Can a causal or time-like structure emerge without assuming a metric ?

[DavidMartin]

In most relativistic frameworks, time and causality are defined through an underlying spacetime metric with Lorentzian signature.

I’m wondering whether there are approaches where a notion of time ordering or causal structure can emerge prior to assuming a metric structure.

For example, can asymmetry in relational or informational structures be sufficient to define a time-like direction, with a metric description appearing only as an effective or secondary construct?

I’m not looking for a new theory claim, but rather for existing frameworks, models, or references where causality or time is treated as emergent rather than postulated.

Any pointers to known approaches or critical arguments against this idea would be appreciated.

 

[Ibix]

I'd have said SR itself fits the bill, at least if you follow Einstein's original postulates rather than starting by postulating Minkowski spacetime or something like that. You postulate the invariance of the speed of light and the principle of relativity and the causal structure emerges from the properties of the Lorentz transforms that you discover.

 

[DavidMartin]

I agree that in Einstein’s original formulation, causal structure is not postulated geometrically but follows from the Lorentz transformations derived from the two physical postulates.

My interest is precisely in understanding how minimal those postulates can be: whether some form of asymmetry or relational structure could play a role analogous to the invariance of ccc, with metric notions appearing only at a later stage.

Do you know of approaches where the Lorentz structure itself is derived from more primitive relational or informational assumptions?

 

[robphy]

Do you know of approaches where the Lorentz structure itself is derived from more primitive relational or informational assumptions?

AA Robb studied the “conical order” in terms of “before” and “after”.

 

[DavidMartin]

Thanks, that’s helpful.


If I understand correctly, Robb’s “conical order” is essentially an order-theoretic notion of “before” and “after”, defined purely in terms of causal accessibility rather than a metric or clock time.

In that sense, the light-cone structure encodes a primitive asymmetry, and notions like time orientation and Lorentzian geometry can be reconstructed from this causal order rather than postulated upfront.

Would it be fair to say that Robb’s work already points toward causality being more fundamental than the metric, with geometry emerging as a secondary description?

 

[robphy]

Would it be fair to say that Robb’s work already points toward causality being more fundamental than the metric, with geometry emerging as a secondary description?

I think that’s a fair statement.

 

[robphy]

You might be interested in David Malament’s dissertation:
“Does the Causal Structure of Space-Time Determine its Geometry”
https://digitalcommons.rockefeller.edu/student_theses_and_dissertations/496/
and
"The class of continuous timelike curves determines the topology of spacetime"
J. Math. Phys. 18, 1399–1404 (1977)
https://doi.org/10.1063/1.523436
https://pubs.aip.org/aip/jmp/articl...lass-of-continuous-timelike-curves-determines

 

[renormalize]

Would it be fair to say that Robb’s work already points toward causality being more fundamental than the metric, with geometry emerging as a secondary description?

Take a look at https://en.wikipedia.org/wiki/Causal_sets:
"The causal sets program is an approach to quantum gravity. Its founding principles are that spacetime is fundamentally discrete (a collection of discrete spacetime points, called the elements of the causal set) and that spacetime events are related by a partial order. This partial order has the physical meaning of the causality relations between spacetime events."