# M-theory

**M-theory**is a new idea in small-particle physics that is part of . The idea, or theory, is the source of debate among scientists, becuse there is no way to test it to see if it is true. If ever proven true, M-theory and string theory would mean big progress for science.

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## String theory

To understand M-theory it is necessary to first get some understanding of string theory. For hundreds of years physics has operated on the paradigm that the fundamental particles, like the familiar electron, are point-like or (in mathematical jargon) 0-dimensional. If string theory was to be summed up in a single idea, it is that this assumption physicists have made is incorrect. Instead, string theory posits that the Universe is fundamentally composed of**1-dimensional objects**- things that are similar to a string. These strings would be so small that on even the tiny scale of particles they would seem like points. In string theory, each fundamental particle is created in some sense by different patterns of

*vibration*of the strings. One might ask why physicists have constrained themselves to 0-dimensional points for all this time; the answer is that 1-dimensional objects are much harder to work with and often cause technical problems with causality and violations of special relativity's mandate that information not travel faster than the speed of light.

String theory's development has come primarily because of an extremely important problem that has faced physics for almost 100 years. The problem is that **general relativity**, the theory developed by Albert Einstein that explains things on very large or cosmological scales, is irreconcilable with **Quantum Mechanics** and the Standard Model, which describe the Universe on the small subatomic scale. Additionally, there are problems with the Standard Model: it has around *20 free parameters* that must be plugged in by hand, and has a *large number of particles* it declares fundamental (there are three copies of every particle organized in what are termed as "families" whose only difference from one another is mass). Also, because it can't be reconciled with General Relativity, it lacks a description of gravity, the most familiar of the four fundamental forces.

It turns out that using 1-dimensional objects instead of point particles solves many of these problems. The number of free parameters in the theory drops from 20 to *one* (a parameter that corresponds to the size of the strings), and there is hope that details of the theory will explain *why the three families* of particles exist. Most importantly, string theorists were delighted to find that string theory necessarily contains gravitons, the particle that causes gravity. This has led Edward Witten, the founder of M-theory, to joke that string theory does have the remarkable experimental evidence that gravity exists all around us. Thus, string theory **successfully unites** General Relativity with Quantum Mechanics.

However, there are some problems with string theory. First of all, it requires 10 dimensions for the strings to vibrate in as supposed to the 4 (3 space and 1 time) dimensions that we commonly observe. This may seem ludicrous; it is, however, possible if the extra 6 dimensions are extremely tiny and curled up. For example, if you look at a tube from a great distance it seems to be just a line (1-dimensional). Closer inspection of the tube reveals 2-dimensions, though: one that is along the tube (the one we saw from far away) and one that is going around the tube. Thus, the tube is really a 2-dimensional *surface* despite the fact that it appears to be a line from far away.

Another problem with string theory is that there are **5 different formulations of it**. This is a key to understanding where M-theory comes in. The 5 theories differ in what kind of strings they allow and in how they implement supersymmetry, a technical part of string theory that leads to the often-used name *super*string theory. These 5 different theories (esoterically called Type I, Type IIA, Type IIB, SO(32), and E_{8}×E_{8}) are something of an embarrassment of riches for string theorists. Because string theory claims to be a theory of everything, there should really only be one consistent formulation of the theory, but instead there are 5. Here is where M-theory steps in to the rescue.

## M-theory

In 1995, Edward Witten initiated what has been called the *Second Superstring Revolution* by introducing M-theory to the world. This theory combines the 5 different string theories (along with a previously abandoned attempt to unify General Relativity and Quantum Mechanics called 11D-Supergravity) into one theory. This is accomplished by knitting together a web of relationships between each of the theories called dualities (specifically, S-duality, T-duality, and U-duality). Each of these dualities provides a way of converting one of the string theories into another.

T-duality is probably the most easily explained of the dualities. It has to do with the size, denoted by R, of the curled up dimensions of the string theories. It was discovered that if you take a Type IIA string theory that has a size R and change the radius to 1/R then you will end up getting what is equivalent to a Type IIB theory of size R. This duality, along with the others, creates connections between all 5 (or 6, if you count supergravity) theories.

The fact that these dualities existed had been known before Witten had come up with the idea of M-theory. What Witten actually did was to predict that the fact that all these different theories were connected was a result of there being **some underlying theory to which they were all approximations** of. Additionally, it was found that the equations that required string theory to exist in 10 dimensions were actually approximations as well. The proposed M-theory would instead be a theory that took place in *11 dimensions*. This theory is somewhat nebulous in nature and has not been pinned down. Additional amusement has come for many in guessing what the M might stand for (possibilities include Matrix theory, Muffin theory, Mystery theory, and Mother theory). Regardless of what the M might possibly mean, M-theory has become one of the most interesting and active areas of research in theoretical physics today.

*For a more technical explanation, see .*

## Books and links

- Brian Greene has written a superb book explaining string theory and M-theory for the layman called
**The Elegant Universe** - The Official String Theory Website has excellent references on string theory for the layman and expert