Tears In Space-time In String Theory

Wednesday, December 05, 2018

Tears In Space-time In String Theory

Tears In Space-time

General relativity says that the space-time cannot tear. It uses Riemannian geometry which requires smooth space-time to work properly. There can be no creases, punctures, gaps etc...

Before string theory had even been developed, physicists had wondered if space-time could tear and there are two ways which have been the most popular among physicists.

Black Holes

Black holes are areas where space-time has extreme curvature and space-time actually appears to be pinched at it's center. Some say that space-time is actually punctured by the black hole at this point but because it is beyond the event horizon, we are protected from any catastrophic effects a puncture could have.

Wormholes

Wormholes are a theoretical way to pass through space-time. They connect two far away places in space-time by creating a new region of space. This also involves the puncturing of space-time.

An illustration of a worm hole

So now we are thinking about string theory, a good question might be: are there other ways in which space-time can puncture?

Flop Transitions

Imagine a sphere inside a Calabi-Yau space. Imagine it shrinking until it goes down to a point, tearing the space at that point, and then opening up that point by putting a new sphere in and blowing it up. This is called a flop-transition and the new Calabi-Yau space will be topologically distinct from the first space (meaning we can't go from shape one to shape two without tearing at some point in the process).

This transformation seems pretty random and pointless but we may want to know what happens if the Calabi-Yau space that occupies our universe undertook a flop-transition.

Mirror Symmetry

Mirror symmetry is a symmetry between Calabi-Yau shapes. Calabi-Yau shapes are 6D and so can have holes in a variety of dimensions, e.g, a hole in three dimensions of the shape would be a sphere. In 1988, Brian Greene found that by transforming a Calabi-Yau shape using certain rules, the number of odd-dimensional holes in the transformed shape was equal to the even-dimensional holes in the original and vice versa. This means that the total number of holes remained unchanged and so the number of particle families stayed the same through the transformation. After further investigation, he found that the rest of the physical properties are also kept under the transformation.

This means for every Calabi-Yau shape, there is a mirror Calabi-Yau space to describe the system where the physics are identical. This was major for string theorists as it allowed impossible calculations to be attempted using the mirror perspective. Sometimes in mathematics, simply rearranging the steps taken to perform a calculation can make it a lot easier and mirror Calabi-Yau shapes often did this naturally.

Flop Transitions And Mirror Symmetry

With our knowledge on mirror symmetry, we may want to ask what happens during a flop transition in the mirror perspective.
It turns out that there is no tearing in the mirror perspective and the physics in the mirror space does not change. Since nothing spectacular happens, we can open up the possibility that the Calabi-Yau space we live in has undergone a flop-transition and therefore space-time has torn at some point in time.
This is because we can describe ourselves to be in a Calabi-Yau space which evolves smoothly over time. Mirror symmetry means that there is also an additional mirror space which is just as valid to claim that we live in. This space may undergo a flop-transition and so it would be equally valid to claim that the space we live in was not evolving smoothly over time, but instead undertook a flop-transition.

Why Do Tears Not Cause Physics To Break?

If we had a point particle theory, the particles would only travel adjacent to a tear and in this case, there would be a disaster. String theory is more versatile however because strings are extended objects. This means they can encircle the tears in space-time and shield the universe from any catastrophe. Even if there are no strings around when a tear occurs, and even though strings are infinitely thin, they can shield the universe because of quantum mechanics. Strings travel by looking at every possible trajectory they can take. The motion we observe is just the combination of all these possibilities. If there is a tear, it is encircled by strings that have possible paths that encircle the tear. Even if no strings are immediately nearby, quantum mechanics takes into account all paths and so there are infinite paths that encircle a tear. In this way, we avoid the laws of physics breaking.
Modelling the fundamental constituents of the universe as strings once again opens up the possibilities for what is possible in the universe.

Impacts Of Tears In Space-time

Flop-transitions do not change the number of holes in a Calabi-Yau space and so the number of families and types of particles in each family will not change. The possible energies of vibrations and therefore the values of masses of elementary particles can change however. It turns out that masses change continuously through flop transitions and there is no catastrophic jump ion mass. This means the moment of tearing actually has no distinct feature.

Has a tear occurred before?

The masses of particles seem stable at the moment. but some point particle theories suggest that the masses of elementary particles have changed over time. This does hint at the possibility that flop-transitions have occurred and therefore space-time has torn in the past. Masses of particles seem stable now as far as we can see however and so this implies that if tears do occur, they are happening at an increasing slow rate, too slow for our equipment to notice.

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