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Update 2022-03-15 10:07

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Jean-Sébastien
2022-03-15 10:07:27 +01:00
parent 4808df71e6
commit 55f0de8197
193 changed files with 2416 additions and 2082 deletions
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build/red_rm_pt.html
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-03-07 Mon 20:38 -->
<!-- 2022-03-15 Tue 08:10 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1310,10 +1310,6 @@ Table of contents
</summary>
<ul>
<li>
<a href="./d_m.html#d_m">Diagnostics: Mathematical Preliminaries</a><span class="headline-id">d.m</span>
</li>
<li>
<a href="./d_ems.html#d_ems">Diagnostics: Electromagnetostatics</a><span class="headline-id">d.ems</span>
</li>
@@ -1352,6 +1348,10 @@ Table of contents
<li>
<a href="./d_red.html#d_red">Diagnostics: Relativistic Electrodynamics</a><span class="headline-id">d.red</span>
</li>
<li>
<a href="./d_m.html#d_m">Diagnostics: Compendium - Mathematics</a><span class="headline-id">d.m</span>
</li>
</ul>
@@ -1616,7 +1616,7 @@ Table of contents
<p>
If you move at velocity \(u\), then, as compared to a ground clock,
your time will go slower. For a ground clock time interval \(dt\),
your {\bf proper time} interval is
your <b>proper time</b> interval is
\[
d\tau = \sqrt{1 - u^2/c^2}~dt.
\]
@@ -1625,16 +1625,16 @@ of your position \({\boldsymbol l}\) with respect to ground time:
\[
{\boldsymbol u} = \frac{d {\boldsymbol l}}{dt}
\]
and this is called the {\bf ordinary velocity}.
The {\bf proper velocity} is defined as the hybrid-frame quantity
and this is called the <b>ordinary velocity</b>.
The <b>proper velocity</b> is defined as the hybrid-frame quantity
(distance as measured on the ground) divided by (proper time interval):
</p>
<div class="core div" id="orgca53eae">
<div class="core div" id="orgc6b970d">
<p>
{\bf Proper velocity}
<b>Proper velocity</b>
\[
{\boldsymbol \eta} \equiv \frac{d {\boldsymbol l}}{d\tau}
\]
{\boldsymbol \eta} \equiv \frac{d {\boldsymbol l}}{d\tau}
\]
</p>
</div>
@@ -1651,16 +1651,16 @@ By adding the zeroth component
\]
we can define the
</p>
<div class="core div" id="orgbf33865">
<div class="core div" id="orgc1354f8">
<p>
{\bf four-velocity} or {\bf proper velocity four-vector}
<b>four-velocity</b> or <b>proper velocity four-vector</b>
\[
\eta^\mu \equiv \frac{dx^\mu}{d\tau}
\]
\eta^\mu \equiv \frac{dx^\mu}{d\tau}
\]
which transforms as
\[
\bar{\eta}^\mu = \Lambda^\mu_\nu \eta^\nu
\]
\bar{\eta}^\mu = \Lambda^\mu_\nu \eta^\nu
\]
</p>
</div>
@@ -1699,7 +1699,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
</div>
<div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-03-07 Mon 20:38</p>
<p class="date">Created: 2022-03-15 Tue 08:10</p>
<p class="validation"></p>
</div>