A real ensemble interpretation of quantum mechanics (1104.2822v1)

Abstract: A new ensemble interpretation of quantum mechanics is proposed according to which the ensemble associated to a quantum state really exists: it is the ensemble of all the systems in the same quantum state in the universe. Individual systems within the ensemble have microscopic states, described by beables. The probabilities of quantum theory turn out to be just ordinary relative frequencies probabilities in these ensembles. Laws for the evolution of the beables of individual systems are given such that their ensemble relative frequencies evolve in a way that reproduces the predictions of quantum mechanics. These laws are highly non-local and involve a new kind of interaction between the members of an ensemble that define a quantum state. These include a stochastic process by which individual systems copy the beables of other systems in the ensembles of which they are a member. The probabilities for these copy processes do not depend on where the systems are in space, but do depend on the distribution of beables in the ensemble. Macroscopic systems then are distinguished by being large and complex enough that they have no copies in the universe. They then cannot evolve by the copy law, and hence do not evolve stochastically according to quantum dynamics. This implies novel departures from quantum mechanics for systems in quantum states that can be expected to have few copies in the universe. At the same time, we are able to argue that the centre of masses of large macroscopic systems do satisfy Newton's laws.

• The paper posits that quantum states are actual ensembles, offering a deterministic framework that reinterprets standard quantum mechanics.
• It introduces copy dynamics and beables to model system evolution and reproduce key features of Schrödinger dynamics.
• The approach implies that quantum mechanics is an approximation for small subsystems with numerous copies, challenging dual ontologies.

A Real Ensemble Interpretation of Quantum Mechanics

In "A Real Ensemble Interpretation of Quantum Mechanics," Lee Smolin proposes a novel interpretation of quantum mechanics that posits the real existence of ensembles associated with quantum states. This approach addresses several foundational issues in quantum theory, particularly the measurement problem and the nature of probabilities in a quantum context. By explicitly associating quantum states with ensembles of systems that objectively exist in the universe, Smolin provides a framework that aims to reconcile quantum mechanics with a coherent ontology.

Key Hypotheses and Arguments

The paper introduces several core hypotheses that form the basis for this interpretation:

1. Ensemble Realism: Quantum states are not merely epistemic tools but correspond to actual ensembles of identically prepared systems across the universe. These ensembles consist of systems with the same constituents, preparation, and environment.
2. Theory of Beables: Smolin builds on the notion of 'beables' from hidden variable theories to provide a real and deterministic account of quantum systems. Each microscopic system in the ensemble is described by beables, which include values of certain observables and phases.
3. No Double Ontology: The paper seeks to avoid a dual ontology wherein both particles and wavefunctions are real entities influencing system dynamics. By doing so, it adheres to principles such as explanatory closure and no unreciprocated action, prevalent in theoretical physics.
4. Copy Dynamics: A novel mechanism is introduced for the evolution of beables. Systems within an ensemble can 'copy' the state of other systems randomly, with probabilities depending on ensemble distributions. This non-local interaction replaces the mysterious influence of wavefunctions in other theories.
5. Approximation to Cosmological Theory: Quantum mechanics is viewed as an approximation that applies to small subsystems of a universe dense with identical copies. It does not apply to macroscopic systems like cats or humans, which are unique and lack such ensembles.

Numerical and Theoretical Implications

The formalism leads to a stochastic and continuous evolution of systems' states, mirroring quantum mechanical predictions. Smolin demonstrates that this framework can reproduce quantum kinematics and dynamics, providing a correspondence to Schrödinger's equation under certain conditions. The approach insists on time-reversal symmetry and respects the large N limit, similar to classical statistical mechanics.

The paper speculates on the emergence of classical mechanics from this framework by neglecting quantum potential at the limit $\hbar \to 0$. Smolin argues that macroscopic bodies can obey classical dynamics, even if their precise quantum states are unique. The concept of phase alignment is explored as essential for deriving Schrödinger dynamics from the evolution of beables.

Challenges and Future Directions

Several issues remain open for further investigation:

• Definition and Nature of Ensembles: A precise characterizing of ensembles in purely physical rather than quantum terms is needed, particularly for systems lacking a large number of copies.
• Composite and Hierarchical Systems: How beables function within systems of nested hierarchies, such as atoms within molecules, requires clarification to address issues like entanglement.
• Phase Alignment: Current mechanisms proposed for phase alignment remain speculative. More robust models are needed to stabilize phase alignment rigorously within the theory.
• Node Problem: Ensuring $n > 0$ for all states to avoid breakdowns in predictions is non-trivial and demands additional solutions beyond simply adding spectator states.

Conclusion

Smolin's real ensemble interpretation suggest novel approaches to resolving longstanding quantum mechanical conundrums, such as the measurement problem and non-local influences. While compelling, the hypothesis requires extensive theoretical development and empirical validation. Research must address unanswered questions about the nature of ensembles, stability of solutions, and potential empirical deviations from conventional quantum mechanics. By doing so, it may offer profound insights into the transition between quantum and classical realms, and the underlying ontology of the quantum world.