Chern Simons Theory Explained

Chern Simons Theory Explained

The Chern-Simons theory can have different definitions for different people. In general terms, however, it refers to the 3D topological quantum field theory. It is a sigma-model TQFT which has target space in the smooth moduli stack and a background gauge field is a circular 3-bundle with connections to the moduli stack.

The properties of the field configuration within the Chern-Simons theory depend upon the properties of its gauge group. If the gauge group is connected to the Lie group, then the configuration space is isomorphic. The properties are different for general gauge groups.

Each, however, can be interpreted as a string theory background.

How Is the Universe Constructed?

The more we discover about the various planes of existence and reality in the universe, the more questions we tend to discover. What we do know about the universe is that it has a specific structure to it. This framework, which uses 1D objects that are referred to as “strings,” interact with each other and look like any ordinary particle.

The difference is that as the strings vibrate, they correspond to gravitons and this carries a gravitational force. What Chern-Simons theory provides is a background of the planar dimensions to help justify the existence of the various strings, branes, and other fundamental objects in their current state of being.

We can begin to do this through this theory by tying magnetic flux to an electric charge. Where one is, then the other must be. They must be proportional locally and be proportionally constant when using the Chern-Simons coupling parameters.

This couples the two through the motion of the particles as they interact with one another. When combined, what we get are matter fields (or quantum fields or smooth tensor fields, if you prefer).

Each field has its own unique properties. The one that we’re going to address with the Chern-Simons Theory is the zero-point field.

Why Energy Is Important to the Chern-Simons Theory

With a matter field, energy almost creates a hierarchy for the types of fields that can exist. On the lowest end of the spectrum, we have the vacuum state. It contains the lowest possible energy because there are no physical particles present. This presents the energy in a ground state, which is how we get to zero-point energy.

Zero-point energy, by definition, is the state of energy in a system that has a temperature of zero.

Yet we still have one problem: every system maintains fluctuations, even in a ground state. Strings that are at absolute zero will therefore continue to vibrate.

Everything has a zero-point energy, no matter what type of field it may be.

It also implies that a vacuum state has energy even though it seems to have nothing at all. Can this energy be measured? Would finding its measurement be useful?

Next Comes the Uncertainty Principle in the Chern-Simons Theory

The uncertainty principle lets us know that for any specific particle, we cannot now its momentum or its position at the exact same time. This is because of the wave-like nature of how the universe tends to exist with its matter and energy.

Many things can be measured in waves. We have sound waves. We have light waves. Your thoughts even have waves that are measureable.

Do we see the waves of sound as they approach us? Of course not. We are aware of their existence because we have the evidence of their existence with our senses. You do not hear something unless a sound wave produced it from an external source.

Yet some people can “hear” sounds that are triggered internally. How can this be if there isn’t an actual sound wave?This is how a thought can present itself. The waves of a thought can produce energy. We can see this in thought toys, bionic limbs, and other concepts. This presents us with a unique perspective. If thoughts can produce energy, and energy can produce matter, then thoughts can produce matter. How we get there is by the calculation of the zero-point field that each thought produces.

Through this process, virtually anything can manifest itself under the correct conditions. How we achieve those conditions is a matter of great debate.

Paradoxes and the Chern-Simons Theory

As we look at our planes of existence and how particles interact with one another, we come to places where certain paradoxes begin to arise. This is particularly problematic when dealing with the idea of a black hole, the movement of gravity, and why the universe is continuing to expand at a greater pace rather than slowing down or beginning to collapse in on itself.

Think of a cube. A cube has six sides to it, is rigid, and contains space within it. If you are inside the cube, you cannot see outside of it. If you are outside the cube, you cannot see into it. You must change the structure of the cube in order to gain a different perspective.

Each is a different reality to the person inside or outside the cube.

Now when the Chern-Simons theory works with modern string theory, what you have are 26 dimensions. Instead of a six-sided cube, you have a structure with 25 different planes and the dimension of time with it.

Other theories, such as M-theory, suggest 11 dimensions exist instead.

No matter what the number may be, what would happen if the reality inside the cube you’ve pictured is able to interact with the reality that is outside of the cube? Bridges, wormholes, and other similar structures open that possibility.

Which brings us back to one of the original questions: how is the universe constructed?

Fundamental Particles Create a Fundamental Reality

We do not have a reality if we do not have particles that have formed and interact with each other to create that reality. The Chern-Simons theory works with string theory, along with a number of additional theories, to describe the fundamental forces and matter forms that are self-contained within our reality.

It can be used as a way to mathematically calculate the movement or curvature of the particles within various environments or states. It can be used to determine energy output, identify waves, or calculate the structures that contain the particles which form our version of reality as wel know it.

The Chern-Simons theory complements a subject that is broad, varied, and complex that attempts to discover the fundamental basics of our universe, our reality, and even the dimension of time itself. If we can discover how to make specific particles form a specific reality, then the potential to create anything comes into play.

Which is why there is a deep connection between science and the spiritual. It opens the possibilities of much more than a simple evolutionary process. It is a chance to get a glimpse into what it truly means to be a creator.