Recent content by DavidMartin

Thank you guys, the causal sets brings me to recent research that may be linked to my personal research and framework starting from a network of abstract and a single axiom: minimizing global incompatibilites. From this, causal order emerges as a consequence — directed constraint weights...

Let V be a finite set and let R⊆V×V be a directed binary relation. Assume that R is not assumed to be transitive or acyclic a priori. Equivalently, think of R as the edge set of a directed graph G=(V,E), possibly containing directed cycles. I am interested in the following general question...

Back to origin : Suppose we have a directed weighted relation and define a stability condition that suppresses cycles. Under what conditions would transitivity appear as a stable configuration?

Type two hyphens (--) it generaly convert to em dash. I use that format in Visual Studio editor and .md files.

I don’t mean metaphysically fundamental — I mean structurally weaker. Szekeres’ signal relation is already assumed to satisfy certain axioms (e.g. reflexivity and other order-like properties). What I’m wondering about is whether one can start with a weaker structure — for example: • a...

I’m not asking whether partial orders can model spacetime (as in causal sets), but whether they can emerge from non-order relations ?

Could we come back to the sens of my question and ignore the emerging remaining ? :smile: Let me restate the core question more concisely. Suppose one starts with a directed relational structure 𝑅(𝑎,𝑏) that is not assumed to be transitive or acyclic. Are there known mathematical results...

That’s a fair request and didn's saw it sorry. By a law, I mean a dynamical rule governing evolution — for example Newton’s second law, Maxwell’s equations, or the Schrödinger equation. These specify how physical states change in time. By a relation, I mean a structural property between...

Let me sharpen the question slightly. Suppose one starts with a directed relational structure R(a,b) that is not assumed to be transitive or acyclic a priori. Are there known results characterizing when such a structure can dynamically or structurally induce a genuine partial order (i.e...

Suppose one starts not from a partial order, but from a non-symmetric compatibility relation R(a,b)≠R(b,a), with no metric assumed. Under what conditions would such a relation induce a consistent partial order (i.e. acyclic and transitive)? Is there any general result characterizing when a...

So the question becomes: is there any intermediate structure — weaker than a full Lorentzian metric — that is sufficient to induce a natural partial order? For example, could some non-symmetric compatibility or signaling relation serve that role without already assuming a metric?

That seems close in spirit to what I’m asking about — although in that framework the S relation itself is still taken as primitive. My question is whether there are approaches where even that non-symmetric signal/causal relation arises from something more primitive, rather than being postulated...

That’s a good point — in classical dynamics the second law is indeed the only fundamental time-asymmetric principle. My question is slightly different, though. I’m not necessarily referring to time-asymmetric laws, but to asymmetric relations. For example, a relation R(a,b) that is not...

My question is slightly more “upstream”: are there approaches where causal order is derived from some underlying relational structure — for example through instability, asymmetry, or symmetry breaking — rather than being postulated as a primitive partial order?