In
theoretical physics, particularly
string theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interac ...
and
M-theory, the notion of a flop-transition is basically the shrinking of a
sphere in a
Calabi-Yau space to the point of tearing. Based on typical
spacetime topology, this is not possible due to mathematical technicalities. On the other hand,
mirror symmetry allows for the mathematical similarity between two distinct Calabi-Yau manifolds. If one undergoes a flop-transition, the mirror of it should result in identical mathematical properties, which it does.
Definition
If there is a given Calabi-Yau manifold (basically a space with 6 or more dimensions curled up in a special way) then a sphere in the center can shrink down to an infinitesimal point that resembles a
singularity. After reaching the singularity-like point, the sphere tears and then a new sphere "blows up" to replace the torn one. The sphere in the mirror image (from
Mirror symmetry) merely undergoes
topologically smooth transition
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ho ...
. The mathematical results from the separate manifolds result in the same physics, so no laws of physics or mathematics are violated.
Why is it possible?
Theoretical physicist
Edward Witten proposed that the reason no flop-transition has ever caused universally catastrophic results is because the world-sheet of the strings will surround the flop-transitioning sphere and virtually cancel out the effects. The
path integral formulation of
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
says that the string (and therefore its world sheet) traverse virtually every possible path, and therefore for any flop-transition, a string world-sheet will be present to cancel out its effects.
See also
*
String theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interac ...
*
M-theory
*
Mirror symmetry
*
Calabi-Yau space
References
{{reflist
String theory