This is my exploration of Yang-Mills theory and the Mass Gap Hypothesis.
Yang-Mills theory was intended as a TOE and my answer to this question is quoted below.
This page is just to start the conversation, it gives a general idea of my theory.
My description of Yang-Mills theory is written as I understand it for myself and particularly how I see it with regards to a TOE, I apologise for any relative inaccuracies.
My answers to the other Millennium Problems are here if you would like a comparison...
http://www.protheory.com/Millenium%20Problems.htm
Thanks
PRO.
Quote:
| 7. 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. 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. 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. 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. 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. 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. 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. 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. 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. |
This is a purely experimental view of extreme logic when applied to Yang-Mills theory and therefore the concept of "everything" by definition.
As I stated previously this page is an introduction to my thoughts on the potentials within the TOE in general.
I look forward to an interesting discussion
PRO.
EDIT - I'm sorry for the "Am I wrong?" stuff, it's the only way I can find at the moment to try and communicate how literally I mean my three potentials argument.