Numerical Clock Networks

Purpose

This lab explores a single organising question: What does it mean for something to be a clock? Students move from isolated oscillator models to a unified research logic: phase comparison → network geometry → observable constraint. The organising principle is the causal-geometry framework, where clocks are unified not by their oscillator physics but by the geometry of phase comparison within networks.

Students will simulate, benchmark, and critically evaluate clocks of different kinds — atomic, engineered, geophysical, and astronomical — within a common comparison network. The lab develops both frequentist and Bayesian statistical reasoning alongside the physical concepts.

Programme Context

The Master Laboratory Applied Physics is a compulsory module (8 ECTS, 10% of final grade) in the M.Sc. Applied Physics. It must be completed within the first two semesters and is a prerequisite for the Research Traineeship.

For the full programme structure, see the M.Sc. Applied Physics Module Handbook (PO 2016, version 01.04.2025).

Structure

The lab is organised across four linked resources. Work through them in order; each builds on the previous.

Learning Goals

• Reflect critically on the concept of time and what constitutes a clock.
• Express phase, frequency, and stability mathematically within both frequentist and Bayesian frameworks.
• Understand the causal-geometry framework: clocks unified by comparison geometry, not oscillator physics.
• Connect numerical models across scales — from quantum oscillators to pulsars.
• Design, simulate, and benchmark a clock comparison network.
• Practise open, collaborative research documentation.
• Communicate scientific results in a short report and seminar presentation.

Prerequisites

• Classical mechanics including Lagrangian formulation (Theo I)
• Quantum mechanics including perturbation theory (Theo II/III)
• Fourier transforms in the context of signal analysis
• Basic statistical methods: χ² fitting, uncertainty propagation
• Python with NumPy/SciPy
• Enrolment in the M.Sc. Applied Physics programme (or equivalent, confirmed by the examination office)

Essential Reading

Metrology and Clock Networks

• Fritz Riehle, Frequency Standards: Basics and Applications, Wiley-VCH, 2003.
• W. J. Riley, Handbook of Frequency Stability Analysis, NIST SP 1065.
• D. W. Allan, N. Ashby, C. C. Hodge, The Science of Timekeeping, HP Application Note 1289.
• Calonico et al., “Optical clock networks for geodesy,” Rep. Prog. Phys. 81, 2018.
• Chou et al., “Optical Clocks and Relativity,” Science 329, 1630 (2010).

Statistical Methods

• D. S. Sivia and J. Skilling, Data Analysis: A Bayesian Tutorial, 2nd ed., Oxford, 2006.
• Feldman and Cousins, “Unified Approach to the Classical Statistical Analysis of Small Signals,” Phys. Rev. D 57, 3873 (1998).

Software Tools

• allantools — Allan deviation and related stability measures
• NumPy / SciPy — Numerical computing
• Matplotlib — Visualisation
• NetworkX — Graph / network analysis
• PyMC or emcee — Bayesian inference

Repository

All materials, notebooks, and data live in a public GitHub repository:

github.com/adv-labs-ufr/numerical_clock_networks

numerical_clock_networks/
│── notes/          ← research plans, reflections, references
│── notebooks/      ← numerical implementations
│── figures/        ← generated plots and schematics
│── report/         ← evolving research summary
└── requirements.txt

Fork the repo, work in your directories, and push final results. Each contribution becomes part of a growing, open scientific record on time and frequency.