Physical and psychical sectors: SMM/DTT and superselection sectors

01What sector means mathematically

Let a Hilbert space decompose as H = H₁ ⊕ H₂ and suppose every allowed observable is block diagonal: A = A₁ ⊕ A₂. The theory’s operational restriction prevents those observables from detecting a relative phase between the two blocks. This is an algebraic fact about the chosen observable set. It does not identify either block as mental, spiritual or nonphysical. To propose that interpretation, a model must explain why a particular sector has the relevant experiential character and why these are the allowed operations. ^[1]

02What the SMM/DTT distinction contributes

SMM begins with one nonspatial generative source. DTT distinguishes its inner production from the outer order in which completed results become accessible. The six inner levels are nested functional dependencies within that production; the seventh denotes outer completion. They are not six independent clocks, six spatial directions, or six simultaneously occupied temporal axes. This distinction makes the framework more specific than a general claim that everything changes: it asks how a world of persistent relations can be generated before its spatial representation is taken for granted.

Psychical and physical can name two kinds of description, two kinds of property, two modes of access, or two distinct realms of being. These are different positions. SMM/DTT’s attraction is the possibility that a single generative source supports both an outwardly measurable world and inwardly meaningful experience. A clear comparison begins by stating what the distinction means. Otherwise a shift from first-person experience to an additional spatial dimension can occur without argument.

An experience of red and a measurement of reflected light are related but answer different questions. The measurement specifies a public procedure and result. The experience concerns how something appears to a subject. A single-source ontology may seek to ground both, yet common dependence does not itself establish an identity between them or a law connecting them. If the psychical is given an autonomous causal role in physical events, the role must be specified. If it is a different aspect of the same events, the task is to explain the correspondence and the limits of each description. ^[2]

03Worked indistinguishability example

Take normalized states |a⟩ in H₁ and |b⟩ in H₂. For |ψθ⟩ = (|a⟩ + exp(iθ)|b⟩)/√2, the expectation of any block-diagonal A is one half of ⟨a|A₁|a⟩ + ⟨b|A₂|b⟩, independent of θ. The same expectation is obtained from the incoherent mixture of the two states. Thus the phase is invisible to that algebra. If an off-diagonal operation becomes physically available, the restriction can change. The example explains restricted observability; it provides no evidence for consciousness in the hidden phase or for an empirically established psychical sector.

04The specific SMM/DTT opportunity

DTT could derive different access algebras from its completion architecture. An observer might obtain only a subset of the source’s correlations, with other distinctions inaccessible after readout. That would be a concrete physical claim about access. A psychical interpretation would be a further bridge identifying first-person significance with some feature of the generated organization. This separation is valuable: it permits a rigorous sector model without declaring every inaccessible variable spiritual. The six inner levels remain nested functions of production, rather than six superselected worlds.

05A philosophical comparison with clear limits

Superselection and psychical privacy both involve a boundary on what can be accessed, but the boundaries have different meanings. An algebraic boundary is specified through operations and measurable expectations. First-person privacy concerns the ownership and character of experience. A common source can motivate a relation between them, yet the relation needs its own argument. The strongest SMM contribution would explain why particular access boundaries arise and how they coexist with reliable physical interaction. That would sharpen the discussion of realms without treating mathematical invisibility as sufficient evidence of a metaphysical domain.

06A further conceptual benchmark

A person silently imagines a triangle and later draws it. The imagined triangle is not a small physical object hidden behind the eyes; the drawing is not identical to the act of imagining. Both can be related through a person’s capacities, intentions and bodily actions. An account can treat these as two aspects of one process, as causally interacting states, or as different levels of description. Each interpretation must explain the same ordinary sequence without confusing representation with represented object. SMM/DTT’s source unity can frame the relation, but the transition from imagination to drawing still calls for a specified account of agency and physical action.

THE SAME QUESTION, DIFFERENT STARTING POINTS

The comparison at a glance

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