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<!DOCTYPE html>
<html>
<head>
<title>Understanding Einstein - The Special Theory of Relativity</title>
<meta charset="utf-8"/>
<link href="http://netdna.bootstrapcdn.com/twitter-bootstrap/2.3.2/css/bootstrap-combined.min.css" rel="stylesheet">
<link rel="stylesheet" href="css/layout.css" type="text/css"/>
<link rel="stylesheet" href="css/style.css" type="text/css"/>
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<script type="text/javascript"
src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
</head>
<body class="body">
<header class="mainHeader">
<nav><ul>
<li class="active"><a href="">Understanding Einstein: The Special Theory of Relativity</a></li>
</ul></nav>
</header>
<div class="mainContent">
<div class="content">
<article class="topContent">
<content>
<div id="twin-paradox-1" style="min-width: 300px; height: 300px; margin: 0 auto"></div>
</content>
</article>
<article class="bottomContent">
<content>
<div id="twin-paradox-2" style="min-width: 300px; height: 300px; margin: 0 auto"></div>
</content>
</article>
<article class="bottomContent">
<content>
<div id="twin-paradox-3" style="min-width: 300px; height: 300px; margin: 0 auto"></div>
</content>
</article>
<article class="bottomContent">
<content>
<h5>Lorentz Equations</h5>
<h4 class="special_text">Calculating Alice's results in Bob's values</h4>
<div><span class="special_text">Outbound</span>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<mrow>
<mrow>
<msub>
<mi>x</mi>
<mi>r</mi>
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<mo stretchy="false">=</mo>
<mo stretchy="false">γ</mo>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<mrow>
<msub>
<mi>x</mi>
<mi>l</mi>
</msub>
<mo stretchy="false">−</mo>
<msub>
<mi mathvariant="italic">vt</mi>
<mi>l</mi>
</msub>
</mrow>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
</mrow>
<annotation encoding="StarMath 5.0">x_r=%gamma(x_l-vt_l)
</annotation>
</semantics>
</math>
</div>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<mrow>
<mrow>
<msub>
<mi>t</mi>
<mi>r</mi>
</msub>
<mo stretchy="false">=</mo>
<mo stretchy="false">γ</mo>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<mrow>
<msub>
<mi>t</mi>
<mi>l</mi>
</msub>
<mo stretchy="false">−</mo>
<mrow>
<msub>
<mi mathvariant="italic">vx</mi>
<mi>l</mi>
</msub>
<mo stretchy="false">/</mo>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
</mrow>
<annotation encoding="StarMath 5.0">t_r=%gamma(t_l-vx_l/c^2)</annotation>
</semantics>
</math>
</div>
<div><span class="special_text">Inbound</span>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<mrow>
<mrow>
<msub>
<mi>x</mi>
<mi>r</mi>
</msub>
<mo stretchy="false">=</mo>
<mo stretchy="false">γ</mo>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<mrow>
<msub>
<mi>x</mi>
<mi>l</mi>
</msub>
<mo stretchy="false">+</mo>
<msub>
<mi mathvariant="italic">vt</mi>
<mi>l</mi>
</msub>
</mrow>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
</mrow>
<annotation encoding="StarMath 5.0">x_r=%gamma(x_l+vt_l)
</annotation>
</semantics>
</math>
</div>
<div><math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<mrow>
<mrow>
<msub>
<mi>t</mi>
<mi>r</mi>
</msub>
<mo stretchy="false">=</mo>
<mo stretchy="false">γ</mo>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<mrow>
<msub>
<mi>t</mi>
<mi>l</mi>
</msub>
<mo stretchy="false">+</mo>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<mrow>
<mi>v</mi>
<mo stretchy="false">/</mo>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
</mrow>
<msub>
<mi>x</mi>
<mi>l</mi>
</msub>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
</mrow>
<annotation encoding="StarMath 5.0">t_r=%gamma(t_l+(v/c^2)x_l)</annotation>
</semantics>
</math></div>
</div>
</div>
<h4 class="special_text">Calculating Bob's results in Alice's values</h4>
<div><span class="special_text">Outbound</span>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<mrow>
<mrow>
<msub>
<mi>x</mi>
<mi>l</mi>
</msub>
<mo stretchy="false">=</mo>
<mo stretchy="false">γ</mo>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<mrow>
<msub>
<mi>x</mi>
<mi>r</mi>
</msub>
<mo stretchy="false">+</mo>
<msub>
<mi mathvariant="italic">vt</mi>
<mi>r</mi>
</msub>
</mrow>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
</mrow>
<annotation encoding="StarMath 5.0">x_l=%gamma(x_r+vt_r)
</annotation>
</semantics>
</math>
</div>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<mrow>
<mrow>
<msub>
<mi>t</mi>
<mi>l</mi>
</msub>
<mo stretchy="false">=</mo>
<mo stretchy="false">γ</mo>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<mrow>
<msub>
<mi>t</mi>
<mi>r</mi>
</msub>
<mo stretchy="false">+</mo>
<mrow>
<msub>
<mi mathvariant="italic">vx</mi>
<mi>r</mi>
</msub>
<mo stretchy="false">/</mo>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
</mrow>
<annotation encoding="StarMath 5.0">t_r=%gamma(t_l+vx_l/c^2)</annotation>
</semantics>
</math>
</div>
<div><span class="special_text">Inbound</span>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<mrow>
<mrow>
<msub>
<mi>x</mi>
<mi>l</mi>
</msub>
<mo stretchy="false">=</mo>
<mo stretchy="false">γ</mo>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<mrow>
<msub>
<mi>x</mi>
<mi>r</mi>
</msub>
<mo stretchy="false">-</mo>
<msub>
<mi mathvariant="italic">vt</mi>
<mi>r</mi>
</msub>
</mrow>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
</mrow>
<annotation encoding="StarMath 5.0">x_l=%gamma(x_r+vt_r)
</annotation>
</semantics>
</math>
</div>
<div><math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<mrow>
<mrow>
<msub>
<mi>t</mi>
<mi>l</mi>
</msub>
<mo stretchy="false">=</mo>
<mo stretchy="false">γ</mo>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<mrow>
<msub>
<mi>t</mi>
<mi>r</mi>
</msub>
<mo stretchy="false">-</mo>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<mrow>
<mi>v</mi>
<mo stretchy="false">/</mo>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
</mrow>
<msub>
<mi>x</mi>
<mi>r</mi>
</msub>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
</mrow>
<annotation encoding="StarMath 5.0">t_l=%gamma(t_r+(v/c^2)x_r)</annotation>
</semantics>
</math></div>
</div>
</div>
</content>
</article>
<article class="bottomContent">
<h4 style="color:#0088cc">Browser Support</h4>
<p>This page is supported on Google Chrome, Safari and Firefox latest versions. Tested on Mac OS X 10.8.3. MathML Support is required for displaying equations</p>
</article>
</div>
</div>
<aside class="top-sidebar">
<article>
<h4 style="color:#0088cc">The Equation</h4>
<p>When something travels in no time then that will result in infinite amount of energy. We are aware energy can neither be created nor be destroyed but it can transfer from one form to another. With respect to Einstein's E = MC^2 equation, there are three possibilities </p>
<ol>
<li class="pull-left" style="color:#0088cc">There exists something with infinite mass, which results in Infinite energy</li>
<li class="pull-left" style="color:#0088cc">Light travels @ infinite speed which results in infinite energy, which is not true</li>
<li class="pull-left" style="color:#0088cc">Something travels in no time. ie Velocity = Distance Travelled(d) / Time Taken(t). If t = 0 then E is infinite.</li>
</ol>
<p>What is that which travels in no time?
Are we agreeing that there is inifinte amount of energy out there? What is a thought experiment? From where does thought arises? Do thought travels? <span class="special_text">If it travels then @ what speed?</p>
</article>
</aside>
<aside class="top-sidebar">
<article>
<h4 style="color:#0088cc">About</h4>
<p>This web page on Einstein and related information is developed while taking <span style="color:#0088cc">Understanding Einstein: The Special Theory of Relativity</span> course by <span style="color:#0088cc">Prof. Larry Lagerstorm</span> from <span style="color:#0088cc">Stanford University</span> in <span style="color:#0088cc">Coursera Platform.</span> The design and development is completely done by Gowri Shankar over a period of 2 days during the summer of 2013. There are no coyprights, no licenses of any kind involved. You can use this design, code in your projects. If you like this design, just send a note to me, I have updated my contact detail below. </p>
<p><span style="color:#0088cc">Gowri Shankar</span></p>
<div><a href="http://in.linkedin.com/in/gowrishankarin" target="_blank">linkedin</a>
<a style="padding-left:15px" href="https://www.facebook.com/shankar.chari" target="_blank">facebook</a>
<a style="padding-left:15px" href="https://twitter.com/gowrishankarin" target="_blank">twitter</a></div>
</article>
</aside>
<aside class="middle-sidebar">
<article>
<h4 class="special_text">The Twin Paradox</h4>
<p>My intention is to make the <span class="special_text">velocity(V)</span> and the <span class="special_text">distance travelled(by Alice)</span> to be fed by the user and redraw the graphs accordingly. However, at presesnt I have drawn the graphs have <span class="special_text">Velocity V=0.6c</span> and <span class="special_text">Distance Travelled Tb=10 Light Year in Bob's Perspective.</span></p>
</article>
</aside>
<aside class="bottom-sidebar">
<article>
<h4 style="color:#0088cc">Quote 1</h4>
<p>Imagination is more important than knowledge. </p>
</article>
</aside>
<aside class="bottom-sidebar">
<article>
<h4 style="color:#0088cc">Quote 2</h4>
<p>A human being is a part of a whole, called by us _universe_, a part limited in time and space. He experiences himself, his thoughts and feelings as something separated from the rest... a kind of optical delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest to us. Our task must be to free ourselves from this prison by widening our circle of compassion to embrace all living creatures and the whole of nature in its beauty.</p>
</article>
</aside>
<aside class="bottom-sidebar">
<article>
<h4 style="color:#0088cc">Quote 3</h4>
<p>Not everything that counts can be counted, and not everything that can be counted counts.</p>
</article>
</aside>
<footer class="mainFooter">
<p>Copyright ©: <a href="#" title="tribe21">Gowri Shankar</a></p>
</footer>
</div>
<script src="http://ajax.googleapis.com/ajax/libs/jquery/2.0.1/jquery.min.js"></script>
<script src="./libs/bootstrap-transition.js"></script>
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text: 'Distance - Bobs World Line (Light Year)'
},
plotLines: [{
value: 0,
width: 1,
color: '#808080'
}]
},
yAxis: {
title: {
text: 'Bobs Time in Years'
},
plotLines: [{
value: 0,
width: 1,
color: '#808080'
}]
},
tooltip: {
valueSuffix: 'Year'
},
legend: {
layout: 'vertical',
align: 'right',
verticalAlign: 'top',
x: -150,
y: 50,
borderWidth: 0
},
series: [{
name: 'Alice - Space',
data: [0, 0, 0, 0, 0, 0, 0, 0, 0, -0.8, -1.6, -2.4, -3.2, -4, -4.8, -5.6, -6.4, -7.2, -8]
}, {
name: 'Alice - Time',
data: [10, 8.75, 7.5, 6.25, 5.0, 3.75, 2.5, 1.25, 0]
}, {
name: 'Origin',
data: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
}/*, {
name: 'London',
data: [3.9, 4.2, 5.7, 8.5, 11.9, 15.2, 17.0, 16.6, 14.2, 10.3, 6.6, 4.8]
}*/]
});
});
</script>
</body>
</html>