In Quantum Electrodynamics (QED), a quantum field theory that describes the interactions of electrons, positrons, and photons, the problem of infinities arises in certain calculations. These infinities arise due to the self-interactions of particles, leading to divergent quantities that cannot be physically interpreted.
To address this issue, a technique called renormalization was developed. Renormalization involves subtracting the infinities from the calculations by redefining the fundamental parameters of the theory, such as the mass and charge of the electron, in a way that preserves the agreement between theoretical predictions and experimental observations. The remaining finite terms give meaningful and physically meaningful results.
Renormalization has been successful in providing precise predictions in QED and has been extensively tested and verified experimentally. It is important to note that renormalization is a mathematical procedure and not a physical interpretation of the infinities. It effectively allows physicists to "tame" the infinities and obtain finite and meaningful results, but the underlying reason for these infinities remains an open question.
It is worth mentioning that the problem of infinities is not unique to QED but is a general feature of quantum field theories. The development of renormalization techniques has been extended to other quantum field theories as well, such as the electroweak theory and quantum chromodynamics.
While renormalization has been highly successful in making predictions in QED and other quantum field theories, it is recognized that it is not a complete solution. The search for a more fundamental theory that goes beyond the standard model of particle physics, which includes QED, is an active area of research. The ultimate goal is to find a theory that can incorporate gravity and provide a unified description of all fundamental interactions.
Various proposals, such as supersymmetry, string theory, and quantum gravity theories, have been put forward as potential candidates for such a theory. However, there is no definitive experimental evidence or consensus on which theory will replace or extend QED. Research in theoretical physics continues to explore these possibilities and seek a more complete understanding of the fundamental laws of nature.