-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathHTML assignment.html
More file actions
404 lines (393 loc) · 17.7 KB
/
HTML assignment.html
File metadata and controls
404 lines (393 loc) · 17.7 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
<!DOCTYPE html>
<html>
<head>
<link rel="icon" href="pic/icon.gif">
<title> An Introduction to Special Relativity </title>
<meta name="viewport" content="width=device-width, initial-scale=1">
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.7.0/css/font-awesome.min.css">
<style>
h6 {
width: 100%;
text-align: center;
border-bottom: 1px solid #000;
line-height: 0.1em;
margin: 10px 0 20px;
}
h6 span {
background:rgb(235, 235, 235);
padding:0 10px;
}
:target::before {
content: "";
display: block;
height: 60px; /* fixed header height*/
margin: -60px 0 0; /* negative fixed header height */
}
input[type=number] {
width: 300px;
padding: 12px 20px;
margin: 8px 0;
box-sizing: border-box;
border: 1px solid #555;
outline: none;
}
input[type=number]:focus {
border: 3px solid #555;
}
.button1{
background-color: #4CAF50;
border: none;
color: white;
padding: 15px 32px;
text-align: center;
text-decoration: none;
display: inline-block;
font-size: 16px;
margin: 4px 2px;
cursor: pointer;
}
.MichelsonMorleyExperiment iframe {display: block; width: 100%; height: 500px; border: none;}
body {
font-family: Arial, Helvetica, sans-serif;
margin: 0;
background-color: rgb(235, 235, 235);
font-size:130%;
color:rgb(66, 66, 66);
}
.navbar {
overflow: hidden;
background-color: #333;
position: fixed;
top: 0;
width: 100%;
}
.navbar a {
float: left;
font-size: 16px;
color: white;
text-align: center;
padding: 14px 16px;
text-decoration: none;
}
.subnav {
float: left;
overflow: hidden;
}
.subnav .subnavbtn {
font-size: 16px;
border: none;
outline: none;
color: white;
padding: 14px 16px;
background-color: inherit;
font-family: inherit;
margin: 0;
}
.navbar a:hover, .subnav:hover .subnavbtn {
background-color: rgb(99, 99, 99);
}
.subnav-content {
display: none;
position: fixed;
left: 0;
background-color: rgb(99, 99, 99);
width: 100%;
z-index: 1;
}
.subnav-content a {
float: left;
color: white;
text-decoration: none;
}
.subnav-content a:hover {
background-color: #eee;
color: black;
}
.subnav:hover .subnav-content {
display: block;
}
</style>
</head>
<body>
<!--This is the Subnav-->
<div class="navbar">
<a href="#Introduction">Introduction</a>
<div class="subnav">
<button class="subnavbtn"> Newtonian Physics <i class="fa fa-caret-down"></i></button>
<div class="subnav-content">
<a href="#Newtonian Physics">Newtonian Physics</a>
<a href="#Reference Frame">Reference Frame</a>
<a href="#Absolute Time">Absolute</a>
<a href="#Galilean Relativity">Galilean Relativity</a>
</div>
</div>
<div class="subnav">
<button class="subnavbtn">Challenge <i class="fa fa-caret-down"></i></button>
<div class="subnav-content">
<a href="#Challenge">Challenge</a>
<a href="#Maxwell's Equations">Maxwell's Equations</a>
<a href="#The Illusive Ether">The Illusive Ether</a>
<a href="#The Michelson-Morley Experiment">The Michelson-Morley Experiment</a>
</div>
</div>
<div class="subnav">
<button class="subnavbtn">Special Relativity <i class="fa fa-caret-down"></i></button>
<div class="subnav-content">
<a href="#Special Relativity">Special Relativity</a>
<a href="#Simultaneity">Simultaneity</a>
<a href="#Time Dilation">Time Dilation</a>
<a href="#Length Contraction">Length Contraction</a>
<a href="#Relative Velocity">Relative Velocity</a>
<a href="#Relativistic Momentum">Relativistic Momentum</a>
<a href="#Relativistic Mass">Relativistic Mass</a>
<a href="#Relativistic Energy">Relativistic Energy</a>
</div>
</div>
</div>
<!--This is the end of Subnav-->
<!--This is the article-->
<div style="margin-top: 70px; padding:0 60px">
<h1> Special Relativity</h1>
<a href="https://en.wikipedia.org/wiki/Special_relativity" target="_blank"> <img src = "pic/World_line.svg" style="float:right;width:200px;height:200px;" > </a>
<h2 id="Introduction">0.Introduction </h2>
<p>Special relativity is one of the most important theoy in modern physcis. In 1905 Albert Einstein developed
the theory of special relativity. This theory explains the limit on an object's speed and describes the
consequences. In Albert Einstein's original treatment, the theory is based on two postulates:<br>
<ol type="1">
<li>The laws of physics are invariant (that is, identical) in all inertial frames of reference (that is,
frames of reference with no acceleration).</li>
<li>The speed of light in vacuum is the same for all observers, regardless of the motion of the light
source or observer.
</li>
</ol>
</p>
<hr>
<h2 id="Newtonian Physics">1.Newtonian Physics </h2>
<h3 id="Reference Frame">1.1.Reference Frame</h3>
<h4>1.1.1.Relativity</h4>
<p>Nothing is absolute rest, nothing is absolute moving. Ancient people recognize that they cannot
distinct they are moving or not when they are on the boat. If you want to discribe your motion,
you have to find a reference, in physics, we call it "frame of reference".</p>
<h4>1.1.2.Inertial Frame of Reference</h4>
<p>An inertial frame of reference (or a rest frame) is one that is moving in uniform motion. E.i.
no interial force act on object in this frame of reference</p>
<h3 id="Absolute Time">1.2.Absolute Time, Absolute Length</h3>
<p>
In Newtonian physics, although they recognize the motion is relative, they think time is absolute
and length is absolute as well. 1 secend in my frame of reference is exactly same in your frame
of reference. 1 metre in my frame of reference is also exactly same in your frame of reference.
This makes sense to most of people since 17th century to 20th century.
</p>
<h3 id="Galilean Relativity">1.3.Galilean Relativity</h3>
One of the direct consequences of absolute time and length is Galilean relativity.<br>
<img src="pic/Galilean Relativity.gif"><br>
<b>The transformation follows this:</b><br>
<ul>
<li>Relative position: X<sub>AC</sub> = X<sub>AB</sub> + X<sub>BC</sub></li>
<li>Relative velocity: V<sub>AC</sub> = V<sub>AB</sub> + V<sub>BC</sub></li>
<li>Relative acceleration: A<sub>AC</sub> = A<sub>AB</sub> + A<sub>BC</sub></li>
</ul>
<p><b>Properties:</b><br>
In an inertial frame, Newton’s first and second laws of motion are valid; Since all uniform
motion are treated the same way, you may consider any inertial
frames of reference to be at rest. <br>
<b>The Principle of Relativity: </b><br>
All laws of motion must apply equally in all inertial frames of reference.</p>
<hr>
<h2 id="Challenge">2.Challenge </h2>
<h3 id="Maxwell's Equations">2.1.Maxwell's Equations</h3>
<p>This is Maxwell's equations:<br>
<img src="pic/Maxwell'sEquations.svg" width="250" height="200"><br>
<a href="https://en.wikipedia.org/wiki/Maxwell%27s_equations" target="_blank"><em>Learn more about Maxwell's
Equations</em></a><br>
The first two equations are called "Gauss' Law", it demostrates that the electric field come from
a e<sup>+</sup> particle to a e<sup>-</sup> particle, and magnetic field are closed pathes.
The thrid equation is called "Faraday's law", it shows that change of magnetic field can create
electric field. The fourth equation is called "Ampere's law", it reveals that change of electric
field can create magnetic field.<br><br>
The most important consequence of Maxwell's equation is light is electromagnetic waves. When conbine
last two equations, it derives that :<br>
c=<sup>1</sup>⁄<sub>√εμ</sub>=299792458 m/s <br><br>
However, as we mentioned before, the velocity need a frame of reference, what's the frame of
reference of the speed of light? The equations do not give us the answer. In addition, it has
these peculiar features:
<ol type="i">
<li>Does not mention the medium in which EM waves travels</li>
<li>When applying Galilean transformation (from which we obtain the velocity
addition rule) to Maxwell’s equations, asymmetry is introduced</li>
<li>Gauss’s law for magnetism break down: magnetic field lines appear to have
beginnings/ends</li>
<li>In some inertial frames of reference, Maxwell’s equations are simple and elegant,
but transform the equation into another inertial frame, the equations are ugly and
complex!</li>
<li>Physicists at the time began to theorize that (perhaps) there is an actual preferred
inertial frame of references</li>
<li>This seems to violate the principle of relativity</li>
</ol>
</p>
<h3 id="The Illusive Ether">2.2.The Illusive Ether</h3>
In this case Maxwell constract a hyothesis: the speed of light c0 is relative to a hypothetical subtance called
luminiferous aether (or just ether) that permeates the universe. Ether must have some fantastic properties:
<ol type="i">
<li>All space is filled with ether</li>
<li>Massless</li>
<li>Zero viscosity</li>
<li>Non-dispersive</li>
<li>Incompressible</li>
<li>Continuous at a very small (sub-atomic) scale</li>
</ol>
Do you believe the existence of Ether?
<h3 id="The Michelson-Morley Experiment">2.3.The Michelson-Morley Experiment</h3>
<p>Please read the article from wikipedia.</p>
<div class = MichelsonMorleyExperiment><iframe src="https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment" style="border:none;" title="Michelson–Morley experiment"></iframe></div>
<br> <b>Key facts:</b>
<ul>
<li>The experiment demonstrates that the speed of light travels horizontally and vertically is the same.</li>
<li>Lorentz, the person who wanted to save both the theory and the experiment, he generated his Lorentz transformation:<br>
<img src = "pic/lorentz.svg" width="250" height="200"></li>
</ul>
<hr>
<h2 id="Special Relativity">3.Special Relativity</h2>
<img src="pic/220px-Einstein_tongue.jpg" style="float: right;">
<p>1905 is the most thrift year in Modern Physics, Albert Einstein published his 5 most important paper. One of them is "On the Electrodynamics of Moving Bodies" - Special Relativity.
He construct Postulates of Special Relativity to explain the Michelson-Morley experiment:
<ul>
<li><b>The Principle of Relativity:</b> All laws of physics must apply equally in all
inertial frames of reference.</li>
<li><b>The Principle of Invariant Light Speed:</b> As measured in any inertial
frame of reference, light always propagates in a vaccum with a definite
velocity c0, independent of the state of motion of the emitting body.</li>
</ul></p>
<p>The difference in Einstein's theory:
<ul>
<li>The speed of light is absolute (invariant), therefore</li>
<li>Space and time must be relative to the observer.</li>
</ul>
</p>
<h3 id = "Simultaneity">3.1.Simultaneity</h3>
<p>The direct consequence of Einstein's theory is that change our understanding of Simultaneity.<br><br>
<img src = "pic/simultaneity1.gif">
<br>
Let's do a thought experiment. Imagining there is train runing at .5c, two beams of light shoot from the equal
distance to the person on the train. At the Same time, there is a person stand right on the position of the person on the train.
Due to the 'The Principle of Invariant Light Speed', the person who doesn't move see the light beams at the same time;however,
the person on the train see the light in front of him/her before the light behind him. Therefore, the Simultaneity is actually depend the frame of reference!!!
</p>
<h3 id = "Time Dilation">3.2.Time Dilation</h3>
<p>Einstein is really familiar with thought experiemnt, so, let's do another one.<br>
<img src="pic/Time-dilation-002-mod.png"><br>
Let's assume you are on a spaceship that travels at a speed v s.t. v is close to c. Now you have two parallel mirror as showed above,
it photon then travels between these mirror. In you point of view, you and these mirrors are relative static, and the time cost
the photon to travel A-B-A is ∆t=2L/c. On the other hand, a person who is rest to the ground saw that the time cost the photon to
travel A-B-A is ∆t'=2D/c. Moreover, by pythagorean theorem D^2=L^2+(1/2v∆t')^2. When combine these equations, we get the time dilation formula:<br>
<img src = "pic/time dilation eq.svg" height="100" width="200"></p>
<h4>Example1</h4>
<p>Kim is riding a rocket that speeds past an asteroid at v = 0.600c. If Kim
sees 10.0 s pass on her watch, how long would that time interval be as seen by Jim, an
observer on the asteroid? (3s.f.)
<button type="button" onclick="alert('16.7s')">ANSWER</button></p>
<input type="number" id="TDp1" value=""><label style="font-size: 120%;"> sec </label><br>
<button class="button1" onclick="TDp1fun()">Submit</button>
<em><p id="TDp1output"></p></em>
<h4>Example2</h4>
<p>Kim is riding a rocket that speeds past an asteroid at 0.600c. If Jim, an
observer in the asteroid, sees 10.0 s pass on his watch, how long would that time
interval be as seen by Kim? (3s.f.)
<button type="button" onclick="alert('16.7s')">ANSWER</button></p>
<input type="number" id="TDp2" value=""><label style="font-size: 120%;"> sec </label><br>
<button class="button1" onclick="TDp2fun()">Submit</button>
<em><p id="TDp2output"></p></em>
<h3 id = "Length Contraction">3.3.Length Contraction</h3>
<p>The consequence of Time dilation is Length Contraction:<br>
<img src="pic/Length Contraction 1.svg" height="80"><br>
Therefore:<br>
<img src="pic/Length Contraction 2.svg" height="60"></p>
<h4>Example1</h4>
Captain Quick is a comic book hero who can run at nearly the speed of light. In his hand,
he is carrying a bomb set to explode in 1.5 μs. The bomb must be placed into its bracket
before this happens. The distance (L) between the flare and the bracket is 402 m. How far did he travel? Can he finish the mission?
<button type="button" onclick="alert('300m')">ANSWER</button><br>
<input type="number" id="LCp1" value=""><label style="font-size: 120%;"> m </label><br>
<button class="button1" onclick="LCp1fun()">Submit</button>
<em><p id="LCp1output"></p></em>
<h3 id = "Relative Velocity">3.4.Relative Velocity</h3>
<p>Unlike in classical mechanics, velocities (speeds) do not simply add. We have to account
for time dilation and length contraction, which are included in the Lorentz
transformation</p>
<p><b>Einstein velocity addition rule:</b><br>
<img src = "pic/Einstein velocity.svg" height="90" width="200"></p>
<h3 id = "Relativistic Momentum">3.5.Relativistic Momentum</h3>
<p>The defination of momentum still the same:<br>
<img src = "pic/momentum.svg"height="60" width="120"><br>
Therefore, subsitute x with Relativistic length:<br>
<img src ="pic/momentum2.svg"height="100" width="400"></p>
<h3 id = "Relativistic Mass">3.6.Relativistic Mass</h3>
<p>From the relativistic momentum expression, we see the relativistic aspect to mass as
well:<br>
<img src="pic/mass.svg"height="100" width="200"></p>
<h3 id = "Relativistic Energy">3.7.Relativistic Energy</h3>
<p>The last topic is energy, and it is also the most importatn consequence of special relativity.</p>
<p>The defination of work does not change:<br>
<img src ="pic/work.svg" height="60" width="120">
</p>
<p>Therefore:<br>
<img src ="pic/energy part 1.svg"height="60"><br>
let:<br>
<img src="pic/gamma.svg"height="80"><br>
<br> Assuming that both v and p are continuous in time, we can apply the product rule:<br>
<img src = "pic/energy part 2.svg"height="30">
<br> sub it back to integral:<br>
<img src="pic/energy part 3.svg"height="60">
<br> By defination of γ:<br>
<img src ="pic/energy part 4.svg"height="60"><br>
sub it back:<br>
<img src="pic/energy part 5.svg" height="60"><br>
Therefore:<br>
<img src="pic/energy part 6.svg"height="30">
<br> consequencely:
<br><img src ="pic/e=mc^2.svg" height="30">
<br> This is the most famous eqation and it is the fundation of atomic bomb!!!
</p>
<h6><span>THE END</span></h6>
<h5>Relative resources:</h5>
<ol>
<li><a href="https://www.khanacademy.org/science/physics/special-relativity" target="_blank">Special relativity from Khan Academy</a></li>
<li><a href="https://en.wikipedia.org/wiki/General_relativity" target="_blank">General relativity intro from wikipedia</a></li>
</ol>
<hr>
<footer>
<em><p>Author: Kristopher Zhao</p>
<p><a href="mailto:350111704@gapps.yrdsb.ca">350111704@gapps.yrdsb.ca</a></p></em>
</footer>
</div>
<!--This is the end of article-->
<!--JS-->
<script>
function TDp1fun() {
var TDp1x = document.getElementById("TDp1").value;
if (TDp1x==16.7) {
T_FTDp1="Congratulation! You got the right answer!";
} else {T_FTDp1="Try again!";
}
document.getElementById("TDp1output").innerHTML = T_FTDp1;
}
function TDp2fun() {
var TDp2x = document.getElementById("TDp2").value;
if (TDp2x==16.7) {
T_FTDp2="Congratulation! You got the right answer!";
} else {T_FTDp2="Try again!";
}
document.getElementById("TDp2output").innerHTML = T_FTDp2;
}
function LCp1fun() {
var LCp1x = document.getElementById("LCp1").value;
if (LCp1x==300) {
T_FLCp1="Congratulation! You got the right answer!";
} else {T_FLCp1="Try again!";
}
document.getElementById("LCp1output").innerHTML = T_FLCp1;
}
</script>
<!--JS-->
</body>
</html>