Introduction to M-theory
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In non-technical terms, M-theory presents an idea about the basic substance of the universe. So far no experimental evidence exists showing that M-theory is a description of the real world. Interest in this theory is mainly driven by mathematical elegance.
In the early years of the 20th century the atom – long believed to be the smallest building-block of matter – was proven to consist of even smaller components called protons, neutrons and electrons, which are known as subatomic particles. Starting in the 1960s, other subatomic particles began being discovered. In the 1970s, it was discovered that protons and neutrons (and other hadrons) are themselves made up of smaller particles called quarks. The Standard Model is the set of rules that describes the interactions of these particles.
In the 1980s, a new mathematical model of theoretical physics, called string theory, emerged. It showed how all the particles and all of the forms of energy in the universe could be constructed by hypothetical one-dimensional "strings", infinitesimal building-blocks that have only the dimension of length, but not height or width.
However, to make string theory mathematically consistent, the universe the strings exist in must have ten dimensions. This contradicts the experience that our real universe has four dimensions: three space dimensions (height, width, and length) and one time dimension. To "save" their theory, string theorists therefore added the explanation that the additional six dimensions exist but cannot be detected directly; this was explained by sophisticated mathematical objects called Calabi–Yau manifolds. The number of dimensions was later increased to 11 based on various interpretations of the 10-dimensional theory that led to five partial theories, as described below. Supergravity theory also played a significant part in establishing the necessity of the 11th dimension.
These "strings" vibrate in multiple dimensions, and depending on how they vibrate, they might be seen in three-dimensional space as matter, light or gravity. It is the vibration of the string which determines whether it appears to be matter or energy, and every form of matter or energy is the result of the vibration of strings.
String theory, as mentioned above, ran into a problem: another version of the equations was discovered, then another, and then another. Eventually, five major string theories were developed. The main differences between the theories were principally the number of dimensions in which the strings developed, and their characteristics (some were open loops, some were closed loops, etc.). Furthermore, all these theories appeared to be workable. Scientists were not comfortable with five seemingly contradictory sets of equations to describe the same thing.
Speaking at the string theory conference at University of Southern California in 1995, Edward Witten of the Institute for Advanced Study suggested that the five different versions of string theory might be describing the same thing seen from different perspectives. He proposed a unifying theory called "M-theory", in which the "M" is not specifically defined but is generally understood to stand for "membrane". The words "matrix", "master", "mother", "monster", "mystery" and "magic" have also been claimed. M-theory brought all of the string theories together. It did this by asserting that strings are really one-dimensional slices of a two-dimensional membrane vibrating in 11-dimensional spacetime. Vibrations of higher-dimensional objects (as in three-dimensional vibrating blob or sphere or even more possible dimensions) are certainly a part of M-theory  but the basic theory of branes is still in progress. Higher-dimensional objects are much harder to mathematically calculate than a point in classical physics or a one-dimension string in string theory or two-dimensional membranes in M-theory.
M-theory is not complete, but the underlying structure of the mathematics has been established and is in agreement with all the string theories. Furthermore, it has passed many tests of internal mathematical consistency.
However, so far no experimental support of the M-theory exists. Some physicists are skeptical that this approach will ever lead to a physical theory describing our real world due to fundamental issues.
Nevertheless, some cosmologists are drawn to M-theory because of its mathematical elegance and relative simplicity, triggering the hope that the simplicity is a reason why it may describe our world. Physicist and author Michio Kaku has remarked that M-theory may present us with a "Theory of Everything" which is so concise that its underlying formula would fit on a T-shirt. Stephen Hawking originally believed that M-theory may be the ultimate theory but later suggested that the search for understanding of mathematics and physics will never be complete. However, Hawking later changed his mind and stated, "M-theory is the only candidate for a complete theory of the universe." Hawking and Leonard Mlodinow, in the popular-science book The Grand Design, take a philosophical position to support a view of the universe as a multiverse, and define it in the book as model-dependent realism which along with a sum-over-histories approach (see path integral formulation of quantum mechanics) to the universe as a whole, is used to claim that M-theory is the only candidate for a complete theory of the universe, mainly due to lack of viable alternatives.
- University of Southern California, Los Angeles, Future Perspectives in String Theory, March 13-18, 1995, E. Witten: Some problems of strong and weak coupling
- Lee Smolin, April 2007:Response to review of The Trouble with Physics by Joe Polchinski.
- Kaku, M. "M-Theory: The Mother of all SuperStrings". Retrieved 2013-08-06.
- Hawking, S. (3 October 2003). "Gödel and the end of physics". Retrieved 2013-08-06.
- Hawking, Stephen (2010). The Grand Design. Bantam Books. ISBN 055338466X.
- Greene, B. (1999). The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. W.W. Norton. ISBN 0-375-70811-1.
- Greene, B. (2004). The Fabric of the Cosmos: Space, Time, and the Texture of Reality. Alfred A. Knopf. ISBN 0-375-41288-3.
- Miemic, A.; Schnakenburg, I. (2006). "Basics of M-theory". Fortschritte der Physik. 54 (1): 5–72. arXiv: . Bibcode:2006ForPh..54....5M. doi:10.1002/prop.200510256.
- Musser, G. (2008). The Complete Idiot's Guide to String Theory. Alpha Books. ISBN 978-1-59257-702-6.
- Smolin, L. (2006). The Trouble with Physics. Houghton Mifflin. ISBN 978-0-618-55105-7.
- Woit, P. (2006). Not Even Wrong: The Failure of String Theory and the Continuing Challenge to Unify the Laws of Physics. Basic Books. ISBN 0-465-09275-6.
- The Elegant Universe - A Three-Hour miniseries with Brian Greene by NOVA (original PBS Broadcast Dates: October 28, 8-10 p.m. and November 4, 8-9 p.m., 2003). Various images, texts, videos and animations explaining string theory and M-theory.
- Superstringtheory.com - The "Official String Theory Web Site", created by Patricia Schwarz. Excellent references on string theory and M-theory for the layperson and expert.