Effect Propagation Process: A Philosophical Framework for Post-Quantum Causality

The concept of causality, fundamental to our understanding of the world, has evolved from ancient philosophical inquiries identifying multiple necessary factors for a cause to be true. This classical view required a spatiotemporal background, as argued by Seneca. However, this notion faced philosophical debate from relationalists like Leibniz and later critiques from Bertrand Russell regarding its status in physics.

The advent of quantum gravity, however, suggesting spacetime may be emergent from a deeper reality and causal structures can be indefinite, poses a profound challenge to traditional causality which relies on a defined background spacetime.

In response, the author proposes the “Effect Propagation Process” as a philosophical framework for post-quantum causality. In this framework, causality is viewed not as discrete links between events in a fixed spacetime, but as the fundamental continuous transfer of influence from within a deeper quantum structure. The “Effect Propagation Process” framework attempts to provide a unified perspective for post-quantum causality that remains compatible with classical causality and aligns with leading theories in quantum gravity.

History of Causality

In Timaeus (c 360 BC), one of the first known attempts to understand why things come into being, Plato explores the cause (aitia) and “contributing causes” (sunaitiai). Plato stipulates that multiple indispensable factors, the model, the maker (Demiurge), the material, and the space (receptacle), explain how the physical world with all the things in it are made¹.

Aristotle (c 350 BC) formalized the notion of causality in his Metaphysics² which serves as the foundation of the classical framework of the “Four Causes”³. These are:

1. The material cause or that which is given in reply to the question “What is it made out of?”

2. The formal cause or that which is given in reply to the question “What is it?”. What is singled out in the answer is the essence of the what-it-is-to-be something.

3. The efficient cause or that which is given in reply to the question: “Where does change (or motion) come from?”. What is singled out in the answer is the whence of change (or motion).

4. The final cause, the end purpose, is given in reply to the question: “What is its good?”. What is singled out in the answer is that for the sake of which something is done or takes place.

Aristotle moved beyond simplistic notions of causality to identify multiple, distinct factors necessary for explaining how things come into being and change.

Seneca (c 56 AD) argues in letter 65⁴ that cause and effect operate within a stage (space) and follow an order (time). Remove the stage or the order, and the conventional understanding of ‘making something’ or ‘causing something’ breaks down. His argument highlights time and place as indispensable conditions for ‘making something’, identifying the need for a spatiotemporal context as a prerequisite for classical causality. This focus on space and time as necessary conditions served as a precursor to later physical concepts treating spacetime as a background for causal processes.

The idea of space and time as an independent background did not go unchallenged in philosophy, even before the advent of modern physics. Gottfried Wilhelm Leibniz (1646-1716), in his famous debate with Isaac Newton’s representative, rejected the concept of absolute space and absolute time as independent, fundamental containers. Instead, Leibniz proposed⁵ a relational view, arguing that space is merely the order of coexisting things (simultaneity), and time is merely the order of successive things. For Leibniz, space and time were not substances or backgrounds that existed on their own, but systems of relations between the objects and events that constitute reality. He arrived at this conclusion through rigorous philosophical reasoning, arguing from fundamental metaphysical principles, such as the Principle of Sufficient Reason, that the concept of absolute space and time was logically untenable. This relational perspective offered a significant historical philosophical alternative to the pre-eminent Newtonian worldview of his time.

The impact of General Relativity on Causality

Einstein’s theory of General Relativity⁶ (GR) maintained the requirement for a spatiotemporal context as a prerequisite for causality, echoing Seneca’s insight. However, GR fundamentally transformed this prerequisite from the static, absolute background of earlier physics into a dynamic spacetime manifold, warped and influenced by matter and energy. Unlike a passive stage, the spacetime of GR is an active participant in the causal processes unfolding within it.

Bertrand Russell (1872 - 1970) wrote in his 1912 essay “On the Notion of Cause”⁷:

“The law of causality, I believe, like much that passes muster among philosophers, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm.” Bertrand Russell

For Russell, the traditional idea of causality, a necessary, temporal asymmetrical link between distinct events, did not match the sophisticated, law-based descriptions used in successful physics. Russell’s argument is rooted in his observation that physics describes how the state of a system evolves. The focus is on the state of a system (e.g., position, velocity, field strength across space) and how that entire state changes continuously, rather than isolating specific, discrete events as “causes” and “effects.”

Many fundamental physical laws are symmetrical in time or involve reciprocal relationships. If state S1 at time t1 is related to state S2 at time t2 by a law, it’s equally true that state S2 at time t2 is related to state S1 at time t1 by the same law. The relationship isn’t a one-way street from a necessary “cause” to a dependent “effect.” Knowing the state at any time allows you (ideally, in a deterministic system) to calculate the state at any other time, past or future. Therefore, which one is the “cause” and which is the “effect” becomes arbitrary, and Russell demonstrated remarkable foresight with this assessment.

The impact of Quantum Gravity on Causality

The emergence of Quantum Gravity with its Dynamic Causal Structure⁸ directly challenges the traditional separation of cause and effect, removes the spacetime frame of reference and introduces indefinite causal structures with time symmetry⁹. Therefore, the fundamental conceptualization of cause, effect, time, and space has been fundamentally challenged.

Seneca defines the necessary conditions for causality as space and time that provide location and ordering. In general relativity, the necessary conditions have been converged into a single spacetime manifold that serves as a frame of reference to determine location and order. However, Quantum Gravity requires a fundamental set of rules from which spatiotemporal relationships and causal order can emerge. Space and time are not necessary external conditions, but potential emergent properties of the necessary internal structure of reality itself. The problem isn’t anymore whether spacetime is static or dynamic, but that spacetime itself may emerge from the quantum level and thus positions itself as a higher-order effect of a generative process.

Instead of asking “Where and When does this cause operate?”, quantum gravity asks “What is the underlying process from which the notions of ‘where’ and ‘when’, and thus causal order, emerge?”

Russell saw physics moving towards laws governing states, a view echoed in quantum gravity’s search for fundamental rules or principles governing the structure from which spacetime and causal order emerge. At this stage, the understanding of causality evolved from a structure that required the existence of space and time as pre-given conditions for emergent causality. This emergent causality does not rely on a pre-existing spacetime, but is grounded in a more fundamental level of reality—a set of underlying rules or principles (i.e., conceptualized as a ‘generating function’) that determine the fundamental potential for existence, relation, and the eventual manifestation of spatiotemporal properties.

If this fundamental level (or its ‘output’ in terms of emergent properties) didn’t include states that resemble classical spacetime, then the conditions Seneca deemed necessary for “making things” (definite causal links) wouldn’t appear.

From the quantum perspective, ‘space and time’ that Seneca identified as necessary are not fundamental inputs to causality, but are outputs or emerging properties from a deeper quantum process grounded in this fundamental level.

The conceptualization of this fundamental level as a “generating function” captures the idea of a deeper source from which the necessary condition of classical causality’s spatiotemporal structure arises. It’s a shift from asking “What causes X given spacetime?” to “What process generates spacetime (and thus enables X to be caused)?”.

Causality as Effect Propagation Process

Logically, the understanding of causality evolves further towards an effect propagation process. Framing causality as an “effect propagation process” means:

1. Focus on the Transfer of Influence: It emphasizes the process by which a change, information, energy, or correlation at one point (in the fundamental structure) influences or leads to changes at another point. This is less about a discrete “cause A produces effect B” event linked by external space and time, and more about a continuous or discrete transfer through the underlying reality.

2. Detachment from Fixed Spacetime Paths: In quantum gravity, where spacetime geometry (and thus smooth paths) can be in a superposition or non-existent at the fundamental level, “propagation” isn’t necessarily movement along a geodesic in a fixed manifold. It’s the spreading of influence or correlation through the network, states, or elements defined by the fundamental structure.

3. Alignment with Emergence: When the fundamental structure gives rise to classical spacetime, this fundamental “effect propagation” would manifest as propagation through spacetime (e.g., waves, particles, forces traveling from one spatiotemporal point to another). Classical cause-and-effect becomes the macroscopic limit of this deeper process.

4. Handling Indefinite Causal Structures: In situations where the causal structure itself is indefinite (a superposition of different possible spacetimes or causal orders), “effect propagation” can be understood as the influence propagating through a superposition of possible pathways or relationships dictated by the fundamental structure. The “effect” isn’t tied to a single, definite causal link but is a result of the propagation through all possible (weighted) connections.

Russell correctly pointed out that the asymmetric relation between a cause and its effect depends on the presence of a temporal order (i.e., the arrow of time). In the Effect Propagation Process framework, due to the detachment from a fixed spacetime, this fundamental temporal order is absent. Consequently, the entire classical concept of causality, where cause must happen before effect (‘A happened before B’), cannot be fundamentally established. The distinction between a definitive ‘Cause’ and a definitive ‘Effect’ becomes untenable, just as Russell foresaw regarding the time-symmetry of fundamental laws. Instead of abandoning causality altogether in an indefinitive causal realm, the framework suggests merging the traditional notions of ‘cause’ and ’effect’ into a single, fundamental entity: the effect propagation process itself. This conceptualization, where causality is defined in terms of this uniform influence transfer rather than an asymmetric sequential link, is consistent with operational frameworks in quantum foundations, such as that proposed by Hardy⁸, which describe causal structure without presupposing a fixed spacetime background.

In this post-quantum context, the term “propagation” does not imply movement through a pre-existing space or over a defined time interval in the classical sense. Instead, it refers to the fundamental process by which influence, correlation, or causal efficacy is transferred or unfolds within the underlying structure of reality itself. This fundamental process is what gives rise to the appearance of propagation through spacetime in the classical, emergent limit. Furthermore, while classical causality relies on a definite temporal order and the apparent arrow of time (cause preceding effect), within the framework of the ’effect propagation process’, this directedness is understood as an emergent property, arising from the fundamental process in the classical limit, rather than being a fundamental feature of the process itself.

While the ’effect propagation process’ involves the transfer of influence or correlations within the fundamental structure, it is crucial to distinguish this from mere accidental correlation. The process reflects the fundamental way the underlying structure of reality mandates or constrains dependencies between its components, giving rise to the non-accidental relationships we recognize as causal connections in the emergent, classical world. This fundamental determination, rather than simple co-occurrence, is what the “effect propagation process” captures at the deepest level.

Replacing the notion of causality as requiring a pre-defined stage of space and time with the notion of causality being an effect propagation process then grounds post-quantum causality into a deeper quantum generative process. The notion of post-quantum causality as an effect propagation process remains agnostic of the exact quantum generative process.

Consequently, causality is understood as an effect propagation process that emerges from the fundamental structure or set of rules (akin to a generating function) from which spatiotemporal relationships emerge. Operating within this same fundamental structure, the process dictates how fundamental degrees of freedom relate and evolve.

The notion of the effect propagation process excludes the operational details of any particular physics theory and offers a coherent way of thinking about causality that aligns with the emergent nature of spacetime and the potential indefiniteness of causal order in the quantum realm. In doing so, it provides a unifying perspective for post-quantum causality by acknowledging the philosophical arguments for dynamic/relational reality which is rooted in process philosophy and relationalism.

This philosophical concept of the effect propagation process finds support in various areas of philosophy and physics. For example, the effect propagation process finds support in physical theories that propose fundamental structures underlying spacetime such as Causal Set Theory, and generalizes the idea of influence transfer present in standard physics (i.e., Quantum Field Theory). Lastly, the notion of causality as an effect propagation process offers a philosophical interpretation for mathematical tools that describe non-classical causal behavior, such as Process Matrices and Operational Frameworks like Hardy’s Causaloids.

The Teleology of the Effect Propagation Process:

Within the Effect Propagation Process framework, the traditional notion of a fundamental Final Cause or inherent purpose (like Aristotle’s teleology or Plato’s Demiurge acting for the Good) is not incorporated as a primary mechanism of causality at the deepest level. The framework focuses on describing the fundamental process of influence transfer and emergence based on the underlying structure’s rules, rather than explaining why that process occurs or for what end. Instead, teleological descriptions, if applicable, would likely be viewed as emergent properties of complex systems that arise from the fundamental Effect Propagation Process, or as a distinct layer of explanation relevant to the organization and behavior of macroscopic entities, rather than a fundamental aspect of causality itself.

The Ontology of the Effect Propagation Process:

The Effect Propagation Process framework fundamentally reconfigures our understanding of what is real at the deepest level. While classical causality operates within a spacetime ontology, the proposed framework suggests that fundamental reality is not spacetime itself, but an underlying structure or set of rules (conceptualized as a ‘generating function’). This fundamental level determines the potential for existence, relation, and eventual manifestation of spatiotemporal properties. The Effect Propagation Process is understood as the dynamic process operating within this fundamental structure, representing how influence transfers and how degrees of freedom relate and evolve, thereby constituting the very emergence and coming into being of the reality we observe, including spacetime and classical objects.

The Epistemology of the Effect Propagation Process:

The Effect Propagation Process framework is fundamentally an epistemological proposal, offering a new way to conceptually grasp and organize our understanding of causality in the post-quantum era. It provides a coherent framework that aligns with the challenges posed by quantum gravity, where traditional spacetime-dependent causal understanding breaks down. By shifting the focus from discrete events in spacetime to the fundamental process of influence transfer within an underlying structure, the framework provides a new lens through which to interpret observations and physical theories. It redefines the key questions of causality, moving from asking where and when causes operate to inquiring into the nature of the fundamental process from which causal order and spatiotemporal notions emerge, thereby guiding the search for knowledge in a spacetime-independent reality.

Epilogue

In classic causality, the key questions are: why do things exist, how do they change, and how do things come into being?

In post-quantum causality, the key questions are: why do things exist, how effects propagate, and how effects emerge into being?

Shifting the understanding of causality from a focus on discrete spacetime-bound events towards a spacetime-agnostic continuous effect propagation process may offer valuable insights for analyzing and advancing complex systems, which are an increasingly omnipresent reality.

By adopting the perspective of causality as an effect propagation process, DeepCausality aims to provide a more fundamental, flexible, and robust framework. It is designed to be agnostic to the specifics of whether effects propagate through physical spacetime, a network of social relations, or an abstract conceptual space. Instead, it focuses on the structural and functional definition of how influence is transferred and transformed within any given modeled system. This approach is crucial for building intelligent systems that can reason effectively in the diverse and often non-classical geometries of complex real-world problems.

About

DeepCausality is a hyper-geometric computational causality library that enables fast and deterministic context-aware causal reasoning in Rust. Learn more about DeepCausality on GitHub and join the DeepCausality-Announce Mailing List.