The manifestation of physical matter when vibrating quantum fields interact is rooted in the framework of quantum field theory (QFT). In QFT, all fundamental particles and their interactions are described as excitations or vibrations of underlying quantum fields that permeate all of spacetime.
According to quantum field theory, particles are considered as quanta of their corresponding fields. These fields are pervasive throughout space and are associated with different types of particles, such as electrons, photons, quarks, and so on. When these fields interact, they exchange energy and momentum, leading to the creation or destruction of particles.
To understand the manifestation of physical matter, let's consider an example: the electron field. The electron field permeates all of spacetime, and an electron is an excitation or a localized disturbance in this field. When the electron field interacts with other fields, such as the electromagnetic field, it can exchange energy and momentum. This exchange manifests as the creation or annihilation of electrons and other particles.
In quantum field theory, the behavior of these fields and their excitations is described by mathematical equations, such as the Dirac equation for electrons or the Klein-Gordon equation for scalar fields. These equations govern the dynamics of the fields and determine how they propagate and interact.
Quantum field theory also incorporates the principles of quantum mechanics, including superposition and uncertainty. As a result, particles can exist in superpositions of different states until measured or interacted with, and their properties become probabilistic until observed.
It's important to note that the manifestation of physical matter from vibrating quantum fields is a complex and abstract concept that requires a deep understanding of quantum field theory and its mathematical formalism. While the framework of QFT has been highly successful in describing and predicting the behavior of fundamental particles and their interactions, the underlying mechanisms and philosophical interpretations are still subjects of ongoing research and debate in theoretical physics.