Re: Is there any such phenomena as space tear?

The idea of spacetime as a "fabric" arose as a consequence of Einstein's
theories of Relativity, which showed that space and time are intimately
connected and provide a dynamical, "curved" arena in which material objects
move.  The analogy with a fabric also naturally leads to the question,
could space-time tear, and if so what would it be like?  Could one be
travelling through space and suddenly reach an end?

In a sense black holes, and specifically the singularities which Einstein's
General Theory of Relativity (GR) tells us they contain, represent an end
to space-time (if you fall into a black hole space and time twist round so
that your passage through time forces you inexorably to the singularity, at
which point time ends!).

Superstring theory, which is the subject of Greene's (excellent) book,
considers a rather different, and in a way even more radical kind of
tearing of spacetime, one which can change its topology.  To understand
this we go back to GR and the idea of curved spacetime.  If something can
curve it is natural to ask whether it could curve all the way round and
join back on itself.  It is in such a way that it is thought that even our
whole 3-dimensional universe might "wrap round" and reconnect, so that if
we were to head off in one direction in a straight line and go enormously
far, we would come back to our starting point.  We don't know if our
Universe really behaves like this, but it is regarding as a logical
possibility, and people have searched for observational evidence, so far
without success.

Now, a key additional ingredient which is required by superstring theory
(and actually by other unified field theories) is that they are framed in
more than just 3 space dimensions.  In the case of superstring theory in 10
space dimensions.  The question is where are these extra dimensions if they
exist - why can't we see them and move in them?  The favoured answer is
that they exist, but in their cases they do curve round on tiny
sub-microscopic scales, and join back on themselves.  Thus all particles
and us do inhabit them, but in a sense we "fill" them and so don't notice
they are there.  Interestingly having allowed that some dimensions of space
may curve back and rejoin, it is then possible to consider that they could
rejoin to make a complex kind of shape.  An analogy we can easily picture
is that a simple shape would be like a sphere, whereas a more complex shape
could be something like a torus (think of a tyre inner tube!).  

Of course, there could be infinitely many such complex configurations of
curled-back space, and string theory actually requires the curled up
dimensions to be of a particular type (a so-called Calabi-Yau space). 
However, there are still many possible Calabi-Yau spaces, and it is not
obvious which, if any, string theory would favour.  What Greene and others
found was that it is possible for one Calabi-Yau space to transform into
another one: this was a surprise since they potentially have different
topologies.  It would be like transforming a beach ball into a tyre inner
tube.  It's easy enough to maul a beach ball around to make a variety of
shapes, but to make anything like an inner tube (or a figure of eight, or a
pretzel shape etc. etc. with more holes in) one would have to actually cut
and restitch the material of the ball.

So, the breakthrough was the realisation that mathematically string theory
allowed for such transformations which actually altered the topology of
space-time, in a way which remained consistent with the laws of physics and
relativity in particular, despite requiring a particular extreme kind of
tearing and rejoining of space.  Does this mean that such tears really
exist?  We don't know.  String theory remains a very active area of
research, and seems to have enormous richness of possibilities, but it is
still very difficult to make connections between the theory (which remains
incompletely formulated) and experiment.  Even if such space tearing can
occur, it seems most likely it would have been a feature of the very early
universe, and indeed take place on such microscopic scales, that we could
only know it had occurred due to changes it brought about in the particles
and forces in the universe.