8 Beyond the Standard Model
513
by quantum mechanics. In GR one is familiar with singularities which are
stationary (time-like) such as the singularity of a charged black hole and those
which form or disappear at a given instance instant such as the big bang and
the big crunch (space-like). What happens in string theory to black holes big
crunches or big bangs? A good question. Consider first the motion a particle on
a circle of some radius and the motion of the string on a segment of some length.
The circle is smooth, the segment has edges. For a point particle probe the first is
smooth and the second is singular. In some cases, viewed by stringy probes, both
are actually equivalent, i.e. both are smooth. The string resolves the singularity.
Moreover there are black holes for which a string probe can’t distinguish between
the black hole’s horizon and its singularity. There are many other cases in string
theory where time-like singularities are resolved. The situation in the case of
space-like singularities is more involved and is currently under study. Some
singularities are in the eyes of the beholder.
• Commutativity—The laws of quantum mechanics can be enforced by declaring
that coordinates do not commute with their conjugate momenta. It is however
taken for granted that the different spatial coordinates do commute with each
other and thus in particular can be measured simultaneously. The validity of this
assumption is actually also subject to experimental verification. A geometry can
be defined even when coordinates do not all commute with each other. This is
called non-commutative geometry. There are cases when strings moving on a
commutative manifold would report the same observations as strings moving on
a non-commutative manifold. It seems many certainties can become ambiguities,
when observed by string probes. Stated differently, string theory has an incredible
amount of symmetry. This may indicate that the space-time one is familiar with,
is in some sense suited only for a “low” energy description. At this stage each
of these pieces of magic seems to originate from a different source. The hardwired mind seeks a unified picture for all this tapestry. This review may reflect
ambiguous feelings, challenges, success and magic each have their share. All in
all, string theory has been an amazingly exciting field, vibrating with new results
and ideas, as bits and pieces of the fabric of space time are uncovered and our
idea of what they really are shifts.
8.4.7 Human Effort and Closing Remarks
One may estimate that more than 10,000 human years have been dedicated up to
now to the study of string theory. This is a global effort. It tells an amazing story
of scientific research. In the mid eighties a regime/leadership change occurred. The
scientific leaders which had nursed the standard model, have been replaced by a
younger generation of string theorists. Some of those leaders complained that the
field had been kidnapped from them. Mathematical methods of a new type were
both applied and invented, many pieces of a vast puzzle were uncovered and a
large number of consistency checks were used to put parts of the puzzle together
513
by quantum mechanics. In GR one is familiar with singularities which are
stationary (time-like) such as the singularity of a charged black hole and those
which form or disappear at a given instance instant such as the big bang and
the big crunch (space-like). What happens in string theory to black holes big
crunches or big bangs? A good question. Consider first the motion a particle on
a circle of some radius and the motion of the string on a segment of some length.
The circle is smooth, the segment has edges. For a point particle probe the first is
smooth and the second is singular. In some cases, viewed by stringy probes, both
are actually equivalent, i.e. both are smooth. The string resolves the singularity.
Moreover there are black holes for which a string probe can’t distinguish between
the black hole’s horizon and its singularity. There are many other cases in string
theory where time-like singularities are resolved. The situation in the case of
space-like singularities is more involved and is currently under study. Some
singularities are in the eyes of the beholder.
• Commutativity—The laws of quantum mechanics can be enforced by declaring
that coordinates do not commute with their conjugate momenta. It is however
taken for granted that the different spatial coordinates do commute with each
other and thus in particular can be measured simultaneously. The validity of this
assumption is actually also subject to experimental verification. A geometry can
be defined even when coordinates do not all commute with each other. This is
called non-commutative geometry. There are cases when strings moving on a
commutative manifold would report the same observations as strings moving on
a non-commutative manifold. It seems many certainties can become ambiguities,
when observed by string probes. Stated differently, string theory has an incredible
amount of symmetry. This may indicate that the space-time one is familiar with,
is in some sense suited only for a “low” energy description. At this stage each
of these pieces of magic seems to originate from a different source. The hardwired mind seeks a unified picture for all this tapestry. This review may reflect
ambiguous feelings, challenges, success and magic each have their share. All in
all, string theory has been an amazingly exciting field, vibrating with new results
and ideas, as bits and pieces of the fabric of space time are uncovered and our
idea of what they really are shifts.
8.4.7 Human Effort and Closing Remarks
One may estimate that more than 10,000 human years have been dedicated up to
now to the study of string theory. This is a global effort. It tells an amazing story
of scientific research. In the mid eighties a regime/leadership change occurred. The
scientific leaders which had nursed the standard model, have been replaced by a
younger generation of string theorists. Some of those leaders complained that the
field had been kidnapped from them. Mathematical methods of a new type were
both applied and invented, many pieces of a vast puzzle were uncovered and a
large number of consistency checks were used to put parts of the puzzle together