Projectional Dissipation and Phase Perturbations in Black Hole Mergers — A TAP Perspective

1. Introduction

The arrow of time remains one of the deepest unresolved questions in modern physics [1,2]. While the fundamental equations of both classical and quantum mechanics are symmetric under time reversal, our macroscopic experience and thermodynamic laws exhibit an unambiguous directionality. General Relativity (GR) elegantly describes how mass and energy curve spacetime [5], but it offers no explanation for why physical processes unfold irreversibly from past to future. Similarly, quantum mechanics permits time-reversed evolution at the microscopic level, yet observation and decoherence consistently select a preferred direction of causality [6,7].

Black hole thermodynamics provides an especially sharp manifestation of this paradox. The Bekenstein–Hawking entropy relation establishes a deep correspondence between horizon area and information content [8,9], suggesting that irreversibility is somehow embedded in spacetime geometry itself. However, these results are descriptive rather than explanatory: they quantify entropy growth but do not reveal its physical origin. As Penrose emphasized [3], the second law of thermodynamics assumes an initial low-entropy state of the universe, but why such a state existed—or why the universe evolves irreversibly from it—remains unsolved. Even within statistical mechanics, the reduction from microscopic reversibility to macroscopic asymmetry is still conceptually incomplete [4,10].

The Thermodynamic Asymmetry from Projection (TAP) framework [13] proposes that temporal asymmetry arises from projectional dissipation: a process in which higher-dimensional informational structures are geometrically projected into lower-dimensional spacetimes. During this projection, not all correlations among the higher-dimensional degrees of freedom can be preserved; the resulting information loss manifests as entropy growth, and the asymmetry of that loss defines the arrow of time. Unlike the holographic principle [11,12], which assumes unitary boundary encoding, TAP explicitly allows non-unitary, dissipative mappings— thereby providing a geometric origin for thermodynamic irreversibility.

In this interpretation, every irreversible process corresponds to an incomplete projection of higher-dimensional coherence. Black hole mergers, with their extreme curvature and boundary dynamics, represent natural laboratories for testing this concept: they act as localized “projection events” in which information loss, horizon-area growth, and gravitational-wave emission are tightly coupled [14]. If TAP is correct, these events should leave measurable traces in the form of faint post-merger oscillations or phase micro-perturbations that encode the dissipation rate of the projection process itself.

This paper develops that idea in a quantitative form. Section 2 establishes the geometric foundation of projectional dissipation; Section 3 draws analogies from known dissipative systems; Section 4 derives testable predictions for gravitational-wave observations; and Section 5–6 extend the discussion to cosmological scales and philosophical implications. In doing so, we aim not only to propose a falsifiable model of time’s arrow, but also to unify thermodynamics, information theory, and spacetime geometry within a single projectional framework.

2. Theoretical Framework: TAP and Projectional Dissipation

At the heart of the TAP framework (Thermodynamic Asymmetry from Projection) lies a simple but radical proposition:

The arrow of time and the growth of entropy are both consequences of how a higher-dimensional informational structure projects into a lower-dimensional spacetime.

This projection is not merely a mathematical mapping — it represents a physical reduction of dimensional information capacity. When a complete higher-dimensional manifold is observed through a lower-dimensional interface, part of its informational coherence becomes inaccessible. That loss manifests within the lower-dimensional frame as an increase of entropy, and its direction defines temporal irreversibility.

2.1. Informational Projection and Dissipation

Let ${\mathcal{I}}_n$ denote an information-complete structure embedded in n-dimensional space. When projected into a lower-dimensional observational domain ${\mathcal{M}}_3$, a fraction of its internal correlations becomes inaccessible:

$${\mathcal{I}}_n⟶{\mathcal{M}}_3:dS=-d{I}_{\mathrm{accessible}}>0$$

(1)

The inequality expresses the fundamental TAP statement:

$${\displaystyle \frac{dS}{dt}}>0⟺{\displaystyle \frac{d{I}_{\mathrm{accessible}}}{dt}}<0$$

(2)

Entropy, therefore, is not an abstract measure of disorder but a projectional metric of lost correlations. Every irreversible process — whether the cooling of a star, the merging of two black holes, or the evolution of consciousness — can be traced to the same geometric cause: the dissipation of information during dimensional reduction.

2.2. Geometric Expression in Black Hole Mergers

In General Relativity, when two black holes merge, the total event horizon area A after merger satisfies the area theorem:

$$A_{\mathrm{final}}\ge A_1+A_2$$

(3)

TAP interprets this inequality not as a thermodynamic coincidence but as a manifestation of information dissipation across the projection boundary. The excess area can be expressed as:

$$\Delta A=A_{\mathrm{final}}-(A_1+A_2)$$

(4)

This $\Delta A$ corresponds to the geometric residue of irretrievable information — the spatial imprint of time’s directionality. Hence, a geometric–informational equivalence emerges:

$$\Delta A\propto \Delta S\propto -\Delta I$$

(5)

The irreversible increase of horizon area thus encodes the same principle that governs the thermodynamic arrow of time, but now generalized to spacetime geometry itself.

2.3. Physical Meaning of Projectional Dissipation

Projectional dissipation is not a metaphor; it is a structural phenomenon. Whenever a system’s boundary conditions constrain the full dimensional description, information must be compressed or discarded. The observer within the reduced dimensionality perceives this as “time passing” — the continuous conversion of potential configurations into realized states.

This perspective redefines causality: cause and effect are not discrete events linked by an external time, but rather the sequential disclosure of higher-dimensional geometry through an irreversible projection process.

2.4. The TAP Principle Restated

In compact symbolic form, the TAP principle can be written as:

$$\begin{array}{|c|}\hline \begin{array}{cc}\hfill \mathrm{Higher}-\mathrm{Dimensional}\mathrm{Information}\text{:}& {\mathcal{I}}_n\hfill \\ \hfill \mathrm{Projection}\mathrm{Operator}\text{:}& {\mathcal{P}}_{n\to 3}\hfill \\ \hfill \mathrm{Observed}\mathrm{Entropy}\mathrm{Growth}\text{:}& dS=-d{I}_{\mathrm{accessible}}\hfill \\ \hfill \mathrm{Arrow}\mathrm{of}\mathrm{Time}\text{:}& \mathrm{Orientation}\mathrm{of}\left({\mathcal{P}}_{n\to 3}\right)\mathrm{under}\mathrm{information}\mathrm{loss}.\hfill \end{array}\\ \hline\end{array}$$

(6)

This represents the central symmetry-breaking mechanism of TAP: time’s direction does not arise from stochastic fluctuations but from a geometric bias in the projection operator itself.

The next section compares this projectional asymmetry with analogous dissipative structures observed in other physical systems.

3. Analogy Across Dissipative Systems

The projectional asymmetry proposed by TAP finds structural analogues in multiple dissipative systems across physics. While these systems differ vastly in scale—from optical cavities to macroscopic spacetime—they all exhibit a unifying pattern: irreversibility emerges when a system loses information through constrained boundary coupling.

3.1. Driven–Dissipative Quantum Systems

In driven open quantum systems, steady-state fluctuations and decoherence arise as the environment continuously absorbs information from the system. Recent analyses [18] show that such systems reach non-equilibrium stationary states characterized by persistent microscopic dissipation. The TAP correspondence here is clear: the system’s Hilbert space acts as a high-dimensional information reservoir, while the environment functions as a lower-dimensional projection channel. The irreversible loss of coherence in quantum correlations parallels the projectional dissipation responsible for time’s arrow.

3.2. Optical Microresonators and Dissipative Solitons

Optical microresonators exhibit self-organized pulse structures known as dissipative Kerr solitons [16,24]. These localized waveforms balance nonlinearity, dispersion, and loss to maintain a stable oscillatory form. Each soliton represents a dynamic equilibrium between continuous driving (energy inflow) and dissipation (energy outflow). In the TAP interpretation, this behavior is analogous to tail-wave perturbations following a projection event: the system stabilizes by releasing surplus informational curvature into its dissipative boundary. Just as solitons mark the interface between order and loss, the TAP tail-wave signature traces the re-stabilization of spacetime geometry.

3.3. Nonlinear Duffing Chains and Perturbation Propagation

Classical many-body models such as driven dissipative Duffing chains [17] demonstrate that localized perturbations do not vanish instantly but propagate as exponentially decaying tails. These tails encode the residual energy of coupling between oscillators, forming a memory of the system’s previous configuration. This mirrors TAP’s prediction that post-merger gravitational systems retain faint phase micro-oscillations— a geometric afterimage of the projectional mismatch between pre- and post-merger states.

3.4. Universality of Projection–Dissipation Duality

Across these examples, a universal structure emerges:

$$\mathrm{Projection}⟷\mathrm{Loss}\mathrm{of}\mathrm{Correlations}⟷\mathrm{Emergent}\mathrm{Directionality}.$$

(7)

Whether in optical, quantum, or classical systems, directionality (time, phase, or information flow) is always born from the same condition: an open boundary that limits information return. TAP extends this universality to spacetime itself, proposing that the fabric of reality obeys the same principle that governs dissipative systems—yet on a geometric scale.

Thus, before searching for TAP’s signatures in black hole mergers, we recognize that nature already exhibits analogous projection–dissipation dynamics at every accessible level of complexity.

4. Predicted Observable Signatures

If projectional dissipation is a genuine geometric mechanism, its effects should leave faint but measurable traces in astrophysical observations. Black hole mergers, being among the most extreme dissipative events in the universe, provide an ideal testing ground for TAP predictions.

4.1. Tail-Wave Echoes and Phase Micro-Perturbations

In TAP, when two event horizons merge, the alignment of their respective projection surfaces induces transient mismatches in curvature and informational coherence. This produces short-lived, low-amplitude oscillations following the primary ringdown phase. We denote these as tail-wave echoes or phase micro-perturbations.

The expected form of the signal may be represented as

$$\delta \varphi \left(t\right)\approx f(M,a)e^{-\lambda t}sin({\omega }_{\mathrm{tail}}t+{\psi }_0),$$

(8)

where

• M is the final black hole mass,
• a is the spin parameter,
• $\lambda$ is the geometric dissipation rate (linked to $\Delta A$),
• ${\omega }_{\mathrm{tail}}$ is the effective tail frequency,
• and ${\psi }_0$ is the phase offset from the main ringdown mode.

Unlike standard quasi-normal mode (QNM) oscillations, these micro-perturbations are not inherent eigenmodes of the black hole spacetime, but geometric afterimages of the projection process itself.

4.2. Relation to Horizon Area Surplus

The TAP framework links these perturbations to the non-linear surplus in horizon area,

$$\Delta A=A_{\mathrm{final}}-(A_1+A_2),$$

(9)

interpreted as the irreversible informational residue of the merger. The dissipation rate $\lambda$ is expected to scale with this surplus:

$$\lambda \propto {\displaystyle \frac{\Delta A}{A_{\mathrm{final}}}}.$$

(10)

Hence, the strength and duration of the tail-wave echoes encode the degree of projectional irreversibility. The measurable parameters $(\lambda ,{\omega }_{\mathrm{tail}})$ therefore serve as observable fingerprints of dimensional information loss.

4.3. Potential Observational Targets

Gravitational-wave events such as GW150914 and GW250114 offer ideal datasets for investigating TAP effects. Preliminary analyses [14,15] have already reported possible residual signals consistent with faint, exponentially damped echoes at post-merger timescales of $t\sim 0.1$–$0.3\mathrm{s}$.

TAP refines this interpretation by proposing that:

• The echo structure arises from curvature-phase realignment between two merging projection surfaces.
• The decay constant $\lambda$ corresponds to the geometric dissipation rate, linked to horizon-area growth.
• Multiple mergers can be statistically stacked to reveal consistent phase-tail patterns buried below the current noise floor.

4.4. Detectability and Falsifiability

From an experimental standpoint, TAP introduces a rare feature: it is directly falsifiable. If repeated cross-event analyses and weighted residual stacking fail to reveal any correlated post-ringdown perturbations, then the projectional dissipation model can be ruled out at astrophysical scales.

Conversely, the detection of even weak but phase-consistent echoes would represent the first empirical signature of geometric dissipation in spacetime itself.

Either outcome advances the field:

• No signal detected: spacetime projection is purely geometric and lossless.
• Signal detected: temporal directionality emerges as a measurable physical phenomenon.

In both cases, black hole mergers serve as natural laboratories for exploring the foundational question of why time possesses an arrow.

5. Discussion and Cosmological Implications

The TAP framework, while motivated by local phenomena such as black hole mergers, has implications that extend to the largest observable structures in the universe. If time’s direction and entropy growth arise from projectional dissipation, then the same mechanism must also leave signatures on cosmological scales, where the universe itself behaves as a global projection system.

5.1. From Local to Cosmic Projection

In TAP, the universe can be regarded as a three-dimensional projection of a higher-dimensional information manifold ${\mathcal{I}}_n$. The boundary of this projection corresponds to the observable cosmic horizon. At such a scale, small irregularities in the projection geometry would appear as anisotropies in both energy distribution and phase coherence.

This leads to a unified interpretation: black hole mergers represent localized projection realignments, while cosmological anisotropies reveal slow, large-scale projection curvature. Both arise from the same underlying informational geometry.

5.2. CMB Anomalies as Phase Anisotropies

The Cosmic Microwave Background (CMB) provides the oldest snapshot of the projection boundary observable to us. Although remarkably uniform, it exhibits several well-known anomalies, including the so-called Cold Spot and the Axis of Evil alignment [19,20]. These large-angle deviations from isotropy have resisted complete explanation within the standard $\Lambda$CDM cosmology.

TAP interprets these anomalies as manifestations of weak phase anisotropies in the global projection field. Let $\Phi \left(x\right)$ denote the projected potential field on the three-dimensional observational manifold. A small phase deviation $ϵ\left(x\right)$ from the higher-dimensional structure leads to:

$$\delta \Phi \left(x\right)={\Phi }_{0}sin(\omega t+ϵ\left(x\right)),$$

(11)

where $ϵ\left(x\right)$ encodes spatial variations in projection phase. Regions where $ϵ\left(x\right)$ deviates coherently from zero appear as statistically significant temperature anisotropies in the CMB.

Thus, what we interpret as primordial fluctuations may instead represent geometric ripples in the projection interface. The persistence and alignment of such anomalies suggest that the universe’s large-scale homogeneity is not fundamental but emergent through projectional averaging.

5.3. Informational Irreversibility on the Cosmological Scale

If the arrow of time originates in projectional dissipation, then the universe’s evolution from low to high entropy is not a random thermodynamic process, but a directional unfolding of geometry. Cosmic expansion and entropy increase reflect the same underlying principle observed in black hole mergers: an irreversible information flow from higher- to lower-dimensional states.

In this view, cosmological time $t_{\cos }$ is not a parameter within the projection, but a cumulative measure of information lost from the higher-dimensional domain:

$$t_{\cos }\propto \int d{I}_{\mathrm{lost}}.$$

(12)

The progression of time therefore corresponds to the accumulation of dissipation across the entire cosmic projection.

5.4. Toward an Observational TAP Cosmology

Several observational strategies could help probe this framework:

• Cross-correlation analysis between CMB phase anomalies and large-scale structure (LSS) distributions to test for coherent projectional signatures.
• Spectral distortion searches in the CMB to detect non-thermal relics of projectional dissipation at early epochs.
• Polarization alignment studies to evaluate whether the Axis of Evil corresponds to a preferred projection direction rather than a statistical fluctuation.

If confirmed, such findings would imply that both the cosmic arrow of time and the microscopic arrow observed in black hole systems originate from the same geometric principle: the asymmetry of information projection.

5.5. Broader Theoretical Context

TAP naturally complements existing frameworks:

• It extends the holographic principle by introducing dissipation and directionality absent in standard holography.
• It aligns with thermodynamic cosmology, yet replaces the notion of random entropy increase with structured, geometry-driven information loss.
• It provides a physical underpinning for Prigogine’s dissipative structures, situating them within the geometry of spacetime rather than within chemical or biological systems.

In this synthesis, the universe emerges not as a static hologram but as a continuously evolving projection—a living interface between higher-dimensional coherence and lower-dimensional observation.

5.6. Summary of Cosmological Implications

• The arrow of time arises universally from projectional dissipation.
• Black hole mergers represent localized, high-intensity projection events.
• CMB anomalies encode large-scale geometric irregularities of the same origin.
• Temporal evolution corresponds to the integral of informational loss across the cosmic boundary.

Thus, TAP offers a unifying lens through which local and global irreversibility can be understood within a single geometric–informational framework.

6. Conclusion

The Thermodynamic Asymmetry from Projection (TAP) framework reinterprets the arrow of time, entropy increase, and cosmological structure as emergent consequences of geometric information projection. From the merging of black holes to the background radiation of the cosmos, every irreversible process is unified under one principle: when higher-dimensional information is projected into a lower-dimensional domain, correlations are lost, and that loss defines the direction of time.

6.1. From Geometry to Temporality

Classical physics treats time as a coordinate and entropy as a statistical quantity. TAP reframes both as outcomes of dimensional geometry. The increase of black hole horizon area,

$$\Delta A=A_{\mathrm{final}}-(A_1+A_2)>0,$$

is not simply a manifestation of energy redistribution, but the spatial record of informational dissipation. In the same way, the cosmic expansion and entropy growth express the large-scale unfolding of projectional asymmetry.

Thus, temporality itself becomes a geometric phenomenon— a signature of the universe’s mode of self-disclosure. Time does not flow; it is revealed, slice by slice, through projectional loss.

6.2. Scientific Implications

The TAP perspective offers three experimentally relevant consequences:

• Astrophysical Verification: Detectable tail-wave echoes and phase micro-perturbations in post-merger gravitational-wave data could reveal dissipation at spacetime boundaries.
• Cosmological Corroboration: Persistent anomalies in the CMB, such as the Cold Spot or Axis of Evil, may represent projectional phase anisotropies on cosmic scales.
• Theoretical Integration: TAP provides a geometric–informational basis for the second law of thermodynamics and for the universality of temporal asymmetry.

Each of these consequences is falsifiable. The framework does not rely on metaphysical assumptions but on geometric observables, linking thermodynamics, general relativity, and information theory within one coherent structure.

6.3. Philosophical Reflection: Time, Letting Go, and Awareness

The implications of TAP extend beyond physics. If time’s arrow is the product of informational dissipation, then every irreversible process—including the unfolding of life and consciousness— is part of the same projectional dynamics.

In this context, the act of letting go (Fangxia) takes on a precise scientific meaning: to align with the natural direction of projection, to cease resisting the geometry of irreversibility. What philosophy calls acceptance, TAP defines as minimizing informational turbulence. Awareness becomes the self-reflective moment when the projection recognizes its own unfolding.

Thus, the border between physics and philosophy dissolves. Entropy, causality, and consciousness all arise as different expressions of the same deeper asymmetry— the one that allows the universe to manifest.

6.4. Outlook

Future research may extend TAP in several directions:

• Developing a formal mathematical model of the projection operator ${\mathcal{P}}_{n\to 3}$ and its curvature–dissipation tensor.
• Performing statistical echo searches across multiple gravitational-wave events to constrain the dissipation rate $\lambda$.
• Mapping TAP’s predictions onto early-universe dynamics to test whether projectional anisotropy could serve as an alternative explanation for inflationary or dark-energy phenomena.

Each step moves the theory closer to a unified framework where time’s arrow, information loss, and geometric structure become different facets of a single physical law.

6.5. Final Synthesis

The TAP theory does not seek to replace existing physics, but to illuminate what they all presuppose: the origin of direction, the reason asymmetry exists at all.

If verified, TAP would reveal that the universe’s most fundamental law is not equilibrium, but dissipation; not symmetry, but the geometry of loss.

In that realization, physics meets philosophy: what we experience as the passing of time is the universe continuing to project itself, moment by moment, through every act of transformation, awareness, and release.

“If the world is a projection, then we are its light.”