In
theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...
, particularly
string theory and
M-theory
M-theory is a theory in physics that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1995. Witten's ...
, the notion of a flop-transition is basically the shrinking of a
sphere
A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is th ...
in a
Calabi-Yau space
In algebraic geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has properties, such as Ricci flatness, yielding applications in theoretical physics. Particularly in superstring ...
to the point of tearing. Based on typical
spacetime topology
Spacetime topology is the topological structure of spacetime, a topic studied primarily in general relativity. This physical theory models gravitation as the curvature of a four dimensional Lorentzian manifold (a spacetime) and the concepts of top ...
, this is not possible due to mathematical technicalities. On the other hand,
mirror symmetry
In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry.
In 2D ther ...
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
In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry.
In 2D ther ...
) merely undergoes
topologically smooth transition. 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
Edward Witten (born August 26, 1951) is an American mathematical and theoretical physicist. He is a Professor Emeritus in the School of Natural Sciences at the Institute for Advanced Study in Princeton. Witten is a researcher in string theory, q ...
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
The path integral formulation is a description in quantum mechanics that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional i ...
of
quantum field theory 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
*
M-theory
M-theory is a theory in physics that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1995. Witten's ...
*
Mirror symmetry
In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry.
In 2D ther ...
*
Calabi-Yau space
In algebraic geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has properties, such as Ricci flatness, yielding applications in theoretical physics. Particularly in superstring ...
References
{{reflist
String theory