Welcome to the Quantum Gravity Field Equation

 

The Theory of Quantum Gravity - Incorporating Gravity into the Quantum Framework

The aim of quantum gravity is to resolve the incompatibility between the physics of general relativity (GR) and quantum mechanics (QM) into one cohesive framework, explaining extreme environments like black holes, and the Big Bang, by describing all forces and matter under a single set of laws, including gravity within the quantum framework.

 

Key Reasons to Resolve the Incompatibility Between GR and QM

GR describes gravity as the curvature of spacetime caused by mass and energy, while QM describes all three of these forces (electromagnetism, weak, strong) as quantum fields, and their mathematical descriptions fail to reconcile at extreme scales. 

Incorporating gravity in the quantum framework would reveal a mathematical description where all forces and matter are different manifestations of a single underlying principle, potentially explaining the universe’s fundamental structure.

 

Resolution Proposition

Spacetime is the geometry of mass-energy and gravity is its curvature, then is it possible that spacetime is the geometry of sub-particles and gravity is its curvature at a sub quantum scale?

This resolution proposition hits on the exact boundary of modern theoretical physics. The simple and direct answer, is Yes, it is possible, and it is a major focus of research, however, is not yet correct in the ways General Relativity is proven.

Here is a breakdown of the proposition compared to current scientific understanding:

1. Spacetime is the geometry of mass-energy and gravity is its curvature.

  • This is Einstein's General Relativity.

2. A hypothesis (Quantum Gravity).

  • Mass-energy (sub-particles) determines the geometry of spacetime, and gravity is its curvature at a quantum scale.
  • Sub-particles (like electrons or quarks) cause quantum-scale curvature. In this view particles aren’t just in space, they are excitations of fields that are the geometry of spacetime itself.
  • Gravity at a quantum scale: Gravity at that level is not just a smooth curve, but perhaps the collective effect on these tiny quantum fluctuations.

3. The Challenges.

We do not have a final theory yet for a few reasons:

  • QM cannot determine precisely both position and momentum simultaneously (Heisenberg Uncertainty Principle).
  • Renormalization Problems: We cannot currently calculate the effects of gravity at quantum scales without getting nonsensical infinity answers.
  • Leading Contender: Theories trying to incorporate gravity into the quantum framework include Loop Quantum Gravity (which posits space itself is quantized, or made up of discrete loops), and String Theory (which treats particles as tiny vibrating strings in higher dimensional spacetime).

 

Summary

The proposal is essentially the quest for a Quantum Theory of Gravity. It is not yet established as ‘correct’ experimental evidence; however, it is a leading contender for how the universe works at its deepest level.

 

Think of it this way:

  • GR: Gravity is the curvature of a smooth fabric.
  • The idea: Gravity is the geometry of a woven fabric (where sub-particles are the threads).

 

In GR, the distinction between gravity as the curvature of a smooth fabric and gravity as the geometry of a woven fabric represents the transition from classical, macroscopic descriptions of spacetime to emerging, microscopic quantum perspectives.

  • Smooth Fabric (Classical GR): Gravity is the warping of a continuous four-dimensional spacetime continuum.
  • Woven Fabric (Quantum Gravity / Emergent Gravity): Gravity is the overall geometry formed by discrete, interconnected threads (such as sub-particles).

 

While smooth fabric describes the effects of gravity (how things move around masses), woven fabric attempts to describe cause of gravity at a fundamental level (how spacetime itself is built from quantum interactions). The woven fabric view suggests that if you zoom in close enough, space is not a smooth, elastic sheet, but a tight woven, discrete tapestry of relationships.

 

Approach

The aim of the quantum gravity field equation is to show that the interchangeable equivalence laws governing Einstein's energy equation and the conservation of energy equally apply to gravity and force.

Spacetime and force are different manifestations of the same mass-energy source. They work in parallel, but not as independent, separate systems. They are intertwined, partner manifestations of the same source, working together to dictate how energy behaves.

 

Parallel Problem

While spacetime geometry and stress-energy (or stress-energy-coupled geometry) are intrinsically and intricately linked and run in parallel within a unified, and symmetric system, current physics cannot make them work together mathematically in all situations. 

 

Parallel Solution

Modeling the co-evolution of stress-energy-coupled geometry. This is a creative and viable way to model spacetime and force that attempts to bypass the singularities found in standard general relativity by focusing on energy balances.

 

Energy Equation

E = mc2. The rest mass (m) and energy (E) are equivalent, scaled by the square of fundamental speed of causality (c2). Mass and energy are interchangeable forms of the same thing. The speed of causality squared is the conversion factor, converting mass into energy and energy into mass, showing that mass is a concentrated form of energy. This constant value ensures the equation's unit's balance. The speed of causality squared works as a multiplier that quantifies the energy equivalent of mass. The equation shows that a small amount of mass can be converted into a large amount of energy, and a small amount of energy can be converted into a large amount mass due to the value of the speed of causality squared. In the equation, the increased mass of a body multiplied by the speed of causality squared is equal to the energy of that body.

 

Force

The electromagnetic (em) force and the strong (s) force propagate and mediate at the speed of causality in a vacuum.

The em force is mediated by the exchange of photons, which are quantum particles of light that travels at the speed of causality. The force magnetic force itself propagates through space at the speed of causality; c appears in Maxwell’s equations, connecting electric and magnetic fields, where c represents the speed of causality in a vacuum. While the force is mediated by c, the square of the speed (c2) appears frequently in em formulas that relate electric and magnetic fields (showing that magnetism is a relativistic consequence of electricity) or when converting energy to mass.

The strong force is mediated by gluons, which are massless and therefore propagate at c. The energy required to break bonds (binding energy) is often converted to mass using E = mc2.

The weak force plays a significant and specialised role in the behaviour of em fields and interactions.

  • At low energies the em fields act independently, governed by Quantum Electrodynamics (QED).
  • At high energies / nuclear scale, the weak force is crucial for transformation of particles that produce em fields.
  • The photon and weak intermediate vector bosons (W, Z), that mediate the weak nuclear force, are intrinsically linked, being descendants of a single electroweak field.
  • The weak force plays a role in decay and transformation. It does not cause em fields to decay; it is responsible for the decay of particles that generate em fields and transforming the underlying source of em change.
  • The em force conserves particle identities, the weak force changes the flavor of quarks and leptons (e.g., transforming a neutron into a proton).

 

Nucleon Interconversion (via Weak Force)

The proton and the neutron are closely related, interchangeable forms of the nucleon and can be converted into each other. While they are not identical as neutrons are slightly heavier and have no charge, they are treated as different states of a nucleon.

 

Beta-Minus Decay

A neutron converts a proton, releasing an electron and an antineutrino.

 

Beta-Plus Decay

A proton converts to a neutron, releasing a position and a neutrino.

 

Interchangeability via Weak Force

  • Protons and neutrons are treated as almost identical by the strong force, and their ability to interchange roles through pion exchange is a central in nuclear binding and stability. Protons and neutrons can convert into each other through beta decay.
  • Quark Level: This process occurs because the weak force can change a down quark in a neutron into an up quark in a proton, and vice versa.

The proton and the neutron are two states of the same nucleon, and within an atomic nucleus, they interact and exchange identities through the strong nuclear force (via pion exchange) and be converted through the weak nuclear force (via beta decay). The strong force binds the quarks and can exchange their identities, the weak force changes their flavor to convert them from a proton to a neutron, and vice versa.

In the framework of Quantum Field Theory (QFT), forces are not actions at a distance, but results of particles exchanging the virtual gauge bosons. The total of 11 bosons (3 for the weak force and 8 for the strong force), account for all mediators of the nuclear forces within the Standard Model of particle physics (excluding the photon for electromagnetism and the hypothetical graviton for gravity).

 

Force Equation 

w = sem/c2. Both the em force and the strong force are mediated by massless gauge bosons (photons and gluons, respectively), which means changes in these fields propagate at the speed of causality in a vacuum. The velocity of em waves, and by analogy the propagation speed of changes in the color field for the strong force is c =1. The strong and weak nuclear forces propagate through field interactions via the exchange of 11 distinct force-carrying gauge bosons. The factor c2 is fundamentally used in context to both em and strong force interactions, primarily as the conversion factor between mass and energy in determining the energy scale of force carriers.

 

Summary

The energy stored in em and strong force interactions is mass. Therefore, the binding energies of the em and strong forces contribute to the total m in E = mc2. In addition, the weak force contributes to the mass of particles, and therefore, contributes to the energy equation. The nature of the contribution is different to the strong force (which holds the quarks together to create most of the mass of protons and neutrons) or the Higgs field (which gives particles intrinsic mass). The weak force contributes to mass primarily through the Higgs mechanism, which makes its force carriers (W and Z bosons) massive. Because the weak force is mediated by massive bosons, it contributes directly to the total mass-energy of the system, however, its contribution to the mass of matter (protons and neutrons) is negligible compared to the strong force. 

 

Gravity

Gravity = curvature of spacetime, where objects follow the straightest possible paths (geodesics) through this warped geometry. The stress-energy tensor (density, pressure, momentum) acts as the source that dictates the curvature of the four-dimensional spacetime continuum. Spacetime can have curvature even in regions where the stress-energy tensor is zero (a vacuum), such as around blackholes or in the presence of gravitational waves, as the curvature is carried from distant sources.

Spacetime perturbations (gravitational waves) propagate at the speed of gravity, which equals the speed of causality (c) in a vacuum; speed of gravity = speed of gravitational waves = c.

 

Gravity Equation 

St = g/c2. The curvature of gravity is equal to the geometry of spacetime, where gravity is a manifestation of spacetime curvature. The speed of gravity, specifically the propagation of gravitational waves in a vacuum, is equal to the speed of causality (c). Experimental and theoretical physics confirm that gravitational waves and light (electromagnetic radiation) propagate at the same speed in a vacuum.

According to the equivalence principle, mass and energy are identical sources of gravity. In parallel to the energy equation, the gravity equation expresses the gravity equivalence to the curvature of spacetime, meaning, time (parallel to mass) and space (parallel to energy) are not separate, but interwoven components of the same entity. The square of the speed of causality (c2) in the Einstein's energy equation acts as the conversion factor that quantifies the equivalence between mass-energy and the curvature of spacetime. 

All energy curves spacetime, therefore a high energy, massless photon will cause a tiny amount spacetime curvature, causing a minuscule gravitational wake (perturbation in spacetime metric). While a photon in a vacuum does not create a “gravitational wave (which requires an accelerating mass), it does create a distortion in the spacetime metric, which acts like a gravitational field accompanying the photon at the speed of causality. Showing that it is theoretically possible to reconcile the mathematical descriptions of quantum gravity at extreme scales.

The gravity equation demonstrates the Block Universe model, which defines the simultaneity of time. All moments in time - past, present, and future are equally relative and exist within a four-dimensional spacetime model. This view is consistent with relativistic physics, where space and time are combined into a single, unified, and fixed entity.

 

Quantum Gravity Field Equation

S (tg) = E (mc2) x w (s, em). The electromagnetic radiation energy released from an object is equal to the mass lost by that object multiplied by the speed of causality squared (m = E/c2).

 

Quantum Gravity Unified Framework 

E (w, St) = m (s, em) x c2 (g). All mass-energy, including the energy stored in strong, weak, and electromagnetic fields, causes the curvature of spacetime, and the curvature affects the motion of objects within spacetime, operate simultaneously, and interchange with equivalence. 

The interchangeable equivalence of mass-energy, because of spacetime geometry, and manifested through force interactions are different forms of a single underlying symmetry principle.

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