What is the difference between classical and quantum physics?

Introduction

Classical and quantum physics are two fundamental frameworks for understanding the physical world. Classical physics, which includes theories like Newtonian mechanics and Maxwell's electromagnetism, describes macroscopic phenomena. Quantum physics, on the other hand, deals with the behavior of particles at the atomic and subatomic levels. Understanding the differences between these two frameworks is crucial for comprehending the transition from macroscopic to microscopic phenomena.

Key Insights

Nature of States:
- Quantum states are discrete, while classical states are dense. The classical limit is achieved when the density of states becomes infinite, making quantum symmetries invisible.
Probability and Symmetry:
- Both classical and quantum theories share common properties in areas such as the logic of propositions, symmetry, and probabilities. However, the essential distinction lies in joint decidability versus smoothness.
Emergence of Classical Physics from Quantum Physics:
- Classical physics can emerge from quantum physics in several ways:
  - In the limit of small Planck's constant (h -> 0).
  - In the limit of a large system with many degrees of freedom (N -> infinity).
  - Through decoherence and consistent histories, where classical states are robust against environmental coupling.
Measurement and Observation:
- The classical world is not created by observation but rather by the lack of it. Classicality results from the elimination of certain states and observables from quantum theory.
Intertheoretic Reduction:
- Classical mechanics can be seen as a special case of quantum mechanics under certain conditions. However, the classical limit does not constitute a proof of reduction, and the two theories are weakly equivalent over a domain of applicability.

Conclusion

Classical and quantum physics differ fundamentally in the nature of their states, with quantum states being discrete and classical states being dense. While they share some common properties, the key distinction lies in their approach to probability and symmetry. Classical physics can emerge from quantum physics under specific conditions, but this emergence is not a straightforward reduction. Instead, it involves the elimination of certain quantum states and observables, leading to the approximate appearance of classical behavior.

What is the difference between classical and quantum physics?

Summary

Introduction

Key Insights

Conclusion

Sources and full results

On quantum vs. classical probability

Quantum theory shares many properties with classical probability theory, but the essential distinction is joint decidability versus smoothness, and beyond quantum theory there are no other generalisations relevant to physics.

Between classical and quantum

Classical physics emerges from quantum physics through the elimination of certain states and observables, rather than observation itself.

Quantum and classical statistics

Quantum particles obey discrete single-particle states, while classical particles obey dense single-particle states, with the classical limit making underlying quantum symmetries invisible.

The relation between classical and quantum mechanics

Classical mechanics reduces to quantum mechanics in a restricted sense, reflecting the domain of applicability and highlighting the need for weaker intertheoretic reduction.

Information and computation: Classical and quantum aspects

Quantum physics allows for efficient information coding and processing, surpassing classical computers in both transmission and processing efficiency.

Quantum and classical logic: Their respective roles

Quantum mechanics uses a non-distributive lattice logic, which is derived from classical logic by dropping distributive laws for 'and' and 'or' and replacing them with weaker connections.

Quantum mechanics from classical statistics

Quantum mechanics can emerge from classical statistics, with Heisenberg's uncertainty relation, entanglement, and Bell's inequalities following from the classical statistical system's particularities.

Categorical Quantum Mechanics II: Classical-Quantum Interaction

Quantum theory exhibits entanglement, GHZ-state and W-state entanglement, and 'genuine quantumness' in classical-quantum interactions, with 'phase spiders' providing a first glimpse of quantum non-locality.

Quantum particles and classical particles

Quantum particles and classical particles can interact to produce stationary states with discrete energies and serve as measuring instruments for determining quantum particle physical variables.

Quantum particles from classical statistics

Quantum particles and classical particles can be described in a common statistical framework, leading to potential cross-fertilization between classical statistics and quantum physics.

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