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Version vom 2009-02-14
author Klaus Thoden <kthoden@mpiwg-berlin.mpg.de>
date Thu, 02 May 2013 11:08:12 +0200
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1 <?xml version="1.0" encoding="utf-8" ?>
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4 <!--http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd-->
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5 <html>
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7 <head><title></title>
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9 <meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/mn.html)" />
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10 <meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/mn.html)" />
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12 <meta name="src" content="Einst_Ueber_de_1907_02.tex" />
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13 <meta name="date" content="2005-02-25 10:10:00" />
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14 <link rel="stylesheet" type="text/css" href="Einst_Ueber_de_1907_02.css" />
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15 </head><body >
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17 <!--l. 12--><p class="noindent"><pb/></p>
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18 <div class="center" >
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20 <!--l. 13--><p class="noindent">
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21 </p><!--l. 14--><p class="noindent"><span
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22 class="cmr-12">12. </span><span
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23 class="cmbxti-10x-x-120">Über die M</span><span
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24 class="cmbxti-10x-x-120">öglichkeit </span> <br/><span
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25 class="cmbxti-10x-x-120">einer neuen Pr</span><span
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26 class="cmbxti-10x-x-120">üfung des</span>
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27 <span
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28 class="cmbxti-10x-x-120">Relativit</span><span
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29 class="cmbxti-10x-x-120">ätsprinzips; </span> <br/><span
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30 class="cmbxti-10x-x-120">von A. Einstein.</span></p></div>
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31 <div class="center" >
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33 <!--l. 18--><p class="noindent">
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34 </p><!--l. 19--><p class="noindent">--------</p></div>
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35 <!--l. 22--><p class="indent"> In einer letztes Jahr erschienenen wichtigen Arbeit<sup ><span
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36 class="cmr-7">1</span></sup>) hat <br/>Hr. J. Stark dargetan, daß die bewegten positiven Ionen der <br/>Kanalstrahlen Linienspektra emittieren, indem er den Doppler-<br/>Effekt nachwies und messend verfolgte. Er stellte auch Unter-<br/>suchungen an in der Absicht, einen Effekt zweiter Ordnung <br/>(proportional
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37 <img
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38 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Ueber_de_1907_02/fulltext/img/Einst_Ueber_de_1907_020x.png" alt="(v/V )" class="left" align="middle" /><sup ><span
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39 class="cmr-7">2</span></sup> nachzuweisen und zu messen; die nicht <br/>speziell für diesen Zweck eingerichtete Versuchsanordnung ge-<br/>nügte jedoch nicht zur Erlangung eines sicheren Resultates.
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40 </p><!--l. 30--><p class="indent"> Ich will im nachfolgenden kurz zeigen, daß das Relativitäts-<br/>prinzip in Verbindung mit dem Prinzip der Konstanz der Ge-<br/>schwindigkeit des Lichtes jenen Effekt vorauszubestimmen <br/>gestattet. Wie ich in einer früheren Arbeit<sup ><span
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41 class="cmr-7">2</span></sup>) gezeigt habe, <br/>geht aus jenen Prinzipien hervor, daß eine gleichförmig be-<br/>wegte Uhr, vom ,,ruhenden&#8220; System aus beurteilt, langsamer <br/>läuft als von einem mitbewegten Beobachter aus beurteilt. <br/>Bezeichnet <span
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42 class="cmmi-10"><img
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43 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Ueber_de_1907_02/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /> </span>die Anzahl der Schläge der Uhr pro Zeiteinheit <br/>für den ruhenden, <span
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44 class="cmmi-10"><img
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45 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Ueber_de_1907_02/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /></span><sub ><span
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46 class="cmr-7">0</span></sub> die entsprechende Anzahl für den mit-<br/>bewegten Beobachter, so ist
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47 </p>
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48 <center class="par-math-display" >
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49 <img
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50 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Ueber_de_1907_02/fulltext/img/Einst_Ueber_de_1907_021x.png" alt=" V~ ---(--)2- -n = 1- -v n0 V " class="par-math-display" /></center>
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51 <!--l. 46--><p class="nopar">
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52 </p><!--l. 50--><p class="noindent">oder in erster Annäherung
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53 </p>
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54 <center class="par-math-display" >
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55 <img
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56 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Ueber_de_1907_02/fulltext/img/Einst_Ueber_de_1907_022x.png" alt="n---n0 1(v-)2 n0 = - 2 V . " class="par-math-display" /></center>
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57 <!--l. 56--><p class="nopar">
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58 </p><!--l. 59--><p class="noindent">Das Strahlung von bestimmten Frequenzen aussendende und <br/>absorbierende Atomion der Kanalstrahlen ist nun als eine <br/>rasch bewegte Uhr aufzufassen, und es ist daher die soeben <br/>angegebene Beziehung auf dasselbe anwendbar.
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59 </p><!--l. 65--><p class="noindent">----------
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60 </p><!--l. 68--><p class="indent"> 1) J. Stark, Ann. d. Phys. <span
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61 class="cmbx-10">21. </span>p. 401. 1906.
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62 </p><!--l. 70--><p class="indent"> 2) A. Einstein, Ann. d. Phys. <span
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63 class="cmbx-10">17. </span>p. 903. 1905. <pb/>
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64 </p><!--l. 76--><p class="indent">
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65
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66 </p><!--l. 77--><p class="indent"> Es ist aber zu beachten, daß die Frequenz <span
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67 class="cmmi-10"><img
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68 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Ueber_de_1907_02/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /></span><sub ><span
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69 class="cmr-7">0</span></sub> (für den <br/>mitbewegten Beobachter) unbekannt ist, so daß die obige Be-<br/>ziehung der experimentellen Prüfung nicht direkt zugänglich <br/>ist. Es ist aber anzunehmen, daß <span
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70 class="cmmi-10"><img
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71 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Ueber_de_1907_02/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /></span><sub ><span
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72 class="cmr-7">0</span></sub> auch gleich ist der <br/>Frequenz, welche dasselbe Ion im ruhenden Zustand emittiert <br/>bez. absorbiert, und zwar aus folgendem Grunde. Aus der <br/>Tatsache, daß dasselbe Linienspektrum unter sehr verschiedenen <br/>Bedingungen entsteht, entnehmen wir, daß die Frequenz <span
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73 class="cmmi-10"><img
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74 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Ueber_de_1907_02/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /></span><sub ><span
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75 class="cmr-7">0</span></sub>
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76 nicht <br/>abhängig ist von Wechselwirkungen zwischen bewegten Ionen <br/>und ruhendem Gas, sondern daß sie dem Ion allein eigentüm-<br/>lich ist; hieraus folgert man direkt mit Hilfe des Relativitäts-<br/>prinzips, daß <span
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77 class="cmmi-10"><img
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78 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Ueber_de_1907_02/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /></span><sub ><span
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79 class="cmr-7">0</span></sub> gleich sein muß der Frequenz der von einem <br/>ruhenden Ion emittierten bez. absorbierten Strahlung.
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80 </p><!--l. 94--><p class="indent"> Die Gleichung
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81 </p>
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82 <center class="par-math-display" >
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83 <img
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84 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Ueber_de_1907_02/fulltext/img/Einst_Ueber_de_1907_023x.png" alt="n--n0- 1 (v-)2 n0 = -2 V " class="par-math-display" /></center>
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85 <!--l. 99--><p class="nopar">
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86 </p><!--l. 103--><p class="noindent">gibt also direkt den gesuchten Effekt zweiter Ordnung.
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87 </p><!--l. 106--><p class="indent"> Die von Hrn. Stark für den Effekt angegebenen Zahlen-<br/>werte sind mehr als zehnmal so groß als die aus der an-<br/>gegebenen Formel hervorgehenden. Es erscheint mir wahr-<br/>scheinlich, daß sichere Resultate in der vorliegenden Frage <br/>erst dann zu erwarten sind, wenn es gelungen ist, (nicht-<br/>leuchtende?) Kanalstrahlen im völlig gasfreien Raume zu er-<br/>zielen.
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88 </p><!--l. 114--><p class="indent"> Bern, März 1907.
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89 </p>
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90 <div class="center" >
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92 <!--l. 116--><p class="noindent">
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93 </p><!--l. 117--><p class="noindent">(Eingegangen 17. März 1907.)</p></div>
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94 <div class="center" >
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96 <!--l. 121--><p class="noindent">
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97 </p><!--l. 122--><p class="noindent">-----------</p></div>
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99 </body></html>
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