semi-automatic waffle

Thursday, 13 November 2025

Sure — let’s take Causal Set Theory (CST) apart carefully. It’s one of the most elegant and conceptually radical approaches to quantum gravity, precisely because it rethinks spacetime itself as discrete and fundamentally relational rather than continuous.

1. The core intuition

Causal Set Theory begins with two basic ideas:

Spacetime is discrete, not continuous — like a fabric made of individual “atoms” of spacetime.
Causality, not geometry, is fundamental — the structure of cause-and-effect between events is what gives rise to spacetime geometry.

That means: instead of imagining spacetime as a smooth manifold (as in general relativity), CST imagines a set of events with a causal order — “who can influence whom.”

Everything else — distance, dimension, curvature — is supposed to emerge from this bare causal structure.

2. The mathematical structure

Formally, a causal set (or causet) is:

A set of elements (think “events”),
Equipped with a partial order ≺ that represents causality,
That satisfies two conditions:
1. Transitivity — if A ≺ B and B ≺ C, then A ≺ C.
2. Acyclicity — no loops (you can’t have A ≺ A).
3. Local finiteness — between any two events, there are only finitely many intermediate events (this enforces discreteness).

So mathematically:

A causal set is a locally finite partially ordered set (poset).

3. How spacetime geometry emerges

In general relativity, spacetime is a smooth 4D manifold with a metric tensor that encodes causal relations and distances.
CST inverts that logic: start from causal relations, and recover the geometry statistically.

The order encodes the causal structure (light cones, time flow).
The number of elements corresponds to spacetime volume (since it’s discrete).

Roughly, if you “sprinkle” points randomly in a region of spacetime (using a Poisson distribution), their causal relations will approximate a causal set. Conversely, given a causal set that approximates a smooth spacetime, you can reconstruct the geometry from the order and count of elements.

That’s the slogan:

Order + Number = Geometry.

⚛️ 4. Why this matters for quantum gravity

CST aims to reconcile general relativity and quantum mechanics by discretizing spacetime without breaking Lorentz invariance (special relativity’s symmetry).

In a lattice or grid model, Lorentz symmetry is broken. But in a causal set, because it’s just an unordered sprinkling of events governed by causal relations, Lorentz symmetry can be preserved statistically.

The hope is that by summing over possible causal sets (like a “path integral” over spacetimes), one could obtain a quantum theory of gravity that naturally explains the emergence of the smooth spacetime we experience.

5. Conceptual implications

CST proposes a universe that is:

Discrete (no infinite divisibility, no continuous manifold).
Relational (only causal order matters, no background space).
Dynamic (the causal set “grows” by new events coming into being).

In some versions (like the Classical Sequential Growth models), the universe literally grows one element at a time, with each new event causally linked to the existing set — almost like a cosmic blockchain of causality.

6. Challenges and open questions

How exactly does quantum superposition of causal sets work?
How does continuum spacetime (and Einstein’s equations) emerge from a causal set?
Can CST make testable predictions, e.g. about discreteness at the Planck scale or violations of locality?
Does time truly flow (ontological becoming), or is that just an artifact of the growth model?

These are still open — CST is elegant but incomplete.

🜍 7. Philosophical side note

Instead of points in space, there are events.
Instead of pre-given structure, there’s emergent order from relations.
Instead of smooth continuity, there’s granular becoming.

Spacetime, in this view, is not the container of events — it is the causal web of events.