[Paper Review] Quantum violation of macroscopic realism and the transition to classical physics

Johannes Kofler|ArXiv.org|Dec 1, 2008

Quantum Computing Algorithms and Architecture7 references3 citations

TL;DR

This dissertation proposes that macroscopic realism emerges not from decoherence or collapse models, but from the fundamental limitation of coarse-grained measurements—where imprecise apparatuses prevent observation of quantum superpositions. It demonstrates that even for arbitrarily large spins, quantum violations of macrorealism persist under ideal measurements, but classical behavior arises naturally when only coarse-grained outcomes are accessible, resolving the quantum-to-classical transition without modifying quantum theory. The key contribution is showing that coarse-graining alone—without environmental decoherence—can enforce macrorealism and classical Newtonian laws, while identifying 'non-classical Hamiltonians' as the sole source of persistent quantum behavior under such measurements.

ABSTRACT

The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems stop to behave quantum mechanically and begin to behave classically is still heavily debated in the physics community and subject to theoretical and experimental research. This dissertation puts forward an approach to the quantum-to-classical transition fully within quantum theory and conceptually different from already existing models: It neither needs to refer to the uncontrollable environment of a system (decoherence) nor to change the quantum laws itself (collapse models), but puts the stress on the limits of observability of quantum phenomena due to the imprecision of our measurement apparatuses. For a certain class of time evolutions it is this mere restriction to coarse-grained measurements which is sufficient to see the natural emergence of macroscopic realism and even the classical Newtonian laws out of the full quantum formalism. But there also exist "non-classical" Hamiltonians for which a classical spatiotemporal description of the system's time evolution remains impossible even under fuzzy measurements or decoherence. It is argued that such Hamiltonians are unlikely to be spontaneously realized in nature because of their high complexity. The last part addresses the question of the origin of quantum randomness and proposes a link with mathematical undecidability.

Motivation & Objective

• To resolve the long-standing question of how the classical world emerges from quantum mechanics without relying on environmental decoherence or collapse models.
• To investigate the role of measurement precision in determining whether macroscopic systems can exhibit quantum behavior or must appear classical.
• To identify conditions under which quantum systems with large spins can still violate macrorealism, even under coarse-grained measurements.
• To explore the connection between quantum randomness and mathematical undecidability, proposing that irreducible quantum randomness may stem from Gödelian undecidability in axiomatic systems.
• To examine whether entanglement between macroscopic observables can persist under coarse-graining, and whether such entanglement conflicts with macrorealism.

Proposed method

• Uses the Leggett-Garg inequality as a diagnostic tool to test macrorealism in quantum systems, particularly for large spins.
• Analyzes time evolution under coarse-grained measurements using positive operator-valued measures (POVMs), modeling measurement imprecision as a fundamental limit on observability.
• Applies the concept of statistical mixtures to represent classical ensembles of states, showing that such mixtures can reproduce classical laws when measurements are coarse.
• Identifies 'non-classical Hamiltonians' as those that cannot be described by classical time evolution even under coarse-grained measurements, using the example of an oscillating Schrödinger cat state.
• Proposes a link between quantum measurement outcomes and mathematical decidability, modeling quantum states as encoding axiomatic systems where undecidability leads to random measurement results.
• Investigates entanglement between collective operators in spin ensembles and harmonic chains, using collective spin and field operators to quantify macroscopic entanglement under sharp measurements.

Experimental results

Research questions

• RQ1 Can macroscopic realism be violated even for arbitrarily large quantum systems under ideal (sharp) measurements, and if so, what prevents classical behavior from emerging?
• RQ2 To what extent does coarse-grained measurement alone—without environmental decoherence—suffice to enforce macrorealism and classical Newtonian dynamics?
• RQ3 What types of Hamiltonians lead to violations of macrorealism even under coarse-grained measurements, and why are such Hamiltonians unlikely to occur in nature?
• RQ4 Can quantum randomness be fundamentally linked to mathematical undecidability, such that undecidable propositions in an axiomatic system lead to irreducible randomness in quantum measurements?
• RQ5 Can entanglement between macroscopic observables persist under coarse-graining, and does this contradict the emergence of classical behavior via measurement imprecision?

Key findings

• For any spin size, quantum mechanics violates macrorealism under ideal (sharp) measurements, demonstrating that large quantum numbers alone do not yield classical behavior.
• Coarse-grained measurements—modeling realistic experimental limitations—suffice to enforce macrorealism and classical Newtonian laws, even for large spins, without requiring environmental decoherence.
• Non-classical Hamiltonians exist that lead to time evolutions incompatible with classical laws, even under coarse-grained measurements, and these are shown to be unlikely in nature due to high particle interaction or computational complexity.
• The time evolution of a statistical mixture under coarse-grained measurements can be classical only if the Hamiltonian is compatible with the measurement structure; otherwise, macrorealism is violated.
• Quantum randomness is linked to mathematical undecidability: when a proposition is undecidable within the axiomatic set encoded in a quantum state, the corresponding measurement yields random outcomes.
• Theoretical and experimental results confirm that undecidability in the encoded axiomatic system leads to irreducible randomness, supporting the view that quantum randomness is not a limitation of knowledge but a fundamental feature tied to logic.