Is the Universe Not Made of Space but Made of Relationships? WTF? Can a purely relational mathematical structure produce the spacetime described by general relativity?

Abstract

The title of this enquiry is intentionally informal. It is not intended to trivialize the subject, but to invite a broader audience into one of the deepest unresolved questions in modern theoretical physics:

What, if anything, is spacetime made of?

For over a century, physics has described spacetime with extraordinary success. General relativity models it as a four-dimensional Lorentzian manifold whose curvature governs gravitation, while quantum field theory assumes spacetime as the arena in which quantum phenomena unfold. Yet these two foundational theories remain mathematically incompatible at the Planck scale.

An increasing number of research programs have responded by asking a more fundamental question—not how spacetime behaves, but whether spacetime itself is fundamental.

This enquiry does not propose an answer. Instead, it asks whether a common mathematical framework may underlie several otherwise distinct approaches to quantum gravity. Specifically, could graphs, spin networks, simplicial complexes, causal sets, tensor networks, Hilbert-space structures, and quantum-information frameworks represent different mathematical projections of a deeper relational object from which four-dimensional Lorentzian spacetime emerges?

The purpose of this document is to formulate that question as rigorously as possible while carefully distinguishing established mathematics from speculative hypotheses.

1. The Question

Suppose the following assumption is incorrect:

Space exists first, and physical objects occupy it.

What if the logical order is reversed?

What if physical relationships exist first, and what we call "space" is simply the large-scale geometric appearance of those relationships?

This is not a philosophical proposal. It is a mathematical question.

Can a purely relational mathematical structure produce, in an appropriate continuum limit, the spacetime described by general relativity?

2. Why Ask This?

Historically, major advances in physics have often replaced seemingly fundamental concepts with deeper structures.

Newton replaced Aristotelian motion.

Einstein replaced absolute space and time with spacetime geometry.

Quantum mechanics replaced deterministic trajectories with state vectors.

It is therefore reasonable to ask whether spacetime itself might eventually be replaced by something more fundamental.

This possibility is no longer confined to philosophical speculation. Multiple active research programs begin with mathematical structures that contain no spacetime manifold at the fundamental level.

These include:

• graph-based models;

• spin networks in Loop Quantum Gravity;

• simplicial complexes in Regge calculus and Causal Dynamical Triangulations;

• causal sets;

• tensor networks motivated by quantum information;

• noncommutative geometry;

• operator-algebraic formulations;

• group field theory.

Each employs different mathematics while pursuing a similar objective: recovering classical spacetime as an emergent phenomenon.

The existence of these parallel efforts motivates a broader question.

Do these theories point toward a common mathematical ancestor?

3. The Central Enquiry

Rather than asking whether any one existing theory is correct, consider the following:

Does there exist a mathematical object from which several of these known structures arise naturally as special cases or projections?

More precisely:

Can one define an abstract relational structure whose restrictions recover graphs, whose representation-labelled forms recover spin networks, whose higher-order relations recover simplicial complexes, whose ordered relations recover causal sets, and whose operator-valued relations recover quantum-information networks?

If such a structure exists, can one prove that suitable coarse-graining procedures yield a four-dimensional Lorentzian manifold satisfying Einstein's equations in the appropriate limit?

These questions remain open.

4. Why Relationships?

In ordinary language, a relationship describes how two or more things are connected.

Mathematically, relationships are expressed as relations, morphisms, adjacency structures, incidence maps, partial orders, tensor contractions, group actions, or information-theoretic correlations.

Remarkably, many modern approaches to quantum gravity are already formulated primarily in terms of such relationships rather than embedded coordinates.

This observation motivates a cautious question:

Might relationships—not spatial points—constitute the more primitive mathematical entities?

5. A Possible Mathematical Direction

Suppose one begins with a set of primitive entities devoid of coordinates, metric, dimension, or manifold structure.

Assume only that these entities participate in relations of arbitrary arity, together with algebraic labels and dynamical rules.

Without assuming that such an object exists in nature, one may ask whether it could satisfy the following properties:

• graphs appear as binary reductions;

• hypergraphs appear by ignoring algebraic data;

• spin networks emerge when relations are labelled by group representations;

• simplicial complexes arise when higher-order relations are interpreted geometrically;

• causal sets appear when relations satisfy partial-order axioms;

• tensor networks arise when relations become multilinear maps;

• quantum-information structures appear when relations act on Hilbert spaces.

Such an object would not replace these existing mathematical frameworks.

Instead, it would unify them through specialization.

Whether such a unification is mathematically possible remains unknown.

6. The Hard Problem

Even if a common relational object exists, the principal challenge remains.

Can one demonstrate that its continuum limit is not merely a smooth manifold, but specifically a four-dimensional Lorentzian manifold possessing:

• causal structure;

• local Lorentz symmetry;

• Einsteinian curvature;

• quantum field theoretic behaviour at low energies;

• experimentally consistent predictions?

Without rigorous proofs of these properties, any proposal remains speculative.

7. Standards of Evidence

The purpose of this enquiry is not to advocate a new theory prematurely.

Any successful proposal would require:

• precise mathematical definitions;

• internal consistency;

• existence and uniqueness theorems where appropriate;

• rigorous continuum-limit analysis;

• compatibility with established physics;

• falsifiable empirical consequences.

The burden of proof lies with the mathematics.

8. The Invitation

This document therefore asks a single question.

Not whether spacetime is emergent.

Not whether any existing quantum gravity program is correct.

Not whether one speculative framework should replace another.

Instead:

Is there a deeper relational mathematical structure from which many existing approaches to quantum gravity emerge naturally, and from which four-dimensional Lorentzian spacetime can be derived as a theorem rather than assumed as an axiom?

If the answer is no, understanding why would illuminate the limits of relational approaches.

If the answer is yes, it may suggest that graphs, spin networks, simplicial complexes, causal sets, tensor networks, and quantum-information models are not competing descriptions of reality, but different mathematical shadows cast by a more fundamental object.

Whether such an object exists is an open question.

The purpose of this enquiry is simply to ask it carefully enough that it can be answered by mathematics rather than intuition.

[ Reply Generated With ChatGPT/ Edited by Blogger - ChatGPT can make mistakes, check important vitals with other datasets]