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KFC
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I read a introductory book on symmetry of physics system. The author says symmetry of quantum mechanical system is VERY different from that of classical system. I just wonder what's the main difference?
KFC said:I read a introductory book on symmetry of physics system. The author says symmetry of quantum mechanical system is VERY different from that of classical system. I just wonder what's the main difference?
In classical physics, symmetry refers to the invariance of physical laws under transformations such as translations, rotations, and reflections. In contrast, quantum systems exhibit a broader range of symmetries, including discrete symmetries such as charge conjugation and parity, which do not have classical analogues. Additionally, quantum systems can exhibit symmetries that arise from the superposition and entanglement of states, which are unique to the quantum realm.
Symmetry is a fundamental concept in quantum mechanics, as it allows us to classify and understand the behavior of quantum systems. By studying the symmetries of a system, we can predict its properties and behavior, such as energy levels and allowed transitions between states. Symmetry also plays a crucial role in the development of quantum field theories, which are essential for describing the behavior of particles and fields at a fundamental level.
Yes, symmetries can be broken in quantum systems, just as they can in classical systems. In quantum mechanics, this is known as spontaneous symmetry breaking, and it occurs when the ground state of a system does not exhibit the same symmetries as the underlying laws of physics. This phenomenon is crucial in understanding the behavior of many quantum systems, including superconductors and superfluids.
Quantum entanglement, where two or more particles become correlated in such a way that their properties are dependent on one another, can lead to the emergence of new symmetries in a system. This is because entangled particles exhibit a type of symmetry known as entanglement symmetry, which is fundamental to the study of quantum information and quantum computing.
Yes, understanding the symmetries of quantum systems has several practical applications. For example, symmetries play a crucial role in the design of quantum algorithms and protocols for quantum communication and cryptography, which rely on the entanglement of particles. Additionally, studying the symmetries of quantum systems can also provide insights into the behavior of complex systems, such as materials and biological molecules, which have quantum properties at the microscopic level.