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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
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build/red_rm_rme.html
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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>
@@ -1613,20 +1613,20 @@ 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="org37554a5">
<div class="core div" id="org1fef50a">
<p>
The <b>relativistic momentum</b> \({\boldsymbol p}\) is defined as
\[
{\boldsymbol p} \equiv m {\boldsymbol \eta} =
\frac{m {\boldsymbol u}}{1 - u^2/c^2}.
\frac{m {\boldsymbol u}}{\sqrt{1 - u^2/c^2}}.
\]
The <b>relativistic energy</b> is defined as
\[
E \equiv \frac{m c^2}{\sqrt{1 - u^2/c^2}}.
E \equiv \frac{m c^2}{\sqrt{1 - u^2/c^2}} \equiv c p^0.
\]
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>
@@ -1635,7 +1635,7 @@ p^\mu \equiv m \eta^\mu.
<p>
When the object is stationary, its energy is the
</p>
<div class="core div" id="orgf6b283a">
<div class="core div" id="org2cb0822">
<p>
<b>Rest energy</b>
\[
@@ -1648,7 +1648,7 @@ E_{\mbox{rest}} \equiv m c^2.
When moving, the difference between relativistic and rest energies
is the
</p>
<div class="core div" id="org8d28e60">
<div class="core div" id="org59d0366">
<p>
<b>Kinetic energy</b>
\[
@@ -1661,14 +1661,14 @@ E_{\mbox{kin}} \equiv E - mc^2 = mc^2 \left( \frac{1}{\sqrt{1-u^2/c^2}} - 1 \rig
For velocities much smaller than the speed of light, we can expand
this to
\[
E_{\mbox{kin}} = \frac{1}{2} mu^2 + \frac{3}{8} \frac{mu^2}{c^2} + ...
E_{\mbox{kin}} = \frac{1}{2} mu^2 + \frac{3}{8} \frac{mu^4}{c^2} + ...
\]
</p>
<p>
In a closed system,
</p>
<div class="core div" id="org0b3cfe4">
<div class="core div" id="orge0a6a35">
<p>
<b>Total relativistic energy and momentum is conserved</b>
\[
@@ -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: 2022-03-15 Tue 08:10</p>
<p class="date">Created: 2022-03-22 Tue 10:52</p>
<p class="validation"></p>
</div>