What are the units in the 11 dimensions of strings theory?

Answer 1

Not sure what you mean by "units", but my guess is that you're asking what is the scale of the higher spatial dimensions in String Theory. Basically, the relevant scale for String Theory, both in terms of energies and length, is the Planck scale.

In particle physics and cosmology, the Planck scale is an energy scale around 1.22 x 10^19 GeV (corresponding to the Planck mass) at which quantum effects of gravity become strong. At this scale, the description of sub-atomic particle interactions in terms of quantum field theory breaks down (due to the non-renormalizability of gravity). For energies approaching the Planck scale, an exact theory of quantum gravity is required, and the current leading candidate is String Theory, or its modernized form M-theory. At the Planck scale, the strength of gravity is expected to become comparable to the other forces, and it is theorized that all the fundamental forces are unified at that scale, but the exact mechanism of this unification remains unknown.

Similarly; the term Planck scale also refers to a length scale in the neighborhood of 1.616 x 10^-35 meters, or the Planck length (which is related to Planck energy by the uncertainty principle). At this scale, the concepts of size and distance break down, as quantum indeterminacy becomes virtually absolute. Because the Compton wavelength is roughly equal to the Schwarzschild radius of a black hole at the Planck scale, a photon with sufficient energy to probe this realm would yield no information whatsoever. Any photon energetic enough to precisely measure a Planck-sized object could actually create a particle of that dimension, but it would be massive enough to immediately become a black hole, thus completely distorting that region of space, and swallowing the photon. This is the most extreme example possible of the uncertainty principle, and explains why only a quantum gravity theory reconciling general relativity with quantum mechanics will allow us to understand the dynamics of space-time at this scale.