The superposition principle

In The Principles of Quantum Mechanics (1930), Dirac identified the superposition principle as the distinctive novelty of quantum theory — the feature from which its entire departure from classical physics flows.

The principle states that states of a quantum system form a linear space. If ψ₁ and ψ₂ are possible states of a system, then any complex linear combination

c₁ψ₁ + c₂ψ₂

is also a possible state of that system. Physically, the system in that combined state is neither definitely in state ψ₁ nor definitely in state ψ₂ — and it's not merely a classical ignorance about which one it "really" is. It is in both, so to speak, with weighted amplitudes. The consequences:

• Interference. Classical probability mixtures just add probabilities (positive numbers). Quantum superpositions add amplitudes (complex numbers), which can cancel. This is why the double-slit experiment yields fringes: the two path-amplitudes sum and interfere.
• Measurement and the Born rule. Upon measurement, the superposition yields outcome ψ₁ with probability |c₁|², etc. The measurement problem — why observations yield definite outcomes when the dynamics is linear — is the price of the principle.
• Entanglement. Applied to composite systems, superposition gives states like (|↑↓⟩ − |↓↑⟩)/√2 that cannot be factored into states of the parts. Nonlocality follows.
• Linearity of dynamics. The Schrödinger equation is linear, so it maps superpositions to superpositions, preserving the structure over time.

For Dirac, this was the deep lesson: nature, at bottom, does not consist of things with definite properties evolving deterministically; it consists of state vectors in Hilbert space whose linear combinations are themselves states.

Wave function monism

If superposition is the fundamental principle, a natural metaphysical question follows: what is the world, if quantum theory is complete? Wave function monism (most influentially defended by David Albert, and a natural companion to Everettian many-worlds) answers: the wave function is all there is.

• The claim. Reality consists solely of the universal wave function Ψ — a single, physically real field evolving unitarily via the Schrödinger equation. There are no particles, no fields in 3-space, no objects over and above Ψ.
• Configuration space. Ψ lives not in three-dimensional space but on the 3N-dimensional configuration space of all the particles in the universe (3×10⁷⁰-odd dimensions, on standard counts). The monist embraces this: the fundamental arena is configuration space, and ordinary three-dimensionality is emergent or illusory.
• Emergence of the manifest image. Tables, chairs, and observers are, on this view, patterns or structures in Ψ — quasi-classical "branches" or decoherent worlds. What we take as a world of localized objects in 3-space is how the wave function's structure presents itself to observers who are themselves part of that structure.

Motivations. It takes the quantum state with maximal seriousness: since the state vector (via superposition) already encodes all dynamical behavior, positing anything extra — particles, primitive fields — seems ontologically redundant. And it avoids the dualism of interpretations (like Bohmian mechanics or GRW with a flash/primitive-matter ontology) that add a second "matter" component over and above the wave function.

Objections. Critics (Maudlin, Allori, and others) press two worries: first, the wave function is complex-valued and unsituated in ordinary space, so it's obscure how it could be the concrete physical world rather than merely describe it; second, the recovery of the three-dimensional manifest image from 3N-dimensional configuration space looks suspiciously like a miracle of emergence — the very appearance the theory was supposed to explain.

The connection

The two ideas are two sides of one coin. The superposition principle makes the quantum state a complete, linear object: nothing about the system needs to be added to Ψ, because every superposition is already a legitimate state and the linear dynamics never requires anything more. Wave function monism simply takes that at metaphysical face value: if Ψ does all the dynamical work and nothing else is needed, then nothing else exists. Dirac's principle is thus the engine; wave function monism is one way of drawing the ontological map that results.