One example of a phenomenon that violates the laws of classical mechanics but not quantum mechanics, while still obeying special relativity, is the phenomenon of particle-antiparticle annihilation and creation.
In classical mechanics, particles are treated as distinguishable and separate entities with well-defined trajectories. However, in the realm of quantum mechanics, particles are described by wave functions that can exhibit behaviors such as superposition and entanglement.
According to quantum field theory, particles and antiparticles can spontaneously annihilate and create pairs of particles and antiparticles. This phenomenon is governed by the principles of quantum mechanics and is supported by experimental observations.
In this process, a particle and its corresponding antiparticle collide and cease to exist, converting their mass into energy. This energy can then be transformed back into particle-antiparticle pairs. Such processes occur in particle accelerators, where high-energy collisions can create particle-antiparticle pairs, and in natural phenomena such as the decay of radioactive substances.
These phenomena can be described using quantum field theory, which combines quantum mechanics with special relativity. Special relativity ensures that the conservation laws, such as conservation of energy and momentum, are upheld during the annihilation and creation processes.
Therefore, particle-antiparticle annihilation and creation is an example of a phenomenon that violates classical mechanics but is consistent with both quantum mechanics and special relativity.