory that Einstein
worked on was due to two mathematicians: a Pole, Theodor
Kaluza, and a Swede, Oskar Klein. Kaluza did all the ground work
and, in 1919, sent a paper to Einstein in which he proposed a way
of explaining electromagnetic radiation within the framework of
general relativity.
Kaluza showed that what was needed to achieve this was to
write his equations not in 4D but 5D spacetime by including an extra space dimension. Although this sounds arbitrary and far
removed from what we might consider as reality, it is relatively
easy to do mathematically, wherewe can add as many dimensions
as we like. But was this fourth dimension of space that Kaluza was
proposing real? We are certainly not aware of it if it is out there. But
when he included this extra dimension Kaluza found that light,
instead of being an oscillating electromagnetic field through 3D
space, was in fact a vibration of this fifth dimension. So there you
go. But don’t worry, I don’t really understand what this means
either. All we can say is that it tries to explain the origin of light at a
more fundamental, geometrical level in the same way that Einstein
had described gravity as a curvature of 4D spacetime. Not only
that, but this fifth dimension does not extend in a straight line like
the other three dimensions of space but is ‘curled up’ on itself. A
simple way to visualize what this means is to think of 2Dworld.
Imagine flat 2D space curled round to make a cylinder. One of
the dimensions—the one that points along its length—remains
unaltered, whereas the other one has looped around into a circle.
The problem of course was that, despite the elegance of
the mathematics of Kaluza’s theory, there was not a scrap
of experimental evidence whatsoever to suggest that this fifth
dimension really existed. Even Einstein, while impressed with
the way Kaluza had unified light and gravity, was unwilling to
believe in the reality of a fifth dimension. After all, he had been
rather reluctant to even take on board the idea of four-dimensional
spacetime to begin with. At least the four dimensions (one of time
and three of space) were real. The main reason for Einstein’s and
others’ scepticism was because we never see this extra dimension.
This question was answered in 1926 when Oskar Klein suggested
that the reason it could not be detected was because it was curled
up into a circle so tiny that it was billions of times smaller even
than an atom. Think again of one of the dimensions of 2Dworld
curled round to form the surface of a cylinder. Klein said that the
cylinder would be so thin that it would look like a line. That is,
2Dworld would look one-dimensional and we would say that the
second dimension was hidden. I am afraid I cannot give you a
higher dimensional example than this because, as we saw back in You aint seen nuthin’ yet! Read on.
After many decades in the wilderness, Kaluza–Klein theory
made a comeback in the late 1970s. By then the unified theory that
the most ambitious theoretical physicists were searching for had
to be all singing and all dancing. It was not enough for it to unify
gravity and light. By that time it had been established beyond
doubt that all phenomena in nature could, at the most fundamental
level, be described by four forces. The force of gravity was one
and the electromagnetic force another. This latter is the attractive
force between electric charges which holds all atoms together
by keeping the negatively charged electrons in the grip of the
positively charged atomic nucleus. It is also the force of attraction
exerted by magnets on each other and on certain metals. I should
point out that, despite electric and magnetic forces appearing to
be quite separate, this is really only superficial. Michael Faraday
had shown in the nineteenth century that they were intimately
connected and had their origin in the same electromagnetic force.
Almost all phenomena we see around us are due ultimately to
one of these two forces: gravity and electromagnetism. We now
know there are, in addition to these, two other forces that act only
within the tiny confines of the atomic nucleus, but which are just as
important as the first two as far as the fundamental laws of nature
are concerned.
So the ultimate theory being searched for in the late ’70s
was one that not only unified gravity with electromagnetism,
as Kaluza–Klein theory did, but which also encompassed the
two nuclear forces. Such a theory would be called a ‘theory of
everything’, since it would show how all four forces of nature are
aspects of just one ‘superforce’. The reason Kaluza–Klein theory
came back into fashion was because of its clever way of being able
to unify forces when higher dimensions of space were included
in the equations. Of course with four forces to deal with, instead
of just two, more than one extra dimension would be required.
Finally, by the mid-1980s a candidate theory was discovered. It was dubbed superstring theory and quickly developed into the
most sophisticated, elegant, complicated, powerful and obscure
theory ever devised. After all, it was a theory of ten dimensions.
If correct, it stated that we lived in a ten-dimensional universe.
But now all six extra spatial dimensions would be curled up into a
tiny high dimensional sphere that we could never detect, leaving
just the four dimensions of spacetime. Superstring theory was so
named because it suggested that everything is ultimately made
of tiny strings which vibrate in ten dimensions. This may sound
crazy but it does achieve the unification of general relativity with
quantum mechanics which is, after all, the holy grail of physics.
So if superstring theory is the ultimate theory of quantum
gravity physicists have been looking for, is the hunt up? And,
more importantly for you dear reader, do its equations contain the
answer to whether time travel is allowed or not? I am afraid it
is still too early to tell yet. Many physicists describe superstrings
as a theory of the twenty first century which has been discovered
too early: beforewe have had the chance to develop mathematical
tools of the required sophistication. It seems that it is just too
hard for anyone to fully comprehend. Its mathematics are beyond
the current ability of most, if not all, mathematicians. Not only
that, but by the early 1990s there were five different versions of
superstring theory and no one knew which was the correct version,
or indeed whether there was a unique version.
Then in 1995, a scientist who has been dubbed ‘the smartest
person on Earth’ found an answer, maybe THE answer. His name
is EdwardWitten and he works at the Institute forAdvanced Study
in Princeton,NewJersey (whichwaswhere Einstein spent his latter
years). Together with a colleague, Paul Townsend of Cambridge
University, Witten believes he has discovered why there are so
many versions of superstring theory. The price that has to be
paid is relatively cheap under the circumstances. Witten asks for
just one more dimension! With eleven dimensions instead of ten
many of the problems of superstring theory go away. Now the
tiny strings are replaced by sheets known as membranes and the
new theory of Witten and Townsend is called membrane theory,
or M-theory for short. However, the ‘M’ is often taken to stand for ‘Magic’, ‘Mystery’ or even ‘Mother’, since this really would be the
mother-of-all-theories.
But could we just keep on going? What if other versions of
M-theory were discovered? Maybe adding a twelfth dimension
would cure things. In fact, why not just chuck in another handful
of dimensions just to be on the safe side! It turns out that this
is not possible. There is something mathematically very special
about the ten dimensions of superstring theory and the eleven
dimensions of M-theory.
Physicists are already making strides in understanding the
meaning of M-theory, although I expect it to take several decades
before all its magic and mystery is unravelled. One of the main
questions to be answered of course is why and how all the extra
dimensions get curled round and squeezed down leaving just the
four dimensions we see. Current thinking is that this would have
happened at the moment of the Big Bang. This implies that there
was something before the Big Bang. Maybe our three dimensions of
space and one of time were part of a much grander ten- or elevendimensional
universe in which all the forces of nature were unified
into one. The Big Bang then caused six or seven dimensions of
space to be crushed down to a size that we would never be able to
access.