Difference between classical physics and quantum physics
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Fundamental Concepts: Classical Physics vs. Quantum Physics
Classical physics describes the world using variables like position and velocity, which are assumed to have definite values at all times. In this framework, the state of a system is fully determined by these measurable quantities, and it is always possible to ask about the value of any physical property at any moment 56. In contrast, quantum physics uses operators instead of simple variables, and the state of a system is described by a wave function or quantum state, which often does not assign definite values to all properties at once 356.
Measurement and Probability: Law of Total Probability vs. Born Rule
A key difference lies in how probabilities are assigned. In classical physics, probabilities follow the Law of Total Probability, which is straightforward and intuitive. Quantum physics, however, uses the Born Rule, which introduces a new way of calculating probabilities based on the quantum state. This difference is fundamental: while classical probabilities simply add up, quantum probabilities can interfere with each other, leading to phenomena like superposition and interference that have no classical counterpart 149.
Superposition, Interference, and Nonlocality: Unique Quantum Features
Quantum physics allows for superposition, where a system can exist in multiple states at once, and for interference, where probabilities can combine in ways that are sensitive to phase relationships. These effects are not possible in classical physics, where systems are always in one definite state. Quantum nonlocality, where measurements on one part of a system can instantly affect another part, also has no classical analog 46.
Emergence of Classical Behavior from Quantum Physics
Classical physics can be seen as an approximation that emerges from quantum physics under certain conditions, such as when Planck’s constant becomes very small, when dealing with large systems, or through processes like decoherence. In these cases, quantum effects become negligible, and the world appears classical. However, the classical world is not a sharply defined objective reality, but rather an approximate appearance that arises from the underlying quantum description 23.
Student Understanding and Misconceptions
Students often struggle with the transition from classical to quantum physics because many classical ideas do not carry over. For example, the expectation that all properties have definite values leads to misconceptions about quantum states and measurements. Students also find it harder to connect quantum physics to real-world experiences and to combine mathematical and conceptual reasoning, compared to classical physics 6710.
Mathematical Language and Abstraction
The mathematical language of quantum physics is more abstract than that of classical physics. While classical physics uses familiar concepts like position and velocity, quantum physics requires new mathematical tools and a different way of thinking about states and measurements 53.
Conclusion
The main differences between classical and quantum physics are found in their treatment of probability, measurement, and the nature of physical reality. Classical physics assumes definite properties and straightforward probabilities, while quantum physics introduces superposition, interference, and a fundamentally different way of assigning probabilities. These differences lead to unique quantum phenomena and require a shift in both mathematical language and conceptual understanding 12345679+1 MORE.
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