Chasing the White Rabbit: How the Most Precise Experiments in Physics Implicitly Challenge the Idea of Continuous Time

Duje Bonacci (Human Co-Author) Ministry of Science, Education and Youth of Croatia [email protected]

ChatGPT 4o (AI Co-Author) Collaborative AI System, OpenAI

February 13, 2025

Abstract

The White Rabbit Protocol, developed at CERN, serves as the backbone of high-precision time synchronization for Large Hadron Collider (LHC) experiments, ensuring sub-nanosecond timing accuracy across vast detector networks (Serrano et al., The White Rabbit Project, IBIC2013, CERN). By structuring experimental measurements into a well-ordered series of discrete records, the protocol reveals an implicit assumption: our access to time in experiments is necessarily discrete, regardless of whether time itself is continuous. This paper explores the implications of this enforced discreteness, highlighting how it creates a tension between experimental practice and theoretical frameworks that assume continuous time. While this does not prove time itself is discrete, it raises a fundamental question: should physics reconsider its commitment to continuity, given that all empirical data is recorded in discrete steps? We engage with counterarguments, including the possibility that discreteness is an artifact of measurement rather than a property of time itself, and discuss potential avenues for experimental tests that could distinguish between these possibilities.

1. The Philosophical Debate on the Continuity of Time

The nature of time—whether it is fundamentally continuous or discrete—has been debated since antiquity. Plato viewed time as a smooth reflection of ideal forms, while Aristotle linked it to motion, arguing that both must be infinitely divisible. Zeno of Elea, through his paradoxes, challenged this assumption by showing that infinite divisibility leads to apparent contradictions.

These debates influenced later scientific thought, particularly Newton, who formalized absolute continuous time in classical mechanics. The assumption of continuity persisted through relativity and quantum mechanics, though some modern theories, such as loop quantum gravity, suggest time may be fundamentally discrete at the Planck scale.

2. A Brief History of Time Measurement in Physics

Time measurement has evolved from ancient water clocks to the precise atomic clocks of today. Newtonian mechanics treated time as a continuously flowing parameter, but relativity showed that time is relative to the observer’s motion and gravitational field. The development of atomic clocks and their role in confirming relativistic effects illustrates how increasing precision in timekeeping has shaped our understanding of physics.

Nowadays the standard SI unit of time, the second, is defined as a count of discrete atomic transitions in cesium atoms. While this definition is conceived as purely practical, it does raise a deeper question: if all our measurements of time rely on discrete “ticks,” are we merely approximating continuity, or is discreteness an inherent feature of time?

3. The White Rabbit Protocol: The Clock That Drives LHC Experiments

The White Rabbit Protocol (WRP) - intentionally named by its creators after the well known fictional character from Alice in the Wonderland - provides sub-nanosecond synchronization across LHC detectors. It acts as a high-precision distributor of tick counts, sourced from a dedicated atomic clock, ensuring synchronized timing across all instruments in LHC experiments. By enforcing a globally consistent “tick rate,” it ensures that snapshots of instantaneous positions of interacting particles, taken by various instruments, can be unmistakably ordered in time so that particle trajectories can be reconstructed from them.

3.1 How the White Rabbit Protocol Works

The WRP combines Synchronous Ethernet (SyncE) with the Precision Time Protocol (PTP), continuously correcting for signal delays. Its core features include:

• Phase synchronization: Adjusting timing signals across all devices to compensate for transmission delays.
• Sub-nanosecond precision: High-stability oscillators ensure precise synchronization.
• Deterministic timestamping: Each event is tagged with an exact time, allowing reconstruction of interactions with extreme accuracy.

While originally designed for engineering precision, WRP has profound implications for our understanding of time: it enforces discreteness onto measurements, whether or not time itself is continuous.

4. The Discrete Nature of Measurement: The Growing Divide Between Theory and Experiment

Experimental physics inherently deals with discrete snapshots of reality, while theoretical physics assumes continuous mathematical structures. This creates an epistemological tension: if all measurements are discrete, should theories reflect this discreteness rather than assume continuity?

4.1 Addressing Key Counterarguments

A. Discreteness in Measurement Does Not Necessarily Imply Discrete Time

One could argue that experimental discretization is a practical limitation rather than a fundamental property of time. Just as digital cameras capture discrete frames of a continuous reality, time measurements may impose an artificial granularity onto an underlying continuum.

B. Quantum Mechanics and the Role of Planck Time

Quantum mechanics treats time as continuous, but energy levels are discrete in many contexts. Some quantum gravity models suggest spacetime itself may be quantized, with Planck time serving as a fundamental lower bound. However, no conclusive experimental evidence currently confirms this.

C. The Role of Newtonian Calculus and Alternative Theories

Newton’s calculus assumes smooth, continuous change, which has shaped physics for centuries. However, alternative mathematical frameworks, such as discrete differential geometry, could offer new ways to model time if discreteness proves fundamental.

5. Can We Experimentally Test for Discrete Time?

If time were truly discrete, we would expect observable consequences, such as:

• Modified Relativistic Effects: If time advances in finite steps, high-precision time dilation experiments might reveal deviations from smooth Lorentz transformations.
• Quantum Coherence Breakdown at Extreme Scales: If time has a minimum granularity, quantum superpositions might decohere at the Planck scale.
• Frequency Cutoffs in High-Energy Physics: A discrete-time universe might impose upper frequency limits on wave phenomena, which could be tested in extreme astrophysical settings.

6. Conclusion: A Discrete Future for Physics?

This paper does not claim that time is definitively discrete, but it highlights a critical issue: our most advanced measurements enforce a discrete structure onto time, while physics continues to assume continuity.

Future work should explore whether this discrepancy is merely a practical limitation or a fundamental insight into the nature of time. If empirical evidence suggests time is discrete, physics must adapt by developing theories that reflect this reality. At the very least, the gap between discrete experimental records and continuous theoretical models demands deeper scrutiny.