Pro Answers > Claymath Millennium Problems > Yang-Mills Theory And The Mass Gap Hypothesis
This is the archive version of www.protheory.com hosted as a mirror on my forum.
Discuss Yang-Mills Theory And The Mass Gap Hypothesis
Yang-Mills Theory and the Mass Gap Hypothesis
Introduction
1. We need to solve the equations that are thought to govern the whole of our universe.
2. We must also solve a technical property within any resulting solution called the mass gap.
Yang-Mills Theory
Yang and Mills created a set of ideas and equations that attempt to explain every possible property of the universe.
Everything
This was an attempt at a theory of everything.
Geometry
Yang and Mills used an approach that is also found in geometry.
Fundamentals
The two researchers were trying to encompass the four fundamental forces which are as follows.
Top of Page
1. The Strong Force
The strong interaction is thought to be responsible for the stability of the atomic nucleus.
2. The Weak Force
The weak force or interaction affects the atomic nucleus and can affect the decay of particles and nuclei.
3. The Electromagnetic Force
The electromagnetic interaction is responsible for parts of atomic structure, chemical reactions, and other electromagnetic phenomena such as light.
4. The Gravitational Force
The main principle of gravity is that every particle of matter in the known universe attracts every other with a quantifiable force.
Observations
These four interactions or forces are thought to account for all of the universal energy changes that we currently observe and we need to unify them to create a singular theory of everything.
Top of Page
Part 1
Yang-Mills Theory
There are classical and quantum versions of Yang-Mills theory because both general relativity and quantum mechanics cannot currently be correct as a complete answer to everything.
Gauge
A gauge group means the assumption that for every situation in physics there is an associated set or group of properties that, when successfully calculated and understood, will explain all behaviours of any given instance.
Hidden
A hidden equation that can explain everything.
Gauge
The gauge group performs the same function as a real life gauge which means that it measures things.
Symmetries
In this case, it measures the supposed symmetries and behaviours of the universe.
Top of Page
Current
The current version of the original Yang-Mills idea is a theory that is known as quantum chromodynamics.
Chromodynamics
This is a model of the fundamental interactions (and therefore all energy in the universe) which proposes that all matter and energy is composed of quarks and their opposites (antiquarks)
Massless
These interactions are thought to be mediated by the exchange of massless energy quanta called gluons.
Gluon
The gluon is thought to be the force or energy that actually interacts with other quarks.
Travel
It is a way to explain how energy seems to travel between these particles.
Top of Page
Solve
We need to find the gauge group of all atomic and sub-atomic particles and solve the resulting equations to explain everything.
Part 2
The Mass Gap Hypothesis
When we study the strong interactions of elementary particles there is a specific inconsistency which we must also solve.
Gap
Yang-Mills theory proposes the existence of a so called "mass gap" in relation to the strong interactions of elementary particles.
Classical
Classical versions of this theory describe waves with no mass that propagate at the speed of light.
Quantum
Quantum mechanics describes every particle as a certain kind of wave so the mass gap is a major contradiction between the two versions of Yang-Mills theory.
Top of Page
Nuclear
The strong and weak nuclear forces are both thought to be carried by particles containing mass.
Missing
Something is missing and this is called the "mass gap."
Massless
The mass gap implies that in certain situations within physics a given quanta of energy may seem to create massive amounts of energy from something that is theoretically massless.
Something seems to be created from nothing essentially.
Possess
We still do not possess a theory of everything that can fully explain why there seems to be a gap in the first place.
Top of Page
Interactions
We still do not have a theory that can successfully unify the four fundamental forces.
Summary
Can we solve and explain the gauge group of all particle physics?
Is there a mathematically provable gap in the energy exchange process of the universe?
The Millennium Problem
The Millennium problem is to solve the gauge group of all physics, and the concept of a "mass gap" must be proven and understood from a mathematical point of view.
For the exact problem description please refer to Claymath.org
The Answer
Conjecture
Yang-Mills theory presents us with two options, either we can solve the gauge group of all physics and explain the observed gap in mass or we cannot, and asks us to choose one of them.
Top of Page
Boundless
Imagine a boundless black box containing a glowing sphere.
Pure
Inside the box there are no forces, values, or measurements in existence except the sphere which itself exists only in example.
Singular
The singular sphere may move in any relative direction and for any relative distance.
Potentially
Wherever the sphere eventually resides, it will always be potentially able to perform the exact opposite to each change in position because it is the only presence within the box.
Conditions
If another sphere is added under the same condition as before, the two spheres will always be opposite to each other, despite distance or position, as they have no relative boundaries to prevent this.
Top of Page
Results
Whichever way the two spheres move the opposite is still be possible in theory.
Third
If a third sphere were added to the example a neutral point could be achieved.
Defined
This point is defined as the position between the two original spheres.
Fourth
If a fourth sphere were to be added to the box, it could only repeat any of the three previously defined actions or positions.
Quality
The fourth sphere may be regarded as being opposite or neutral in relation to the others, but it adds no unique quality to the example.
Top of Page
Option
The fourth sphere has the option of attracting another sphere, repulsing another sphere, or neutralising itself in relation to another sphere at any given moment but its potential behaviours are simply a repeat of the original three.
Regardless
We could choose to add an infinite number of spheres to the same example, but regardless of the relative "amount" of spheres, they all possess the same three theoretical potentials.
Atoms
1. Electrons are negative.
2. Protons are positive.
3. Neutrons are neutral.
Sub-atomic
Sub-atomic level is a fractional version of the same principle.
Charges
All sub-atomic particles may carry three possible charges at any relative point in time, regardless of what words may be used to describe them.
Top of Page
Difference
The amount of a certain charge may vary, relatively creating what we define as "difference" but this does not change the fact that quarks possess the same three potentials as atoms and literally everything else.
Mass
The reason that there appears to be a gap in mass is because all energy changes in three ways simultaneously, energy can either contain mass, not contain mass or be neutral in potential.
Destroyed
Energy is not "created" or "destroyed" it is changed.
Singular
There is no unchangingly singular "beginning" or "end" to change.
Part 1
Yang-Mills Theory
Can we solve the gauge group of all physics?
1. We can solve the gauge group of all physics.
2. We cannot solve the gauge group of all physics.
3. There is a neutral possibility.
Simultaneously.
Top of Page
Part 2
The Mass Gap Hypothesis
Is there a mass gap?
1. Energy may contain mass.
2. Energy may not contain mass.
3. Energy may be neutral.
Simultaneously.
Am I wrong?
I simultaneously oppose, agree with, and neutralise all criticism ad infinitum.
My point is literal.
There is no point creating a theory of everything that doesn't work.
NEXT > Mathematics Answers
Interested?
If you're interested in a positive discussion about everything the whole of protheory.com is mirrored on my Theory Of Everything Forum
Discuss Yang-Mills Theory And The Mass Gap Hypothesis