§4.4. and §4.5 of (Vimal, 2025v5.1): Emergence of Spacetime in DPV∼ICRDAM (§4.4) and Extending Einstein’s GR’s field equations to incorporate the s-aspect of DAS of the spacetime
Ram Lakhan Pandey Vimal
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§4.4. and §4.5 of (Vimal, 2025v5.1): Emergence of Spacetime in DPV∼ICRDAM (§4.4) and Extending Einstein’s GR’s field equations to incorporate the s-aspect of DAS of the spacetime (§4.5) in <https://drive.google.com/file/d/1yLzMiYF0WTeFxoLOdwZJbSaMUk7xBpew/view?usp=sharing>
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4.4. The Emergence of Spacetime in DPV∼ICRDAM: How Space, Time, and Spacetime Arise from Trans_spatiotemporal Param Brahman — A Comparison with Einstein's Spacetime Formulation
Q. How does both space, time, and spacetime in S1-PBspatiotemporal arise from PBtrans_spatiotemporal? Compare with Einstein’s spacetime formulation.
Abstract
A central puzzle in DPV∼ICRDAM (Dvi-Pakṣādvaita Vedānta ~ Inseparable-Complementary-Reflective Dual-Aspect Monism; Vimal, 2026c) is how space, time, and spacetime — features of the manifested dual-aspect Saguṇa Brahman (SB) domain — arise from the fully symmetric, neutral, trans_spatiotemporal Param Brahman (PBtrans_spatiotemporal). PBtrans_spatiotemporal corresponds in the scientific register to the pre-Big Bang quantum vacuum field with potential protoconsciousness fluctuations and quantum fluctuations (preBB-QVF-potential-PCFs/QFs) at cosmic state S1 in the Heptagonal Cyclic Cosmology (HCC).
PBtrans_spatiotemporal (SD-SRPT,ontological)↔(SD-SBPT,ontological) <S1-PBspatiotemporal ~ S1-preBB-QVF-potential-PCFs/QFs>, where SRPT represents symmetriy-recovering phase-transition.
This article clarifies the ontological mechanism of this emergence through four analytic steps: (1) the precise characterization of PB as trans_spatiotemporal (PBtrans_spatiotemporal) via the catuskoti (tetralemma) analysis; (2) the stability-driven symmetry-breaking phase transition (SD-SBPT) as the ontological actualization of PB’s internal instability; (3) the appearance of S1-PBspatiotemporal as the first minimally-differentiated spatiotemporal configuration (DEM = 0); and (4) the full spacetime manifold of S2–S6 (SB) as the product of sequential symmetry-breaking through Heptagonal Cyclic Cosmology (HCC).
These steps are then compared with Einstein’s (1916, 1920) formulation of spacetime as a dynamical field curved by mass-energy, showing that DPV∼ICRDAM operates at a deeper ontological register: where Einstein presupposes a pre-existing spatiotemporal manifold, DPV∼ICRDAM accounts for the very arising of that manifold from its trans_spatiotemporal ground.
4.5. Toward a Dual-Aspect Field Theory of Spacetime: Coupling Curvature to Effective Integrated Information in DPV~ICRDAM
Abstract
General relativity (GR) describes how mass-energy curves a spacetime manifold whose own ontological origin it does not address. The spirituality-based Dvi-Pakṣādvaita Vedānta ~ science-based Inseparable-Complementary-Reflective Dual-Aspect Monism framework (DPV~ICRDAM; Vimal, 2026c) supplies an account of that origin: spacetime arises through a stability-driven symmetry-breaking phase transition (SD-SBPT) from a trans-spatiotemporal source-ground, Param Brahman (PB) ~ PreBB-QVF-potential (pre-Big_Bang quantum vacuum field that has potentialitity of everything), and is, from its first actualization, a dual-aspect structure in which a subjective or protoconscious pole (s-aspect) is inseparable from, complementary to, and mutually reflective of a non-subjective physical pole (ns-aspect). This article takes up the research program implied by that comparison: extending the Einstein field equations (EFE) to incorporate the s-aspect of spacetime through a coupling between curvature and the degree of integration of the s-aspect, formalized as Effective Integrated Information (EII). We review three independent precedents that already treat spacetime geometry as responsive to information-theoretic or entropic quantities-Jacobson's (1995) thermodynamic derivation of the EFE, Verlinde's (2011) entropic gravity, and the entanglement-builds-geometry program inaugurated by Van Raamsdonk (2010) and Ryu and Takayanagi (2006)-and argue that these results, while developed independently of any consciousness-theoretic motivation, are structurally compatible with, and can be read as partial formalizations of, the dual-aspect coupling that DPV~ICRDAM motivates on ontological grounds. We then construct a candidate dual-aspect extension of the EFE (DA-EFE), in which an EII-stress tensor TEIIμν is added to the matter-energy stress tensor, and show that the standard EFE, the Jacobson equation of state, and a modified Friedmann equation are recovered as limiting or special cases under explicit assumptions relating EII to horizon entropy and to the Degree of Effective Māyā (DEM, complexity) scale of the Heptagonal Cyclic Cosmology (HCC). We argue throughout that the ontological grounding relation (PB → S1, in the register of Ultimately Mind-Independent Reality, UMIR) must not be conflated with the dynamical, empirically testable proposal for a curvature-EII coupling within manifested spacetime (the register of Conventional Mind-Dependent Reality, CMDR); the former is a metaphysical thesis, the latter a falsifiable physical hypothesis. We close by specifying what observational or experimental signatures would distinguish the DA-EFE from standard GR, and by situating the proposal relative to integrated information theory interpreted in DPV~ICRDAM (Vimal, 2022), panprotopsychism, and the combination problem.
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RāmLakhan Pāndey Vimal, Ph.D.
Abstract
A central puzzle in DPV∼ICRDAM (Dvi-Pakṣādvaita Vedānta ~ Inseparable-Complementary-Reflective Dual-Aspect Monism; Vimal, 2026c) is how space, time, and spacetime — features of the manifested dual-aspect Saguṇa Brahman (SB) domain — arise from the fully symmetric, neutral, trans_spatiotemporal Param Brahman (PBtrans_spatiotemporal). PBtrans_spatiotemporal corresponds in the scientific register to the pre-Big Bang quantum vacuum field with potential protoconsciousness fluctuations and quantum fluctuations (preBB-QVF-potential-PCFs/QFs) at cosmic state S1 in the Heptagonal Cyclic Cosmology (HCC).
PBtrans_spatiotemporal (SD-SRPT,ontological)↔(SD-SBPT,ontological) <S1-PBspatiotemporal ~ S1-preBB-QVF-potential-PCFs/QFs>, where SRPT represents symmetriy-recovering phase-transition.
This article clarifies the ontological mechanism of this emergence through four analytic steps: (1) the precise characterization of PB as trans_spatiotemporal (PBtrans_spatiotemporal) via the catuskoti (tetralemma) analysis; (2) the stability-driven symmetry-breaking phase transition (SD-SBPT) as the ontological actualization of PB’s internal instability; (3) the appearance of S1-PBspatiotemporal as the first minimally-differentiated spatiotemporal configuration (DEM = 0); and (4) the full spacetime manifold of S2–S6 (SB) as the product of sequential symmetry-breaking through Heptagonal Cyclic Cosmology (HCC).
These steps are then compared with Einstein’s (1916, 1920) formulation of spacetime as a dynamical field curved by mass-energy, showing that DPV∼ICRDAM operates at a deeper ontological register: where Einstein presupposes a pre-existing spatiotemporal manifold, DPV∼ICRDAM accounts for the very arising of that manifold from its trans_spatiotemporal ground.6. Comparison with Einstein’s Spacetime Formulation
6.1. Einstein’s Spacetime: Key Features
Einstein’s general theory of relativity (1916) reformulated spacetime in four essential ways:
(1) Spacetime as a dynamical field: rather than Newton’s absolute space and absolute time as fixed containers, Einstein established the four-dimensional pseudo-Riemannian manifold (M, gμν) as dynamical — curved by the distribution of mass-energy through the Einstein field equations (EFE): Gμν + Λgμν = (8πG/c⁴)Tμν.
(2) Unification of space and time: following Minkowski (1908), Einstein treated space and time as aspects of a single four-dimensional continuum in which the spacetime interval ds² = −c²dt² + dx² + dy² + dz² is the invariant quantity. No observer-independent ‘space’ or ‘time’ exists separately.
(3) No privileged reference frame: the principle of general covariance makes all coordinate systems equally valid; the geometry of spacetime is the physical reality, not its coordinate representation.
(4) Spacetime as the arena of physics: all physical processes, fields, and matter distributions occur within and curve the spacetime manifold. Spacetime does not have a ground outside itself in Einstein’s framework (Einstein, 1920; Janssen & Renn, 2022).
6.2. The Ontological Register Difference
The fundamental difference between DPV∼ICRDAM’s account of spacetime emergence and Einstein’s formulation is one of ontological depth:
Einstein’s general relativity operates entirely within the CMDR (conventional mind-dependent reality) register: it is a theory of the dynamics of spacetime once spacetime exists. It does not address — and does not need to address, for its scientific purposes — the question of why there is a spatiotemporal manifold at all.
DPV∼ICRDAM operates at the UMIR (ultimate mind-independent reality) register: it accounts for the very arising of the spatiotemporal manifold from its trans_spatiotemporal ontological ground (PB). The two accounts are therefore not rivals but complementary, addressing different depths of the same reality (Vimal, 2026c, §13.4: complementarity thesis).
Table 2. Comparison of Einstein’s GR Spacetime and DPV∼ICRDAM Spacetime Emergence.
|
Dimension |
Einstein (GR) |
DPV∼ICRDAM |
|
Ontological register |
CMDR: dynamics within existing spacetime |
UMIR: arising of spacetime from PB; CMDR: dynamics once S1 exists |
|
Nature of spacetime |
Dynamical pseudo-Riemannian manifold (M, gμν) |
Manifested dual-aspect SB; spatiotemporal structure arising from PB’s sarva-saṃbhāvanā |
|
Pre-spacetime ground |
None posited (spacetime is fundamental) |
PBtrans_spatiotemporal: fully symmetric, neutral, trans_spatiotemporal |
|
Mechanism of spacetime dynamics |
Einstein field equations (Gμν + Λgμν = 8πG/c⁴ Tμν); curvature by mass-energy |
SD-SBPT (UMIR: ontological actualization); CCC conformal rescaling (CMDR: aeon boundary); temperature-driven SBPT (TD-SBPT) (CMDR: S1→S2→…→S7→S1) |
|
Space and time |
Unified in 4D spacetime interval ds²; no observer-independent separation |
Inseparable aspects of PB’s potentiality; differentiated at S3–S4 through symmetry-breaking |
|
Consciousness |
Not addressed (physicalist framework) |
Dual-aspect: every spacetime state is a DAS with inseparable s-aspect (protoC or CSE) and ns-aspect |
|
Cosmological cycle |
No cyclic framework (though inflationary and cyclic models are developed by others) |
HCC: S1→S2→…→S7→S1; grounded in Penrose’s CCC (Penrose, 2010) |
|
Relation to quantum theory |
Unresolved (GR and QM not fully reconciled) |
preBB-QVF-potential-PCFs/QFs at S1; quantum fluctuations as ns-aspect of PB’s potentiality; preBB-QVF-actualized-PCFs/QFs at S2; points toward quantum gravity at S3 |
|
Buddhist/Vedantic compatibility |
Not addressed |
Trans_spatiotemporal PB compatible with sūnyatā-sūnyatā (Vimal, 2026c, §12); PB as catuskoti-negated ground |
6.3. Where the Frameworks Converge
Despite the ontological register difference, several convergences are noteworthy:
(1) Spacetime is not absolute: both Einstein and DPV∼ICRDAM reject Newton’s fixed absolute space and absolute time. For Einstein, spacetime is dynamical; for DPV∼ICRDAM, spacetime is the manifested expression of PB’s potentiality; then spacetime is dynamical, which is consistent with Einstein, and carries DEM > 0.
(2) Space and time are unified: Minkowski’s unification is anticipated by DPV∼ICRDAM’s treatment of space and time as inseparable aspects of PB’s sarva-saṃbhāvanā (all-potentiality)[i], jointly actualized at the SD-SBPT boundary.
(3) Matter-energy and spacetime are interdependent: Einstein’s EFE establish that matter-energy curves spacetime and spacetime determines matter-energy motion. In DPV∼ICRDAM, the dual-aspect structure of SB means that the spatiotemporal (ns-aspect) and the protoconscious/conscious (s-aspect) are equally fundamental and mutually reflective through the ICR structure (Vimal, 2026c, §2.3).
(4) The cosmological constant and PB: Einstein’s cosmological constant Λ (representing vacuum energy) has a structural parallel in DPV∼ICRDAM’s preBB-QVF-potential at S1: both represent a pre-matter vacuum state with non-zero energy content. DPV∼ICRDAM interprets this vacuum energy as PB’s sarva-saṃbhāvanā in its first spatiotemporal actualization.
6.4. Where the Frameworks Diverge
The frameworks diverge decisively but in a complementary manner in three respects:
First, DPV∼ICRDAM posits a pre-spatiotemporal ontological ground (PB) that has no analog in Einstein’s framework. For Einstein, spacetime is the starting point; for DPV∼ICRDAM, it is the product of SD-SBPT from PB.
Second, DPV∼ICRDAM is explicitly dual-aspect: every spatiotemporal state is a DAS with both s-aspect (protoC or CSE) and ns-aspect (physical/neural). Einstein’s GR is a purely ns-aspect framework; consciousness and subjectivity play no role.
Third, DPV∼ICRDAM’s HCC cycle provides an account of the cosmological boundary (S7→S1) grounded in PB, while general relativity’s standard formulation does not address what precedes or grounds the Big Bang, though Penrose’s CCC (Penrose, 2010) — incorporated into HCC — partially addresses the aeon boundary.
7. The Dual-Aspect Character of Emergent Spacetime
A distinctively DPV∼ICRDAM feature of the account of spacetime emergence is that spacetime, from its first actualization at S1, is not a purely physical (ns-aspect) structure but a dual-aspect structure (DAS). Even at S1, the QVF-potential includes both:
• s-aspect: potential protoconsciousness fluctuations (PCFs), the proto-mental pole of the pre-Big Bang vacuum
• ns-aspect: potential quantum fluctuations (QFs), the physical pole of the pre-Big Bang vacuum
These are not yet actualized at S1 (DEM = 0; no actualized PCFs/QFs), but their joint potentiality is already present as the inseparable, complementary, and mutually reflective (ICR) dual-aspect structure of PB’s sarva-saṃbhāvanā (all-potentiality). This means that the emerging spacetime at S2 is already dual-aspect from its inception: matter/energy fields (ns-aspect) and their inseparable protoconscious counterparts (s-aspect) arise together from the SD-SBPT.
This dual-aspect character of spacetime at its origin is the DPV∼ICRDAM solution to the hard problem of consciousness (Chalmers, 1995): consciousness does not emerge from a purely physical spacetime at some later stage of cosmic evolution; rather, the proto-mental is co-present with the physical from the very first spatiotemporal actualization at S2, as the inseparable s-aspect of the manifested DA-SB (Vimal, 2026c, §2.2).
8. Discussion: Implications and Open Questions
The DPV∼ICRDAM account of spacetime emergence has several significant implications:
(1) It provides an ontological grounding for quantum gravity approaches. The trans_spatiotemporal PB ground and the SD-SBPT correspond structurally to what quantum gravity theories seek at the Planck scale: the pre-geometric, pre-spatiotemporal domain from which spacetime emerges. DPV∼ICRDAM is not a quantum gravity theory, but it is ontologically consistent with the aspiration of such theories (Rovelli, 2004; Penrose, 2010; Barbour, 1999; Ashtekar et al., 2006; Ashtekar 2020).
(2) The anirvacanīyā boundary is not a theoretical gap but an ontological feature. The inexpressibility of the PB→S1 boundary is not a deficiency of the framework but a principled consequence of the fact that any description of the boundary already uses temporal categories that only become available after the boundary. This is consistent with the findings of Kant (1781/1998) that space and time are conditions of possible experience rather than features of the thing-in-itself.
(3) The dual-aspect character of spacetime from S2 onward implies that a complete physics must include both the ns-aspect (the subject matter of current physics) and the s-aspect (protoconsciousness and consciousness) as equally fundamental. This is consistent with, and extends, the dual-aspect monist tradition of Velmans (2008, 2021, 2026) and Atmanspacher (2012).
(4) The comparison with Einstein’s spacetime suggests a research program: extending GR’s field equations to incorporate the s-aspect of spacetime. Just as Einstein extended Newton’s absolute spacetime to a dynamical curved manifold, DPV∼ICRDAM points toward a further extension: a dual-aspect field theory in which the curvature of spacetime is coupled to the degree of protoconsciousness integration (EII: Effective Integrated Information; Vimal, 2026c, §2.3).
9. Conclusion
This article has clarified, within the DPV∼ICRDAM framework (Vimal, 2026c), how space, time, and their union as spacetime arise from the trans_spatiotemporal Param Brahman (PB):
(1) PBtrans_spatiotemporal is the fully symmetric, neutral, equipollent source-ground characterized by maximum potentiality and minimum entropy, transcending all spatiotemporal predicates through the catuskoti analysis.
(2) The SD-SBPT is PB’s ontological self-actualization — the internal instability of perfect symmetry — that inaugurates S1-PBspatiotemporal as the first minimally-differentiated spatiotemporal configuration (DEM = 0) in the UMIR register.
(3) The transition PBtrans_spatiotemporal →(SD-SBPT, ontological, UMIR) <S1-PBspatiotemporal ~ S1-preBB-QVF-potential-PCFs/QF> has no spatiotemporal ‘when’; it is ontological grounding (UMIR), not temporal efficient causation (CMDR).
(4) Full spacetime — as the dynamical dual-aspect manifold of S2–S4 — arises through the sequential temperature-driven SBPT sequence of HCC, with the CMDR temporal efficient causation (S7 → S1 via CCC) completing the cycle.
(5) Compared with Einstein’s general relativity, DPV∼ICRDAM operates at a deeper ontological register: where GR describes the dynamics of spacetime once it exists, DPV∼ICRDAM accounts for the very arising of the spatiotemporal manifold and its dual-aspect character from the trans_spatiotemporal PB ground.
The comparison underscores the complementarity thesis (Vimal, 2026c, §13): Einstein’s spacetime, Penrose’s CCC, quantum gravity approaches, and DPV∼ICRDAM are not rivals but partial crystallizations of PB, each capturing a different depth and register of the same underlying dual-aspect reality.
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RāmLakhan Pāndey Vimal, Ph.D.