jscaux/pqed_html
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Update 2022-03-15 10:07

Browse Source
This commit is contained in:
Jean-Sébastien
2022-03-15 10:07:27 +01:00
parent 4808df71e6
commit 55f0de8197
193 changed files with 2416 additions and 2082 deletions
Download Patch File Download Diff File Expand all files Collapse all files
build/red_rm_rme.html
+31 -31
View File
@@ -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>
@@ -1613,21 +1613,21 @@ Table of contents
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a><span class="headline-id">red.rm.rme</span></h4>
<div class="outline-text-4" id="text-red_rm_rme">
<div class="core div" id="org0915366">
<div class="core div" id="org37554a5">
<p>
The {\bf relativistic momentum} \({\boldsymbol p}\) is defined as
The <b>relativistic momentum</b> \({\boldsymbol p}\) is defined as
\[
{\boldsymbol p} \equiv m {\boldsymbol \eta} =
\frac{m {\boldsymbol u}}{1 - u^2/c^2}.
\]
The {\bf relativistic energy} is defined as
{\boldsymbol p} \equiv m {\boldsymbol \eta} =
\frac{m {\boldsymbol u}}{1 - u^2/c^2}.
\]
The <b>relativistic energy</b> is defined as
\[
E \equiv \frac{m c^2}{\sqrt{1 - u^2/c^2}}.
\]
These can be combined into the {\bf energy-momentum four-vector}
E \equiv \frac{m c^2}{\sqrt{1 - u^2/c^2}}.
\]
These can be combined into the <b>energy-momentum four-vector</b>
\[
p^\mu \equiv m \eta^\mu.
\]
p^\mu \equiv m \eta^\mu.
\]
</p>
</div>
@@ -1635,12 +1635,12 @@ These can be combined into the {\bf energy-momentum four-vector}
<p>
When the object is stationary, its energy is the
</p>
<div class="core div" id="orgb6d41ac">
<div class="core div" id="orgf6b283a">
<p>
{\bf Rest energy}
<b>Rest energy</b>
\[
E_{\mbox{\tiny rest}} \equiv m c^2.
\]
E_{\mbox{rest}} \equiv m c^2.
\]
</p>
</div>
@@ -1648,12 +1648,12 @@ When the object is stationary, its energy is the
When moving, the difference between relativistic and rest energies
is the
</p>
<div class="core div" id="org38aad5f">
<div class="core div" id="org8d28e60">
<p>
{\bf Kinetic energy}
<b>Kinetic energy</b>
\[
E_{\mbox{\tiny kin}} \equiv E - mc^2 = mc^2 \left( \frac{1}{\sqrt{1-u^2/c^2}} - 1 \right).
\]
E_{\mbox{kin}} \equiv E - mc^2 = mc^2 \left( \frac{1}{\sqrt{1-u^2/c^2}} - 1 \right).
\]
</p>
</div>
@@ -1661,25 +1661,25 @@ is the
For velocities much smaller than the speed of light, we can expand
this to
\[
E_{\mbox{\tiny kin}} = \frac{1}{2} mu^2 + \frac{3}{8} \frac{mu^2}{c^2} + ...
E_{\mbox{kin}} = \frac{1}{2} mu^2 + \frac{3}{8} \frac{mu^2}{c^2} + ...
\]
</p>
<p>
In a closed system,
</p>
<div class="core div" id="org7f507cd">
<div class="core div" id="org0b3cfe4">
<p>
{\bf Total relativistic energy and momentum is conserved}
<b>Total relativistic energy and momentum is conserved</b>
\[
E^2 - c^2 p^2 = m^2 c^4
\]
E^2 - c^2 p^2 = m^2 c^4
\]
</p>
</div>
<p>
N.B.: don't confuse an {\bf invariant} quantity with a {\bf conserved} quantity.
N.B.: don't confuse an <i>invariant</i> quantity with a <i>conserved</i> quantity.
</p>
</div>
</div>
@@ -1702,7 +1702,7 @@ 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>