Farewell to Reality (32 page)

The M-theory conjecture and the second superstring revolution

As theories proliferated and superstring theory lost any sense of uniqueness, interest began to wane. British superstring theorist Michael Duff explained it like this:

Theorists love
uniqueness;
they like to think that the ultimate
Theory of Everything
will one day be singled out, not merely because all rival theories are in disagreement with experiment, but because they are mathematically inconsistent. In other words, that the universe is the way it is because it is the only possible universe.
⁹

There were also rumblings from some theorists that, based on calculations using supergravity, the right number of spacetime dimensions is actually eleven, not ten. It all seemed to be getting rather out of hand. Then, at a superstring theory conference at the University of Southern California in March 1995, Witten made a bold conjecture. Perhaps the five different ten-dimensional superstring theories are actually instances or approximations of a single, overarching eleven-dimensional structure. He called it M-theory. He was not specific on the meaning or significance of ‘M'.

This was a conjecture, not a theory. Witten demonstrated the equivalence of a ten-dimensional superstring theory and eleven-dimensional supergravity but he could not formulate M-theory; he could only speculate that it must exist.

This is a simple fact that many readers of popular presentations of superstring theory somehow tend to miss.
M-theory is not a theory.
Nobody knows what M-theory looks like, although many theorists have tinkered with structures that they believe it could or should possess. So, on top of a foundation built from a sequence of assumptions, we now erect the biggest assumption of all. We assume that a unique eleven-dimensional superstring theory is possible in principle, although we don't yet know what this theory is.

I think this is a truly remarkable state of affairs. Of course, this kind of speculative theorizing goes on all the time in physics, and there are plenty of examples from history. We might look again at the sequence of assumptions that have led us here and conclude that theorists who commit themselves to M-theory are either brave or foolhardy or both. We might express some concern for their future career development, but we might be ready and willing to acknowledge that the very idea of academic freedom means that there will always be some few committed to what seem to us to be mad or trivial pursuits.

But M-theory is not the preserve of a few theorists who have become addicted to its beauty and the tightness of its structure, as Danish historian Helge Kragh explains:

With M-theory and what followed, new recruits were attracted to the field. It is estimated that the string community amounts to some 1,500 scientists worldwide, a remarkably large number given the abstract and purely theoretical nature of string physics. Incidentally, this means that there are as many string theorists today as the total number of academic physicists in the world about 1900, all countries and fields of physics included.
¹⁰

Given that we can trace the first superstring revolution back nearly thirty years and the second revolution began seventeen years ago, we might well ask what all these theorists have been up to during this time.

One of the big revelations of Witten's M-theory conjecture concerns so-called
dualities
that prevail between different versions of superstring theory. For example, S-duality, or strong-weak duality, allows states with a coupling constant of a certain magnitude in one type of theory to be mapped to states with a coupling given by the reciprocal of this constant in its dual theory. This means that strong couplings which reflect the influence of strong forces in one theory would be weak couplings in the dual theory. So, the perturbation theory techniques used so successfully in QED, normally applicable only for systems of low energy and weak coupling, could now be applied to the dual theory to deal with problems involving high-energy, strong-coupling regimes.

A lot of previously intractable calculations suddenly became tractable.

Branes and braneworlds

There was a lot more, however. Introducing the extra dimension in M-theory opened up an extraordinarily rich structure of mathematical objects. Superstring theory was no longer limited to one-dimensional strings. It could now accommodate higher-dimensional objects, called
membranes,
or ‘branes', which quickly took over from strings as the primary focus of investigation, leading Duff to refer to it as ‘the theory formerly known as strings'.
¹¹

Branes may have up to nine dimensions. A string is a ‘one-brane'. Two-dimensional membranes (sheets) are referred to as two-branes. Three-branes are actually three-dimensional spaces. Generically, these objects are referred to as
p
-branes, where
p
refers to the number of dimensions.

Branes lie at the heart of superstring theory's dualities. For example, particles in one version of the theory become branes in the dual theory. This kind of interrelationship lends credibility to the assumption that these are more than just mathematical curiosities — that branes reflect or represent physically real properties and behaviours of our universe. This is a perfectly logical inference, but we should be clear once again that there is no single piece of experimental or observational evidence to suggest that the fundamental elements of reality are multidimensional membranes.

Branes are the principal objects of a theory which is conjectured to exist but which has yet to be written down. Exploring the mathematical relationships between and involving branes in various forms and connecting these with physically meaningful properties and behaviours requires another big assumption.

A subcategory of
p
-branes, called ‘D-branes', are particularly interesting because they represent locations in space where open strings can end.
^*
Such objects not only represent different ways in which the various spatial dimensions can be occupied; they also possess shape and particlelike properties such as charge. Branes are dynamic objects; they move around and interact and are susceptible to forces.

In fact, Witten and Czech theorist Petr Ho
ř
ava constructed a model universe from two parallel ten-dimensional D-branes separated in the direction of the eleventh dimension. The space between branes is referred
to as the ‘bulk'. They demonstrated that this structure is equivalent to a strong-coupling version of the original heterotic E
₈
× E
₈
superstring theory first devised by the Princeton String Quartet.

The fascination with such ‘braneworlds' derives from the fact that models can be created in which all material particles, which are composed of open strings, are permanently fastened to one or other of the D-branes, the spaces where the open strings end. Models can be set up so that these particles cannot detach from the brane and so cannot explore other spatial dimensions that exist ‘at right angles' to the dimensions of the D-brane. In other words, the particles cannot travel ‘at right angles to reality'.

A ten-dimensional D-brane can be thought to consist of three ‘conventional' spatial dimensions which extend off to infinity, six dimensions curled up and tucked away in a Calabi—Yau space, and time. The model demands that, once fixed to the D-brane, all the material particles of the standard model are then constrained to move in the three-dimensional space that we ourselves experience.

But particles formed from closed strings, such as the graviton, are not so constrained. The gravitational force can therefore in principle explore
all
the spatial dimensions of the theory, including the eleventh dimension of the bulk. And because the standard model particles of familiar experience are stuck to one of the D-branes, there is no restriction in principle on the size of the eleventh dimension. It could be small, wrapped up into a tiny cylinder. Or it could be large.

This was something of a revelation. It offers the possibility of using the difference between material particles and the standard model force-carriers (open strings) and the graviton (closed strings) to explain why gravity is so very different from the electromagnetic, weak and strong nuclear forces. The latter act on particles fixed to a D-brane. Gravity is free to roam.

Could this be an answer to the hierarchy problem? It didn't take superstring theorists too long to come up with some proposals. In 1998, theorists Nima Arkani-Hamed, Savas Dimopoulos and Gita Dvali (collectively referred to as ADD) devised a braneworld model in which the great gulf between the electro-weak mass-energy scale and the Planck mass-energy scale could be explained by the
dilution
of the force of gravity compared to other standard model forces.

The ADD model uses a single D-brane on which all the standard model particles can be found, and introduces hidden dimensions which
are considerably larger than had been considered permissible in superstring theories to this point. Just a couple of large extra dimensions are needed to dilute the force of gravity sufficiently. Physicists (who are made of standard model particles) will therefore only ever measure gravity as it is manifested on the D-brane and will conclude that it is much weaker than the other forces of nature.

How large is ‘large'? Well, contemporary experiments have verified Newton's classical inverse-square law of gravity down to millimetre dimensions. We would expect the effects of large hidden dimensions to show up as deviations from this law. This means that the hidden dimensions could be of the order of tenths of a millimetre, and we wouldn't know.

Now that's much, much larger than the Planck length.

A further braneworld model devised by American theorist Lisa Randall and Indian-born American Raman Sundrum uses two parallel D-branes, as in the original Ho
ř
ava-Witten braneworld, but dilutes the effects of gravity not by using large hidden dimensions but by constructing a model in which the spacetime of the bulk is strongly warped by the energy it contains. On one brane, gravity is strong — as strong as the other standard model forces. But the warped spacetime between the branes dilutes gravity such that when it reaches the second brane, the force is considerably weaker. This second brane is where we are to be found, measuring a force of gravity that is now much weaker than the other forces, causing us to scratch our heads as we wonder how this can be.

I suspect that your reaction to braneworld scenarios such as these is really a matter of taste. Perhaps you're amazed by the possibility that there might be much more to our universe than meets the eye; that there might exist dimensions ‘at right angles to reality' that we can't perceive but whose influence is manifested in the behaviour of those particles that we can observe. The revelation that there might be multidimensional branes, bulk and hidden dimensions — large, small or warped — might prompt more than one ‘Oh wow!' moment.

But it doesn't do it for me, I'm afraid. I really can't read this stuff without thinking that I've accidentally picked up a Discworld novel, by the English author Terry Pratchett. Discworld is a fictional place not unlike earth, except that it is a flat disc, balanced on the backs of four elephants who in turn stand on the back of Great A'Tuin, a giant turtle
which swims slowly through space. Magic is not unusual on Discworld, which has its own unique system of physics. I would speculate that people will be talking about Pratchett's Discworld long after the various braneworlds of M-theory have been quietly forgotten.

My problem is that branes and braneworld physics appear to be informed not by the practical necessities of empirical reality, but by imagination constrained only by the internal rules of an esoteric mathematics and an often rather vague connection with problems that theoretical physics beyond the standard model is supposed to be addressing. No amount of window-dressing can hide the simple fact that this is all
metaphysics,
not physics.

In his book
Facts and Mysteries in Elementary Particle Physics,
published in 2003, Martinus Veltman did not even wish to acknowledge supersymmetry and superstrings:

The fact is that this is a book about physics, and this implies that the theoretical ideas discussed must be supported by experimental facts. Neither supersymmetry nor string theory satisfy this criterion. They are figments of the theoretical mind. To quote Pauli: they are not even wrong. They have no place here.
¹²

Sheldon Glashow has wondered if superstring theory might be a more appropriate subject for mathematics departments, or even schools of divinity. ‘How many angels can dance on the head of a pin?' he asked. ‘How many dimensions are there in a compactified manifold, 30 powers often smaller than a pinhead?'
¹³

The reality check

Am I being too harsh? After all, I made a big fuss in the opening chapter about the metaphysical nature of reality and the fact that we must be content with an empirical reality of things-as-they-appear or things-as-they-are-measured. Surely this means that any attempt to build a structure which goes beyond appearances and measurement is going to be metaphysical? And didn't I say that facts are in any case contaminated by theoretical concepts and that any path to a theory — no matter how speculative — is acceptable provided it yields a theory that works?

Yes, this is what I said. But if we accept the six Principles described in Chapter 1, then we must acknowledge that the determination of what is or what is not true in relation to a theory must be judged on the basis of the theory's empirical tests.