From bed1b10f2c48275b890481f1adc2ca4308c48852 Mon Sep 17 00:00:00 2001 From: medusa Date: Tue, 28 May 2024 04:15:31 +0000 Subject: [PATCH] Update random/planck-unit.md --- random/planck-unit.md | 30 ++++++++++++++++++++++++++++++ 1 file changed, 30 insertions(+) diff --git a/random/planck-unit.md b/random/planck-unit.md index b642763..a709fb4 100644 --- a/random/planck-unit.md +++ b/random/planck-unit.md @@ -1,3 +1,33 @@ +Absolutely! Here's the information presented in mathematical form using LaTeX compatible with GitHub markdown: + +**Planck Time:** + +The Planck time denoted by $t_P$ is a unit of time theorized to be the smallest measurable time interval. It is expressed as: + +$$t_P = \sqrt{\frac{\hbar G}{c^3}} \approx 5.39 \times 10^{-44} \text{ seconds}$$ + +* $\hbar$ (h-bar) represents the reduced Planck constant (approximately 1.054 x 10^-34 Joule-seconds). +* $G$ represents the gravitational constant (approximately 6.674 x 10^-11 meters cubed per kilogram per second squared). +* $c$ represents the speed of light in a vacuum (approximately 299,792,458 meters per second). + +**Planck Length:** + +The Planck length ($l_P$) is the distance light travels in a Planck time. It can be derived using: + +$$l_P = c \times t_P \approx 1.616 \times 10^{-35} \text{ meters}$$ + +**Comparison with Nanosecond:** + +A nanosecond (ns) is one billionth of a second (10^-9 seconds). The difference in scale between Planck time and nanoseconds can be shown as: + +$$\frac{1 \text{ ns}}{t_P} \approx \frac{10^{-9} \text{ s}}{5.39 \times 10^{-44} \text{ s}} \approx 1.85 \times 10^{34}$$ + +This indicates that a nanosecond is roughly 1.85 x 10^34 times larger than a Planck time. + +**Note:** The statement about counting Planck times exceeding the universe's age is a simplified explanation. While mathematically true, the vast difference in scales emphasizes the extreme smallness of the Planck time. + +--- + # Understanding the Planck Units: Exploring the Smallest Scales of Our Universe Introduction: