Time from a Timeless Universe
The
Emergence of Time from a Timeless Universe: A Relational Quantum
Ontology
Author: Rowan Brad Quni-Gudzinas
Affiliation: QNFO Contact:
rowan.quni@qnfo.org ORCID: 0009-0002-4317-5604
ISNI: 0000 0005 2645 6062 DOI:
10.5281/zenodo.17414448 Publication Date: 2025-10-22
Version: 1.0
Abstract: The problem of time in physics stems from
a foundational conflict between the static, geometric reality described
by fundamental theories and the dynamic, flowing time of human
experience. Physicalist models that attempt to reify this experiential
time, such as the Evolving Block Universe (EBU), suffer from systemic
failures, including logical circularity, empirical emptiness, and
incompatibility with relativity. This paper argues for a paradigm shift
from a substance-based ontology of time to a relational one grounded in
quantum information. We deconstruct the failures of the substance
ontology and construct a relational framework from the first principles
of quantum mechanics, postulating a universal, timeless quantum state
governed by the Wheeler-DeWitt equation. Within this framework, we
formally derive the time-dependent Schrödinger equation as an effective,
emergent description of the correlations between a subsystem designated
as a “clock” and the rest of the universe. This derivation demonstrates
that the ‘present moment’ is a conditional, observer-dependent state and
the ‘passage of time’ is the measurable evolution of this state. The
paradoxes of time are thereby resolved as category errors, and the Block
Universe is reinterpreted as a static map of the timeless quantum
correlations that constitute the fundamental territory of reality.
Keywords Evolving Block Universe, Relational Quantum
Mechanics, Page-Wootters Formalism, Problem of Time, Emergence of Time,
Timelessness, Wheeler-DeWitt Equation, Quantum Ontology
1.0
Introduction: A Paradigm Shift for the Ontology of time
The problem of time in physics is not a specific technical issue but
a symptom of a flawed underlying ontology that reifies subjective
temporal experience (Riggs, 2024; Rovelli, 2018). Models that attempt to
build a physical reality upon the intuitive notions of a flowing
‘passage’ of time or a universal ‘present moment’ consistently fail,
generating irresolvable paradoxes and requiring ad-hoc mechanisms that
lack empirical support. This paper will demonstrate that a complete,
coherent, and predictive model of time emerges when this ontology is
replaced with a relational one based on the principles of quantum
information. The central argument will be validated by a formal
derivation of the time-dependent Schrödinger equation from a timeless
universal state, showing that the temporal world of experience is not a
fundamental reality but an effective description for observers embedded
within it.
1.1
The Ontological Fork: Time as Substance vs. time as
relation
The history of the philosophy and physics of time is defined by a
tension between treating time as a fundamental container for reality
versus a relational structure derived from reality’s contents (Rovelli,
2018). The substance-based view posits time as a fundamental aspect of
the objective world—the “territory” itself. This approach inevitably
leads to paradoxes when the properties of this supposed substance
conflict with the known laws of physics, such as relativity. Relational
ontology, in contrast, treats time as a “map”—an effective, high-level
language for describing the correlations and relationships within the
territory. This distinction is crucial: relational ontology avoids
paradoxes by deriving the properties of the map (experienced time) from
the fundamental, timeless structure of the territory (physical
reality).
1.2
Argumentative Strategy: Deconstruction, Construction, and Formal
validation
The argument will proceed in three stages: demonstrating the
incoherence of the old paradigm, building the new one from first
principles, and validating it with a formal derivation. First, the
substance ontology will be deconstructed by analyzing the systemic
failures of its representative models. Second, a relational ontology
will be constructed from the foundational principles of quantum
mechanics. Third, this new paradigm will be validated through a rigorous
mathematical proof that derives all of temporal dynamics from a timeless
quantum state.
2.0
Deconstruction of the Substance Ontology: The Failure of Physicalist
Models of Flowing time
Physicalist models that presuppose an objective ‘passage of time’ are
fundamentally unable to provide coherent, non-circular, and empirically
verifiable definitions for their core temporal concepts (Riggs, 2024).
These models attempt to project the human experience of temporal flow
onto the fabric of reality, but in doing so, they clash with the
established principles of modern physics and fail to produce a logically
consistent framework.
2.1
Case Study: The Internal Incoherence of the Evolving Block Universe
(EBU)
The Evolving Block Universe (EBU) model is a prime example of a class
of theories that fail because they require ad-hoc, physically
unmotivated mechanisms to reconcile the static geometry of relativity
with the dynamic experience of time (Riggs, 2024). The EBU posits that
spacetime grows as the ‘present moment’ advances, converting an
indeterminate future into a determinate past. While attempting to
capture the intuition of a flowing time, this model collapses under the
weight of its own internal contradictions. The model’s definition of the
present is circular: the ‘collapse’ events that supposedly generate the
passage of time are themselves described as occurring sequentially in
time (Riggs, 2024). Furthermore, the model’s entire structure is
contingent on a ‘collapse’ interpretation of quantum mechanics, which is
not empirically established and is one of several competing, viable
interpretations (Riggs, 2024). The astronomical number of local
‘collapse’ events would produce a disordered ‘present,’ not the single,
ordered ‘now’ of experience, a problem made intractable by the
relativity of simultaneity (Riggs, 2024; Einstein, 1905).
2.2 The
Empirical Emptiness of Temporal ‘passage’
The ‘passage of time’ is an empirically empty, metaphysical concept,
not a physical observable, because its defining characteristic—its
rate—is immeasurable. No known physical instrument can measure a ‘rate
of passage’ for time; clocks measure duration, a relational quantity
between events (Riggs, 2024). The concept of a ‘rate of time’s passage’
is a tautology (one second per second) devoid of empirical content,
signaling its non-physical nature.
2.3
Synthesis of Failure: The Need for a New ontology
The failures of models like the EBU are not technical but
foundational, stemming from the incorrect assumption that time is a
substance. The identified problems of circularity, empirical emptiness,
and incompatibility with relativity are not isolated flaws but systemic
failures of the underlying substance ontology, thus motivating the
necessity of a paradigm shift.
3.0
Construction of the Relational Ontology: Time from Timeless
information
A coherent model of time is possible if, and only if, time is
understood not as a fundamental substance but as an emergent property of
quantum correlations between physical subsystems (Page and Wootters,
1983). This section constructs such a model from the first principles of
quantum mechanics, showing how a complete description of time can be
built from timeless quantum information.
3.1
Foundational Postulate: The Timeless, Static Universal Quantum
state
The fundamental description of the universe is a static state vector
\(|\Psi\rangle\) that is an eigenstate
of the total Hamiltonian \(H\) with
eigenvalue zero (DeWitt, 1967):
\[
H|\Psi\rangle = 0 \quad (1)
\]
This equation, known as the Wheeler-DeWitt equation in quantum
cosmology, contains no time variable. It describes a reality that, when
viewed as a whole, is static and timeless. This postulate embraces the
timeless nature of fundamental physics rather than attempting to fight
it.
3.2
Principle 1: Emergence via Subsystem partition
Observable dynamics are not properties of the universe as a whole but
of the relationships between its constituent parts. To describe the
experience of an observer within the universe, we partition the total
system into subsystems, such as a “clock” and a “system” that is
observed. This allows for a description of the system *relative
to* the clock, which is the foundational step for recovering a
temporal narrative from a timeless state.
3.3
Principle 2: Entanglement as a Static Record of dynamics
Static quantum entanglement between subsystems serves as the complete
informational record of a system’s dynamical history relative to a
clock. The universal state \(|\Psi\rangle\) is a static superposition of
entangled states, each term of which correlates a specific state of the
clock with a corresponding state of the system. This static web of
correlations contains all the information of a complete dynamical
history, ready to be “read” by an internal observer.
4.0
Formal Validation: The Derivation of Dynamics from a Timeless
state
The entire mathematical framework of time-dependent quantum mechanics
can be derived as an effective, relational description from within a
globally timeless quantum state, proving the mathematical viability of
the relational ontology (Page and Wootters, 1983). This section outlines
the core of this derivation, which is presented in full in Appendix
A.
4.1
The ‘present moment’ Formalized as a Conditional state
The ‘present moment’ for an observer at time \(t\) is formally defined as the conditional
state \(|\psi(t)\rangle_S\), obtained
by projecting the universal state \(|\Psi\rangle\) onto the clock’s eigenstate
\(|t\rangle_C\):
\[
|\psi(t)\rangleS := \langle t|C |\Psi\rangle \quad (2)
\]
This provides a rigorous, physical definition of “now” not as a
universal hyperplane, but as the state of the system that is correlated
with the state of the observer’s clock. It is crucial to note that this
projection is a mathematical tool for defining the conditional state; it
is not a model of physical wavefunction collapse. The Page-Wootters
formalism provides a powerful solution to the problem of time, but it
does not, by itself, claim to solve the quantum measurement problem,
which remains a distinct challenge for the foundations of quantum
mechanics.
4.2
The Derivation of the Time-dependent Schrödinger equation
The mathematical operation of conditioning the system’s state on the
clock’s state transforms the static Hamiltonian constraint (\(H|\Psi\rangle = 0\)) into the familiar
time-dependent Schrödinger equation for the system. As shown in Appendix
A, the action of the clock’s Hamiltonian on the conditional state
becomes equivalent to a time-derivative operator, while the system’s
Hamiltonian acts on the state itself. This directly yields the equation
governing all quantum evolution.
4.3
Implications of the Derivation: From Mathematics to
physics
The success of the derivation demonstrates that a temporal
description of the world is not fundamental but is the effective,
high-level language for observers embedded within a timeless reality.
This elevates the relational ontology from a philosophical preference to
a mathematically validated physical model. Time is not a postulate of
physics but a derivable consequence of its timeless quantum
foundation.
5.0
Resolution of Paradoxes: A Direct Mapping from Substance to
relation
The relational framework provides physically grounded,
non-paradoxical definitions for concepts that are ill-defined in
substance-ontology models, thereby solving the problem of time. Each
paradox of the substance ontology is resolved by mapping it to a
coherent physical principle in the relational ontology.
5.1 The Problem of
the Preferred present
The ontological error of the substance view is the assumption that
the ‘present’ is a universal, absolute hyperplane. The relational
framework corrects this by defining the ‘present’ as a local, physical
state of a system conditioned on its correlation with an observer’s
clock. The resolution, therefore, is that the locality and
observer-dependence of the present are its defining physical features,
not a flaw.
5.2 The Problem of
Temporal passage
The ontological error of the substance view is the assumption that
‘passage’ is a metaphysical flow with an intrinsic, yet immeasurable,
rate. The relational framework corrects this by defining ‘passage’ as
the physical evolution of a system’s conditional state relative to a
clock, a process governed by the emergent Schrödinger equation. The
concept is thereby transformed from an unobservable metaphysical flow
into a measurable, relational dynamic.
5.3 The Problem of
the Block universe
The ontological error of the substance view is the conflation of the
geometric representation of history (the map) with the fundamental
reality itself (the territory). The relational framework corrects this
by identifying the geometric Block Universe as a static map of the
timeless quantum correlations that constitute the territory. The paradox
of a static block containing a dynamic experience dissolves as a
category error: the map is static, but an observer’s processing of
information from the map is a dynamic, temporal process.
6.0 Implications and
Future directions
The relational paradigm offers a new foundation for tackling
long-standing problems in quantum gravity and cosmology. By providing a
framework where dynamics can emerge without a pre-existing spacetime
background, it opens new avenues for research.
6.1 Implications for
Quantum gravity
The Page-Wootters mechanism provides a concrete example of how
dynamics can emerge in a background-independent theory, where spacetime
itself is not a fixed stage (Rovelli, 2004). This is a key requirement
for theories of quantum gravity, and the relational approach provides a
powerful conceptual and mathematical toolkit for constructing such
theories.
6.2 Implications for
the Arrow of time
The directionality of time is not a fundamental law but an emergent
feature of the specific universal state \(|\Psi\rangle\), which is constrained by a
low-entropy past boundary condition (Carroll, 2010). Within the
relational framework, the ‘arrow of time’ is understood as a
thermodynamic and informational asymmetry related to the boundary
conditions of the universe, allowing an observer to form memories of one
“temporal” direction but not the other. While the Past Hypothesis
provides the necessary global condition, formally demonstrating the
emergence of a consistent thermodynamic arrow for all internal observers
within this framework is a non-trivial subject of ongoing research.
6.3
Limitations and Generalizations of the Relational Model
It is important to acknowledge the idealizations upon which the
simple derivation in Appendix A rests. The assumption of a
non-interacting Hamiltonian (\(H = H_C +
H_S\)) and the existence of a “perfect” clock are significant
simplifications. In a more realistic scenario, interactions between the
clock and system would introduce a term \(H_{int}\), and any physical clock would be
imperfect. These factors complicate the emergent dynamics and are the
subject of active research aimed at generalizing the model.
Furthermore, the partition of the universe into a “clock” and a
“system” is arbitrary. This ambiguity is not a flaw but a core feature
of the relational ontology. Different partitions can lead to different,
equally valid “temporal narratives” for the same underlying reality.
This reinforces the conclusion that time is not a universal, monolithic
background but an emergent, perspective-dependent description of
relationships between parts of the universe.
7.0
Conclusion: The Success of the Relational paradigm
The relational framework successfully unifies the static, timeless
view of the universe suggested by fundamental physics with the dynamic,
temporal world of observation. By replacing metaphysical postulates with
derivable physical mechanisms, the relational ontology solves the
problem of time and provides a coherent foundation for future research.
The successful derivation of the Schrödinger equation from a timeless
state validates this paradigm, demonstrating that the rich, evolving
world we experience can emerge from a reality that is, at its most
fundamental level, static and eternal.
**Appendix A: Formal Proof of Emergent Temporal
dynamics** |
This appendix provides a self-contained, rigorous proof of the
central theorem: the derivation of the time-dependent Schrödinger
equation from the timeless Wheeler-DeWitt equation via the Page-Wootters
formalism. |
Axioms and Definitions |
- Axiom 1 (Timeless Universe): The universe is a
closed system described by a static state vector \(|\Psi\rangle\) such that \(H|\Psi\rangle = 0\), where \(H\) is the total Hamiltonian (DeWitt,
1967). |
\[
H|\Psi\rangle = 0 \quad (A)
\] |
- Axiom 2 (Subsystem Partition): The universe is
partitioned into a non-interacting clock (C) and system (S), with \(H = HC + HS\). - **Definition 1
(Ideal Clock):** An ideal clock C has a Hamiltonian \(H_C\) that generates translations along the
eigenstates \(|t\rangle_C\) of a time
observable \(T_C\). -
Definition 2 (The Present Moment): The state of the
system at time \(t\) is the conditional
state \(|\psi(t)\rangleS := \langle t|C
|\Psi\rangle\). |
Theorem |
The evolution of the conditional state \(|\psi(t)\rangle_S\) with respect to the
clock parameter \(t\) is governed by
the time-dependent Schrödinger equation (TDSE): |
\[
i\hbar \frac{\partial}{\partial t} |\psi(t)\rangleS = HS
|\psi(t)\rangle_S \quad (A)
\] |
Proof |
- Project the Constraint: We begin by applying the
projection operator \(\langle t|_C\) to
the Hamiltonian constraint: |
\[
\langle t|C (HC + H_S) |\Psi\rangle = 0 \quad (A)
\] |
- Evaluate System Term: Since \(H_S\) acts only on the system’s Hilbert
space, it commutes with the projection operator: |
\[
\langle t|C HS |\Psi\rangle = HS (\langle t|C |\Psi\rangle) = H_S
|\psi(t)\rangle_S \quad (A)
\] |
- Evaluate Clock Term: By the definition of \(H_C\) as a generator of translations in its
own time-eigenstate basis, its action can be shown to be equivalent to a
time-derivative operator on the conditional state: |
\[
\langle t|C HC |\Psi\rangle = -i\hbar \frac{\partial}{\partial t}
|\psi(t)\rangle_S \quad (A)
\] |
- Assemble the Equation: Substituting the results
from (A) and (A) into the projected constraint (A) yields: |
\[
-i\hbar \frac{\partial}{\partial t} |\psi(t)\rangleS + HS
|\psi(t)\rangle_S = 0 \quad (A)
\] |
- Conclusion (Q.E.D.): Rearranging the terms of
(A) yields the TDSE (A): |
\[
i\hbar \frac{\partial}{\partial t} |\psi(t)\rangleS = HS
|\psi(t)\rangle_S \quad (A)
\] |
This demonstrates that temporal dynamics for a subsystem are a
necessary consequence of the timeless correlations in the universal
state (Page and Wootters, 1983; Rovelli, 2004). |
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