Supersymmetry, String Theory, M-Theory

The plague of infinities is similar to the problem that occurs in the theories of the strong, weak, and electromagnetic forces, except in those cases renormalization removes the infinities.

The closed loops in the Feynman diagrams for gravity produce infinities that cannot be absorbed by renormalization because in general relativity there are not enough renormalizable parameters (such as the values of mass and charge) to remove all the quantum infinities from the theory.

This leaves a theory of gravity that predicts that certain quantities, such as the curvature of space-time, are infinite. This is no way to run a habitable universe.

That means the only possibility of obtaining a sensible theory would be for all the infinities to somehow cancel, without resorting to renormalization.

In 1976, a possible solution was found as supergravity. The “super” refers to a kind of symmetry the theory possesses, called supersymmetry.

Supersymmetry

In physics, a system has a symmetry if its properties are unaffected by a certain transformation such as:

• rotating it in space or
• taking its mirror image.

For example, if you flip a plain donut, it looks exactly the same.

Supersymmetry is a more subtle kind of symmetry that cannot be associated with a transformation of ordinary space.

It implies that force particles and matter particles, and hence force and matter, are really just two facets of the same thing:

• each matter particle, such as a quark, should have a partner force particle.
• each force particle, such as the photon, should have a partner matter particle.

This can solve the problem of infinities:

• The infinities from closed loops of force particles are positive
• The infinities from closed loops of matter particles are negative

In this way, the infinities in the theory arising from the force particles and their partner matter particles tend to cancel out.

Unfortunately, the calculations required to find out whether there would be any infinities left uncanceled in supergravity:

• were so long and difficult
• had such potential for error

This is why no one did them.

Nonetheless, most physicists believed that supergravity was probably the right answer to the problem of unifying gravity with the other forces.

You might think that validating supersymmetry would be easy–just examine the properties of the existing particles and see if they pair up.

But no such partner particles have been observed.

But physicists have performed various calculations. These show that the partner particles of those existing particles should be 1,000 times as massive as a proton, if not even heavier.

That is too heavy for such particles to have been seen in any experiments to date. But there is hope that such particles will eventually be created in the Large Hadron Collider in Geneva.

The idea of supersymmetry was the key to the creation of supergravity.

String Theory

But the concept had actually originated years earlier with theorists studying a fledgling theory called string theory.

According to string theory, particles are not points, but patterns of vibration that have length but no height or width, like infinitely thin pieces of string.

String theories also lead to infinities, but it is believed that in the right version they will all cancel out.

They have another unusual feature: They are consistent only if space-time has 10 dimensions, instead of the usual 4.

We do not notice these extra dimensions because they are curved up into a very small space.

Imagine a 2D plane, as a straw.

Another 2D space is the surface of a straw. To locate a point on that space, you need to know:

• where along the straw’s length the point is
• where along its circular dimension.

But if the straw is very thin, you would get a very good approximate position employing only the coordinate that runs along the straw’s length, so you might ignore the circular dimension.

If the straw were a million-million-million-million-millionth of an inch in diameter, you wouldn’t notice the circular dimension at all.

That is the picture string theorists have of the extra dimensions—they are highly curled, on a scale so small that we don’t see them.

In string theory, the extra dimensions are curled up into the “internal space”, as opposed to our usual 3D space.

These internal states are not just hidden dimensions swept under the rug—they have important physical significance.

In addition to the question of dimensions, string theory suffered from another awkward issue: There appeared to be at least 5 different theories and millions of ways the extra dimensions could be curled up.

It was an embarrassment of possibilities for a theory of everything.

Then, around 1994, people started to discover dualities—that different string theories, and different ways of curling up the extra dimensions, are simply different ways of describing the same phenomena in 4 dimensions.

Moreover, they found that supergravity is also related to the other theories in this way.

String theorists are now convinced that the 5 different string theories and supergravity are just different approximations to a more fundamental theory, each valid in different situations.

M-Theory

That more fundamental theory is called M-theory.

People are still trying to decipher the nature of M-theory, but that may not be possible. It could be that the physicist’s traditional expectation of a single theory of nature is untenable, and there exists no single formulation.

It might be that to describe the universe, we have to employ different theories in different situations.

Each theory may have its own version of reality, but according to modeldependent realism, that is acceptable so long as the theories agree in their predictions whenever they overlap, that is, whenever they can both be applied.

Whether M-theory exists as a single formulation or only as a network, we do know some of its properties.

First, M-theory has eleven spacetime dimensions, not ten. String theorists had long suspected that the prediction of ten dimensions might have to be adjusted, and recent work showed that one dimension had indeed been overlooked.

Also, M-theory can contain:

• vibrating strings
• point particles
• two-dimensional membranes
• three-dimensional blobs
• other objects that are more difficult to picture and occupy even more dimensions of space, up to nine.
  • These objects are called p-branes (where p runs from zero to nine).

What about the enormous number of ways to curl up the tiny dimensions?

In M-theory, those extra space dimensions cannot be curled up in just any way. The mathematics of the theory restricts the manner in which the dimensions of the internal space can be curled.

The exact shape of the internal space determines both the values of physical constants, such as the charge of the electron, and the nature of the interactions between elementary particles.

In other words, it determines the apparent laws of nature.

We say “apparent” because we mean the laws that we observe in our universe—the laws of the four forces, and the parameters such as mass and charge that characterize the elementary particles.

But the more fundamental laws are those of M-theory.

The laws of M-theory therefore allow for different universes with different apparent laws, depending on how the internal space is curled.

M-theory has solutions that allow for many different internal spaces, perhaps as many as 10,500, which means it allows for 10500 different universes, each with its own laws.

To get an idea how many that is, think about this: If some being could analyze the laws predicted for each of those universes in just one millisecond and had started working on it at the big bang, at present that being would have studied just 1020 of them.

And that’s without coffee breaks.

Centuries ago Newton showed that mathematical equations could provide a startlingly accurate description of the way objects interact, both on earth and in the heavens.

Scientists were led to believe that the future of the entire universe could be laid out if only we knew the proper theory and had enough computing power.

Then came quantum uncertainty, curved space, quarks, strings, and extra dimensions, and the net result of their labor is 10500 universes, each with different laws, only one of which corresponds to the universe as we know it.

The original hope of physicists to produce a single theory explaining the apparent laws of our universe as the unique possible consequence of a few simple assumptions may have to be abandoned. Where does that leave us? If M-theory allows for 10500 sets of apparent laws, how did we end up in this universe, with the laws that are apparent to us?

And what about those other possible worlds?