A common generative source must reproduce the quantum joint distribution while preserving local control of observable signals. The decisive calculation combines Bell correlations, no-signalling and physically defined completion times.
The experimental problem concerns joint probabilities
Two observers prepare an entangled pair, separate its components and independently choose measurement settings. They later compare outcomes. Bell’s theorem shows that certain quantum correlations cannot be reproduced by a class of models in which outcomes depend only on the local setting and a shared classical variable, with the settings statistically independent of that variable. [2]
Bell tests therefore probe a precise combination of assumptions, rather than merely asking whether two distant objects are correlated. In the 2015 experiment of Hensen and collaborators, electron spins separated by 1.3 kilometres were used in a test addressing both locality and detection loopholes. Its observed violation supplies a concrete empirical benchmark for any proposed source model. [4]
The challenge for DTT is to calculate the same setting-dependent joint distribution and explain why an observer still cannot use the correlations alone to send a chosen message outside the observed causal cone.
Spatial separation need not mean independent generation
The original DTT account treats separated objects as appearances within one process of repeated creation. A completed spatial configuration contains relations among its components, while their formation belongs to the nested inner levels. An entangled pair can therefore be regarded as a jointly generated system even after its observed components become distant. The older article compares the universe to a coordinated field of excitations and interprets conservation and synchronization through that shared source. [1]
It contrasts ordinary macroscopic propagation through many coupled constituents with a small coherently prepared system whose correlations concern the whole state. This is the central idea to retain: measured distance and generative dependence answer different questions. The six inner stages are dependent construction levels, and the seventh role makes an observable result available. The most useful mathematical development assigns a joint state to the source and local instruments to the two observers, so that the correlation and signalling questions are solved within one model. [1]
A singlet supplies an explicit correlation target
Take the normalized two-spin singlet |ψ⟩ = (|01⟩−|10⟩)/√2. Let each observer measure spin along a unit direction, with outcomes labelled +1 and −1. The singlet has zero local mean in every direction and the joint correlation E(a,b) = −a·b. Its rotationally invariant anticorrelation gives a compact target for the source’s joint completion rule.
Equal directions give perfect anticorrelation. Perpendicular directions give four equally probable outcome pairs. Choosing a = z, a′ = x, b = (z+x)/√2 and b′ = (z−x)/√2 yields
The corresponding local hidden-variable bound is S ≤ 2. The CHSH formulation makes this a direct comparison between a proposed probability law and the statistics of a realizable experiment. [3]
Changing an unread local measurement leaves the distant marginal fixed
Summing the singlet distribution over the first observer’s outcome gives p(t|b) = 1/2, independently of a. This already shows that the setting at the first apparatus cannot encode a message in the second apparatus’s unconditioned outcome frequencies.
The same conclusion follows for any joint quantum state ρ and any trace-preserving local instrument with operators Ms. For a distant observable B, the expectation after ignoring the local outcome is
Conditioning on a particular reported outcome changes the predicted distant state, but using that information requires access to the outcome record. The trace calculation gives the temporal-source programme an exact consistency condition: inner coordination may generate a joint distribution, while every allowed local operation must preserve the distant unconditioned marginal.
A shared classical seed is insufficient for the target
A classical source can easily prepare opposite bits and send one to each observer. That reproduces perfect anticorrelation for one fixed measurement. It does not reproduce all singlet correlations when the observers independently choose several directions. If each output is only a function of its local setting and a shared setting-independent seed, the CHSH bound follows. [2, 3]
Consequently, a serial generative model must identify the physical structure that changes this analysis. It may realize an entangled quantum state with compatible local instruments, or it may propose a different dependence structure and calculate its observable consequences. Saying that the pair shares one origin leaves this choice open. The source state, admissible operations and probability rule are the ingredients that decide it.
The existing phase-and-composition target addresses an essential part of the quantum route: explaining why independently controlled subsystems combine in the required state space.
Keep hidden generation and measured propagation connected
Entangled correlation, tunnelling and ordinary transport require different operational descriptions. A tunnelling probability is a transition amplitude through a specified barrier; it should not be replaced by an unsupported statement about an instantaneous traversed path. Likewise, a distant correlation is measured by comparing records, not by watching an object travel between the detectors.
DTT can sharpen its original account by assigning physical clock readings to preparation and completion events and calculating the distribution of their delays. If the inner mechanism selects an ordering invisible to observers, show why allowed experiments cannot reveal a preferred frame through those delays or through controllable influence. If a residual timing effect is predicted, specify its size and its dependence on the prepared state.
This makes the relation between emergent spatial distance and generative dependence a quantitative research question.
One model should pass the joint test
Build the smallest autonomous source that prepares the singlet, accepts independently chosen detector settings, produces stable local outcomes and retains the records used for comparison. Compute the complete joint probability table, including unsuccessful preparations and completion-time selection. Then prove the no-signalling identity for every permitted local instrument.
A meaningful new prediction would link a small departure from the singlet law to a separately measured source-memory or completion parameter. A meaningful exact result would show that the same source dynamics enforcing local transport also produces the quantum correlation law. Both directions preserve the original SMM/DTT insight that observable separation need not imply independent formation, while confronting the strongest experimental and mathematical constraints on how that formation can work.
Books, papers and further reading
- Mohamed Haj Yousef, Duality of Time, Chapters V and VI
Original nonlocality account: repeated spatial creation, joint synchronization, conservation and the relation between macroscopic motion and small entangled systems.
- John S. Bell, On the Einstein Podolsky Rosen paradox (1964)
Local-response assumptions and the quantum correlation obstruction.
- John F. Clauser, Michael A. Horne, Abner Shimony and Richard A. Holt, Proposed Experiment to Test Local Hidden-Variable Theories (1969)
The CHSH inequality and an operational correlation test.
- B. Hensen and collaborators, Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres (2015)
Primary experimental benchmark; author manuscript available as arXiv:1508.05949.