The aim of quantum gravity is to develop a theoretical framework that reconciles spacetime and gravity with the principles of quantum mechanics. Theoretically a photon can curve spacetime causing a miniscule gravitational effect, semi-classically quantifying gravity in the quantum framework. Energy density (including pressure, stress, and momentum) curves spacetime, and gravity is modeled by this curvature. Electromagnetic, strong, and weak forces contribute to the total energy that causes spacetime to curve. 

 

Relationship Between Mass-Energy and Quantum Fields

The Origin of Matter

The Big Bang is considered the origin of the observable universe’s matter, space, and time. This event produced the primordial matter and energy, and the Higgs field became active and produce mass to the universe shortly after.

 

The Origin of Mass

The Higgs field is an invisible energy field that fills the entire universe, which is the source of rest mass to elementary particles such as fermions (like electrons and quarks). While the Higgs field gives inertia mass to elementary particles, it accounts for approximately 1-2% of the mass of ordinary matter. The remaining 98-99% of nucleon mass (protons and neutrons) is sourced from the strong nuclear force energy, binding quarks together.

 

The Structure of a Proton

Quarks make up protons and neutrons. The primary mass, sourced from the Higgs field are very small. The combined rest mass of the three quarks that make up protons (uud), is approximately 10 Me V/c², and the total mass of a proton is approximately 938 Me V/c². Electrons are lighter, contributing less than 0.1% or 0.511 Me V/c² to the total mass of atoms.

 

Mass - Atoms are the building blocks of matter

Everything with mass is made up of atoms. Atoms are composed of subatomic particles: the nucleus is made up of positively charged protons and neutrons, and the negatively charged electrons which orbit the nucleus. 

 

Elements and Atoms

Elements have a unique number of protons in their atoms. All atoms of a particular element are identical, whereas atoms of a different element have unique or different characteristics. 

 

Formulation of Molecules

Atoms can connect with other atoms to form larger objects called molecules.

 

Atoms and Energy

Atoms contain energy, including the energy stored in electrons, the kinetic energy of their movements, and the nuclear energy within the nucleus.

 

The Speed of Causality - The Universal Constant

The speed of causality in a vacuum is a universal constant meaning it is the same unchanging value for all observers regardless of their own motion and represents the absolute speed limit for anything with mass or energy in space. As an object approaches the speed of causality, its mass increases infinitely, and time slows down, requiring energy to further accelerate. 

 

E = mc² Explained - Speed of Causality Squared

Mass and energy are interchangeable forms of the same thing. The speed of causality squared is the conversion factor, converting mass (kg) into energy (joules) and energy into mass, showing that mass is a concentrated form of energy. This constant value ensures the equation's unit's balance.

In Einstein's energy equation E = mc², the speed of causality squared (c²) works as a multiplier that quantifies the energy equivalent of mass. 

 

According to E = mc², energy has mass. The binding energy holds an atom together (strong force), the energy within a photon (electromagnetism), and the energy of radioactive decay (weak force) all contribute to the stress-energy tensor on the right side of the energy equation.

 

Understanding E = mc²

E: represents energy measured in joules.

m: represents mass (amount of matter) measured in kilograms.

c: represents the speed of causality in a vacuum, 299,792,458 metres per second.

c² represents the speed of causality squared, which quantifies the scale of conversation, meaning a very small amount of mass can be converted into a very large amount of energy, and a very small amount of energy can be converted into a very large amount of mass, such as high energy photons (like gamma rays) can collide and convert particle-antiparticle pairs. For example, an electron and a position.

 

Standard Model

First generation particles - orbit: positron (e+) and electron (e-) particle interaction.

Second generation particles - nucleus: up quark (u) and down (d) particle interaction.

Third generation particles - charm (c) and strange (s) / muon particle interaction (produced in particle accelerators).

Fourth generation particles - top (t) and bottom (b) / tau (τ) particle interaction (produced in particle accelerators).

 

Electromagnetic Spectrum

Radio waves, visible light, ultraviolet light, X-rays, and gamma radiation are all forms of emr that constitute the em spectrum, and the photon is their quantum particle. They are produced by the acceleration of charged particles, including atomic interactions, and electrical circuits.  

 

Atomic Sources of Electromagnetic Radiation

• Radio waves are produced by accelerated charged particles, primarily electrons.
• Visible light is produced by electrons releasing energy as photons.
• Ultraviolet light is produced by photons that are emitted when electrons in an atom move between orbital states in the atom, such as from a higher orbital state to a lower orbital state.
• X-rays are primarily produced by electrons, which are usually emitted outside the nucleus of an atom.
• Gamma radiation is primarily produced by the photon, emitted from the nucleus of the atom.

 

Quantum Chromodynamics

The color charge is the fundamental property of quarks and gluons, which act as the source of the strong force. The exchange of gluons between quarks, which carry the color charge, generates the strong force. This force binds quarks together to form protons, neutrons, and other hydrons. Quarks carry one of three colors (red, green, or blue) and antiquarks carry one of three anticolors (anti-red, anti-green, or anti-blue).

Gluons carry a combination of a color and a different anticolor charge, which allows them to mediate the strong force by changing the color of quarks. There are 8 gluon combinations (red-antigreen, red-antiblue, green-antired, green-antiblue, blue-antired, blue-antigreen, red-antired / green-antigreen combination, and red-antired / green-antigreen / blue / antiblue combination).

 

Beta-Minus Decay

In beta decay processes (specifically beta-minus decay), the weak force causes a neutron (ddu quark combination) to convert into a proton a proton (uud), emitting an electron and antineutrino. A down quark (d) in the neutron changes into an up quark (u), transforming udd to uud. This alters the net electrical charge of the nucleus, changing the respective em field.

The proton remains in the nucleus, increasing the atomic number (Z) by 1. 

 

Beta-Plus Decay

The weak force is the rate-limiting step that enables the formation of deuterium in the proton-proton chain, permitting stellar nucleosynthesis to start, which creates the heavier elements needed for chemistry, and structure of em interactions. The resulting atoms consist of nuclei surrounded by electron, which interact via em to form molecules and complex structures. Quantum tunnelling works alongside the weak force to help protons to overcome Coulomb repulsion and initiate fusion, specifically in context to the sun and stars. 

 

Summary of General Relativity and Standard Model

Mass-energy governs how spacetime curves, while quantum fields (QFT) govern the behaviour of mass-energy within that space.

 

Relationship Between the Strong Force, the Weak Force, and Electromagnetism

Strong Force

The strong force is responsible for binding quarks together, mediated by gluons. The strong force acts between protons and neutrons to hold the entire atomic nucleus together, overcoming electromagnetic repulsion. It operates at very short distances, usually within the nucleus of the of atoms. In the same way the electromagnetic force acts on electric charge, the strong force acts on a property called color charge (red, blue and green). The strong force holds subatomic particles together to form larger subatomic particles, converting some of their mass into energy.

 

Weak Force

The weak force is responsible for the radioactive decay of subatomic particles and for changing one type of particle into another. It allows quarks to change their type. For example, it can convert a down quark into an up quark, which converts a neutron into a proton. The weak force transforms particles flavors (the different varieties of quarks and leptons), frequently converting the kinetic energy of reactions into the mass of new particles. The weak force acts as a transformer that changes particles identities, transforming one particle flavor into another. 

 

Electromagnetic Force

The em force affects subatomic particles and other objects that contain electrical charge. The em force exhibits em fields such as magnetic fields, and light. It is the fundamental reason electrons bind to the nucleus and are responsible for the complete structure of the nucleus. Light is a form of em radiation, meaning that they are fundamentally the same. Electromagnetism produces speed by accelerating charged particles, primarily through electric and magnetic fields. Electromagnetic waves and radiation consisting of oscillating electric and magnetic fields, travel at the speed of causality.

While often called a single force, the electroweak theory does not unite them into a single gauge group, but two-gauge groups, which combine to produce the photon and W/Z bosons.

The electroweak unified force only applies at high energies such as in the early universe or modern particle colliders.

 

Electroweak Theory

The electroweak theory (or Weinberg-Salam model) unified the electromagnetic and weak interactions into a single framework, revealing them as different facets of a single force at high energies. It explains phenomena such as radioactive beta decay and solar nuclear reactions.

In high energies-energy phase, the four gauge bosons of three W’s and one B, are massless and travel at the speed of causality. However, in a low-energy environment, the W and Z bosons are massive and do not travel at the speed of light.

While often referred to as a single force, the electroweak theory does not unite them into a single simple gauge group, but rather a product of two-gauge groups, which combine to produce the photon and W/Z bosons.

 

w = sem/c² Explained - Speed of Electromagnetic Radiation

The electromagnetic force and the strong force (specifically in terms of gluons) propagate and mediate at the speed of causality in a vacuum. The strong and weak nuclear forces propagate through field interactions via the exchange of gauge bosons. The factor c² is fundamentally used in context to both electromagnetic and strong force interactions, primarily as the conversion factor between mass and energy in determining the energy scale of force carriers.

 

Understanding w = sem/c² 

w: represents the weak force. The weak force plays a role in converting mass into energy. 

s: represents the strong force. The strong force plays a role in converting energy into mass.

em: electromagnetism defines how electric and magnetic fields behave and interact.

emr: represent the propagation of electromagnetic fields through a vacuum. 

c² represents the speed of causality squared. Because both em and strong force involve fields that propagate at c and relate to energy-mass equivalence, c² is a universal constant applicable to relativistic descriptions.

 

Relationship Between Spacetime and Gravity

St = g/c² Explained - Speed of Gravity

Space and time are interwoven complementary facets of a single unified entity known as spacetime. The speed of gravity (the speed at which changes in the gravitational field propagate in a vacuum) is equal to the speed of causality, acting as the conversion factor between space and time, showing that time and space are two components of a unified four-dimensional spacetime. In the gravity equation St = g, the speed of gravity acts as the speed of causality (the maximum propagation speed) and a unit conversion factor in Einstein’s gravity.

The speed of causality squared acts as the fundamental conversion factor that ensures the units of mass-energy, and spacetime curvature are balanced. 

 

Space

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

The nature of spacetime is a four-dimensional structure, and presence of mass-energy alters its geometry causing objects to naturally follow these curved pathways (geodesics). Mass-energy curves spacetime because the stress-energy tensor (comprising of mass-energy density, momentum, pressure, and stress).

As a conceptual framework, mass-energy is the content and spacetime is the context that dictates how the content behaves. In modern physics they are not entirely separate. Spacetime itself can have energy (vacuum energy / dark energy), and the geometry of spacetime that hold energy, in which mass-energy works in parallel to spacetime.

  

Space Is Made Up Of

• Dark energy, which causes universe expansion. Spacetime itself can have a small amount of energy even in a complete vacuum (dark energy), meaning that even when all matter (atoms, molecules, particles) is removed from a space, the space itself is not truly empty.
• Dark matter, which influences galaxy formation.
• Cosmic microwave background radiation.
• Interstellar gas, dust, and plasma.

 

The Fabric of Spacetime

The fabric of spacetime is a four-dimensional concept, rather than a literal fabric. The fabric represents a unification of three-dimensional space and one-dimensional time, showing a four-dimensional continuum (spacetime continuum). Spacetime acts as a reference system for physical events.

 

Spacetime Misconception

• Spacetime is not a literal fabric, it is an analogy applied to show how spacetime curves.
• The universe is not expanding into a pre-existing space, rather than the fabric itself is growing.

 

Time

The speed of causality dictates how time behaves and connects to space. For non-relativistic (slow-moving) objects, the warping of time is the primary cause of acceleration (weak gravity), not the warping of space. For relativistic objects (close to speed of causality) or black holes, the roles reverse and the warping of space becomes significant (weak gravity).

Time dominates at low speeds; space becomes significant at high speeds. Time runs slower closer to massive objects like earth compared to being at a distance. This is known as gravitational time dilation, where stronger gravitational fields warp spacetime more significantly, causing time to pass more slowly.

 

Gravity

The speed of causality is the speed of gravity, which acts as the universal speed limit for casual information, unifying space and time into a single, four-dimensional framework.

The presence of mass-energy and quantum fields curves spacetime causing a gravitational field, and gravity is its curvature.

The interchangeable equivalence of mass-energy (E = mc²) plays a central role in curving spacetime, causing gravity.

The presence of mass-energy and quantum fields curve spacetime, meaning gravitational acceleration is actual inertial motion (free fall) along geodesics through this curved geometry.

 

Understanding St = g/c²

S: represents occupied space. The gravitational field that causes the geometry of gravity is spacetime. Simply, spacetime is the geometry of gravity. Space is warped or stretched near mass, which changes the measurement of distances, known as spatial curvature. Near mass the fabric of space itself is stretched or distorted. The result is the shortest path between two points is no longer a straight line, but a curve that follows the dip. Because of the dip, radial distances are longer and circumference is shorter.

t: represents time. Mass-energy curves spacetime, which causes clocks closer to mass to run slower and distances space geometry; this warped spacetime is what we experience as gravity. This is known as gravitational time dilation.

g: represents the speed of gravity in a vacuum. The presence of mass-energy curves spacetime causing a gravitational field and gravity is its curvature. Gravity acts like a distortion lens for space. Because the space is stretched, a metre near a black hole covers more physical space than a metre at a distance.

c² represents the square of the speed of causality which acts as the fundamental conversion factor that quantifies the equivalence between mass-energy and the curvature of spacetime.