In quantum mechanics, the conservation laws play a fundamental role in describing the behavior of physical systems. The conservation of information, as well as the conservation of energy and momentum, are deeply ingrained principles in the theory. Violations of these conservation laws would have profound consequences and would challenge our understanding of the fundamental principles of physics.
According to our current understanding, there is no known mechanism or scenario in quantum mechanics that allows for the simultaneous violation of both conservation of information and conservation of energy/momentum. Let's consider each conservation law separately:
Conservation of Information: Information in quantum mechanics is typically associated with the state of a physical system, which is described by its wave function. The evolution of the wave function is governed by the Schrödinger equation, which is a unitary and deterministic process. Unitarity ensures that information is conserved throughout the evolution of the system, meaning that the total amount of information encoded in the wave function remains constant.
Conservation of Energy/Momentum: Conservation of energy and momentum are consequences of certain symmetries of nature, such as time translation symmetry and spatial translation symmetry, respectively. These conservation laws are deeply rooted in the mathematical structure of quantum mechanics and have been extensively tested and confirmed by numerous experiments.
While it is always important to keep an open mind in science, there is no experimental evidence or theoretical framework that suggests the simultaneous violation of conservation of information and conservation of energy/momentum in quantum mechanics. It is worth noting that the foundations of quantum mechanics are still an active area of research, and our understanding of the theory may evolve with future discoveries.