Time as Irreversible Causal Record A Mathematical Derivation from Causality and Passivity

Before the Frame of Reality: Why Time Must Be an Irreversible Causal Record In recent years, the idea of viewing reality through the notion of a frame has gained increasing attention across physics, philosophy, and information theory. From block-universe interpretations in relativity to correlation-based views of time in quantum foundations, many contemporary approaches suggest that reality may be better understood not as something that flows, but as something that exists all at once, structured into a static or quasi-static whole. This shift has been productive. It has helped clarify why simultaneity depends on observers, why time does not appear as a fundamental variable in some formulations of quantum gravity, and why many physical laws remain time-symmetric despite our everyday experience of irreversibility. Yet, even within this increasingly popular “frame of reality” perspective, a critical question remains open: if reality is framed, what determines the order in which that frame is accessed, updated, or experienced? In most existing discussions, the frame itself is taken as given. The ordering of events is either assumed, delegated to external parameters, or attributed to correlations without specifying why some correlations become effective while others do not. As a result, the notion of time risks being reintroduced implicitly—smuggled back in through assumptions about sequence, observation, or evolution—rather than explained. This work proposes a step before the frame. Instead of starting with a pre-defined temporal or informational frame, we ask a more basic question: what minimal structure is required for any ordering to exist at all? The answer we explore is that time should not be understood as a background parameter, a flowing substance, or even merely an emergent coordinate—but as an irreversible causal record produced by finite, constrained interactions. In this view, not all potential events participate equally in reality. Physical systems do not respond continuously to infinitesimal changes; they update only when sufficient causal conditions are met. This is already familiar from quantum physics, where energy, action, and interaction occur in discrete units, and from thermodynamics, where irreversibility arises not from the laws themselves but from constraints on memory, dissipation, and accessibility. We extend this logic more generally. A “moment” of time is not a slice of a universal flow, nor simply a coordinate in spacetime. It is the accumulation of causal updates that have crossed admissibility thresholds and left a persistent record. Events that fail to meet these thresholds are not partially real—they are simply non-events. What we call the present is the current boundary of this accumulated record; the past is what has already been irreversibly stored; the future is what has not yet become causally accessible. Crucially, this ordering does not require a global clock, an external observer, or a preferred frame. It arises naturally once three conditions are enforced: finite signal propagation, passive response (no free energy creation), and bounded memory. Under these constraints, causal influence propagates within finite cones, updates occur only after delays, and records grow monotonically. Time, in this sense, is not something added to physics—it is what remains when physics is forced to respect its own limits. Seen this way, the frame of reality is not fundamental but retrospective. Frames summarize what has already been recorded; they do not explain why records form in a particular order. The arrow of time, likewise, is not imposed by entropy alone, nor by consciousness, but by the impossibility of erasing or reordering causal records once they have formed. This perspective does not replace quantum mechanics, classical physics, or relativity. Instead, it clarifies their common ground. Quantum discreteness explains why partial updates do not occur. Relativity explains why causal access is bounded and observer-dependent. Classical irreversibility emerges when records accumulate faster than they can be undone. What unifies these regimes is not a shared notion of time as a variable, but a shared commitment to causality with memory. In short, before we speak of frames, flows, or timelines, we must account for the simple fact that reality only changes when something happens, and something only happens when it leaves a trace that cannot be undone. Time is that trace. It does not flow. It records. Seen from this angle, the familiar question—“Does time exist?”—is misplaced. The more precise question is: what can be causally recorded, and what cannot? The answer to that question, not the choice of frame, is what ultimately orders reality.