Core Equations and Proton Mass Derivation in EQST-GP

Overview of the Theory (EQST-GP)

This paper presents a new theory called "Expanded Quantum String Theory with Gluonic Plasma" (EQST-GP). The primary goal of this theory is to unify all of nature's fundamental forces (gravity, electromagnetism, strong nuclear forces, and weak nuclear forces) into a single, consistent mathematical framework in eleven dimensions (11-D).

Explanation of the main sections and ideas:
1. Key Innovations:

1. Expanded energy equation\[
   E_{\text{total}} = mc^2 + \hbar\omega + \Lambda(t) V_{\text{plasma}}
   \]

(QGP)Gluonic Plasma Dark Matter:

The idea here is that dark matter, which makes up most of the universe's mass and is invisible to us, may consist of a strange state of gluon plasma (particles that transmit the strong nuclear force). Equation (1) gives the density of this dark matter based on the properties of the quark-gluon plasma.

This is an innovative solution, as it attempts to explain dark matter using components from the Standard Model itself rather than postulating exotic new particles.

11D Non-Commutative Geometry:

To introduce gravity (general relativity) into a quantum framework, the theory uses the idea that spacetime coordinates do not interchange (i.e., [X^μ, X^ν] ≠ 0). Equation (2) shows that exchanging two spacetime coordinates gives an imaginary value related to the Planck length (l_p), the scale at which quantum gravity effects become important.

Dimension 11 is the dimension at which supergravity theory becomes particularly simple and promising for unification.

2. Derivation of fundamental constants (e.g., the mass of the proton):

The theory aims to accurately calculate the proton mass (and other constants) from quantum chromatic atom theory (QCD) with the addition of a gluon plasma "mirror."

Puzzle: The proton's mass (m_p) is much larger than the sum of the masses of its constituent quarks. Most of its mass comes from the binding energy between the quarks via gluons.

Proposed solution (Equation 4): The equation divides the proton's mass into three parts:

Constituent quark mass: This is affected by the value of the "quark condensate" (⟨q̄q⟩), a non-zero value in vacuum that gives the quarks an effective mass.

Negative exponential (exp(-π/α_s)): This represents the effect of "asymptotic freedom" in QCD, where the strong nuclear force becomes weaker at high energies.

Mirror plasma correction factor: This is the additional fraction introduced by the new theory, and comes from interactions with the proposed plasma state.

Table 1 shows the contribution of each fraction to the final mass, with 65.7% of the mass attributed to the QCD condensate.

3. Cosmological Framework:

The theory modifies the fundamental Friedmann equations that describe the expansion of the universe.

Equation (5) adds a new term (Ω_p) for the gluon plasma energy, which behaves like negative-pressure dark matter, affecting the expansion of the universe.

It also adds a term for dark energy (Ω_Λ) that is dynamic (varying with redshift z) and not constant like Einstein's cosmological constant (Λ). This is one proposed solution to the Hubble tension problem.

4. Testable Predictions:

For a theory to be credible, it must predict new phenomena that can be confirmed or disproved by experimental tests.

Equation (6) predicts an exact value for the collision cross-section σ for the pp → γγ process (two-photon production) at the LHC at 14 TeV. If experiments (such as ATLAS and CMS) find this value, this supports the theory. If they do not find it, the theory needs to be revised.

Summary and Evaluation:

What is it?
A very ambitious theoretical framework that aims to be a "theory of everything" by combining quantum mechanics and general relativity in 11 dimensions.

How does it do this?
It uses ideas from string theory, non-commutative geometry, and adds a new component (gluon plasma) to explain dark matter and the mass of the proton.

Is it rigorous?

Pros: The method is systematic, provides precise numerical calculations, and predicts testable experiments. It is the gold standard in science.

Challenges: String theory in 11 dimensions is complex and has not been experimentally proven. The idea that gluon plasma could be dark matter is new and unconventional and requires strong evidence.