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Discrete Spacetime from the Photoelectric Effect and Special Relativity? An Ontological Reading of the Lorentzian Null Interval

Fibonacci Fahrenheit

Published May 4, 2026• 0 citations
Publisher

Abstract

We present an ontological reading of the discrete-time framework obtained from the joint application of two of Einstein's 1905 results — the photoelectric effect (energy-quantum hypothesis) and special relativity — and apply it to the frame-proper behaviour of the photon. The framework treats time as the discrete sequence of interaction events between energy packets, with characteristic tick T = h/mc2 for a packet of mass m. We argue that the present has internal structure: a past-of-the-present (the most recent scar), an in-between (the ongoing resolution), and a future-of-the-present (binary potentials).The in-between of any resolution is identified, structurally, with the Bohr quantum leap (Bohr 1913, Nobel 1922): no intermediate state, no intermediate position, empirical correctness in the cases tested. We give the constant c its ontological reading as the metrological signature of the leap as observed in any massive frame, while explicitly stating that the framework does not derive c's numerical value or its frame-invariance, both of which are taken as empirical input. Heisenberg's indeterminacy is recovered as a consequence of position belonging to the past-of-the-present and momentum belonging to the future-of-the-present (different ontological modes). Seven empirical signatures are listed under which the framework would be falsified.

DOI
10.6084/m9.figshare.32163087

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•Oct 31, 2026•0 citations

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•Sep 18, 2026•0 citations
We present an ontological reading of the discrete-time framework obtained from the joint application of two of Einstein's 1905 results — the photoelectric effect (energy-quantum hypothesis) and special relativity — and apply it to the frame-proper behaviour of the photon. The framework treats time as the discrete sequence of interaction events between energy packets, with characteristic tick T = h/mc2 for a packet of mass m. We argue that the present has internal structure: a past-of-the-present (the most recent scar), an in-between (the ongoing resolution), and a future-of-the-present (binary potentials).The in-between of any resolution is identified, structurally, with the Bohr quantum leap (Bohr 1913, Nobel 1922): no intermediate state, no intermediate position, empirical correctness in the cases tested. We give the constant c its ontological reading as the metrological signature of the leap as observed in any massive frame, while explicitly stating that the framework does not derive c's numerical value or its frame-invariance, both of which are taken as empirical input. Heisenberg's indeterminacy is recovered as a consequence of position belonging to the past-of-the-present and momentum belonging to the future-of-the-present (different ontological modes). Seven empirical signatures are listed under which the framework would be falsified.
We derive the discreteness of time from two empirically established results of Einstein (1905): the photoelectric effect (energy is quantized) and special relativity (time is relative to the observer's frame). The Planck–Einstein relation E=hf and mass–energy equivalence E=mc2 jointly yield a characteristic frequency f=mc2/h and a minimum temporal resolution T=h/mc2 for any energy packet of rest mass m. Combined with a principle of ontological parsimony excluding unobservable continuous background time , we propose that time does not exist as a continuous substrate but emerges as the discrete sequence of causal interaction events between energy packets.
Holographic Informational Ontology Framework: Relativity and Quantum Field Theory (HIOF-PnQFT) Incompatibility as a Problem of Positioning* This is a short, non-technical companion to the 5-paper HIOF-PnQFT series (Prelude and Papers I to IV). It is written for readers in physics, philosophy of physics, or the foundations of quantum theory, not for readers already familiar with the author's wider framework. The core idea, stated plainly Relativity and quantum field theory are usually treated as two correct theories that still need a bridge. The series asks a prior question: what exactly are they being asked to make compatible? In the reading of this framework, a spacetime stage and randomness of outcomes are manifest features, not fundamental ones. The compatibility problem is therefore read as a problem of positioning. This is a repositioning, not a claim that any technical obstacle has been removed. Two layers The information layer has no coordinates, no spatiotemporal character, and no relative relations; it only exists. The manifest layer is what appears after information is read, expanded, and set in flow: past, present, space, fields, energy, carriers, relations, and determinate results. The order of manifestation is information, then energy, then matter. This order is an inference, not a verified conclusion. Past, present, future The past is information. The present is the reading of consciousness, where consciousness is the direction and path along which an "I" manifests. The future is not stored in advance. Spacetime is not a pre-existing stage. Five readings of the incompatibility Relative relations belong to the manifest layer. Spacetime is manifestation, not a stage. The quantum has no randomness, only uncertainty from a limited arc window. The spooky distance of entanglement is a category error: the spacetime in which distance is defined is imposed on information that has none. The speed of light is read as the upper limit of reading, with causal structure as its consequence. This is an inversion at the ontological level only: within the arc window, every observable result agrees with special relativity. The measurement chain The quantum itself is not read at any layer. A source of interference forces the quantum to hand out a posture (coercion, not transaction). The posture and the instrument transact; the instrument and the observer transact. The constitution of an instrument determines its arc window, including what it does not know that it does not know. A response is established when an instrument reads a posture and yields a stable record that can be read again. The single result and the Born rule are taken as axioms. Fermi theory as a case study A low-energy theory is read as the successful marking of wide-domain information through a narrow arc window. In Fermi theory the coupling constant carries the fingerprint of the W boson mass, and its dimension forecasts where the window gives way. The mathematics is that of effective field theory; the difference lies in ontological commitment only. What the series does not do It supplies no alternative dynamics, no new field equation, and no distinguishable observational prediction. It does not derive the Born rule, does not claim to meet microcausality, Lorentz invariance, or unitarity, and does not claim that consciousness influences the ontological information. Algebraic quantum field theory, the thermal time hypothesis, emergent spacetime, and relational quantum mechanics are compared with the series and never treated as support for it. Any test template involving symmetry groups, topology, or lattices would be an independent model at the manifest layer, not an inference of the framework. What the series covers Prelude: why this series, and why the two theories do not fitPaper I: spacetime, past, present, futurePaper II: the sources of incompatibilityPaper III: the interface and relationsPaper IV: arc windows and effective theories A note on method Each paper separates standard published results from the framework's own readings and states what it does not claim. Readers are encouraged to treat the readings as hypotheses to be compared with existing theory and experiment, not as settled fact. Keywords: relativity, quantum field theory, information ontology, arc window, measurement problem, effective field theory, entanglement, emergent spacetime, philosophy of physics AuthorWai-Hung Tam (Pan), Independent ResearcherORCID: 0009-0002-7789-8464Email: panxtam@protonmail.com
This paper presents a foundational thought experiment and proposes a radical ontological framework for interpreting quantum mechanics and the nature of time. It moves beyond conventional interpretations by testing them against a novel scenario: a hypothetical "time machine" (device 𝒲) capable of passively reading the past state of a quantum system without interacting with it. The central testbed is the classic double-slit experiment. In Stage 1, performed at time T_0, the experiment is run without any path detection, yielding the standard interference pattern. In Stage 2, at a later time T_0 + ΔT, the device 𝒲 is used to retroactively "read" the precise state of the system at the moment the electron passed the slit plane. The pivotal question is: What information about the electron's path will 𝒲 find? The analysis demonstrates that established interpretations face significant paradoxes: The Copenhagen Interpretation risks falling into retrocausality, as the mere potential for future path-information readout could retroactively collapse the interference pattern. The Many-Worlds Interpretation leads to internal inconsistency, as the deterministic, single-path history observed within a given branch by 𝒲 contradicts the interference pattern observed in that same branch's past. The de Broglie-Bohm (dBB) Interpretation, while positing a hidden trajectory, struggles with the mechanism of how 𝒲 could read this information without interacting with the guiding pilot wave, which is essential for the interference effect. As a resolution, the paper proposes a new ontological model based on a geometric, discrete conception of reality. The core tenets are: Fundamental Entities: Reality is a dynamic network of "p-gluons," postulated as geometric quanta of spacetime. Discrete Frames: Observable reality is not continuous but consists of a sequential generation of discrete, global "frames" (K_i). Each frame is a complete geometric snapshot of the entire p-gluon network's configuration. The Axiom of Record Economy (AOZ): This is the central formal postulate. At each generative step, at most one frame from the space of locally possible states (ℋ_poss) is physically realized. A frame is generated if and only if it satisfies a condition of global consistency with the entire history, as determined by a fundamental "algorithm of reality" (𝒜). Crucially, states in ℋ_poss that are not selected for generation attain no ontological status whatsoever; they are abstract possibilities, not unrecorded facts. Emergent Time: Observable time is not a fundamental background parameter but an emergent measure of the rate (Ḳ) at which these global frames are generated. Within this Frame-Recording Ontology, the time-machine paradox finds an elegant and decisive solution: In the double-slit experiment without a detector, the only configuration consistent (via algorithm 𝒜) with the future observation of an interference pattern is a global superposed state. This state, describable as an extended pattern of geometric correlations in the p-gluon network encompassing both slits, is the one and only frame generated (K_T0). Deterministic "path" frames (electron at S_1 or S_2) are not generated; they remain unrealized abstractions. Therefore, when device 𝒲 reads the past, it accesses the sole ontological record: frame K_T0. It finds no geometric data corresponding to a classical path because such data was never physically recorded. The answer is not "the information is hidden" (epistemology), but "the corresponding fact was never generated" (ontology). The paper elaborates on the non-anthropomorphic, non-teleological nature of algorithm 𝒜, framing it as a constraining structure akin to a variational principle rather than a conscious selector. It discusses the model's implications for the measurement problem (reinterpreted as the generation of a "classical" frame), nonlocality, and its philosophical shift from epistemic to ontological indeterminacy. Methodology: The work is developed using the author's "Pencil Case Philosophy" or "Sonar Modeling" approach. This methodology begins by constructing minimal axiomatic building blocks (p-gluons, AOZ, 𝒜), activates the system, and rigorously traces its logical consequences without prior commitment to reproducing existing theoretical frameworks.
Holographic Informational Ontology Framework: Relativity and Quantum Field Theory (HIOF-PnQFT) Incompatibility as a Problem of Positioning* This is a short, non-technical companion to the 5-paper HIOF-PnQFT series (Prelude and Papers I to IV). It is written for readers in physics, philosophy of physics, or the foundations of quantum theory, not for readers already familiar with the author's wider framework. The core idea, stated plainly Relativity and quantum field theory are usually treated as two correct theories that still need a bridge. The series asks a prior question: what exactly are they being asked to make compatible? In the reading of this framework, a spacetime stage and randomness of outcomes are manifest features, not fundamental ones. The compatibility problem is therefore read as a problem of positioning. This is a repositioning, not a claim that any technical obstacle has been removed. Two layers The information layer has no coordinates, no spatiotemporal character, and no relative relations; it only exists. The manifest layer is what appears after information is read, expanded, and set in flow: past, present, space, fields, energy, carriers, relations, and determinate results. The order of manifestation is information, then energy, then matter. This order is an inference, not a verified conclusion. Past, present, future The past is information. The present is the reading of consciousness, where consciousness is the direction and path along which an "I" manifests. The future is not stored in advance. Spacetime is not a pre-existing stage. Five readings of the incompatibility Relative relations belong to the manifest layer. Spacetime is manifestation, not a stage. The quantum has no randomness, only uncertainty from a limited arc window. The spooky distance of entanglement is a category error: the spacetime in which distance is defined is imposed on information that has none. The speed of light is read as the upper limit of reading, with causal structure as its consequence. This is an inversion at the ontological level only: within the arc window, every observable result agrees with special relativity. The measurement chain The quantum itself is not read at any layer. A source of interference forces the quantum to hand out a posture (coercion, not transaction). The posture and the instrument transact; the instrument and the observer transact. The constitution of an instrument determines its arc window, including what it does not know that it does not know. A response is established when an instrument reads a posture and yields a stable record that can be read again. The single result and the Born rule are taken as axioms. Fermi theory as a case study A low-energy theory is read as the successful marking of wide-domain information through a narrow arc window. In Fermi theory the coupling constant carries the fingerprint of the W boson mass, and its dimension forecasts where the window gives way. The mathematics is that of effective field theory; the difference lies in ontological commitment only. What the series does not do It supplies no alternative dynamics, no new field equation, and no distinguishable observational prediction. It does not derive the Born rule, does not claim to meet microcausality, Lorentz invariance, or unitarity, and does not claim that consciousness influences the ontological information. Algebraic quantum field theory, the thermal time hypothesis, emergent spacetime, and relational quantum mechanics are compared with the series and never treated as support for it. Any test template involving symmetry groups, topology, or lattices would be an independent model at the manifest layer, not an inference of the framework. What the series covers Prelude: why this series, and why the two theories do not fitPaper I: spacetime, past, present, futurePaper II: the sources of incompatibilityPaper III: the interface and relationsPaper IV: arc windows and effective theories A note on method Each paper separates standard published results from the framework's own readings and states what it does not claim. Readers are encouraged to treat the readings as hypotheses to be compared with existing theory and experiment, not as settled fact. Keywords: relativity, quantum field theory, information ontology, arc window, measurement problem, effective field theory, entanglement, emergent spacetime, philosophy of physics AuthorWai-Hung Tam (Pan), Independent ResearcherORCID: 0009-0002-7789-8464Email: panxtam@protonmail.com
Holographic Informational Ontology Framework: Relativity and Quantum Field Theory (HIOF-PnQFT) Incompatibility as a Problem of Positioning* This is a short, non-technical companion to the 5-paper HIOF-PnQFT series (Prelude and Papers I to IV). It is written for readers in physics, philosophy of physics, or the foundations of quantum theory, not for readers already familiar with the author's wider framework. The core idea, stated plainly Relativity and quantum field theory are usually treated as two correct theories that still need a bridge. The series asks a prior question: what exactly are they being asked to make compatible? In the reading of this framework, a spacetime stage and randomness of outcomes are manifest features, not fundamental ones. The compatibility problem is therefore read as a problem of positioning. This is a repositioning, not a claim that any technical obstacle has been removed. Two layers The information layer has no coordinates, no spatiotemporal character, and no relative relations; it only exists. The manifest layer is what appears after information is read, expanded, and set in flow: past, present, space, fields, energy, carriers, relations, and determinate results. The order of manifestation is information, then energy, then matter. This order is an inference, not a verified conclusion. Past, present, future The past is information. The present is the reading of consciousness, where consciousness is the direction and path along which an "I" manifests. The future is not stored in advance. Spacetime is not a pre-existing stage. Five readings of the incompatibility Relative relations belong to the manifest layer. Spacetime is manifestation, not a stage. The quantum has no randomness, only uncertainty from a limited arc window. The spooky distance of entanglement is a category error: the spacetime in which distance is defined is imposed on information that has none. The speed of light is read as the upper limit of reading, with causal structure as its consequence. This is an inversion at the ontological level only: within the arc window, every observable result agrees with special relativity. The measurement chain The quantum itself is not read at any layer. A source of interference forces the quantum to hand out a posture (coercion, not transaction). The posture and the instrument transact; the instrument and the observer transact. The constitution of an instrument determines its arc window, including what it does not know that it does not know. A response is established when an instrument reads a posture and yields a stable record that can be read again. The single result and the Born rule are taken as axioms. Fermi theory as a case study A low-energy theory is read as the successful marking of wide-domain information through a narrow arc window. In Fermi theory the coupling constant carries the fingerprint of the W boson mass, and its dimension forecasts where the window gives way. The mathematics is that of effective field theory; the difference lies in ontological commitment only. What the series does not do It supplies no alternative dynamics, no new field equation, and no distinguishable observational prediction. It does not derive the Born rule, does not claim to meet microcausality, Lorentz invariance, or unitarity, and does not claim that consciousness influences the ontological information. Algebraic quantum field theory, the thermal time hypothesis, emergent spacetime, and relational quantum mechanics are compared with the series and never treated as support for it. Any test template involving symmetry groups, topology, or lattices would be an independent model at the manifest layer, not an inference of the framework. What the series covers Prelude: why this series, and why the two theories do not fitPaper I: spacetime, past, present, futurePaper II: the sources of incompatibilityPaper III: the interface and relationsPaper IV: arc windows and effective theories A note on method Each paper separates standard published results from the framework's own readings and states what it does not claim. Readers are encouraged to treat the readings as hypotheses to be compared with existing theory and experiment, not as settled fact. Keywords: relativity, quantum field theory, information ontology, arc window, measurement problem, effective field theory, entanglement, emergent spacetime, philosophy of physics AuthorWai-Hung Tam (Pan), Independent ResearcherORCID: 0009-0002-7789-8464Email: panxtam@protonmail.com
This paper begins with a question concerning the physical meaning of 𝑚0𝑐2 as it appears in the relativistic energy relation 𝐸2 = 𝑝2𝑐2 + 𝑚02𝑐4. The numerical relations 𝐸 = 𝑚0𝑐2 and 𝐸 = 𝛥𝑚𝑐2 are supported by precise experiments, but the ontology to which these mathematical quantities are assigned is a separate issue. This question leads directly to a reconsideration of the standard relativistic picture in which the relativistic time and relativistic length introduced by Einstein in 1905, and later geometrized as spacetime after Minkowski, are attributed to the physical world itself. The same issue appears in quantum theory. The relativistic energy–momentum relation connects to relativistic quantum-wave structures and, in the nonrelativistic regime, to Schrödinger mechanics; however, it does not follow uniquely from the mathematics that the wave function, probability, and uncertainty must be interpreted as properties of reality itself. The present paper identifies a common root of these two problems in the identification of mathematically observed quantities with reality itself. The Nakaza New Relativity Theory (NNRT) places an invariant real spacetime, consisting of universal time and universal space, as its physical basis. It does not, however, assume an absolute rest frame or an ether, and it regards all inertial frames as physically equivalent. In contrast, time, distance, phase, frequency, wavenumber, arrival time, and related quantities constructed through actual measurement are separated as quantities of measurement spacetime. The logical boundary between observational agreement and ontological identification is formulated here as the Observational–Ontological Non-Uniqueness Proposition (OONP). Taking the phase–action correspondence 𝛩 = 𝑆⁄ℏ, 𝑘𝜇(𝛩) = 𝜕𝜇𝛩, and 𝑃𝜇(𝛷) = ℏ𝑘𝜇(𝛩) as a common bridge, the dispersion structure of a single Fourier mode is organized as relativistic observation, whereas the superposition of multiple modes and Fourier duality are organized as quantum observation. In this framework, 𝛥𝑥𝛥𝑝 ≥ ℏ⁄2 is first interpreted as a bandwidth–localization constraint of a phasebased observational representation, while the Born rule, Hilbert space, and unitary evolution are retained as standard quantum mathematics in the quantum-observational layer. Furthermore, 𝑚0𝑐2 is reconstructed as the phase-invariant base scale 𝐵𝛷 = ℏ√𝜔2 − 𝑐2𝑘2 = 𝑚0𝑐2. What this paper changes is neither established mathematics nor experimental values. NNRT explicitly rejects the physical definition according to which relativistic time, relativistic length, and relativistic spacetime are properties of real time and real space themselves. It therefore proposes that these concepts be removed from the foundational description of real spacetime and be confined to the mathematics of measurement and observation.