Observation Limits and the Undifferentiated Origin: An Epistemological Inquiry from Quantum Measurement to Cosmology

This exploratory essay organizes the limits of an observer's ability to distinguish physical states into three phases: a Spacetime-Limit Phase, in which the spacetime framework remains but distinctions become statistically harder; a Dimension-Reduction Phase, in which the number of independently distinguishable directions decreases; and a Zeroth-Order Phase, in which the observer has no means of observation that distinguish differences in time, distance, direction, or causal order. Here "phase" names the state of an observer's description; it does not mean a thermodynamic or quantum phase transition. The essay adopts the epistemological position that states no available measurement can distinguish are treated as the same for that observer. It formalizes the Zeroth-Order Phase as the condition that the outcome distributions of all procedures the observer can perform coincide (Δ_O = 0). From the quantum Fisher information matrix of the state restricted to the observer's observation conditions, it defines an effective dimension D_eff, for given required resolutions and a finite number of measurements, and a rank d_O. Neither D_eff approaching zero nor a vanishing rank is by itself sufficient for the Zeroth-Order Phase. Finite-dimensional toy models in the appendices (records relaxing to thermal equilibrium, clocks and rulers, multilevel rulers, and a setting patterned on the far future of conformal cyclic cosmology) illustrate these definitions and show some of their limitations. As a worked example, the essay applies the known quantum limit on distinguishing one versus two incoherent point sources to cosmological distances under stated assumptions. It separates a limit that the essay treats as one in principle, given upper limits on the observer's resources adopted under stated conditions, from constraints whose strength depends on the history of our universe (optical depth and cosmic variance). Appendix 4 gives the derivation from existing results and examines the effect of propagation. Appendix 2, Section 10 gives a conditional, order-of-magnitude estimate, for a fixed source under explicitly adopted principles, of how the smallest distinguishable separation changes further into the past. The connections between the phases are hypotheses. Section 6 of the essay classifies its claims as results of existing theory, definitions of this essay, or hypotheses of this essay. It is an independent essay that has not been peer reviewed, and it contains no new experimental or observational data. Generative AI tools were used to draft and revise the text, translate it, create the figures, and carry out checks, as described in the essay's Disclosure of AI Assistance; 5garashi.com Design Office made the judgments on the content and is responsible for it. What this essay does not show: It does not derive spacetime, gravity, or gauge fields from distinguishability. Instead, it asks where the observer's means of distinguishing spacetime differences run out, and calls the state in which none remain the Zeroth-Order Phase. That the path toward it passes through the Dimension-Reduction Phase is a hypothesis. The toy models are finite-dimensional examples. No physical process in a cosmological setting is computed, and it is not shown that no means of distinction remains once all allowed operations are taken into account. The two-source limit is an application of existing results (Tsang, Nair and Lu, 2016). The estimate in Appendix 2, Section 10 rests on adopted principles, such as an upper limit on observation time, and on a fixed-source example. A non-integer effective dimension is not a topological dimension. The rank counts the directions distinguishable under continuous changes of the parameters; it encodes neither the metric signature nor global distinctions. Appendix 3 relates the Zeroth-Order Phase to the connecting boundary of conformal cyclic cosmology as a hypothesis and uses a toy model patterned on its far future. CCC is a cosmological model still under study, and the essay makes no claim about its validity. The archive contains the essay and Appendices 1–4 in Japanese (original) and English, and two supplementary notes in Japanese only. Read online: https://5garashi.github.io/zeroPhase/