To understand PF, we first revisit McTaggart’s distinction:

Many physicists, swayed by the block universe interpretation of relativity, argue against the objective reality of the A-series ( Silberstein et al., 2018 ). PF, however, aims to bring the A-series back into the core of reality.

PF posits that reality is not a single, unified spacetime continuum with a universal “now,” but rather a collection of discrete “fragments.”

In PF, the A-series is not an illusion or a subjective construct imposed on an underlying B-series reality; it is real and ontologically fundamental to each quantum fragment.

Prior to Sadra, motion was generally considered to be an accidental property, affecting only the qualities, quantities, positions, or states of a substance, not its underlying essence. Sadra challenged this by positing that the very substance or “quiddity (mahiyya)” or essence/whatness of a contingent being is in a continuous state of flux and renewal ( Zamaniha , 2022 ).

The pivotal aspect of Sadra’s essential movement relevant to our discussion is its source:

Sadra’s philosophy is fundamentally existential. He argued for the “primality of existence” (Asalat al-Wujud), meaning that existence (wujud) is the fundamental reality, while essences (mahiyyat) are secondary. Furthermore, “existence has degrees” (Tashkik al-Wujud), implying that existence is a graded reality, ranging from the weakest contingent existents to the infinite and perfect existence of the Wajib al-Wujud. Essential movement is the process of traversing these degrees.

The Wajib al-Wujud (W) can be understood not as a specific force within the universe, but as the ultimate, foundational reality that grounds the very existence and nature of the quantum universe itself.

Mulla Sadra’s essential movement (M) is the continuous actualization and transformation of existence. In a quantum gravitational context, this becomes the inherent dynamism of the quantum vacuum, the ceaseless dance of virtual particles, the continuous evolution of quantum states, and the very fluidity of spacetime at its most fundamental level.

Here lies the core of the reconciliation: The “inherent existence of the A-series” within a quantum fragment (A_i ∈ F_i) is not a contradiction to an external source of motion (W). Instead, it is the specific, local way in which the universal essential movement manifests at the level of individual quantum systems.

In PF, the alignment of A-series during quantum measurements is crucial for the emergence of a shared macroscopic “now.” This process can be interpreted as a higher-level manifestation of essential movement.

To establish a solid foundation for our deeper mapping, let’s briefly recall the pertinent elements of FCQG as a speculative quantum gravity theory:

$\langle {\Psi }_{\text{final}}|{\Psi }_{\text{initial}}\rangle ={\displaystyle \int D\left[F\right]e^{iS\left[F\right]/\hslash }}$(1)

Now, let’s meticulously map Mulla Sadra’s metaphysical principles onto these specific elements of FCQG, arguing for their intrinsic connection.

Mapping 1: The Necessary Being (W) as the Axiomatic and Telic Principle of FCQG

Furthermore, we can conjecture that the action S[F] might conceptually align with the drive towards “perfection” inherent in Sadra’s teleological understanding of existence. This highly speculative hypothesis invites future philosophical inquiry into the intrinsic aims or directions within the dynamics of reality, distinguishing it from the more direct ontological mappings presented earlier.

$S\left[F\right]=S_{\text{grav}}\left[R\left(F\right)\right]+S_{\text{matter}}\left[F\right]+\lambda N\left(F\right)$(2)

Mapping 2: Essential Movement (M) as the Continuous Quantum Process of FCQG

$i\hslash \text{d}|C\rangle /\text{d}t=H_{\text{FCQG}}|C\rangle$(3)

Mapping 3: The Inherent A-series (A_i) as the Local Intrinsic Evolution of a Fragment’s Causal Structure

${\tau }_i=\text{max\_chain\_length}\left(C_i,\prec i\right)$(4)

$i\hslash \partial /\partial {\tau }_i|{\Psi }_i\left({\tau }_i\right)\rangle =H_i|{\Psi }_i\left({\tau }_i\right)\rangle$(5)

Mapping 4: Shared A-Series via Causal Influence and Emergent Spacetime Coherence

$R_{\alpha \beta \gamma \delta }=8\pi G{C}_{\alpha \beta \gamma \delta }\left(F_i,F_j\right)+{\Lambda }_{g\alpha \beta \gamma \delta }$(6)

This refined section now provides a more detailed and specific mapping, directly engaging with the mathematical and conceptual components of FCQG to instantiate the philosophical ideas. It deepens the “how” of the reconciliation, making the proposed connection more robust.