Can you please explain me the concepts of fourth (or higher!) dimension?
Some theories suggest that, beyond the three spatial dimensions we experience (plus time, which can be regarded and an additional dimension), our Universe has some extra dimensions. These have finite size, so they are curved onto themselves, for instance with the shape of a circle (although, for more than one extra dimensions, more complicated geometries are possible).
This idea was suggested at the beginning of the 20th century, by Kaluza and Klein, in an attempt to unify gravity and electromagnetism. Although the initial proposal did not quite work as expected, the idea of extra dimensions is still with us, and comes up quite naturally in theories like string theory.
Why we do not 'see' them in our everyday life?
The basic reason is that they are too small and we do not have enough energy or precision to detect them, at least with the present experiments. To understand this better, let us give some additional details, to be developed below. To `see' a dimension, one needs to probe it with an object, or a particle which satisfies 1) it can propagate in the extra dimension 2) is small enough to have enough resolution to feel the extra dimension, if the latter is of finite size
How can you detect them?
In some theories, all particles can propagate in the extra dimension (including gravitons, the particles that carry the gravitational force, and all particles we are made of, like electrons and quarks). However, to really detect the extra dimension one needs to probe it with particles with a very high energy. In quantum mechanics, the larger the energy of the particle, the smaller its effective size is. So to detect a small dimension, one needs particles of very high energy. The extra dimensions are actually so small that even our largest particle accelarator have not produced particles of enough energy to see them. However, in some theories the sizes of the extra dimensions are small, but just large enough for particles in the LHC at CERN (which starts running in 2008) to be able to detect them. The detection would occur via processes where `Kaluza-Klein' particles (particles with small enough effective size that can move in the extra dimension) are created.
There are theories that suggest that the matter particles we are made of cannot propagate on the extra dimensions, but are localized and forced to sit a particular location in the extra dimension. If so, we can simply not detect the extra dimensions. Hence, no matter how energetic they are, they cannot detect the extra dimension because in the theory they are not allowed to move into it. In these theories, the size of the extra dimension could be quite large, even of tenths of a milimiter in size. In these theories, the only way to detect the extra dimensions is by using gravitational interactions (since gravitation is related to the geometry of spacetime, and hence gravity particles necessarily can propagate in any dimension, including the extra ones). The simplest way to test the
existence of these dimension is by Cavendish experiments, where one measures the form of Newton's law for gravitational attraction of two massive objects at very short distances (milimiter or below) in a laboratory . The basic idea is that once the distance between the two massive objects is similar to the size of the extra dimension, there would be deviations in the 1/r2 gravitational attraction, because the gravitational field would start feeling the presence of the extra dimensions on which it can propagate. These theories also have interesting implications for accelerator experiments. In these theories, the strength of gravity in the 5-dimensional (or higher-dimensional) description is much more intense than in four dimensions, hence predict the possibility of having creation of black holes in collisions in the LHC. These events would be spectacular, with the black hole decaying almost immediatly into a shower of many particles, and would allow to test properties of quantum gravity in accelerators. In any of these two possible scenarios, the detection of the existence of extra dimensions would an unprecedented discovery, and an astonishing insight into the nature of the Universe!
What is M-theory?
M-theory is a conjecture theory that is defined in 11 dimensions and in different limits reduces to different string theories.
For further reading: http://superstringtheory.com/basics/basic7.html