I was reading an article in this months issue of Physics World magazine on the three main theories of extra dimensions and stumbled across something I didn't quite understand when the author began talking about detecting particles in extra dimensions at a particle lab, such as the LHC in Geneva, Switzerland.
The energy of a particle in 3-dimensional space consists of its rest energy, $E=mc^2$, and the kinetic energy of its motion. If extra dimensions do exist, then the particle will have extra space to move in, so will obtain an additional, independent contribution to its kinetic energy. Since we don't observe the motion of the particle in the extra dimension, this kinetic energy will be interpreted as rest energy, or in other words, the mass of the particle.
This is all understood perfectly fine, but it is this quote that comes next that confuses me:
To us, the particle would not look like one particle, but a set of particles - all with different masses.
Why would the particle look like a set of particles rather than just the one that is being observed?
Furthermore, why would they all have different masses?
How many particles would there be in this set?
Please keep your answers as simple as possible, as I am just a Layman.