The smallest unit of time in nature, excluding quantum particles, is generally considered to be the Planck time. The Planck time is derived from fundamental physical constants, such as the speed of light (c), the gravitational constant (G), and Planck's constant (h). It represents the time it would take for light to travel a distance of one Planck length, which is the smallest measurable length in the universe according to our current understanding.
The value of the Planck time is approximately 5.39 x 10^-44 seconds. This incredibly small timescale is far beyond our current technological capabilities to measure directly. Moreover, at such minuscule time scales, our understanding of physics breaks down, and quantum effects become significant. Therefore, it's important to note that our current understanding of time and the universe may not fully capture the behavior of time at the Planck scale.
It's worth mentioning that quantum particles, such as quarks or electrons, are fundamental constituents of matter, and their behavior is inherently intertwined with quantum mechanics. The concept of time at quantum scales becomes more intricate and involves phenomena such as superposition, quantum entanglement, and uncertainty principles. At these scales, the notion of a discrete smallest unit of time becomes less clear and is subject to ongoing research and theoretical exploration.