The Theory of Band-Limited Relational Time

By Cherry Speicher

9/4/2025 (Updated 9/16/2025)

Abstract

Theoretical and Conceptual

In this paper I will introduce a theoretical framework that may serve as a unifying qualitative language to assist in solving the problem of time. The problem of time being defined by “A conceptual conflict between quantum mechanics and general relativity. Quantum mechanics regards the flow of time as universal and absolute, whereas general relativity regards the flow of time as malleable and relative. This problem raises the question of what time really is in a physical sense and whether it is truly a real, distinct phenomenon. It also involves the related question of why time seems to flow in a single direction, despite the fact that no known physical laws at the microscopic level seem to require a single direction.” Anderson, E. (2012-12-15). "Problem of time in quantum gravity". Annalen der Physik. 524 (12): 757–786

I propose here a novel concept I call “Band-Limited-Relational Time” or BLRT for short. In this framework I assert that time itself is band related; relative to not only the observer, but the observer’s perspective frame rate defined as; how we biologically process time into a coherent flow, which yields a perceivable band of linear time. This band allows us to better understand that, while we may be perceiving correctly, the linear flow of time resides in not only a spatially relative way, but also a perceptively relative way.

In BLRT the observers relative perspective, coupled with frame rate, are important because it gives context for how time is measured, and why in some models, (General Relativity: GR) time works linearly in our equations, while in others (Quantum Mechanics: QM) time does not seem to adhere to the same linear framework; especially in cases of Quantum Entanglement, Simultaneity, and Quantum Gravity. 

9/16/2025- Updates abbreviated:

(1) a Predictive-Sufficiency Principle for choosing a “best clock” or the subsystem that carries the most predictive information under real-world limits; (2) a clear resolution of the band-limit vs. Markovianity critique via smooth filters and explicit coarse-graining (no brick-wall cutoffs); (3) an algebraic/modular construction (filtered modular flow) and a path-integral implementation that interpret spectral filtering as a physically motivated regulator, without pretending renormalization disappears; and (4) a falsifiable experimental pathway: measure human neural filters (EEG/SSVEP) and test whether an observer’s filter shape predicts the decoherence rate of a weakly coupled quantum probe. If the rate tracks the overlap integral I specify, that supports BRT; if it doesn’t, after power matching and attention controls, this particular physiological implementation is constrained.

I also include a minisuperspace toy model to show how “cosmic time” precision depends on passband, plus a conservative SNR/power analysis for lab feasibility. Scope matters: the strong-gravity, highly non-stationary universe is outside the claims here. But for finite observers in weak-coupling regimes: humans, clocks, detectors, BLRT offers a concrete bridge between relational/thermal time ideas and testable lab predictions.

Theoretical Framework and Introduction

In BLRT, bands are born out of an emergent system in which they reside in. (referenced formally later in this paper as the Predictive-Sufficiency Principle). From there, they chemically, elementally and biologically filter into cohesion through relevance. This relevance gives rise to organisms who share similar biological composition. Biologically similar organisms, who have evolved within the same system then (when evolutionarily relevant) develop certain ways of perceiving time. Anything outside of the system, has no evolutionary benefit or necessity to develop in a similar way, and only gains relevance when observed or measured by something beyond its relative time.

I assert that other emergent systems exist in the same way in which we do, and still others far differently, but because they have no relevance to us, they become outside of our band-width. Therefore, bands that are more closely relevant to our own allow us to study their mechanics only at a brief glimpse and causing incongruencies in our understanding of time.

In my framework, I speculate that when we observe systems relatively close to our band, we see them as being Quantum problems within our General Relativity framework. Here I say, “Both or true” (each within its own relativistic band) in the context of this paper I highlight this by showing emergent Lindblad dynamics from band-limited observations.

In BLRT I assert that the only gap between QM and GR, is that the relativistic band in which Quantum physics operates in, doesn’t operate exactly as ours does in GR because it emerged out of a different system of a near linear, or nonlinear band of time. Each band as real, each operating in the grounded principle that reality is real, but time is relational. 

Furthermore, I would say that the only reason we are able to measure it and quantify it by any means at all, is because its band still carries relativity in our own system, and that we are ourselves a part of its system. When I say “it” I would like to further clarify that I don’t impose any notion of consciousness into these states, only that they exist as electron clouds, photons and the like. I postulate that these particles emerged out of a universal state (which is why I reference measuring in terms of Hilbert space), but they do not require the same kind of basic principles of linear time for existence. In these states: (photons, mesons etc.) evolution is not time dependent, therefore it is able to exist in many states at once, just as we study in superposition, and when we study by example of quantum entanglement.

This is all given further depth by describing BLRT in terms of over-dense and under-dense regions in cosmology, in which emergent systems evolved only because they maintained context and were relative to each other. This then, makes the bolder and admittedly, more speculative statement, that while we may exist in a Block Universe, our known reality exists as an emergent band inside it, which would also explain many principles in string theory (speculative but testible within my framework), thus uniting these theoretical frameworks into one understandable unifiable framework. Wherein, only certain terms (particularly in string theory) would be categorized as emergent string sector grammar, because the operational framework of Band Limited Relational Time gives them new context.   

I assert that by measuring and quantifying our own perceptual frame rate, we can then use this information to deduce (by reasonable, quantifiable and calculable means) where our discrepancy lies, as well as, apply it to our current known Lindblad equations to produce meaningful solutions.

Here I introduce the known concept of, Positive Operator-Valued Measure in Hilbert Space, with the additional constraints of spectral filter represented as F(_ω) and bandwidth regimes, from here it is possible to produce equations that reconcile between the gaps of GR and QM.

BLRT is proposed within a Lorentz safe structure, (nothing is faster than the speed of light), a Non-signaling (no “spooky action”) framework, founded in well understood principles that are testable in both the lab, and given as “toy models” here.

Theoretical Implications

If verified in lab studies the implications for its findings could offer new insights into not only the world of QM and GR but also in developing new tools for individuals who suffer Parkinson’s, ADHD, or schizophrenia who often have altered temporal windows. Measuring bandwidth could become a diagnostic marker. If you know someone’s integration window is wider or narrower than average, therapies (like rhythmic stimulation, meds, or even music training) could be tuned to restore balance.

In aging research, older adults’ time windows widen; measuring that can help design interventions to keep attention and coordination sharp.

In technology, human and machine syncopation through VR, AR, and integrated machine presence, depend on matching system delays to our temporal bandwidth. If systems fall outside that band, people feel disoriented. If we could match this in better ways we could improve cars, planes, and surgical robots all which rely on split-second judgments. Knowing the human bandwidth helps design alerts and interfaces that can land inside it.

In personalized tech and improved learning for those with disabilities, imagine headphones, learning apps, or fitness trainers that adapt their pacing to your own temporal processing rhythm.

In short, we already know and understand that we are the universe observing itself, we don’t live independent of it, we live inside a beautiful and complex system. So, I propose that we begin our journey into the universe not by looking out at it, but by viewing ourselves in it, and seeing how our own perspective and relative nature may skew us from answering some of our deepest problems with time.

In the paper that follow, I formalize these concepts into a rigorous and testable framework using band-limited POVMs, modular flows, and optimization principles.