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Update 2022-03-22 10:53

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Jean-Sébastien
2022-03-22 10:53:22 +01:00
parent f8fdc5f8b4
commit 2d1d8d39a4
209 changed files with 1240 additions and 1226 deletions
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build/red_rm_pt.html
+8 -8
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-03-15 Tue 08:10 -->
<!-- 2022-03-22 Tue 10:52 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1629,7 +1629,7 @@ 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="orgc6b970d">
<div class="core div" id="org6b9040e">
<p>
<b>Proper velocity</b>
\[
@@ -1651,7 +1651,7 @@ By adding the zeroth component
\]
we can define the
</p>
<div class="core div" id="orgc1354f8">
<div class="core div" id="org75d23d9">
<p>
<b>four-velocity</b> or <b>proper velocity four-vector</b>
\[
@@ -1659,7 +1659,7 @@ we can define the
\]
which transforms as
\[
\bar{\eta}^\mu = \Lambda^\mu_\nu \eta^\nu
\bar{\eta}^\mu = \Lambda^\mu{}_\nu \eta^\nu
\]
</p>
@@ -1673,9 +1673,9 @@ invariant).
By contrast, the ordinary velocities obey cumbersome transformation rules:
for our usual relative frame velocity of \(v\) in the \(x\) direction,
\[
\bar{u}_x = \frac{d\bar{x}}{dt} = \frac{u_x - v}{1-v u_x/c^2}, \hspace{10mm}
\bar{u}_y = \frac{d\bar{y}}{dt} = \frac{u_y}{1-v u_x/c^2}, \hspace{10mm}
\bar{u}_z = \frac{d\bar{z}}{dt} = \frac{u_z}{1-v u_x/c^2}.
\bar{u}_x = \frac{d\bar{x}}{d\bar{t}} = \frac{u_x - v}{1-v u_x/c^2}, \hspace{10mm}
\bar{u}_y = \frac{d\bar{y}}{d\bar{t}} = \frac{u_y}{\gamma(1-v u_x/c^2)}, \hspace{10mm}
\bar{u}_z = \frac{d\bar{z}}{d\bar{t}} = \frac{u_z}{\gamma(1-v u_x/c^2)}.
\]
</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: 2022-03-15 Tue 08:10</p>
<p class="date">Created: 2022-03-22 Tue 10:52</p>
<p class="validation"></p>
</div>