506
E. Rabinovici
say that point particles allow everything. We mentioned that spin one half particles
can’t be defined on all manifolds but the number of known restrictions is much
smaller. The interactions could be of an infinite (sometimes classifiable) variety, the
color group, which happens to be SU(3), could have been for all the theory cares,
SU(641), the electromagnetic force could have been absent or there could have been
17 photons. Not everything is allowed, but an infinite amount of variations could
have been realized instead of what one actually sees in nature today. The same goes
for many (but not all) of the properties of the space-time arena in which all the
interactions are occurring, in particular effective low energy theories (and one seems
to be constrained to use only such theories for a long time to come) contain many
more free parameters such as masses and some of the couplings. In a string theory
one may have expected that all or most of these parameters are fixed in some manner.
Actually is it more complicated, for some string backgrounds, some parameters are
fixed, while other parameters are not. In addition there seemed to be several string
theories leading to even more possibilities.
8.4.4 The One and Only?
As we have discussed the desire to find the one and only theory encompassing all
fundamental physical phenomena seems hard wired in many scientific minds. Is
string theory an example of such a theory? Before addressing this question let us
reflect upon the limitations of the methods used. What would in fact satisfy the
purest (or extremist) of reductionists? A one-symbol equation? Be her desires, what
they may be, one should recall that one is using mathematics as our tether into the
unknown. This tool, which has served science so well, has its own severe limitations,
even ignoring the issue of using differential equations as tool to probe short distance,
a generic problem in mathematics can’t be solved, maybe the NOH principle will
eventually have its day, one will run out of interesting questions which have answers,
maybe that day is today! (Although some mathematicians suggest to use physicists
as hound dogs that will sniff one’s way towards interesting and solvable problems).
Having this in mind the key question is posed in hope it does have an answer: find the
unique theory describing the fundamental forces. There have been ups and downs
for the proponents of the one and only string theory. The understanding of the
situation has passed several evolutionary stages. From the start it was recognized
that one may need to settle for more than only one string theory. It was thought
that a distinction could been drawn between a theory of only closed strings and a
theory containing both open and closed strings. A theory with only open strings
was realized to be perturbatively inconsistent. Even those theories needed not only
a fixed dimension but in addition an extra symmetry, supersymmetry, to keep them
consistent. It was very quickly realized that actually there are an infinite varieties of
backgrounds in which a string could move. For example, consider 26 dimensional
spaces in which one dimension is actually a circle of radius R. It turned out that all
possible values for the radius, R, of the circle are allowed. It was then realized that
E. Rabinovici
say that point particles allow everything. We mentioned that spin one half particles
can’t be defined on all manifolds but the number of known restrictions is much
smaller. The interactions could be of an infinite (sometimes classifiable) variety, the
color group, which happens to be SU(3), could have been for all the theory cares,
SU(641), the electromagnetic force could have been absent or there could have been
17 photons. Not everything is allowed, but an infinite amount of variations could
have been realized instead of what one actually sees in nature today. The same goes
for many (but not all) of the properties of the space-time arena in which all the
interactions are occurring, in particular effective low energy theories (and one seems
to be constrained to use only such theories for a long time to come) contain many
more free parameters such as masses and some of the couplings. In a string theory
one may have expected that all or most of these parameters are fixed in some manner.
Actually is it more complicated, for some string backgrounds, some parameters are
fixed, while other parameters are not. In addition there seemed to be several string
theories leading to even more possibilities.
8.4.4 The One and Only?
As we have discussed the desire to find the one and only theory encompassing all
fundamental physical phenomena seems hard wired in many scientific minds. Is
string theory an example of such a theory? Before addressing this question let us
reflect upon the limitations of the methods used. What would in fact satisfy the
purest (or extremist) of reductionists? A one-symbol equation? Be her desires, what
they may be, one should recall that one is using mathematics as our tether into the
unknown. This tool, which has served science so well, has its own severe limitations,
even ignoring the issue of using differential equations as tool to probe short distance,
a generic problem in mathematics can’t be solved, maybe the NOH principle will
eventually have its day, one will run out of interesting questions which have answers,
maybe that day is today! (Although some mathematicians suggest to use physicists
as hound dogs that will sniff one’s way towards interesting and solvable problems).
Having this in mind the key question is posed in hope it does have an answer: find the
unique theory describing the fundamental forces. There have been ups and downs
for the proponents of the one and only string theory. The understanding of the
situation has passed several evolutionary stages. From the start it was recognized
that one may need to settle for more than only one string theory. It was thought
that a distinction could been drawn between a theory of only closed strings and a
theory containing both open and closed strings. A theory with only open strings
was realized to be perturbatively inconsistent. Even those theories needed not only
a fixed dimension but in addition an extra symmetry, supersymmetry, to keep them
consistent. It was very quickly realized that actually there are an infinite varieties of
backgrounds in which a string could move. For example, consider 26 dimensional
spaces in which one dimension is actually a circle of radius R. It turned out that all
possible values for the radius, R, of the circle are allowed. It was then realized that