What Is the Substrate Hypothesis?
— Science — Substrate
Part of the Substrate science series for Wherever It Leads.
The Substrate Hypothesis is a fictional scientific theory. It is also built on real open questions in physics.
This post is an attempt to explain what the hypothesis claims, what evidence Leo Alderman constructs it from, and where the boundary sits between the real science and the fiction. The boundary is not where most readers expect it to be.
What the Hypothesis Claims
The Substrate Hypothesis, as Leo Alderman formulates it in Wherever It Leads, makes three connected claims.
First: space is not fundamental. The spatial relationships between events — the distances, the geometry, the structure of spacetime — are emergent from a deeper level of reality rather than being basic features of the world.
Second: the substrate from which space emerges is not itself spatial. It is a network of relationships that have no position, no extension, no location. Space arises from the pattern of these relationships the way temperature arises from the motion of molecules — as a derived quantity that does not exist at the level of the fundamental constituents.
Third: the relationships that constitute the substrate are not purely physical in the standard sense. They are, at their deepest level, something more like information — or something more like experience — than like matter or energy. The substrate is not made of stuff. It is made of something that is prior to the distinction between mind and matter.
This third claim is the one that gets Leo into trouble. The first two are speculative but scientifically respectable. The third is where his colleagues stop following him.
What the Real Physics Says
The first claim — that space is emergent — is not Leo's invention. It is a serious research programme in contemporary physics.
Loop quantum gravity, developed by Carlo Rovelli, Lee Smolin, and others, proposes that space is made of discrete quantum units — quanta of geometry — and that the smooth, continuous spacetime of general relativity is an approximation that emerges at large scales. At the Planck scale, roughly 10^-35 metres, space itself has a granular structure.
Causal set theory takes a different approach: it proposes that the fundamental structure of reality is a discrete set of events connected by causal relationships, and that spacetime geometry emerges from the pattern of these causal connections. Space and time are not the arena. They are what the arena looks like from the outside.
The holographic principle, supported by the mathematics of the AdS/CFT correspondence, suggests that the information content of a region of space is encoded on its boundary rather than in its volume — that three-dimensional space may be, in a precise mathematical sense, a projection of a two-dimensional structure. This is not a metaphor. It is a mathematical result with significant empirical support from the study of black holes and quantum gravity.
None of these programmes is established physics. They are serious, mathematically rigorous research programmes that take the emergence of space seriously. Leo's hypothesis is built on this foundation.
Where the Fiction Begins
The second claim — that the substrate is non-spatial — follows naturally from the first. If space is emergent, then the level from which it emerges is, by definition, not spatial. This is not controversial among physicists who take the emergence of space seriously.
The third claim is where Leo departs from mainstream physics.
The question of what the non-spatial substrate is made of is, in the real physics, left open. Loop quantum gravity describes the quanta of geometry mathematically without asking what they are made of. Causal set theory describes the causal relationships without asking what is doing the relating. The holographic principle describes the encoding without asking what the encoder is.
Leo's hypothesis is that this question — what is the substrate? — cannot be answered within the framework of physics as currently conceived, because physics as currently conceived assumes the primacy of the physical. If the substrate is prior to the distinction between mind and matter, then asking what it is made of in physical terms is like asking what temperature is made of in terms of temperature.
His mathematical framework proposes a specific structure for the substrate: a network of relational properties that he calls "attending" — a term he chose deliberately for its ambiguity between the physical sense (being present to, being in contact with) and the phenomenological sense (paying attention to, being aware of). The attending relationships generate spatial geometry as an emergent property. They also generate, under certain conditions, something that looks like experience.
This is speculative. Leo knows it is speculative. The novel is about what happens when the data starts to look less speculative than expected.
What Sarah Chen Is There to Disprove
Sarah Chen arrives at the Institute for Theoretical Physics with a specific mandate: to find the flaw in Leo's mathematics. She is one of the best mathematical physicists of her generation, and she has been sent by people who are certain the flaw exists.
What she finds instead is that the mathematics is clean. The framework is internally consistent. The predictions it makes about the structure of quantum correlations at cosmological scales are, as far as she can determine, correct.
The question she is left with is not whether the mathematics works. It is what the mathematics means.
The Substrate Hypothesis is a fictional theory. But the questions it is built on are real. The emergence of space is an open problem. The relationship between the physical and the experiential is an open problem. The nature of the substrate — if there is one — is an open problem.
The novel follows these questions honestly. The answers it finds are not the ones anyone expected.