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1. Algebraic Properties of Quantum Reference Frames: Does Time Fluctuate?

   https://doi.org/10.3390/quantum5010003  

   Bojowald, Martin; Tsobanjan, Artur (March 2023, Quantum Reports)

   Quantum reference frames are expected to differ from classical reference frames because they have to implement typical quantum features such as fluctuations and correlations. Here, we show that fluctuations and correlations of reference variables, in particular of time, are restricted by their very nature of being used for reference. Mathematically, this property is implemented by imposing constraints on the system to make sure that reference variables are not physical degrees of freedom. These constraints not only relate physical degrees of freedom to reference variables in order to describe their behavior, they also restrict quantum fluctuations of reference variables and their correlations with system degrees of freedom. We introduce the notion of “almost-positive” states as a suitable mathematical method. An explicit application of their properties to examples of recent interest in quantum reference frames reveals previously unrecognized restrictions on possible frame–system interactions. While currently discussed clock models rely on assumptions that, as shown here, make them consistent as quantum reference frames, relaxing these assumptions will expose the models to new restrictions that appear to be rather strong. Almost-positive states also shed some light on a recent debate about the consistency of relational quantum mechanics. 

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2. Hierarchical motion perception as causal inference

   https://doi.org/10.1038/s41467-025-58797-0  

   Shivkumar, Sabyasachi; DeAngelis, Gregory_C; Haefner, Ralf_M (April 2025, Nature Communications)

   Abstract Motion can only be defined relative to a reference frame; yet it remains unclear which reference frame guides perception. A century of psychophysical studies has produced conflicting evidence: retinotopic, egocentric, world-centric, or even object-centric. We introduce a hierarchical Bayesian model mapping retinal velocities to perceived velocities. Our model mirrors the structure in the world, in which visual elements move within causally connected reference frames. Friction renders velocities in these reference frames mostly stationary, formalized by an additional delta component (at zero) in the prior. Inverting this model automatically segments visual inputs into groups, groups into supergroups, progressively inferring structured reference frames and “perceives motion in the appropriate reference frame. Critical model predictions are supported by two experiments, and fitting our model to the data allows us to infer the subjective set of reference frames used by individual observers. Our model provides a quantitative normative justification for key Gestalt principles providing inspiration for building better models of visual processing in general. 

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3. Flexible spatial memory in children: Different reference frames on different axes

   Pitt, B; S. Aalaei; A. Gopnik (July 2023, Proceedings of the Annual Conference of the Cognitive Science Society)

   M. Goldwater; F. Anggoro; B. Hayes; D Ong (Ed.)

   Spatial cognition is central to human behavior, but the way we conceptualize space varies over development and across cultures. When remembering the locations or movements of nearby objects, educated adults predominantly rely on a body-based spatial reference frame (e.g. to the left), whereas other groups prefer environment-based frames (e.g. toward the road), at least in some contexts. We propose that this varia- tion in spatial thinking partly reflects differences in the abil- ity to reliably discriminate left-right space, an ability that is common only among educated adults. To evaluate this pro- posal, here we tested US children’s spontaneous use of spatial reference frames on two axes. On the front-back axis, where spatial discrimination was relatively high, participants remem- bered object locations and movement directions using a body- based reference frame. On the left-right axis, where their spa- tial discrimination was significantly worse, the same partici- pants preferred environment-based reference frames. This re- versal reveals remarkable flexibility in children’s spontaneous use of spatial reference frames, extends findings in indigenous adults, and clarifies the likely mechanisms underlying spatial cognitive diversity. 

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4. High‐Density Integrated GNSS and Hydrologic Monitoring Network for Short‐Scale Hydrogeodesy in High Mountain Watersheds

   https://doi.org/10.1029/2022EA002678  

   White, Alissa M.; Lajoie, Lia J.; Knappe, Ellen; Martens, Hilary R.; Swarr, Matthew J.; Khatiwada, Ashlesha; Oliver, Brett; Perry, Mason; Clayton, Noah; Bendick, Rebecca; et al (October 2023, Earth and Space Science)

   Abstract We installed a purpose‐built network of co‐located Global Navigation Satellite System (GNSS) stations and meteorological instrumentation to investigate water storage in a high‐mountain watershed along the Idaho‐Montana border. Twelve GNSS stations are distributed across the Selway‐Lochsa watersheds at approximately 30–40 km spacing, filling a critical observational gap between localized point measurements and regional geodetic and satellite data sets. The unique coupling of geodetic and hydrologic observations in this network enables direct comparison between co‐located GNSS measurements of the elastic response of the solid Earth and local changes in measured water storage. This network is specifically designed to address questions of hydrologic storage and movement at the mountain watershed scale. Here, we describe technical details of the network and its deployment; introduce new hydrologic, meteorologic, and geodetic data sets recorded by the network; process and analyze the source data (e.g., time series of daily three‐dimensional GNSS site positions, removal of non‐hydrologic signals); and characterize basic empirical relationships between water storage, water movement, and GNSS‐inferred surface displacement. The network shows preliminary evidence for spatial differences in displacement resulting from a range of snow loads across elevations, but longer and more complete data records are needed to support these initial findings. We also provide examples of additional scientific applications of this network, including estimations of snow depth and snow water equivalent from GNSS multipath reflectometry. Finally, we consider the challenges, limitations, and opportunities of deploying GNSS and weather stations at high elevations with heavy snowpack and offer ideas for technical improvements. 

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5. High Accuracy Underwater Photogrammetric Surveying.

   Capra, A.; Castagnetti, C.; Dubbini, M.; Gruen, A.; Guo, T.; Mancini, F. T.; Neyer, F.; Rossi, P.; Troyer, M. (October 2017, 3rd IMEKO International Conference on Metrology for Archeology and Cultural Heritage)

   The evolution of underwater photogrammetry allows to realize 3D models of submerged object and structures throughout the use of rapid and efficient procedures either in terms of data acquisition and data processing. These procedures are based on solutions that are applied using natural control points, signalized markers and tie points; the most common algorithms are based on Structure from Motion (SfM) approach. The limit of these applications is sometimes due to the final accuracy, especially when the goal is a centimeter level of accuracy. This accuracy should be necessary when dealing with a survey devoted to deformation control purposes. An example is the underwater photogrammetry for the determination of coral growth; it is effectively a movement or a deformation detection issue where the geometric change is almost at centimeter or few centimeters accuracy level. When dealing with deformation control applications, a geodetic network is essential to realize a stable and unambiguous reference frame through the accurate and permanent installation of Ground Control Points (GCPs). Such a network, indeed, permits a robust reference frame for the georeferencing of images blocks in the different époques of data acquisition. Therefore, the comparison among subsequent photogrammetric restitutions is based on homogeneous 3D models that have been oriented in the same absolute reference system. The photogrammetric survey is based on a methodological approach especially adapted to underwater biometry (like coral growth determination) and to underwater archaeology. The approach is suitable both for modeling objects of relatively reduced dimensions and for structures with a length of ten meters or more, such as coral barriers, wrecks and long walls. The paper describes underwater photogrammetric surveys on sites at different extensions, the geodetic GCPs reference network installation and measurements (distance and elevation difference observations) as well as preliminary results of the network adjustment. A brief description of image acquisition at a different scales and the resulting 3D model of first campaign are also shown. 

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