The principle that antiparticles have equal energy as their corresponding particles, but opposite charge and spin, is a consequence of the theory of quantum field theory, specifically the Dirac equation and the concept of antimatter.
In quantum field theory, particles and antiparticles are described as excitations of their respective quantum fields. The Dirac equation, which describes relativistic quantum mechanics for fermions (particles with half-integer spin), predicts the existence of antiparticles as solutions to the equation.
According to the Dirac equation, for every particle with a certain energy and spin, there exists an antiparticle with the same energy magnitude but opposite charge and spin. The negative-energy solutions of the Dirac equation are interpreted as antiparticles, while the positive-energy solutions correspond to particles.
The principle of equal energy for particles and antiparticles arises from the concept of the vacuum. In quantum field theory, the vacuum is not an empty void but a state with a non-zero energy called the zero-point energy. This energy is associated with the fluctuations of quantum fields even in the absence of particles.
When a particle is created or annihilated, it involves a redistribution of the energy of the fields. In the process of particle-antiparticle creation or annihilation, the total energy remains conserved. The energy of the particle is transferred to the field while an antiparticle is created, and vice versa.
As a result, the energy of the particle and its corresponding antiparticle is equal in magnitude but opposite in sign. This principle holds true for all known particles and their antiparticles.
Experimental evidence supports this principle. Particle accelerators, such as the Large Hadron Collider (LHC), have produced and detected a wide range of particles and their antiparticles, confirming their equal energy but opposite charge/spin nature.
Overall, the equality of energy between particles and antiparticles, along with the opposite charge and spin, is a fundamental aspect of quantum field theory and is supported by both theoretical considerations and experimental observations.