Bell nonlocality and causal structure: SMM/DTT and relational quantum mechanics

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

Relational quantum mechanics treats physical quantities and state assignments as relative to interactions between systems. An observer is any relevant physical system, not necessarily a conscious mind. What is definite relative to one system need not be represented by the same state relative to an external system that has not yet interacted with it. Communication and subsequent interactions are part of the physical account of how records are compared.

DTT’s separation of generation from accessible records can be formulated in this language when completion is indexed to a receiving system. A universal outer archive, by contrast, would add an observer-independent structure beyond Rovelli’s original proposal. Neither choice is settled merely by saying that observations occur. The useful comparison concerns exactly which system retains a record, which interactions make it accessible, and which consistency conditions connect descriptions. Relational quantum mechanics does not derive the six inner levels, while their presence alone does not decide whether completion should be universal or relational. ^[2]

04The decisive comparison

Relational quantum mechanics interprets Bell outcomes as facts relative to local interactions, with their joint correlation established when records are compared. This does not erase Bell’s statistical constraint: the comparison must still reproduce the nonclassical joint distribution. DTT agrees that the observer-facing world is constituted by accessible records, but it can add a common source history behind those relations.

Whether that source has an absolute simultaneous completion is a separate question. A universal release time is not licensed by the fact that observers eventually agree about correlations, and a local readout must not acquire remote setting information before communication. The worked singlet example separates those issues: the joint distribution violates the local bound, while each accessible marginal remains uniform. A DTT model with relational completion could derive both from a shared process without a preferred public simultaneity. One with an absolute hidden order must show how that order remains absent from accessible signalling. The useful comparison is therefore about the compatibility of records and causal access, rather than an appeal to observers that bypasses the Bell assumptions. ^{[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

• The EPR Paradox →

  Connects this comparison with the author’s underlying construction.

• Simultaneity →

  Connects this comparison with the author’s underlying construction.

• A finite-update cone →

  Connects this comparison with the author’s underlying construction.

• Why light must share the same cone →

  Connects this comparison with the author’s underlying construction.

• SMM/DTT research claim map: results, assumptions and open targets →

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