Bell nonlocality and causal structure: SMM/DTT and QBism

01The question behind this comparison

Bell inequalities test restrictions on correlations, not the speed of an observed signal. In the usual local causal model, outcomes at two separated laboratories become independent once the relevant common cause and local settings are specified. Measurement-setting independence is another premise. Quantum states can violate the resulting bounds while preserving the inability to transmit a controllable message by changing a distant measurement choice alone.

A Single Monad is naturally a common origin for records, but a common origin by itself does not evade Bell’s argument: the hidden variable in a Bell model already represents an arbitrarily rich common cause. The decisive issue is the form of the conditional probabilities. A DTT account must specify whether its source violates factorization, changes a setting-independence assumption, or uses a different causal structure. An inaccessible inner ordering is not an automatic explanation of the observed correlation law. ^{[3] [4] [5]}

02The SMM/DTT starting point

The Single Monad Model begins with one nonspatial generative source. The Duality of Time Theory distinguishes the source’s inner production from the outer order in which completed records become accessible. Its six inner levels are nested functional roles of one process: a higher role organizes lower-level work. The seventh is the completion or observation interface. They are neither six independent clocks nor six additional time coordinates.

This distinction supplies a useful research question: which features of an observed world can follow from the way a source produces, retains and releases information? A concrete answer needs a state space, an autonomous update, retained memory and a rule connecting completion to an accessible measurement. In the constructions discussed here, those mathematical ingredients are stated explicitly. A successful finite example establishes what its specified mechanism can do; further arguments connect it to physical particles, spacetime or universal laws. ^[1]

03How the comparator works

QBism interprets quantum probabilities as an agent’s personal expectations for the consequences of actions on the world. The quantum state belongs to that probability assignment rather than serving as a complete observer-independent description of the system. The Born rule acts as an additional normative constraint among an agent’s probability judgments. QBism does not deny an external world; it rejects an interpretation in which the state is simply a catalogue of its intrinsic properties.

The Single Monad Model has a much stronger ontological ambition: one source is intended to explain the production of physical multiplicity. A mathematical DTT model can still use an operational probability interface, but equating that interface with QBism would obscure this difference. The informative question is whether a proposed generative law imposes new, testable restrictions on the probabilities an agent should assign. If it does not, the two views can organize the same data while offering substantially different accounts of what the formalism means. ^[2]

04The decisive comparison

QBism describes a Bell experiment through an agent’s probabilities for the outcomes of actions and later record comparisons. Its authors resist interpreting a quantum state update as a physical disturbance propagating to a remote system. DTT instead seeks an underlying source process, which may coordinate the two records before or beneath their spatial description. These interpretational differences do not change the joint statistics that an experiment must reproduce.

The single-source hypothesis must be stated carefully: a shared cause compatible with Bell-local factorization cannot generate the ideal CHSH value under setting independence. A DTT account must identify the exact assumption its deeper process changes, while retaining the observed local marginals. QBism does not supply that hidden mechanism, because doing so is not its explanatory aim. Conversely, an ontic source mechanism does not eliminate the observer’s need for coherent probability assignments. The two approaches become empirically distinguishable only if the source imposes a further measurable restriction. A different vocabulary for collapse or nonlocality is insufficient; the restriction must appear in an operationally defined joint or conditional probability. ^{[2] [3] [4] [5]}

05Worked benchmark

For a spin singlet, the correlation of ±1 outcomes along unit vectors a and b is E(a,b)=−a·b. Choose a=z, a′=x, b=(z+x)/√2 and b′=(z−x)/√2. In the CHSH combination E(a,b)+E(a,b′)+E(a′,b)−E(a′,b′), the four terms add to −2√2, whose absolute value exceeds the local bound 2.

Each local outcome remains equally likely. Indeed the reduced state at either wing is I/2. A distant trace-preserving operation leaves the local reduced state unchanged when its outcome is not conditioned upon. Correlation beyond the Bell bound and no signalling therefore coexist in the same calculation. This is the benchmark for temporal source proposals: a mechanism must reproduce both facts. Explaining only the strong correlation while allowing the remote setting to change a local marginal would describe a different, experimentally constrained theory. ^{[3] [4] [5]}

06What follows for the source programme

The strongest use of DTT here is to make the hidden production architecture precise enough that its causal assumptions can be inspected. A source update that coordinates records may be nonlocal at the underlying level while yielding a relativistically admissible observable interface. That is a substantive possibility, but a claim of compatibility requires the interface calculation. Existing Bell violations support the quantum correlation structure, not a unique ontology of its origin. ^{[3] [4] [5]}

THE SAME QUESTION, DIFFERENT STARTING POINTS

The comparison at a glance

Continue on SMONAD

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  Places the comparison alongside the programme’s published results, assumptions and open targets.