NOTE: This was generated based on my extensive discussion with Gemini chat model.
Abstract: This paper proposes a model of time grounded in Presentism, defining the present moment ("Now") as the set G composed of the unique "latest event" occurring at each individual point in space. Each latest event is determined strictly by the local history of its respective point, independent of events at other locations and explicitly excluding any inherent simultaneity between spatially separated members of the set. We argue that this definition aligns with the intuitive, common understanding of "now" and results in a frame-independent description of the present. This G-based Presentism is posited as the fundamental layer of reality. Concepts from Special Relativity (SR), such as the constant speed of light (c) and relative simultaneity, which require relating spatially separated points, are argued to operate at a secondary layer, describing relationships within the fundamental reality defined by G. This model challenges interpretations like the Block Universe, suggesting they arise from prioritizing SR's relational structure over the proposed foundational nature of locally-determined existence.
Keywords: Presentism, Time, Now, Latest Event, Local Determination, Frame Independence, Special Relativity, Ontology of Time, Foundational Reality, Simultaneity.
1. Introduction
The nature of time and existence remains a profound question at the intersection of physics and philosophy. Presentism, the view that only the present moment is real, aligns closely with common human intuition but faces significant challenges when confronted with the implications of modern physics, particularly Special Relativity (SR) and its consequence, the Relativity of Simultaneity (RoS) [1, 2]. RoS implies that observers in relative motion disagree on which spatially separated events occur "at the same time," undermining the notion of a single, objective, universe-wide present moment often assumed by simple forms of presentism.
Interpretations of SR have often led to ontological models like Eternalism (the Block Universe) [3], where past, present, and future co-exist with equal reality, seemingly accommodating RoS more naturally. However, these models conflict strongly with the intuitive sense of temporal flow and the unique status of the present.
This paper argues that the conflict arises partly from how "now" is conceptualized within physics. We contend that the intuitive or "layperson's" understanding of "now" corresponds to a different, more fundamental concept than the frame-dependent simultaneity slices described in SR. We propose a formal definition of "Now" based purely on local reality – the collection of the latest events occurring at each point in space – and argue this definition avoids the conflicts with SR by explicitly separating the concept of "Now" from the concept of "simultaneity." We further argue that this locally-determined "Now" represents the fundamental layer of existence, upon which the relational structures described by SR are superimposed.
2. Model Definition: The Set G as "Now"
We begin with fundamental premises:
Space can be considered as a set of points {P_i}.
At each point P_i, there is a history H_i consisting of a temporally ordered sequence of events or states occurring locally at P_i.
Within any realized segment of H_i, there exists a unique "latest event" or "latest instant," denoted L_i, which is the final element in that sequence at P_i. No subsequent event at P_i has yet occurred. This definition relies solely on the local temporal order at P_i.
Based on these premises, we define the set G: G = {L_i | L_i is the latest event in the history H_i of point P_i}
Crucially, we then propose the following stipulative definition: "Now" := G
This definition asserts that the word "Now" means precisely this set G. It is vital to note what this definition does not include:
It does not assume or require that events L_i and L_j (for i ≠ j) are simultaneous in any sense.
It does not rely on relating different points P_i and P_j via light signals or any other means.
The set G is formed simply by collecting all entities across space that satisfy the locally determined property of "latestness."
3. Properties of the Model
3.1. Frame Independence: The determination of L_i depends only on the temporal order of events at P_i. The order of events at a single spacetime location (along a worldline) is absolute – all observers agree on the sequence. Therefore, the identification of L_i within its local history H_i is frame-independent. Since each element L_i is frame-independently identifiable, the set G, defined as the collection {L_i}, is itself frame-independent. It represents the same collection of spacetime events regardless of the observer's state of motion.
3.2. Realization of Presentism: This model provides a direct framework for Presentism. If "Now" (G) is defined as above, and we postulate that only what is "Now" exists, then only the collection of latest events G constitutes reality. Past events (those preceding L_i in any H_i) have ceased to exist, and future events (those potential events following L_i) do not yet exist. The entirety of existence is the set G.
4. Relationship to Special Relativity
We acknowledge the empirical success and validity of Special Relativity within its domain. SR provides our best description of spacetime geometry and kinematics, particularly concerning relationships between spatially separated events and observers in relative motion. Key concepts include the constant speed of light (c) and the Relativity of Simultaneity (RoS).
4.1. Conceptual Layering: We argue that the conceptual apparatus required for SR is distinct from and builds upon the concepts required to define G.
Defining G requires only local temporal ordering at individual points.
SR, particularly in defining simultaneity and relating distant events, requires additional concepts: spatial separation between points, temporal intervals between events at different points, and the universal constant c (related to signal propagation). The units of c (distance/time) reflect its role in relating spatially and temporally separated events.
Therefore, we propose that G represents a more fundamental layer of reality (the existing "Now"), while SR describes a secondary layer concerning the propagation of influences and the structure of relationships within or across the fundamental reality described by G. SR details how points in G relate and signal each other, governed by c.
4.2. "Now" vs. Simultaneity: This model explicitly decouples "Now" from "Simultaneity."
Our "Now" (G) is absolute and frame-independent because it makes no claims about simultaneity.
SR's "simultaneity" is relative because its definition inherently relies on c and reference frames to relate distant events in time. They are separate concepts addressing different aspects – G addresses what exists (latest events locally), while SR's simultaneity addresses how events time-correlate across space based on light speed and frame choice. The conflict between Presentism and SR arises only if one insists that "Now" must be a surface of simultaneity in the SR sense. Our definition rejects this insistence.
5. Discussion
This model defines "Now" (G) in a way that aligns with the intuitive notion of a present composed of the latest state of affairs everywhere, while remaining frame-independent and compatible with Presentism. It achieves this by separating the concept of "Now" from the concept of "simultaneity."
This challenges interpretations like the Block Universe (Eternalism). We argue that Eternalism gains traction primarily because simple Presentism struggles to reconcile with RoS. By defining a Presentism based on G that sidesteps RoS (by definition), the motivation for Eternalism derived from SR is weakened; Eternalism becomes an interpretation of a secondary structure (SR spacetime geometry) rather than a description of fundamental reality (G).
The physical nature of the set G warrants further exploration. Since it is not defined as a surface of simultaneity, it would likely represent a complex hypersurface in relativistic spacetime, possibly with some elements being spacelike separated from others, and some timelike or lightlike separated. Understanding the dynamics and evolution of such a surface presents a conceptual challenge. How does the set G evolve? Does L_i tick forward independently at each P_i, constantly redefining G? This requires a theory of dynamics compatible with this ontology.
Furthermore, the objection that c having units disqualifies it from being fundamental (raised in discussion) is addressed by noting that units reflect human convention and the quantity's nature (relating space and time). Its fundamentality within SR stems from its role. In our model, c belongs to the secondary SR layer; the fundamental layer G requires no such constant for its definition.
6. Conclusion
We have proposed a model where "Now" is defined as the frame-independent set G of locally determined latest events at all points in space. This definition is explicitly decoupled from the concept of simultaneity. This G-based "Now" provides a foundation for Presentism that is not in direct conflict with the Relativity of Simultaneity, as RoS addresses a different concept (frame-dependent simultaneity based on light signals). We argue that G represents the fundamental layer of existence, with the relational structure described by Special Relativity operating as a secondary layer. While this model aligns with intuition about the present and avoids standard conflicts, further work is needed to explore the physical characteristics and dynamics of the set G and its compatibility with other areas of physics.
7. References
[1] Einstein, A. (1905). Zur Elektrodynamik bewegter Körper. Annalen der Physik, 322(10), 891–921.
[2] Putnam, H. (1967). Time and Physical Geometry. Journal of Philosophy, 64(8), 240–247.
[3] Rietdijk, C. W. (1966). A Rigorous Proof of Determinism Derived from the Special Theory of Relativity. Philosophy of Science, 33(4), 1 341–344. (Additional relevant references on Presentism, Eternalism, Growing Block, and Philosophy of Time would be included here in a full paper.)
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