In quantum field theory, the conservation of energy is explained through the concept of virtual particles and the principles of quantum mechanics. Virtual particles, including virtual photons, are not directly observable and do not have the same properties as real particles. They are mathematical constructs used to describe the behavior of interacting quantum fields.
According to quantum field theory, all particles, including photons, are considered excitations of their respective quantum fields. These fields permeate all of spacetime and can undergo interactions with each other. When two charged particles interact through the electromagnetic force, they exchange virtual photons.
Virtual photons are not limited by the same constraints as real photons. They can have energies and momenta that do not correspond to the mass-energy relationship of real particles. Instead, they represent a transfer of momentum and energy between the interacting particles. The exchange of virtual photons mediates the electromagnetic force and results in the establishment of an electric field between the charged particles.
The conservation of energy is maintained in this process by the uncertainty principle of quantum mechanics. The uncertainty principle allows for temporary violations of energy conservation, as long as they are within a certain limited timeframe. This principle states that energy can fluctuate within a short time interval, as long as the total energy is conserved when averaged over longer timescales.
In the case of virtual particles, such as virtual photons, the temporary violation of energy conservation is allowed due to the uncertainty principle. These virtual particles can exist for a very short time, on the order of the Heisenberg uncertainty principle, which governs the uncertainty in energy and time. As a result, the energy of the virtual photons can deviate from the usual mass-energy relationship, but the overall conservation of energy is maintained when considering longer time intervals and the contributions of all interactions.
In summary, the conservation of energy in quantum field theory is ensured by the exchange of virtual particles, such as virtual photons, which mediate the interactions between charged particles. While virtual photons can carry energies that do not correspond to their mass-energy relationship, their temporary violation of energy conservation is allowed by the uncertainty principle as long as the overall energy conservation is maintained when considering longer timescales.