Matter and Energy in Quantum Field Theory

In QFT, matter is not a fundamental substance but a form of energy. The universe is a closed system of conserved energy that constantly changes form, with matter being one of its temporary manifestations.

The Origin of Matter: Excitations in Quantum Fields

Matter does not come from some external source. It emerges from the fundamental quantum fields that constitute the universe.

The Two-Step Origin:
1. Universal Fields: Reality is made of omnipresent quantum fields (electron field, quark fields, etc.).
2. Matter as Excitation: A particle of matter is a localized, stable vibration in its corresponding field.

An electron is not a "thing" but a state of the electron field. When we say "create an electron," we mean we have added enough energy to the electron field to create a stable, particle-like excitation.

The Closed System: Conservation of Energy

The Fundamental Law: Energy is Conserved, Matter is Not

Classical conservation of mass is obsolete. Einstein's \( E=mc^2 \) showed mass is a form of energy. QFT provides the mechanism for how energy transforms between different forms, with "matter" being one of those forms.

The total energy in a closed system is constant, but it constantly flows between:

Mass-Energy (matter particles) ↔ Radiative Energy (photons, gluons) ↔ Kinetic Energy (motion) ↔ Potential Energy (field interactions)

The Cycle of Transformation: Matter is not a permanent substance but a temporary vessel for energy.

Process 1: Pair Production (Energy → Matter)

High-Energy Photon (γ) → Electron (e⁻) + Positron (e⁺)

A high-energy photon (pure energy in the electromagnetic field) interacts with the quantum vacuum and converts its energy to create a particle-antiparticle pair. Radiative energy transforms into mass-energy. The number of "matter particles" in the universe increases, but total energy is conserved.

Process 2: Annihilation (Matter → Energy)

Electron (e⁻) + Positron (e⁺) → Photons (γ + γ)

A matter particle and its antimatter counterpart collide and annihilate. Their mass-energy is converted entirely into the energy of photons. Mass-energy transforms back into radiative energy. The number of "matter particles" decreases, but total energy is conserved.

Process 3: Particle Decay (Matter → Different Matter + Energy)

Higgs Boson (H) → Bottom Quark (b) + Anti-Bottom Quark (b̄) + Kinetic Energy

An unstable heavy particle decays into lighter particles. The sum of the mass-energy of the decay products is less than the original particle's mass; the missing mass has been converted into kinetic energy carried by the new particles. Mass-energy transforms into kinetic energy.

Synthesis: The True Nature of "Stuff"

Quantum Field Theory gives us a coherent and powerful picture:

Matter is not a primary substance but a temporary form that energy takes. It is a stable, localized excitation of a quantum field.

The universe is a closed, dynamic system of energy flowing between quantum fields. The total quantity of energy is fixed and conserved, but its manifestations are endlessly changing.

Therefore, the answer to "Where does matter come from?" is: It comes from energy being added to quantum fields. And the answer to whether there's a closed system of matter is: No, there is a closed system of energy, and matter is one of its many forms.

This framework dissolves the classical distinction between "matter" and "energy," revealing a universe that is, at its most fundamental level, a complex dance of vibrating fields whose total energy content is constant.