The problem of determinism, that is, the question of the universal causal conditioning of events, is one of the oldest in philosophy and science. From ancient debates about fate and free will to modern discussions about interpretations of quantum mechanics — this topic retains its relevance.
Classical physics was dominated by Laplacian determinism — the idea that if we knew the exact position and velocity of all particles in the Universe, we could predict any future event. However, with the advent of quantum mechanics, this certainty was shaken.
The goal of this work is not to revive Laplacian determinism in its original form, but to construct a rigorous logical system that allows for a correct analysis of the principle of causality and its consequences. We will consider the concept of "causal closure" as a fundamental property of reality and analyze whether it is compatible with modern scientific ideas.
It should be emphasized that this research does not claim to discover fundamentally new philosophical truths. Its main goal is the systematization and rigorous formalization of classical ideas of determinism, dating back to Spinoza, Leibniz, and Laplace. The presumed novelty of the work lies not in the ideas themselves, but in their composition and the construction of a deductive chain leading from accepted axioms to conclusions about the nature of quantum uncertainty. The subsequent exposition also develops the concept of a multi-level causal structure, which allows explaining apparent stochasticity within the framework of global determinism.
An event is understood as any fact or change in the state of a system, localizable in space-time. The set of all events is denoted as ℰ.
An event is any fact that can be recorded: an apple falling, a person's birth, a chemical reaction. The set of all events is simply the totality of everything that has ever happened, is happening, or will happen.
A causal relation ≺ on the set ℰ is a binary relation satisfying the conditions:
A causal relation is simply a way of saying that one event is the cause of another. It has three natural properties:
These properties correspond to our intuitive understanding of causality.
A configuration level is understood as a separate causal loop or mode of existence of the Universe, characterized by its own set of physical laws and causal relations. The set of all possible levels is denoted as C = {C₁, C₂, ..., Cₙ}, where n is finite.
Imagine that the Universe can exist in different "modes" or "configurations". Each level is like a separate layer of reality with its own laws. For example, our familiar physical world is one level (Cₖ). There may be a finite number of such levels, and together they form the complete reality.
For any finite observer considering two events e₁, e₂ ∈ ℰ, there always exists a consistent narrative explanation linking them into a single causal chain:
The impossibility of constructing such an explanation is a consequence of the fundamental limitation of the observer's knowledge, not the absence of connection in the ontological structure of the world.
This axiom states that any two distinct events in the Universe can be linked by a causal explanation. We are not asserting direct physical influence between distant events, but rather that in a complete description of reality they turn out to be connected through a common causal history.
Between any two causally related events there exists an intermediate event:
This axiom states that causal connection is never instantaneous or immediate. Between cause and effect there are always intermediate events forming a continuous chain.
There is no event isolated from the causal structure of the world:
This axiom states that there are no completely isolated events. Every event is connected by causal relations to at least one other event in the Universe.
Every event is connected by causal relations to the entire structure of the Universe:
This axiom states that each event is connected not just to some other single event, but to a whole network of events constituting the structure of the Universe. The observer and their intentions are also part of this structure and influence events.
Any measurement event includes the state of the observer as an integral part:
This axiom states that the observer is not external to the measured system. Their mental state, including the intention to measure, is as much a part of the causal structure as the physical system itself.
The set of all configuration levels C forms a causally closed system. There are no external causes relative to C that influence events inside any level Cᵢ ∈ C.
This axiom extends the principle of causal closure to the entire hierarchy of reality levels. All possible "worlds", "realities" or "configurations" of the Universe form a single causally closed system. There is nothing "outside" this system that could influence events within it.
The set of all configuration levels C is finite:
This axiom states that although there may be many levels of reality, their number is finite. This prevents infinite regress and ensures the fundamental knowability of the complete structure of reality.
This theorem states that the Universe is causally closed — there are no external causes influencing events within it. All causes and effects are contained within the Universe itself.
This does not mean that we know all the causes of all events, but only that all these causes exist within reality itself, not outside it.
This theorem states that the apparent randomness of quantum measurements arises from our incomplete knowledge. If we knew the complete state of the system, instrument, and observer, the result would be predictable.
Quantum probability reflects not fundamental randomness, but our ignorance of subtle correlations in the unified causal structure.
This theorem explains why quantum uncertainty is fundamentally ineliminable in practice. To completely predict the measurement result, we need to know the state of the observer, but for that we need another observer, and so on ad infinitum.
This creates a fundamental epistemological barrier that protects the theory from experimental refutation.
This theorem states that although our local reality may appear stochastic, the complete reality, including all configuration levels, develops strictly deterministically. All apparent randomness arises from our limited knowledge of the complete state Λ.
Quantum probability describes the behavior of subsystems. The cause of "randomness" is not the absence of causes, but their complexity. The complete system "Universe + Hypothetical Observer with complete knowledge" is deterministic.
Probability in QM is a projection of an N-dimensional deterministic process onto the 3-dimensional subspace of knowledge of a finite observer.
The model presented above does not contradict the idea of the existence of multiple "levels" or "configurations" of reality. We can assume that the Universe exists within a finite set of causal levels C = {C₁, C₂, ..., Cₙ}, where n is finite.
Our observable reality corresponds to one of these levels, Cₖ. The laws of physics, including quantum mechanics, describe the regularities operating precisely at this level. However, the complete deterministic structure of the Universe is described by the global state Λ, which includes the states of all levels:
In such a model:
This model offers an explanation for the apparent variability and stochasticity of our level of reality without introducing fundamental randomness.
Imagine a multi-core processor where each core runs its own program (level Cᵢ). Each program is deterministic, but the cores exchange data through shared memory (interaction between levels). An observer located inside one core sees only their own program and the received data — for them, some events seem random, although the entire system as a whole operates deterministically.
John Bell's theorem (1964) is considered one of the most serious challenges to determinism. It shows that no local theory with hidden parameters can reproduce all the predictions of quantum mechanics.
Bell's theorem proves the impossibility of local hidden parameters. But it not only does not exclude, but indirectly confirms the existence of a single global hidden parameter — the complete state of the Universe Λ(t) at moment t=0.
Non-local correlations are not "influence", but a manifestation of the mutual consistency of all events initially embedded in Λ(0).
where Λ is the global parameter, and PA, PB are deterministic functions taking values 0 or 1.
Bell's theorem does not refute the proposed theory for several reasons:
Imagine an iceberg. Quantum mechanics describes only the visible part — correlations between measurements. Bell's theorem shows that these correlations cannot be explained by local causes in the visible part. But the presented theory claims that the cause lies in the invisible part — the entire global structure of the Universe, including its developmental history, all interconnections, and other configuration levels.
Thus, Bell's theorem does not contradict causal closure, but only shows the limitations of local explanations. The global causal structure can explain quantum correlations without violating causality.
Many believe that quantum mechanics with its uncertainty principle and probabilistic nature of the microcosm refutes determinism. However, this is not necessarily the case.
Quantum uncertainty fits perfectly into the proposed model of causal closure:
Quantum uncertainty can be reinterpreted as a reflection of a fundamental limitation: we cannot know the complete state (S, M, O) because knowing the state O (observer) requires the inclusion of a new observer, and so on ad infinitum (Theorem 3.3).
This creates a fundamental epistemological barrier that is mistakenly interpreted as ontological randomness.
Quantum uncertainty can be interpreted not as an absence of causality, but as a fundamental limitation of our knowledge about the complete causal structure. Even if individual events are unpredictable, the structure in which they occur is causally closed and deterministic.
When we throw dice, the result seems random. But in reality, it is completely determined by the laws of physics: initial position, throwing force, air resistance, etc. Our ignorance of these factors creates the illusion of randomness.
Similarly, quantum uncertainty may not be a fundamental property of nature, but a reflection of fundamental limitations of our cognition, including our ignorance of other levels of reality.
Although the presented theory is primarily a metaphysical construct, it leads to potentially testable predictions:
These predictions, although difficult to test with current technology, show that the theory is not purely tautological and can in principle be falsified.
If the theory is correct, this means that:
As a result of the conducted research, an axiomatic system formalizing the principle of universal causal connection has been proposed. Although the idea of the causal closure of the world is not new, the presented formalism allows for a new perspective on old problems. In particular, it has been shown that the causal closure of the world and the impossibility of absolutely random events follow from this system.
The proposed concept of a multi-level causal structure allows explaining the apparent variability and stochasticity of our level of reality without abandoning the principle of global determinism. The finite set of configuration levels forms a causally closed system in which all evolution is deterministic.
Bell's theorem does not refute the proposed theory, as it considers only local parameters, whereas our theory assumes a global causal structure where the entire Universe, including all its levels, influences every event.
Quantum uncertainty does not contradict the causal closure of the world, but only points to the fundamental limitations of our cognition of causal structures. The observer and their intentions are not external factors, but part of the unified causal network of the Universe.
The proposed theory opens new perspectives for investigating the connection between consciousness and physical reality, offering a consistent deterministic alternative to the generally accepted indeterministic interpretations of quantum mechanics.