Quantum mechanics, as a branch of physics, is primarily concerned with describing the behavior and interactions of particles and systems at the quantum level. It provides a mathematical framework to understand and predict phenomena in the physical world.
When you mention "the set of everything that doesn't exist," it is important to clarify what you mean. In the context of quantum mechanics, the term "existence" typically refers to the observable properties and states of particles or systems. Quantum mechanics describes the behavior of particles and systems that do exist and can be observed or measured.
However, quantum mechanics does have implications beyond the realm of directly observable phenomena. For example:
Quantum field theory: Quantum field theory is a framework that combines quantum mechanics with special relativity to describe the behavior of elementary particles and their interactions. It allows for the creation and annihilation of particles from quantum fields and provides a theoretical understanding of fundamental forces and particles.
Quantum fluctuations and virtual particles: Quantum mechanics allows for the existence of quantum fluctuations, which are temporary changes in the energy of a system due to inherent uncertainty. These fluctuations can give rise to the creation of virtual particles, which exist for a very short time and play a role in various phenomena, such as the Casimir effect and particle interactions.
Quantum cosmology: Quantum mechanics can be applied to cosmology and the study of the early universe. The application of quantum principles to the universe as a whole can provide insights into the origin, evolution, and possible quantum nature of the universe, although many open questions and challenges remain in this field.
It's worth noting that some aspects of quantum mechanics, such as superposition and entanglement, can lead to philosophical and conceptual discussions about the nature of reality, observation, and the role of consciousness. However, these discussions often go beyond the scope of purely scientific inquiry and touch on metaphysical and philosophical questions.
In summary, while quantum mechanics primarily describes the behavior of particles and systems that exist and can be observed, it does have applications and implications that extend to phenomena beyond direct observation, such as quantum fields, fluctuations, and cosmology. However, the concept of applying quantum mechanics to "everything that doesn't exist" would require further clarification or a more specific context.