Bell nonlocality and causal structure: SMM/DTT and Bohmian 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

Bohmian mechanics supplements a wavefunction with an actual configuration, ordinarily particle positions. The Schrödinger equation guides the wavefunction, and a velocity law guides the configuration. When configurations follow the quantum-equilibrium distribution, the theory reproduces the usual quantum statistics in its applicable domain. Apparatus outcomes are ultimately configurations too, so measurement is treated as a physical interaction rather than a separate primitive collapse.

This is an instructive comparison for SMM because it provides an explicit account of definite observed events while retaining an additional, nonclassical level of description. But a Bohmian particle follows a trajectory in a configuration space whose geometry is supplied. The Single Monad proposal instead seeks to explain how spatial and particle records arise at all. The challenge is therefore not to rename a guiding wave as inner time. It is to show what variables replace the configuration, how records obey the equilibrium statistics, and whether the replacement adds an observable consequence. ^[2]

04The decisive comparison

Bohmian mechanics is explicitly nonlocal in its configuration-space guidance for entangled systems, while quantum equilibrium yields the standard no-signalling statistics in its applicable setting. It therefore demonstrates that definite outcomes do not require Bell-local dynamics. DTT’s single-source production could likewise be nonlocal underneath the completed spatial interface without permitting controllable faster-than-light communication.

The correspondence remains incomplete until the source has an equivalent of the equilibrium mechanism. A hidden inner ordering can coordinate outputs, but if an experimenter can use it to change a remote marginal, the model predicts signalling. If the ordering is empirically inaccessible, a proof of that restriction is needed rather than an assurance that it is metaphysical. Bohmian mechanics offers a concrete benchmark because guidance, actual configurations and their distribution are all specified. DTT’s distinctive ambition is to generate the configuration and space themselves. A successful construction would therefore explain not just why outcomes correlate, but why the same source measure produces the singlet statistics and protects operational locality across changes of measurement setting. ^{[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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• Simultaneity →

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• A finite-update cone →

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• Why light must share the same cone →

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

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