The PBR theorem (proposed by Pusey, Barrett, and Rudolph in 2012) is often interpreted as a fatal blow to the view that "the wavefunction is merely knowledge," seemingly proving once and for all that the wavefunction must be part of physical reality (ψ-ontic). However, from the perspective of Natural Quantum Theory (NQT), this conclusion does not hold, as it relies on physically invalid implicit premises and highlights NQT's ontological clarity.
I. Traditional Interpretation: A False Dilemma
The PBR theorem attempts to resolve a fundamental question:
Does the wavefunction describe "the world itself" or "our knowledge of the world"?
To this end, it establishes two models:
ψ-ontic: Each pure quantum state |ψ⟩ uniquely corresponds to a physical state λ. The wavefunction is "real."
ψ-epistemic: Multiple different |ψ⟩ can correspond to the same underlying physical state λ. The wavefunction is merely "incomplete knowledge."
The theorem's core argument is:
If two different states (e.g., |0⟩ and |+⟩ = (|0⟩ + |1⟩)/√2) could share the same λ, then through cleverly designed joint measurements (e.g., specific projections on two independently prepared systems), results contradictory to quantum mechanical predictions would emerge.
Therefore, ψ-epistemic models are excluded, and the wavefunction must be ψ-ontic.
This conclusion is widely regarded as a devastating blow to instrumentalist positions like the Copenhagen interpretation.
II. NQT's Third Way: Beyond the Binary
Natural Quantum Theory fundamentally rejects the binary framework presupposed by the PBR theorem. In NQT's view, the wavefunction is neither "subjective knowledge" (ψ-epistemic) nor "ultimate entity" (standard ψ-ontic), but rather:
A spectral representation of the global eigenmodes formed by classical physical systems (e.g., electromagnetic fields) under constraints.
This implies:
NQT is scientific realist: It firmly believes in an observer-independent physical reality—the continuous, local, classical field and its topological structures.
But the wavefunction is not that reality itself: Like Fourier coefficients, it is a mathematical encoding of the system's permissible vibrational modes.
Thus, the wavefunction possesses objectivity (as it describes objective modes) without ontological priority (it is not a "thing," but a "mode of description").
This positioning allows NQT to completely escape the PBR theorem's logical trap.
III. The Validity of the Preparation Independence Assumption
The PBR theorem's proof relies on a core assumption—Preparation Independence:
If system A is prepared in state |ψ⟩ and system B in state |φ⟩, and they are spatially separated, their joint physical state is λ_A ⊗ λ_B, with no correlation between them.
NQT argues that this assumption is fundamentally invalid in physics.
1. "Preparation" = Establishing a Global Mode
In NQT, so-called "preparing a quantum state" essentially means exciting a coherent global electromagnetic mode through specific experimental apparatus (e.g., lasers, nonlinear crystals, cavities).
This mode is determined by the entire system's boundary conditions, geometry, and initial excitation.
It is inseparable and cannot be decomposed into the sum of independent subsystem properties.
2. Different Wavefunctions Correspond to Different Physical Preparation Processes
Producing a |0⟩ state requires one specific apparatus configuration (e.g., polarizers, phase shifters).
Producing a |+⟩ state requires another, physically distinct configuration.
→ Therefore, the underlying physical states (i.e., global field modes) from these two different apparatus are naturally different.
They cannot share the same λ because, in NQT, the mode itself is the physical state.
3. Guitar String Analogy: Mode = State
Imagine a guitar string:
Plucking method A → excites the fundamental mode (analogous to |0⟩).
Plucking method B → excites the first harmonic (analogous to |+⟩).
Can you say "the string's 'true physical state' is the same for both plucking methods"? Obviously not.
The mode itself is the manifestation of the physical state, not "incomplete knowledge" of some hidden state.
Similarly, in NQT, what the wavefunction tags is the objective vibrational configuration of the physical field.
IV. How Does NQT Explain PBR-Type Experiments?
Even if a PBR-type joint measurement experiment were performed, NQT could provide a consistent explanation:
The two systems, seemingly "independently prepared," actually originate from distinct global field excitation processes.
The joint measurement apparatus introduces new overall boundary conditions, allowing only self-consistent mode combinations to pass.
The observed statistical results reflect deterministic responses of mode matching, not "wavefunction collapse" or "hidden variable determination."
Thus, the phenomena conform to quantum mechanical predictions, while the mechanism remains entirely classical, local, and continuous.
V. Conclusion: The PBR Theorem Becomes Evidence for NQT
In summary, Natural Quantum Theory's critique of the PBR theorem boils down to three points:
PBR attacks the wrong target: It refutes models where "wavefunction = subjective knowledge," a position NQT does not hold.
PBR relies on an invalid assumption: "Preparation Independence" naturally fails under NQT's global-mode worldview.
NQT provides a reasonable explanation for "wavefunction reality": The wavefunction is "real" because it precisely characterizes objectively existing eigenmodes of classical fields—not mysterious quantum entities, but understandable physical structures.
| Theory | View of Wavefunction | Relation to PBR Theorem |
|---|---|---|
| Traditional ψ-ontic (e.g., Many-Worlds) | Wavefunction is the universe's fundamental entity | Supports PBR, but falls into mathematical ontology |
| Traditional ψ-epistemic | Wavefunction is observer's incomplete knowledge | Refuted by PBR |
| Natural Quantum Theory (NQT) | Wavefunction is spectral description of classical field's global modes | Unaffected, exposes PBR's premise flaws |
Ultimately, NQT transforms the PBR theorem from a "victory proclamation" supporting quantum mysticism into an opportunity revealing deep classical-physical unity.
As NQT insists:
Nature was never mysterious; we once described it with the wrong language. When we replace "particles" with "modes" and "fields" with "wavefunction entities," those seemingly counterintuitive "quantum paradoxes" become natural echoes of classical physics under constraints.
The PBR theorem is not an obstacle to NQT but a mirror illuminating its self-consistency—it reflects not the wavefunction's "ontological status," but the urgent call for humanity to update its cognitive paradigm.