Electron-electron interaction

Imagine electrons as tiny magnets with an electric field surrounding them. This electric field affects the space around them.

• When two electrons are close, their electric fields push against each other because they have the same charge (like poles of magnets repel).
• According to the theory of quantum electrodynamics (QED), electrons can’t directly interact with each other. Instead, they exchange energy in the form of a photon, the carrier of the electromagnetic force.
• One electron emits a photon due to a fluctuation in its electric field. This photon carries some energy and momentum.
• The other electron, influenced by the changing electric field of the first electron (carried by the photon), absorbs the photon. This changes the second electron’s energy and momentum.
• So, even though the electrons never directly touch, the exchanged photon acts as a messenger, causing a repulsive force due to the way their electric fields interact.

• Electrons, being charged particles, create an electric field around themselves. When two electrons are present in close proximity, their electric fields interact with each other. This interaction can result in various phenomena, including the exchange of electromagnetic force, exchange of a photon, repulsion or attraction between the electrons, exchange of energy, and momentum transfer.
• This  applies to both real photons, encountered in everyday life, and virtual photons, used as mathematical tools in theoretical physics, is essential for understanding electron-electron interaction:
  • Real photons: Real photons are the ones we encounter in everyday life. They are the carriers of electromagnetic radiation, including visible light, radio waves, microwaves, infrared radiation, ultraviolet radiation, X-rays, and gamma rays. These photons are what we perceive when we see light, feel warmth from the Sun, or use electronic devices that emit or receive electromagnetic signals. Ordinary photons are detectable and observable and form the basis of our understanding of light and electromagnetism.
  • Virtual Photon: Virtual photons are mathematical tools used in theoretical physics, particularly in quantum field theory, to calculate the electromagnetic interaction between charged particles, such as electrons. They are termed “virtual” because they exist as intermediate states in calculations of particle interactions but cannot be directly observed or detected. Virtual photons do not manifest as observable particles in the same way as ordinary photons.
• In some scenarios, electrons can emit or absorb real photons. This can happen during collisions with high enough energy. These real photons can be detected and their properties measured.
• Electron-electron interactions mediated by photons are responsible for many of the properties of matter, such as the electrical conductivity of metals, the colour of objects, and the chemical bonds that hold atoms together.
• More commonly, the interaction happens via virtual photons. These are temporary fluctuations in the electromagnetic field that mediate the force between electrons. They cannot be directly observed because they exist for an extremely short time and violate some properties of real photons (like having no mass).

• Here are four examples of the process of electron-electron interaction mediated by photons:

Colour of objects

• The colour of an object is determined by the wavelengths of light that are absorbed and reflected by the object.
• The absorption and reflection of light is caused by the interaction of photons with electrons in the object. For example, a red object appears red because it absorbs blue and green light, and reflects red photons.

Electrical conductivity of metals

• The electrical conductivity of a metal is determined by the number of free electrons in the metal.
• The free electrons in a metal can be accelerated by an electric field, which causes the metal to conduct electricity. For example, copper is a good conductor of electricity because it has a lot of free electrons.

Møller scattering

• Møller scattering is the name given to electron-electron scattering in quantum field theory.
  • Møller scattering is the process in physics that describes the interaction between two charged particles. It is mediated by the exchange of virtual photons.
  • When two electrons interact with each other through the exchange of a virtual photon, the photon is emitted by one electron and absorbed by the other electron.
  • This exchange of energy and momentum causes the electrons to change their direction of motion. This change in direction is what we observe as the electric force.

Photoelectric emission

• Photoelectric emission is the process of an electron being ejected from a metal surface when light hits the surface. This process can be explained by the exchange of a virtual photon between the electron and the photon. For example, photoelectric emission is used in solar cells to convert sunlight into electricity.