Ratzinger said:
Have experimental findings and theoretical developments in the very recent time (like last three years) been in favour for or against string theory? Has optimism been growing or has it decreased?
String theory seems to be mathematically consistent only when there are extra (to those normally perceived) spatial dimensions. How could these extra spatial dimensions be detected? One way is by look for modifications (for semi-technical reasons why, see below) in Newton's inverse square law for gravity at small distances. There ongoing investigations looking for such modification, but, so far, none have been detected.
I, too, have a question. If evidence for either supersymmetry or extra spatial dimensions is found, string theorists will jump all over the results and claim vindication. But, since (as far as i know) they are not sufficient conditions, will either of these results really be enough?
It seems that superstring theory implies supersymmetry and superstring theory implies extra spatial dimensions, but how likely is that these necessary conditions can be "true" without symmetry being true? Scientific theories are often "verified" (note the scare inverted commas) for a certain domain of validity by a finding a number of necessary conditions. In this case, how much is enough?
For what it's worth, finding *both* supersymmetry and extra spatial dimensions would go a long way towards bringing me around.
Now, why do extra dimensions modify Newton's inverse square law? First, a somewhat wordy motivation for the inverse square force in three spatial dimensions. Consider gravitational lines of force coming from a point mass. Consider two (massless) imaginary balls with radii R and r that both have the point mass at their centres. The lines of force cross the surfaces (boundaries) of the balls at points. The (relative) strength of gravity at these surfaces will be proportional to the number of crossing point per unit area. Since the same lines of force pierce both surfaces, the number of crossing points is the same for the two surfaces. However, the surface areas scale as radius squared, and thus the strength of gravity (number of points per unit area scales inversely to radius squared.
Now consider gravitational lines of for from a point mass in a universe that has four spatial dimensions. A ball now is a 4-dimensional spatia volumel, and the boundary ("surface") of a ball is a 3-dimensional object. Consequently, the number of crossing points per unit "surface area", i.e., the gravitational force, now scales inversely to radius cubed.
In practice, the extra spatial dimensions, if they exist, are probably folded up in a complicated manner, so the precise deviation from Newton's inverse square law is probably impossible to calculate.
Regards,
George