504
E. Rabinovici
such a generalization did eventually reproduce many properties of point particle
interactions and in addition enabled one to formulate what seems as a theory of
gravity. This it should do, following the tradition of subjecting any new theory to the
test of the correspondence principle. The theory is well defined up to several orders
and perhaps to all orders in perturbation theory. The perturbations are small at the
vicinity of a very small distance scale called the string scale, as small as that distance
is, it is sometimes expected to be larger than the Planck length and thus is associated
with lower energies than the Planck energy (it is related to the plank scale by the
string interaction coupling). Interactions among strings are, to a large extent, softer
and fuzzier than those among point particles. Recall that a large number of successes
of particle physics consisted of explaining and predicting the physics of the various
interactions at scales at which they were weakly coupled, otherwise, a large dose
of symmetry was essential. This is perhaps the most significant achievement of
string theory. It is also its major source of frustration, if the string scale is indeed
of the order of 10 −32 cm or even slightly larger, it is not known today how to
verify, experimentally, any prediction resulting from perturbative string theory. It
is very difficult to imagine, for example, how to set up an experiment measuring the
differential cross section of graviton-graviton scattering at the string scale. We will
return to this extremely important issue later on and continue to follow for a while
the path of the theoreticians.
8.4.3 New Questions
The impact of scientific progress can be tested by the type of questions it makes
us aware of, as well as by the answers it eventually provides for them. By studying
string theory new questions do arise. Values taken for granted are subjected to query
and downgraded to being parameters. String theory suggests questioning the values
of some such physical quantities and in some cases offers scientific answers to the
question. A prime example is that of the number of space-time dimensions. In a
point like constituent theory there is a very large degree of theoretical freedom. As
far as we know spin zero point particles, for example, could have propagated in
any number of dimensions, their interactions would have been different depending
on the dimension of space-time but nevertheless they would have been allowed.
A theory of spin one half particles can turn out to be in consistent on certain
type of manifolds but they do not restrict the dimensionality of the space in
which they propagate. Strings are much fussier than particles, (super) strings can
propagate quantum mechanically only in a limited number of dimensions. In fact,
not only are the number of allowed possible dimensions dramatically reduced,
the allowed values of the number of space-time dimensions do not include the
value 4. These dimensions are usually required to be 10 or 26 depending on the
amount of supersymmetry the string is endowed with. The origin of this basic
number is, at this stage, disappointingly technical and one should note that though,
strictly speaking, the number 26 does indeed appear in string theory, it is not
E. Rabinovici
such a generalization did eventually reproduce many properties of point particle
interactions and in addition enabled one to formulate what seems as a theory of
gravity. This it should do, following the tradition of subjecting any new theory to the
test of the correspondence principle. The theory is well defined up to several orders
and perhaps to all orders in perturbation theory. The perturbations are small at the
vicinity of a very small distance scale called the string scale, as small as that distance
is, it is sometimes expected to be larger than the Planck length and thus is associated
with lower energies than the Planck energy (it is related to the plank scale by the
string interaction coupling). Interactions among strings are, to a large extent, softer
and fuzzier than those among point particles. Recall that a large number of successes
of particle physics consisted of explaining and predicting the physics of the various
interactions at scales at which they were weakly coupled, otherwise, a large dose
of symmetry was essential. This is perhaps the most significant achievement of
string theory. It is also its major source of frustration, if the string scale is indeed
of the order of 10 −32 cm or even slightly larger, it is not known today how to
verify, experimentally, any prediction resulting from perturbative string theory. It
is very difficult to imagine, for example, how to set up an experiment measuring the
differential cross section of graviton-graviton scattering at the string scale. We will
return to this extremely important issue later on and continue to follow for a while
the path of the theoreticians.
8.4.3 New Questions
The impact of scientific progress can be tested by the type of questions it makes
us aware of, as well as by the answers it eventually provides for them. By studying
string theory new questions do arise. Values taken for granted are subjected to query
and downgraded to being parameters. String theory suggests questioning the values
of some such physical quantities and in some cases offers scientific answers to the
question. A prime example is that of the number of space-time dimensions. In a
point like constituent theory there is a very large degree of theoretical freedom. As
far as we know spin zero point particles, for example, could have propagated in
any number of dimensions, their interactions would have been different depending
on the dimension of space-time but nevertheless they would have been allowed.
A theory of spin one half particles can turn out to be in consistent on certain
type of manifolds but they do not restrict the dimensionality of the space in
which they propagate. Strings are much fussier than particles, (super) strings can
propagate quantum mechanically only in a limited number of dimensions. In fact,
not only are the number of allowed possible dimensions dramatically reduced,
the allowed values of the number of space-time dimensions do not include the
value 4. These dimensions are usually required to be 10 or 26 depending on the
amount of supersymmetry the string is endowed with. The origin of this basic
number is, at this stage, disappointingly technical and one should note that though,
strictly speaking, the number 26 does indeed appear in string theory, it is not