= Solution
In <Bohmian mechanics>, the corpuscles supply an actual configuration of matter, not a further branch of the <wave function>. Their positions and the guiding wave together specify the physical state. In a common nonrelativistic spinless formulation, the wave obeys the <Schrödinger equation> while the actual configuration $Q=(Q_1,\ldots,Q_N)$ obeys
$$
\dot Q_k=\frac{\hbar}{m_k}\operatorname{Im}\frac{\nabla_k\Psi}{\Psi}(Q,t),
$$
where the expression is applied away from nodes of $\Psi$. These are coupled in the sense that the wave guides the configuration; in the standard theory the wave's Schrödinger evolution does not receive a reciprocal source term from the actual particle positions. This is not a model of classical little balls carrying every ordinary observable as a pre-existing intrinsic attribute.
The point of adding a configuration is especially clear in a measurement. A wave may evolve into several macroscopically separated pointer packets. The apparatus's actual particle configuration lies in one packet, so there is a definite pointer record even though the full wave has not undergone fundamental collapse. The corpuscles thereby connect the mathematical description with the location of actual apparatus, records and observers. <David Bohm>'s original papers provide a theory of individual processes and analyse measurement in this spirit.<A Suggested Interpretation of the Quantum Theory in Terms of Hidden Variables I by David Bohm>[1952, Physical Review 85, pages 166–179: additional variables and continuous individual dynamics]{ref}<A Suggested Interpretation of the Quantum Theory in Terms of Hidden Variables II by David Bohm>[1952, Physical Review 85, pages 180–193: measurement analysis and correlations between separated systems]{ref}
For a subsystem, inserting the actual environment configuration into the universal wave gives a <conditional wave function>, schematically $\psi(x,t)\propto\Psi(x,Y(t),t)$. If the branches are suitably disjoint in the environment's configuration coordinates and remain dynamically isolated, the occupied branch supplies an <effective collapse in Bohmian mechanics>. The unoccupied branches are not simply erased by definition: before permanent separation, wave packets can recombine and affect interference. The conditional and effective wave-function constructions make this distinction precise.<Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory by Detlef Dürr and others>[sections 2.1–2.3, especially Conditional and Effective Wave Functions; conditional wave functions need not always obey an autonomous subsystem Schrödinger equation]{ref}
The <Born rule> also needs an account. The guidance current is $j_k=(\hbar/m_k)\operatorname{Im}(\Psi^*\nabla_k\Psi)$, and both $|\Psi|^2$ and an ensemble of guided configurations satisfy the associated <continuity equation>. Hence an initial <quantum equilibrium> distribution $\rho=|\Psi|^2$ is preserved. Equivariance supports the ordinary statistical predictions, but the guidance law alone does not prove that an arbitrarily prepared ensemble has that distribution.
The corpuscles are therefore neither detectors that a conscious observer adds to the theory nor dispensable labels attached after the statistics have been calculated. They constitute a <primitive ontology> that provides definite configurations, trajectories and records. Whether this is preferable to a wave-only ontology is a further explanatory judgement; its empirical equivalence in quantum equilibrium does not make the two accounts identical in their claims about what exists.
Back to article page
