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arXiv:0911.2416

An experimentally testable proof of the discreteness of time

Guang Ping He

Published Nov 12, 2009• 2 citations
arXivHTMLPDF

Abstract

By proposing a paradox between the impossibility of superluminal signal transfer and the normalization condition of wavefunctions, we predict that when a change happens to the conditions that determining the status of a quantum system, the system will show no response to this change at all, until after a certain time interval. Otherwise either special relativity or quantum mechanics will be violated. As a consequence, no physical process can actually happen within Planck time. Therefore time is discrete, with Planck time being the smallest unit. More intriguingly, systems with a larger size and a slower speed will have a larger unit of time. Unlike many other interpretations of the discreteness of time, our proof can be tested, at less partly, by experiments. Our result also sets a limit on the speed of computers, and gives instruction to the search of quantum gravity theories.

DOI
10.48550/arxiv.0911.2416

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By proposing a paradox between the impossibility of superluminal signal transfer and the normalization condition of wavefunctions, we predict that when a change happens to the conditions that determining the status of a quantum system, the system will show no response to this change at all, until after a certain time interval. Otherwise either special relativity or quantum mechanics will be violated. As a consequence, no physical process can actually happen within Planck time. Therefore time is discrete, with Planck time being the smallest unit. More intriguingly, systems with a larger size and a slower speed will have a larger unit of time. Unlike many other interpretations of the discreteness of time, our proof can be tested, at less partly, by experiments. Our result also sets a limit on the speed of computers, and gives instruction to the search of quantum gravity theories.
We consider the following two questions. Suppose that a quantum system suffers a change of the boundary condition or the potential at a given space location. Then (1) when will the wavefunction shows a response to this change at another location? And (2) how does the wavefunction changes?The answer to question (1) could reveal how a quantum system gets information on the boundary condition or the potential. Here we show that if the response takes place immediately, then it can allow superluminal signal transfer. Else if the response propagates in space with a finite velocity, then it could give a simple explanation why our world shows classicality on the macroscopic scale. Furthermore, determining the exact value of this velocity can either clarify the doubts on static experiments for testing Bell’s inequality, or support the pilot‐wave interpretation of quantum mechanics. We propose a feasible experimental scheme for measuring this velocity, which can be implemented with state‐of‐art technology, e.g., single‐electron biprism interferometry.Question (2) is studied with a square‐well potential model, and we find a paradox between the impossibility of superluminal signal transfer and the normalization condition of wavefunctions. To solve the paradox, we predict that when a change of the potential occurs at a given space location, the system will show no response to this change at all, until after a certain time interval. Otherwise either special relativity or quantum mechanics will be violated. As a consequence, no physical process can actually happen within Planck time. Therefore it gives a simple proof that time is discrete, with Planck time being the smallest unit. Combining with the answer to question (1), systems with a larger size and a slower velocity could have a larger unit of time, making it possible to test the discreteness of time experimentally. Our result also sets a limit on the speed of computers, and gives instruction to the search of quantum gravity theories.
When the boundary condition of a quantum system changes, how fast will it affect the state of the system? Here we show that if the response takes place immediately, then it can allow superluminal signal transfer. Else if the response propagates in space with a finite speed, then it could give a simple explanation why our world shows classicality on the macroscopic scale. Furthermore, determining the exact value of this speed can either clarify the doubts on static experiments for testing Bell's inequality, or support the pilot-wave interpretation of quantum mechanics. We propose an experimental scheme for measuring this speed, which can be implemented with state-of-art technology, e.g., single-electron biprism interference.
This preprint presents a speculative but internally consistent framework in which time is not treated as a fundamental dimension, but as an emergent ordering imposed by finite-capacity state transitions in space. Space is modeled as a discrete lattice of single-occupancy units, each capable of holding exactly one state and transitioning at a bounded rate. Within this model, apparent motion corresponds to pattern propagation rather than physical transport, the relativistic speed limit emerges as a throughput constraint, time dilation follows from update contention, and gravity arises from persistent local saturation of update capacity. Black holes correspond to permanent queue saturation. The framework is further extended to core quantum phenomena, interpreting entanglement, superposition, and measurement as consequences of shared scheduling constraints and pending state resolution rather than non-local information transfer or hidden variables. The work is intended as a foundations-level proposal designed to provoke critical analysis and identify failure modes, rather than as a completed physical theory. Keywords: time, spacetime, information theory, quantum foundations, relativity, gravity, entropy, causality, discrete spacetime, computational models of physics
This paper argues that the quantization of energy and the relationship E = hf are not fundamental axioms of quantum mechanics but structural consequences of two postulates: that time is discrete at the Planck scale, and that each discrete temporal unit carries equal action. Planck's constant is identified as the action content of one Planck-time tick, and the Nyquist-Shannon sampling theorem is applied to derive the maximum physical frequency. The paper further argues that wave-particle duality dissolves under this framework — a photon is always a wave, and point-like detection events are what quantized energy transfer looks like at the receiving end, not evidence for particle ontology. The double-slit experiment, quantum eraser, and interaction-free measurements are re-examined and shown to require no paradoxical interpretation when particle language is abandoned. The paper is a conceptual contribution intended to motivate formal development. Prior work by Caldirola on the chronon is discussed and distinguished.
The conceptual foundations of the special and general theories of relativity differ greatly from those of quantum mechanics. Yet in all cases investigated so far, quantum mechanics seems to be consistent with the principles of relativity theory, when interpreted carefully. In this paper I report on a new investigation of this consistency using a model of a quantum clock to measure time intervals; a topic central to all metric theories of gravitation, and to cosmology. Results are presented for two important scenarios related to the foundations of relativity theory: the speed of light as a limiting velocity and the weak equivalence principle (WEP). These topics are investigated in the light of claims of superluminal propagation in quantum tunnelling and possible violations of WEP. Special attention is given to the role of highly non-classical states. I find that by using a definition of time intervals based on a precise model of a quantum clock, ambiguities are avoided and, at least in the scenarios investigated, there is consistency with the theory of relativity, albeit with some subtleties.