"If we accept that two entangled particles cannot communicate through mechanisms internal to our spacetime, and we do not find a more ontologically satisfactory solution within the current spatiotemporal framework, the most logical and at the same time most parsimonious conclusion is that they are connected in another reality, here denoted as R′..."

Relational Coexistence Theory (TCR): Quantun and Cosmological Foundations - Pag 3 - 8 September 2025

TCR: a relational reality from which space and time emerge

The Theory of Relational Coexistence (TCR) is a scientific proposal born from not accepting physics paradoxes.

To address these paradoxes, through logical and mathematical reasoning, it posits that spacetime is not the universe’s primary entity, but emerges from a network of relations between entities.

These relations form a deeper layer of reality, called R′, from which the observable spacetime (R) arises and evolves.

The world we experience—made of events, distances, times, and measurements—is the manifestation of these fundamental relations.

In other words: TCR does not see space as the “container” and time as the “flow”; rather, it is the evolving of relations that creates time, and entities moving apart that creates space.

  • Unification: entanglement, gravity and expansion as manifestations of relations among entities.
  • Predictions & tests: suggests experiments and data comparisons (e.g., cosmic chronometers).
  • Open rigor: preprints, code and data are open with DOIs for independent verification.
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Author photo

Pietro
Curatola

Independent researcher, author of TCR

Pietro Curatola develops the Theory of Relational Coexistence (TCR), a framework in which spacetime emerges from a more fundamental relational domain. His work connects quantum mechanics and gravity, offering unified interpretations for entanglement, decoherence, cosmic expansion and the arrow of time. Preprints, code and data are published in an open form to promote reproducibility and critical evaluation.

Why it matters now

Three impact tracks, with examples and compact figures.

Low-z cosmology

Alternative interpretation of expansion and inhomogeneities: TCR suggests a measurable directional dependence.

Entanglement & decoherence

Relational coexistence offers a realist account for the origin of decoherence and the arrow of time.

Testable predictions

Directional tests with cosmic chronometers, signals in void/wall regions, experiments on decoherence times.

Publications & Resources (DOI, PDF, code)

Preprints, datasets and repositories for independent verification.

Theory of Relational Coexistence (TCR)

Ontological framework: spacetime emerging from R′; conceptual unification of quantum theory and gravity.

TCR-Cosmo: model and observational tests

Implications for H(z), directional analysis and void/wall comparisons with cosmic chronometers.

How to cite: download the CITATION.cff file from the repository to keep citations consistent in articles and posts.

Evidence & Data preview

Key plots and methodological notes. For details, see the preprints.

Directional H(z) comparison

Hypothesis: higher H(z) along “void” directions than “wall”.

Relational decoherence signal

Decoherence times as a proxy for “relational temperature”.

FAQ explained simply

It’s a simple idea: spacetime is not the “first brick” of reality. First there is a network of relations (R′). What we see as space, time and forces emerges from how these relations organize.

It changes the ontology: it does not add exotic particles or fields; it reorganizes causes. Entanglement, gravity and expansion become aspects of the same “relational coexistence.”

Yes: it proposes directional tests of H(z) (void vs wall) and predictions on decoherence times. Protocols are described in the preprints with open data and code.

Glossary (excerpt)

Coexistence
Relational measure (0–1) of the “bond” between entities. High values indicate strong correlation.
R′
Pre-spacetime relational domain, from which the space and time observed in R emerge.
Decoherence
Loss of relational coherence; in TCR it is linked to the arrow of time.
See full TCR glossary

See full TCR-Cosmo glossary

Media & Press quick kit

Authorized materials for articles, interviews, talks.

Short bio (100 words)

Concise bio text for editors and moderators.

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Images & logos

TCR logotype, author photo, key charts in high resolution.

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Journalist brief

What TCR is, key points, contacts, DOI links.

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Contacts & Collaborations

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Quick references — TCR theory

Quick references — TCR Cosmo