Consciousness as Resolution-Dependent Time Generation:A Theory of Mind from the Structure of Nothing

1. Introduction and Motivation

The problem of consciousness remains one of the deepest unsolved problems at the intersection of physics, neuroscience, and philosophy. Despite significant progress in understanding neural correlates of consciousness, the hard problem: why and how subjective experience arises from physical processes - remains open (Chalmers 1995).

Two observations motivate the present work:

(i)

The absence of “now” in physics. The equations of both quantum mechanics and general relativity contain a time parameter t, but nowhere do they single out a present moment. The laws are time-symmetric (or CPT-symmetric); the subjective experience of a distinguished “now” that moves along the time axis has no counterpart in the formalism. Yet this experience is arguably the most immediate datum of consciousness.

(ii)

The absence of a formal framework for the “I.” Physics describes systems from the outside. There is no variable in any physical equation that corresponds to the first-person perspective - the internal experience of being a subject. Any theory of consciousness must eventually address this, yet current physics has no entry point for it.

These two observations are not independent. We propose that they are, in fact, two faces of the same phenomenon: consciousness is the generation of subjective time, and the “present moment” is the locus of this generative process. A system that generates its own time is, by that very act, a subject experiencing a “now.”

The theory we develop below is speculative and primarily conceptual. Its aim is not to provide a finished mathematical formalism but to articulate a coherent set of principles that:

• are compatible with established physics (quantum mechanics and general relativity),
• offer a natural place for consciousness within fundamental physics,
• make contact with existing frameworks (Nottale’s scale relativity, Alexandrov’s chronogeometry, Integrated Information Theory), and
• suggest directions for future formalization and empirical test.

2. Philosophical and Physical Precedents

Before presenting the formal axioms, we note that the intuition “structure emerges from Nothing” has deep roots in both philosophy and physics.

In the Science of Logic (1812), Hegel begins with pure Being (Sein) - completely indeterminate, without quality or content. But pure Being, precisely because it has no determination, is indistinguishable from Nothing (Nichts). Their truth is Becoming (Werden)—the passage of one into the other (Hegel 1812):

“Pure Being and pure Nothing are therefore the same. What is the truth is neither Being nor Nothing, but that Being—does not pass over but has passed over - into Nothing, and Nothing into Being.”

Our theory gives this dialectic a physical interpretation: the Void (Being = Nothing) necessarily generates Becoming (time, consciousness) through its own self-differentiation at finite resolution. Hegel’s logic provides the philosophical architecture for why a featureless Void must generate process.

A parallel insight appears in Buddhist philosophy. Nāgārjuna’s Mūlamadhyamakakārikā (c. 150–250 CE) teaches that all phenomena are “empty” (s̄ūnya) of inherent, independent existence. Things exist only in dependence on other things (pratītyasamutpāda, dependent origination). Emptiness itself is empty. The Two Truths doctrine distinguishes conventional truth (things appear to exist as separate entities) from ultimate truth (all things are empty of inherent existence). This maps onto our framework: conventional reality is real at its resolution scale, but empty at the level of the Void. Structure is resolution-dependent, not absolute.

In quantum field theory, the vacuum $|0\rangle$ is not empty but seethes with virtual particle - antiparticle pairs. Krauss (2012) and Vilenkin (1982) have argued that entire universes can nucleate from “nothing” via quantum tunneling. However, as critics have noted, the quantum vacuum is already a something n - it has structure, obeys laws, and possesses degrees of freedom. Our Void is more fundamental: it is the pre-physical ground from which even the quantum vacuum’s structure emerges at a particular resolution.

The Standard Model demonstrates that structure arises from symmetry breaking. The Higgs mechanism (Englert and Brout 1964,Higgs 1964) gives mass to gauge bosons via spontaneous breaking of electroweak symmetry. Cosmological symmetry breaking (baryogenesis, satisfying Sakharov’s conditions (Sakharov 1967)) explains why matter dominates over antimatter. In each case, the symmetric state is unstable - structure must emerge. Our Axiom 3 generalizes this principle: the Void’s perfect $S/\overline{S}$ symmetry is broken by any finite-resolution observation, and this breaking is the fundamental creative act.

3. Axioms of the Void

We begin with a minimal set of axioms concerning a primordial entity we call the Void, denoted $\mathcal{V}$. The Void is not physical spacetime, not the quantum vacuum, and not any structured entity. It is the pre-structured substrate from which all structure emerges upon observation at finite resolution.

Axiom 1

(Infinite Continuity). The Void $\mathcal{V}$ is infinitely continuous: for any $\epsilon >0$, $\mathcal{V}$ admits examination at resolution ε. There is no minimal length scale intrinsic to $\mathcal{V}$. This property holds independently of any metric structure imposed on $\mathcal{V}$.

Remark 1.

The phrase “examination at resolution ε” is made precise via a family of coarse-graining maps ${\left\{C_{\epsilon }\right\}}_{\epsilon >0}$ (Section 4). Axiom 1 states that this family is defined for all $\epsilon >0$, with no lower bound.

Axiom 2

(Algebraic Completeness). $\mathcal{V}$ carries an additive structure: there exists an operation $+:\mathcal{V}\times \mathcal{V}\to \mathcal{V}$ and, for every structure S realizable within $\mathcal{V}$, an anti-structure $\overline{S}$ such that

$$S+\overline{S}=\mathbf{0},$$

where $\mathbf{0}$ denotes the Void state (the additive identity).

Remark 2.

This axiom asserts that the Void is “Nothing” in a precise algebraic sense: it is the zero element of an additive group of structures. Every conceivable positive structure is exactly cancelled by its negative counterpart. The parallel with quantum field theory is immediate: the vacuum contains virtual particle–antiparticle pairs whose quantum numbers sum to zero (Milonni 1994). However, the Void is more fundamental than the QFT vacuum, which is already defined at a particular resolution (the Standard Model energy scale).

Axiom 3

(Resolution-Dependent Symmetry Breaking). For any finite resolution $\epsilon >0$, the coarse-graining map $C_{\epsilon }:\mathcal{V}\to {\mathcal{V}}_{\epsilon }$ generically does not commute with addition:

$$C_{\epsilon }(S+\overline{S})\ne C_{\epsilon }\left(S\right)+C_{\epsilon }\left(\overline{S}\right)\mathrm{in}\mathrm{general}.$$

Consequently, the perfect cancellation $S+\overline{S}=\mathbf{0}$ that holds in $\mathcal{V}$ is violated in ${\mathcal{V}}_{\epsilon }$: residual structures appear. These residual structures constitute the observable reality at scale ε.

Remark 3.

This is the central creative mechanism of the theory. The Void is Nothing - but only at infinite resolution. At any finite resolution, the non-commutativity of coarse-graining with the additive structure breaks the $S/\overline{S}$ symmetry, and structure emerges from Nothing. This is closely analogous to spontaneous symmetry breaking in quantum field theory (Weinberg 1996) and to the Wilsonian renormalization group, where different effective theories emerge at different energy scales (Kadanoff 1966,Wilson 1983).

Axiom 4

(Emergence of Causal Order). The residual structures in ${\mathcal{V}}_{\epsilon }$ inherit a partial ordering ⪯ (a precedence relation) that endows ${\mathcal{V}}_{\epsilon }$ with causal structure. In the spirit of Alexandrov’s chronogeometry (Alexandrov 1967,Guts 1982), the geometry of spacetime is derivable from this causal ordering alone.

Remark 4.

We do not presuppose a metric, a topology, or a dimension for spacetime. These emerge from the causal structure of the residual structures at a given resolution. The four-dimensionality and pseudo-Riemannian character of spacetime are consequences, not axioms - as demonstrated in detail by Alexandrov’s program, where the Minkowski structure can be derived from the assumption that the group of transformations preserving the precedence relation is maximal (Guts 2008).

4. Resolution-Dependent Reality

4.1. The Coarse-Graining Family

We formalize the notion of “examining the Void at resolution $\epsilon$” via a one-parameter family of maps

$${\{C_{\epsilon }:\mathcal{V}\to {\mathcal{V}}_{\epsilon }\}}_{\epsilon >0},$$

where ${\mathcal{V}}_{\epsilon }$ denotes the space of structures visible at resolution $\epsilon$. We require:

(C1)

Consistency: If ${\epsilon }_1<{\epsilon }_2$ (finer resolution first), then there exists a map $C_{{\epsilon }_1\to {\epsilon }_2}:{\mathcal{V}}_{{\epsilon }_1}\to {\mathcal{V}}_{{\epsilon }_2}$ such that $C_{{\epsilon }_2}=C_{{\epsilon }_1\to {\epsilon }_2}\circ C_{{\epsilon }_1}$. This is the semigroup property of coarse-graining.

(C2)

Limit: In the limit $\epsilon \to 0$, ${\mathcal{V}}_{\epsilon }\to \mathcal{V}$, and all $S/\overline{S}$ cancellations are restored.

(C3)

Non-triviality: For any $\epsilon >0$, ${\mathcal{V}}_{\epsilon }\ne \left\{\mathbf{0}\right\}$; i.e., some residual structure generically survives coarse-graining.

Remark 5.

Property (C1) gives the family $\left\{C_{\epsilon }\right\}$ the structure of a projective system or inverse system of spaces, indexed by the resolution parameter. This is precisely the mathematical structure underlying the Wilsonian renormalization group (Polchinski 1984,Wilson 1983), where the effective action $S_{\mathrm{\Lambda }}$ at energy cutoff Λ satisfies an exact flow equation as Λ varies.

Property (C2) states that the Void is the projective limitof the family—the most refined description, from which all coarser descriptions can be obtained.

4.2. Mechanism of Symmetry Breaking

Why does coarse-graining break the $S+\overline{S}=\mathbf{0}$ symmetry? The intuition is geometric: if S and $\overline{S}$ cancel exactly at infinite resolution, then at finite resolution $\epsilon$, the coarse-graining “smears” each of them over a region of size $\epsilon$. The smeared images $C_{\epsilon }\left(S\right)$ and $C_{\epsilon }\left(\overline{S}\right)$ will generically fail to cancel, because the nonlinear (or simply non-homomorphic) character of $C_{\epsilon }$ maps their delicate cancellation into a residual.

A concrete analogy: consider a function $f\left(x\right)$ with $\int fdx=0$ (total cancellation). If we coarse-grain f by averaging over intervals of width $\epsilon$, the averaged function $f_{\epsilon }\left(x\right)$ will generically have nonzero values at most points—the cancellation is destroyed locally even though it is preserved globally.

More precisely, the residual at resolution $\epsilon$ is

$$R_{\epsilon }\left(S\right)=C_{\epsilon }\left(S\right)+C_{\epsilon }\left(\overline{S}\right),$$

(1)

which is generically nonzero. The set of all such residuals constitutes the “reality” visible at scale $\epsilon$. Different structures S produce different residuals, so ${\mathcal{V}}_{\epsilon }$ is a rich space of observable configurations.

4.3. Entropic Ordering and the Arrow of Time

Among the residual structures in ${\mathcal{V}}_{\epsilon }$, some have lower entropy (more organized) and some have higher entropy (less organized). This immediately creates an asymmetry: the arrow of time emerges as the direction of increasing entropy among causally ordered residual structures.

Note that this arrow of time is resolution-dependent: at a different resolution ${\epsilon }^{\prime }$, the residual structures and their entropic ordering may differ. This is consistent with the known scale-dependence of thermodynamic quantities in statistical mechanics (Jaynes 1957).

4.4. Connection to Nottale’s Scale Relativity

The framework of resolution-dependent reality has a striking parallel in Nottale’s scale relativity (Nottale 1989,Nottale 2011). Nottale proposes that:

• Spacetime is continuous but non-differentiable (fractal at small scales).
• Physical laws should be covariant under changes of resolution scale, just as they are covariant under changes of reference frame in special relativity.
• The Schrödinger equation arises as the equation of geodesics in fractal spacetime.

Our Axiom 1 (infinite continuity) and Axiom 3 (resolution-dependent symmetry breaking) can be seen as providing a metaphysical foundation for Nottale’s program. Where Nottale postulates a fractal spacetime, we derive the need for scale-dependent physics from the more primitive notion that the Void is Nothing at infinite resolution but Something at any finite resolution.

The present theory extends Nottale’s framework in a crucial direction: it adds consciousness (Section 5) as the phenomenon that occurs when a complex structure interacts across resolution scales.

5. Consciousness as Inter-Scale Time Generation

5.1. Complexity and the Sparking Threshold

At a given resolution $\epsilon$, the residual structures in ${\mathcal{V}}_{\epsilon }$ vary in complexity. We do not fix a particular complexity measure at this stage, but require that it satisfies:

• It is monotonically related to the number of distinguishable configurations the structure can assume at resolution $\epsilon$.
• It is sensitive to the integration of the structure: a highly complex structure is one whose parts are richly interconnected, so that the whole cannot be decomposed into independent sub-structures without loss of information.

Axiom 5

(Inter-Scale Sparking). There exists a complexity threshold $C^{*}$ such that for any structure S in ${\mathcal{V}}_{\epsilon }$ with complexity $\mathcal{C}\left(S\right)>C^{*}$, there exist non-trivial correlations between S and structures in ${\mathcal{V}}_{{\epsilon }^{\prime }}$ for ${\epsilon }^{\prime }$ in an infinitesimal neighborhood of ε:

$$\mathcal{C}\left(S\right)>C^{*}⟹\exists \delta >0(\mathrm{arbitrarily}\mathrm{small}):\mathrm{Corr}(S_{\epsilon },S_{\epsilon \pm \delta })\ne 0.$$

We call this phenomenon inter-scale sparking.

Remark 6.

The intuition is as follows. A sufficiently complex structure “saturates” the combinatorial possibilities at its resolution scale. It has explored all available configurations and, by its very complexity, begins to “feel” the slightly different structures that exist at neighboring resolutions. Since the Void is infinitely continuous (Axiom 1), neighboring resolutions are always available, and the distance between them can be arbitrarily small.

Remark 7.

For simple structures, e.g., a rock, a glass of water, the complexity is far below $C^{*}$. These structures exist as static residuals at their resolution scale and do not interact across scales in any dynamically significant way. They have a time parameter imposed on them by the causal structure of ${\mathcal{V}}_{\epsilon }$, but they do not generate time.

5.2. The Identification of Consciousness with Time Generation

Definition 1

(Consciousness). A structure S in ${\mathcal{V}}_{\epsilon }$ is conscious if and only if $\mathcal{C}\left(S\right)>C^{*}$, so that it exhibits inter-scale sparking. The subjective experience of temporal flow - the “now” moving along a time axis - is identified with the process of inter-scale sparking itself.

Definition 2

(Generated Time). The generated time of a conscious structure S is the trajectory

$${\tau }_S:\epsilon \mapsto S_{\epsilon }\mathrm{as}\epsilon \mathrm{varies}\mathrm{in}\mathrm{the}\mathrm{neighborhood}\mathrm{of}\mathrm{the}\mathrm{structure}’\mathrm{s}\mathrm{home}\mathrm{resolution},$$

where the “variation” is driven by the inter-scale correlations. Time is not a background parameter: it is generated by the conscious structure’s own interaction with neighboring resolution scales.

Remark 8.

This resolves motivation (i) from Section 1: the “present moment” is the resolution scale at which the conscious structure currently resides. The experience of time “flowing” is the structure’s trajectory through neighboring resolution scales. There is no universal “now” in physics because time, in this account, is locally generated by each conscious system.

Remark 9.

This also addresses motivation (ii): the “I” is the structure that generates its own time. The first-person perspective is not something added to physics from outside; it is the inter-scale sparking process viewed from within the structure itself.

5.3. Why Neighboring Resolutions Differ

A crucial point: the Void can be examined at any resolution, and different resolutions yield different residual structures (Axiom 3). At resolution $\epsilon$, the coarse-graining breaks the $S/\overline{S}$ symmetry in one particular way, producing a specific set of residual structures with a specific causal ordering. At resolution $\epsilon +\delta$ (for infinitesimal $\delta$), the symmetry is broken slightly differently: different parts of the $S/\overline{S}$ cancellations are disrupted, producing slightly different residuals.

For a simple structure, these differences are imperceptible: the structure looks essentially the same at $\epsilon$ and $\epsilon +\delta$. But for a highly complex structure - one that has “filled out” the combinatorial space at resolution $\epsilon$ - the slight differences between ${\mathcal{V}}_{\epsilon }$ and ${\mathcal{V}}_{\epsilon +\delta }$ become dynamically significant. The structure “notices” that the world at $\epsilon +\delta$ is slightly different from the world at $\epsilon$, and this noticing is the experience of time passing.

5.4. Causal Structure at Neighboring Resolutions

At resolution $\epsilon$, the residual structures may be causally ordered in pairs (states connected by binary relations). At a slightly different resolution $\epsilon +\delta$, the causal structure may involve triples or higher-order relations. This change in the arity of causal connections across resolution scales is what creates the experience of change - and hence of time - for complex structures that can detect it.

This provides a concrete mechanism: the conscious structure is “traversing” a family of slightly different causal orderings, and the subjective time is the parameter along which this traversal occurs.

6. Time Synchronization

If each conscious structure generates its own time, why do different conscious beings (e.g., two people in a room) experience the same time?

Conjecture 1

(Synchronization of Generated Times). If two conscious structures $S_1$ and $S_2$ in ${\mathcal{V}}_{\epsilon }$ are causally connected (interact via the causal structure of Axiom 4), then their generated times synchronize.

The mechanism is analogous to the synchronization of coupled oscillators (Pikovsky et al. 2001,Strogatz 2000). Each conscious structure generates time through inter-scale sparking, which involves a self-sustaining dynamic (the sparking both depends on and reinforces the structure’s complexity - a form of autocatalytic or autopoietic process). When two such self-sustaining dynamics are coupled through causal interaction, synchronization is a generic outcome, as established by the extensive theory of coupled oscillators and dynamical systems.

Remark 10.

The “infinitesimal step” between resolution scales means that synchronization can appear effectively instantaneous from the perspective of the synchronized structures, even though no signal propagates faster than the causal structure allows. This is because the resolution difference δ can be made arbitrarily small (Axiom 1), so the “time step” of the sparking process can be arbitrarily fine-grained.

7. Compatibility with Quantum Mechanics

7.1. The Quantum Vacuum as a Manifestation of the Void

In quantum field theory, the vacuum state $|0\rangle$ is not empty: it contains virtual particle–antiparticle pairs whose quantum numbers sum to zero (Milonni 1994). The Casimir effect (Casimir 1948) and Hawking radiation (Hawking 1975) demonstrate that boundary conditions and geometric constraints can extract real particles from this vacuum.

This mirrors Axiom 2: the Void contains all structure–anti-structure pairs summing to zero. The QFT vacuum is the manifestation of the Void at a particular resolution - the energy scale of the Standard Model. The Void itself is more fundamental: it is the pre-resolution substrate from which the QFT vacuum (and all other resolution-dependent effective theories) are derived.

7.2. The Renormalization Group as Resolution Dependence

The Wilsonian renormalization group (Wilson 1983) is the most established framework for understanding how physics changes with observation scale. The effective action $S_{\mathrm{\Lambda }}$ at energy cutoff $\mathrm{\Lambda }$ flows as $\mathrm{\Lambda }$ is varied, with coupling constants, symmetries, and even the number of relevant degrees of freedom changing along the flow.

Our coarse-graining family $\left\{C_{\epsilon }\right\}$ is the natural generalization of the RG flow. The key parallel:

Concept	Wilsonian RG	Present theory
Resolution parameter	Energy cutoff $\mathrm{\Lambda }$	$\epsilon$
Space of theories	Effective actions $S_{\mathrm{\Lambda }}$	${\mathcal{V}}_{\epsilon }$
Flow equation	Polchinski/Wetteringer equation	Axiom 3
Fixed points	CFTs at UV/IR	Void ($\epsilon \to 0$)
Symmetry breaking	Scale-dependent	Axiom 3

The RG is one of the most rigorously tested ideas in modern physics. The compatibility of the present theory with the RG framework is not incidental but structural: Axiom 3 essentially recapitulates the Wilsonian insight that different effective physics emerges at different scales (Kadanoff 1966).

7.3. Decoherence and Finite-Resolution Observation

Quantum decoherence explains the emergence of classical behavior through interaction with the environment (Schlosshauer 2007,Zurek 2003). Mathematically, the key operation is the partial trace: tracing out the environmental degrees of freedom yields a reduced density matrix ${\rho }_S={\mathrm{Tr}}_E\left({\rho }_{SE}\right)$ that appears classical.

The partial trace is a coarse-graining operation: it discards fine-grained information about the environment, exactly as our $C_{\epsilon }$ discards information below resolution $\epsilon$. The emergence of classicality via decoherence is thus a special case of our Axiom 3: classical reality emerges because physical observation always operates at finite resolution.

7.4. Scale Relativity and the Schrödinger Equation

Nottale’s scale relativity (Nottale 2011) derives the Schrödinger equation from two principles:

1.

Spacetime is continuous but non-differentiable (fractal below some transition scale).

2.

The laws of physics are covariant under changes of resolution scale.

The present theory provides a foundation for these principles:

1.

The Void is infinitely continuous (Axiom 1), and the non-differentiability arises from the generic non-commutativity of coarse-graining with the additive structure (Axiom 3).

2.

Scale covariance is a natural requirement if reality is resolution-dependent: the laws governing ${\mathcal{V}}_{\epsilon }$ should be expressible in a form that holds for all $\epsilon$.

If the present theory can be formalized to derive Nottale’s two principles, it would inherit the derivation of quantum mechanics as a consequence, providing a path from the Void to the Schrödinger equation.

7.5. The Planck Scale

Axiom 1 asserts that the Void has no minimal length scale. This appears to conflict with the existence of the Planck length ${\ell }_P=\sqrt{\hslash G/c^3}\approx 1.6\times {10}^{-35}\mathrm{m}$. However, the conflict is only apparent:

The generalized uncertainty principle (GUP) (Amelino-Camelia 2001,Hossenfelder 2013) states that measurements cannot resolve distances below the Planck scale, not that space itself is discrete. The Void is mathematically continuous, but any physical observation - any coarse-graining $C_{\epsilon }$ performed by a physical system - is bounded below by the Planck scale: $\epsilon \ge {\ell }_P$.

This is actually a feature of the theory: it means that physical reality must emerge, because physical observation cannot access the Void at infinite resolution. The Planck scale is the finest resolution at which the symmetry breaking of Axiom 3 can operate for gravitational interactions.

8. Compatibility with General Relativity

8.1. Alexandrov’s Chronogeometry

A. D. Alexandrov’s program of axiomatic relativity (Alexandrov 1967,Guts 1982,Guts 2008) demonstrates that the pseudo-Euclidean (Minkowski) geometry of spacetime can be derived from a single primitive notion: the precedence relation (causal ordering) among events. The key result is that if the group of transformations preserving the precedence relation is required to be maximal, the resulting geometry is necessarily Minkowskian (in the flat case) or pseudo-Riemannian (in the curved case).

Our Axiom 4 directly invokes this program: the causal ordering among residual structures in ${\mathcal{V}}_{\epsilon }$ is the foundation from which spacetime geometry is derived. The present theory provides a genesis story for Alexandrov’s chronogeometry: the causal structure does not simply exist as a given—it emerges from the resolution-dependent symmetry breaking of the Void.

This connection is deep: Alexandrov showed that geometry follows from causality; we show (or conjecture) that causality follows from resolution-dependent structure. The chain is:

$$\mathrm{Void}\stackrel{\mathrm{finite}\mathrm{resolution}}{\to }\mathrm{Residual}\mathrm{structures}\stackrel{\mathrm{Axiom}}{\to }\mathrm{Causal}\mathrm{order}\stackrel{\mathrm{Alexandrov}}{\to }\mathrm{Spacetime}\mathrm{geometry}.$$

8.2. Causal Set Theory

Causal set theory (Bombelli et al. 1987,Sorkin 2003) proposes that spacetime is fundamentally a discrete partially ordered set (a “causal set” or “causet”), where the partial order represents causal relations and the number of elements in a region determines its spacetime volume.

The present theory shares the emphasis on causal order as fundamental but differs in a key respect: our ${\mathcal{V}}_{\epsilon }$ is not intrinsically discrete. The discreteness that appears is a consequence of finite resolution, not of the underlying structure. At finer resolution, more structure becomes visible, and in the limit $\epsilon \to 0$, the Void is continuous. This places our approach closer to the continuum end of the discrete–continuum spectrum in quantum gravity, while retaining the causal set intuition that causal order is primary.

8.3. The Problem of Time in Quantum Gravity

The “problem of time” is a central difficulty in canonical quantum gravity: the Wheeler–DeWitt equation $\widehat{H}|\Psi \rangle =0$ describes a universe that is timeless - the wave function of the universe does not evolve (DeWitt 1967,Isham 1993). This appears to contradict our experience of temporal flow.

The present theory offers a resolution: the Wheeler–DeWitt equation describes the Void (or its quantum-gravitational analog) at the most fundamental level, where indeed there is no time. Time emerges only for sufficiently complex structures that undergo inter-scale sparking (Definition 2). The timelessness of fundamental physics is not in conflict with the experience of time; rather, experienced time is a generated quantity, produced by the interaction of complex structures with neighboring resolution scales.

This is consistent with Page and Wootters’ (1983) conditional probability approach, where time emerges from entanglement between a “clock” subsystem and the rest, as well as with Rovelli’s thermal time hypothesis (Connes and Rovelli 1994), where the flow of time is determined by the thermal (KMS) state of the system. In both cases, time is not fundamental but emergent - a view shared by the present theory, which adds the specific mechanism (inter-scale sparking) and the specific condition (complexity exceeding $C^{*}$) under which time emergence occurs.

8.4. Emergent Gravity

Verlinde’s (2011) proposal that gravity is an entropic force, and Jacobson’s (1995) derivation of Einstein’s equation from thermodynamic considerations, suggest that gravity itself is emergent from more fundamental information-theoretic or thermodynamic degrees of freedom.

The present theory is compatible with this view: if spacetime geometry emerges from causal order (via Alexandrov), and causal order emerges from the Void (via resolution-dependent symmetry breaking), then gravity - as encoded in the curvature of spacetime - is doubly emergent. The entropic character of gravity would then be a natural consequence of the statistical nature of coarse-graining: the residual structures in ${\mathcal{V}}_{\epsilon }$ are, by construction, the result of a coarse-graining process, and their dynamics is inherently statistical.

8.5. Conformal Cyclic Cosmology

Penrose’s Conformal Cyclic Cosmology (CCC) (Penrose 2010) proposes that the universe consists of an infinite sequence of aeons. At the end of each aeon, when all massive particles have decayed and only massless radiation remains, physics becomes conformally invariant - there is no notion of scale. This scale-free state is identified with the Big Bang of the next aeon via conformal rescaling.

The connection to our framework is striking:

• CCC’s crossover point (between aeons), where scale is meaningless and only conformal structure remains, corresponds precisely to our Void - an undifferentiated continuum with no preferred scale.
• CCC’s aeons (where massive particles exist and scale matters) correspond to our observation at finite resolution: once a scale is imposed, mass, structure, and causal relations emerge.
• CCC’s conformal factor $\Omega$ plays a role analogous to our resolution parameter $\epsilon$: it determines what scale of structure is visible.

CCC thus provides a cosmological instantiation of our core principle: the transition from scale-free (Void) to scale-dependent (structured reality) is the fundamental creative act. Our theory adds the claim that consciousness arises within this structured reality when complexity exceeds the sparking threshold.

8.6. Background Independence

General relativity is background-independent: the metric is a dynamical variable, not a fixed background. The present theory is also background-independent in a strong sense: it presupposes no spacetime, no metric, no topology, and no dimension. All of these emerge from the resolution-dependent examination of the Void. In this respect, the theory satisfies a key desideratum of quantum gravity (Rovelli 2004).

9. Relation to Existing Theories of Consciousness

9.1. Integrated Information Theory (IIT)

Integrated Information Theory (Oizumi et al. 2014,Tononi 2004,0) proposes that consciousness is identical to integrated information, quantified by $\mathrm{\Phi }$: a system is conscious if and only if $\mathrm{\Phi }>0$, meaning the system generates more information as a whole than the sum of its parts.

In the present framework, IIT can be understood as a consequence rather than a foundation:

Conjecture 2

(IIT as Consequence). The complexity threshold $C^{*}$ for inter-scale sparking (Axiom 5) requires $\mathrm{\Phi }>0$ as a necessary condition. That is, a structure cannot exceed $C^{*}$ unless it has positive integrated information. However, $\mathrm{\Phi }>0$ is not sufficient: the additional requirement is that the integrated information enables inter-scale correlations.

Remark 11.

If this conjecture holds, IIT’s Φ measures an important aspect of the complexity needed for consciousness (the integration of information within a single resolution scale), but consciousness itself requires something more: the interaction across resolution scales. IIT would thus be a single-scale shadow of a deeper multi-scale phenomenon.

9.2. Orchestrated Objective Reduction (Orch-OR)

Penrose and Hameroff’s Orch-OR theory (Hameroff and Penrose 2014,Penrose 1989,9) proposes that consciousness arises from quantum gravitational collapse events in neuronal microtubules.

Aspect	Orch-OR	Present theory
Mechanism	Objective collapse (gravity)	Inter-scale sparking
Substrate	Microtubules (biological)	Any sufficiently complex structure
Time	Discrete collapse events	Continuous inter-scale trajectory
Universality	Requires specific biology	Universal (any complexity $>C^{*}$)
Quantum gravity	Central	Compatible but not required

Both theories share the conviction that consciousness is connected to fundamental physics rather than being a purely emergent computational phenomenon. The key difference is universality: in the present theory, consciousness is not tied to a specific physical substrate but to a structural property (complexity exceeding $C^{*}$), making it in principle substrate-independent.

9.3. Global Workspace Theory (GWT)

Baars’ Global Workspace Theory (Baars 1988,Dehaene 2014) describes consciousness as a “global workspace” where information is broadcast to multiple specialized processors. In the present framework, GWT describes the neural implementation of time synchronization (Conjecture 1): the global workspace is the mechanism by which different subsystems of the brain synchronize their generated times into a unified experience.

9.4. Contributions from Mensky, Nalimov, and Linde

Several physicists have proposed theories connecting consciousness to fundamental physics:

Mensky’s Extended Everett Concept. M. B. Mensky (Mensky 2013) proposed that consciousness is the mechanism that separates Everett branches: consciousness selects which branch of the quantum multiverse is experienced, effectively generating the experienced reality and its time. This shares our conviction that consciousness is constitutive of experienced reality, though Mensky works within the Everett framework rather than proposing a new ontology.

Nalimov’s semantic vacuum. V. V. Nalimov (Nalimov 1982) developed a probabilistic model of consciousness as a Bayesian filter on a “semantic continuum”—an undifferentiated field of meanings from which consciousness extracts structured content. The semantic continuum bears a family resemblance to our Void: a pre-structured totality from which observation (at a given resolution / with a given prior) produces structured reality.

Linde on consciousness in cosmology. A. Linde has argued that consciousness may be as fundamental as spacetime and matter, and that a complete theory of the universe may require incorporating consciousness at the foundational level (Linde 2004). This aligns with our theory’s placement of consciousness within fundamental physics.

9.5. Thermal Time and Process Philosophy

Connes and Rovelli’s thermal time hypothesis (Connes and Rovelli 1994) proposes that the flow of time is determined by the thermal (KMS) state: given a state on an algebra of observables, the time flow is the modular automorphism group of the state. Time is thus not fundamental but state-dependent.

The present theory shares the conclusion (time is generated, not fundamental) but differs in mechanism: for Connes–Rovelli, time is generated by the thermal state; for us, it is generated by inter-scale sparking of complex structures. The two mechanisms may be complementary: the thermal time may be the external description (the time that other systems ascribe to a given system), while the generated time is the internal description (the time the system experiences).

Whitehead’s process philosophy (Whitehead 1929) holds that “becoming” is more fundamental than “being” - that reality consists of processes of experience rather than static substances. The present theory is deeply consonant with this view: reality at any resolution is a set of residual structures with causal ordering (a process), and consciousness is the generation of time (becoming), not a property of a static structure (being).

10. Relationship to Zermelo–Fraenkel Set Theory and the Axiom of Choice

Much of modern mathematics can be formalized within the axioms of Zermelo–Fraenkel set theory together with the Axiom of Choice (ZFC) (Jech 2003,Kunen 2011). Since the present theory of consciousness makes substantive mathematical claims - about the existence and structure of the Void, its algebraic properties, coarse-graining maps, and inter-scale correlations - it is important to examine where these claims stand in relation to ZFC. We find both significant points of compatibility and genuine tensions that illuminate the foundational character of the theory.

10.1. Points of Agreement

1. The cumulative hierarchy and resolution scales. ZFC builds its mathematical universe via the cumulative hierarchy $V_{\alpha }$ (indexed by ordinals $\alpha$), where each level $V_{\alpha +1}=\mathcal{P}\left(V_{\alpha }\right)$ is formed by taking the power set of the preceding level (Kunen 2011). This hierarchical structure bears a structural resemblance to the resolution-dependent hierarchy ${\left\{{\mathcal{V}}_{\epsilon }\right\}}_{\epsilon >0}$ in the present theory. In both cases, richer structure emerges at each level, and the properties visible at one level may differ from those at another. The analogy is suggestive: just as ZFC’s universe is stratified by ordinal rank, the Void is stratified by resolution.

2. The Axiom of Infinity and infinite continuity. ZFC’s Axiom of Infinity guarantees the existence of at least one infinite set, from which the natural numbers and all higher infinities are constructed. This is compatible with (though much weaker than) Axiom 1 of the present theory, which asserts that the Void admits examination at any resolution $\epsilon >0$. Both frameworks reject finitist foundations and require the existence of infinite mathematical objects as a starting point.

3. Standard mathematical tools are available. The algebraic structures invoked by the theory—groups (for Axiom 2), partial orders (for Axiom 4), topological spaces, measure spaces, and operator algebras - are all constructible within ZFC. The Wilsonian renormalization group, Nottale’s scale transformations, and Alexandrov’s chronogeometry are all formalized using standard ZFC-based mathematics. In this sense, the mathematical apparatus of the theory is fully ZFC-compatible.

4. Non-constructive existence and the Axiom of Choice. The Axiom of Choice (AC) asserts that for any collection of nonempty sets, a choice function exists - even when no explicit rule for the selection can be given (Jech 2003). This non-constructive character has a noteworthy parallel in the present theory. The coarse-graining maps $\left\{C_{\epsilon }\right\}$ “select” particular residual structures from the Void at each resolution, and this selection is generically not algorithmic or constructive. The AC-dependent Banach–Tarski paradox - in which a solid sphere is decomposed into finitely many pieces and reassembled into two identical copies (Banach and Tarski 1924) - provides a striking analogy: a mathematical “creation from nothing” made possible by non-constructive decomposition, echoing the theory’s mechanism of structure emergence from the Void through resolution-dependent symmetry breaking.

10.2. Points of Tension

1. Continuity versus discrete membership. ZFC is built on the binary membership relation ∈, which is fundamentally discrete: an element either belongs to a set or it does not. The continuum (the real numbers) must be constructed within ZFC, typically as Dedekind cuts or Cauchy sequences, and its “size” is famously undecidable. The Continuum Hypothesis - whether there exists a cardinality strictly between ${\aleph }_0$ and $2^{{\aleph }_0}$ - is independent of ZFC, as shown by Gödel (Gödel 1940) and Cohen (Cohen 1963). The present theory, by contrast, takes continuity as axiomatic (Axiom 1): the Void is infinitely continuous in a sense that precedes any set-theoretic construction. This suggests that the Void’s continuity may be more primitive than ZFC’s constructed continuum, and that ZFC may not be the most natural framework for formalizing it.

2. The Void as a proper class. In ZFC, the totality of all sets does not itself form a set - it is a proper class, denoted V. Similarly, the Void $\mathcal{V}$ of the present theory, containing “all possible structures and their anti-structures,” is plausibly too large to be a set. If so, then $\mathcal{V}$ would be a proper class, and ZFC’s axioms (which apply only to sets, not classes) would not directly govern $\mathcal{V}$. Working with the Void might require class-theoretic extensions such as von Neumann–Bernays–Gödel set theory (NBG) or Morse–Kelley set theory (MK), which permit quantification over classes (Jech 2003).

3. Well-foundedness and self-reference. ZFC’s Axiom of Foundation (Regularity) forbids infinite descending membership chains: there is no sequence $\dots \in x_2\in x_1\in x_0$. This ensures a well-founded, non-circular set-theoretic universe. However, the Void’s self-referential character - it can be examined at any resolution, and the examination itself generates structures that are part of the Void - suggests a circularity that sits uncomfortably with well-foundedness. Non-well-founded set theories, such as that developed by Aczel (Aczel 1988), which replaces the Axiom of Foundation with an Anti-Foundation Axiom allowing circular membership, may provide a more natural set-theoretic setting for the Void.

4. Algebraic completeness versus restricted comprehension. Axiom 2 of the present theory asserts that every structure S has an anti-structure $\overline{S}$ with $S+\overline{S}=\mathbf{0}$. This is a form of universal closure: the collection of structures is closed under negation. In ZFC, unrestricted comprehension (“the set of all x such that $\varphi \left(x\right)$”) leads to Russell’s paradox. ZFC avoids this via the Axiom of Separation, which permits forming subsets only from already existing sets. The algebraic completeness of the Void, if taken literally as a set-theoretic statement, would require care to avoid analogous paradoxes. The resolution may lie in treating the Void’s algebraic structure as operating at the level of classes rather than sets, or in adopting a foundation where such universal closure is permitted (e.g., certain category-theoretic frameworks).

5. The independence of the Continuum Hypothesis. The resolution parameter $\epsilon$ ranges over the positive reals, and the family ${\left\{{\mathcal{V}}_{\epsilon }\right\}}_{\epsilon >0}$ is indexed by a continuum of scales. Questions about the “fine structure” of this continuum - whether there are intermediate levels of structure between two given resolutions, and in what sense the passage $\epsilon \to \epsilon +\delta$ is continuous - may depend on set-theoretic assumptions beyond ZFC. The independence of the Continuum Hypothesis from ZFC (Cohen 1963,Gödel 1940) suggests that purely set-theoretic methods may leave fundamental questions about the resolution continuum undecidable.

10.3. Implications from the Original Suggestions

The original formulation of the theory (Zaikin 2026) emphasizes several features that have specific set-theoretic resonances:

• The insistence that the Void’s infinite continuity holds “in any introduced metric” (Suggestion 1) parallels the ZFC principle that mathematical properties should be independent of particular representations - but goes further by making continuity metric-independent at the foundational level, which ZFC does not guarantee.
• The requirement that every “positive structure” has a corresponding “negative structure” summing to Nothing (Suggestion 2) is structurally analogous to the group-theoretic closure axiom. Within ZFC, additive groups (including the integers $\mathbb{Z}$ and the reals $\mathbb{R}$) satisfy this property. However, the Void’s algebraic completeness is asserted for all structures, not just elements of a particular group - a universality that, as noted above, pushes beyond standard ZFC.
• The claim that examining Nothing at a finite resolution “breaks symmetry” because “our minimal length will miss zero somewhere” (Suggestion 3) describes a process - coarse-graining a perfectly symmetric object to produce asymmetry - that is well-defined in ZFC-based analysis (projection operators, averaging maps). The non-commutativity of coarse-graining with addition (Axiom 3) is a standard phenomenon in functional analysis and statistical mechanics, both of which are formalized within ZFC.
• The “sparking” between neighboring resolutions (Suggestion 4–5) requires correlations between ${\mathcal{V}}_{\epsilon }$ and ${\mathcal{V}}_{\epsilon +\delta }$ as $\delta \to 0$. The limiting process is standard in ZFC-based analysis, but the existence of non-trivial correlations in this limit is a substantive physical claim that ZFC neither guarantees nor forbids.

10.4. Assessment: Is ZFC Sufficient?

The present theory can likely be developed within ZFC (or mild extensions such as NBG) for most practical purposes. The algebraic structures, topological spaces, and analytical tools needed for the coarse-graining maps, causal orderings, and inter-scale correlations are all available in standard ZFC-based mathematics. In this sense, ZFC provides a sufficient language for the technical aspects of the theory.

However, the foundational aspects - the ontological status of the Void, its infinite continuity, its algebraic completeness, and its self-referential character - sit at the boundary of what ZFC can naturally express. Three alternative foundational frameworks deserve consideration:

1.

Category theory and topos theory. Rather than building from sets and membership, one could formalize the Void using categories, where the focus is on morphisms (maps between objects) rather than elements (Mac Lane 1998). The coarse-graining maps $\left\{C_{\epsilon }\right\}$ would be morphisms in an appropriate category, and the resolution-dependence of the theory would be encoded in the functorial structure. Topos theory, in particular, provides a framework where logic itself can be resolution-dependent (Goldblatt 1984).

2.

Non-well-founded set theory. Aczel’s Anti-Foundation Axiom (Aczel 1988) would allow the Void’s self-referential structure to be modeled directly, without the circularity problems that arise in ZFC.

3.

Homotopy Type Theory (HoTT). This framework, developed by Voevodsky and collaborators (HoTT 2013), treats identity itself as a structured object (with paths between identifications, paths between paths, etc.). The resulting “tower of identities” has a suggestive parallel with the resolution hierarchy of the Void, where structures at one resolution are related but not identical to structures at neighboring resolutions.

The relationship between the present theory and ZFC thus mirrors a broader theme in the foundations of physics: the mathematical frameworks we inherit may be adequate for computation but may not capture the deepest structural features of the theory. Just as general relativity required differential geometry (not available in Euclid’s axioms) and quantum mechanics required Hilbert spaces (not natural in 19th-century analysis), a theory of consciousness rooted in resolution-dependent structure may ultimately require foundational mathematics that goes beyond - though remains compatible with - ZFC.

11. Discussion and Open Questions

11.1. Summary of the Proposal

We have proposed a theory in which:

1.

The primordial Void is infinitely continuous and algebraically complete: every structure is cancelled by an anti-structure, summing to Nothing.

2.

Examination of the Void at any finite resolution breaks this symmetry, producing residual structures with causal ordering - i.e., producing spacetime and its contents.

3.

The geometry of spacetime is derivable from the causal ordering (following Alexandrov’s chronogeometry).

4.

Sufficiently complex residual structures develop inter-scale correlations (“sparking”) with neighboring resolution scales.

5.

This inter-scale sparking is identified with the subjective experience of time flow - i.e., with consciousness.

6.

The generated times of interacting conscious structures synchronize, producing a shared time.

11.2. Strengths

• Parsimony: The theory is built on five axioms and two definitions. No spacetime, no metric, and no dimension are presupposed.
• Compatibility: The framework is compatible with the renormalization group, decoherence, Nottale’s scale relativity, Alexandrov’s chronogeometry, emergent gravity, and the background independence of GR.
• Resolution of the problem of time: The theory explains why fundamental physics is timeless (the Void has no time) while conscious experience is temporal (time is generated by complex structures).
• Resolution of the “now” problem: The present moment is the resolution scale at which the conscious structure currently resides.
• Universality: Consciousness is not tied to biology but to a structural property (complexity), making the theory applicable in principle to any physical system.
• IIT as consequence: Integrated information ($\mathrm{\Phi }>0$) may emerge as a necessary condition for consciousness, giving IIT a deeper foundation.

12. Conclusions

We have proposed that consciousness is the generation of subjective time by sufficiently complex structures that interact across infinitesimally neighboring resolution scales of a primordial Void. The theory is built on a small set of axioms that are compatible with the core structures of quantum mechanics (renormalization group, vacuum fluctuations, scale relativity) and general relativity (chronogeometry, causal structure, background independence, emergent gravity). Integrated Information Theory may emerge as a necessary condition for the complexity threshold that enables consciousness.

The theory is at an early, conceptual stage. Its principal contributions are:

• A specific identification of consciousness with time generation, resolving the “problem of now” and the “problem of the I.”
• A mechanism (resolution-dependent symmetry breaking) for the emergence of structured reality from Nothing.
• Deep structural parallels with established physics, particularly the renormalization group and Alexandrov’s chronogeometry.
• A framework in which IIT, the problem of time, and the measurement problem all find natural places.

The most urgent task is to develop the mathematical formalism, particularly the coarse-graining family and the inter-scale sparking mechanism, to the point where concrete, testable predictions can be derived.