[Paper Review] There is no first quantization - except in the de Broglie-Bohm interpretation

Hrvoje Nikolić|ArXiv.org|Jul 25, 2003

Quantum Mechanics and Applications2 references3 citations

TL;DR

This paper argues that first quantization is inconsistent with relativistic quantum field theory (QFT), as the standard probabilistic interpretation of wave functions fails in this context. Only the de Broglie-Bohm (dBB) interpretation remains consistent because it derives probabilities from deterministic particle trajectories, avoiding reliance on a fundamental probability postulate that breaks down in relativistic settings.

ABSTRACT

The relativistic effects of the integer-spin quantum field theory imply that the wave functions describing a fixed number of particles do not admit the usual probabilistic interpretation. Among several most popular interpretations of quantum mechanics applied to first quantization, the only interpretation for which this fact does not lead to a serious problem, and therefore the only consistent interpretation of first quantization, is the de Broglie-Bohm interpretation.

Motivation & Objective

• To challenge the foundational validity of first quantization in relativistic quantum mechanics.
• To identify which interpretations of quantum mechanics remain consistent when subjected to relativistic QFT constraints.
• To demonstrate that the probabilistic postulates of standard interpretations (e.g., Copenhagen, many-worlds) fail in relativistic contexts.
• To establish the de Broglie-Bohm interpretation as the only consistent interpretation of first quantization under relativistic constraints.
• To show that decoherence alone cannot resolve the measurement problem, but complements dBB by explaining statistical outcomes.

Proposed method

• Analyzes the standard postulates of quantum mechanics applied to first quantization, particularly the probabilistic interpretation via |c_i(t)|².
• Applies relativistic QFT to show that wave functions describing fixed particle numbers do not support a consistent probability interpretation due to non-unitary scalar products.
• Evaluates five major interpretations (Copenhagen, minimal probabilistic, consistent histories, Everett, dBB) for consistency under relativistic constraints.
• Demonstrates that only the dBB interpretation avoids reliance on a fundamental probability postulate by deriving probabilities from deterministic particle trajectories.
• Integrates decoherence into the dBB framework to explain why measurement outcomes appear probabilistic, without postulating wave function collapse.
• Uses the dBB equation of motion (e.g., v = ∇S/m) in a relativistic generalization to show that probabilities can be derived from deterministic dynamics.

Experimental results

Research questions

• RQ1 Why does the standard probabilistic interpretation of wave functions fail in relativistic quantum field theory?
• RQ2 Which interpretations of first quantization remain consistent when subjected to relativistic constraints?
• RQ3 Can the de Broglie-Bohm interpretation consistently derive the Born rule without relying on a fundamental probability postulate?
• RQ4 How does decoherence interact with the de Broglie-Bohm interpretation to explain measurement outcomes?
• RQ5 Why do other interpretations (e.g., Everett, Copenhagen) fail in the context of relativistic QFT?

Key findings

• The probabilistic interpretation of wave functions in first quantization is inconsistent with relativistic QFT because the required unitary scalar product (ψ_i, ψ_j) = δ_ij cannot be maintained.
• The Copenhagen, minimal probabilistic, consistent-history, and Everett interpretations all rely on a fundamental postulate of probability, which fails in relativistic settings.
• The de Broglie-Bohm interpretation is the only interpretation that remains consistent because it derives probabilities from deterministic particle trajectories rather than postulating them.
• In the dBB interpretation, the probability distribution of particle positions is given by |ψ(X,t)|², which is consistent with quantum predictions when combined with the measurement theory based on decoherence.
• Decoherence explains why classical statistics apply to measurement outcomes, but cannot explain why definite values are obtained—this is resolved by the dBB interpretation.
• The dBB interpretation can be extended to relativistic QFT, where nonlinearities in the equations of motion do not lead to inconsistencies, unlike in standard interpretations.