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1446 lines
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<title>A Brief history of Einstein’s special theory of relativity</title>
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<meta name="author" content="Amr Gharbeia">
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<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><font color="#993366"><font face="Verdana, sans-serif"><b>A<img src="data:image/png;base64,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" name="TtsOtkCLStr_03" align="right" hspace="5" width="300" height="29" border="0">
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Brief history of Einstein’s special theory of relativity. </b></font></font>The
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main conclusions of Einstein’s special theory of relativity are the
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Lorentz transformation equations. They are called the “<i>Lorentz</i>
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transformation equations,” because they had already been
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discovered, before Einstein’s first paper, by H. A. Lorentz, taking
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a Newtonian approach. That is where I will pick up the story about
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the Einsteinian revolution in physics, since spatiomaterialism is
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merely following in the footsteps of Lorentz. What I will call the
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four “Lorentz distortions”are sufficient to explain all the of
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the predictions by which Einstein’s special theory of relativity
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has been confirmed. </font></font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><font face="Verdana, sans-serif">L<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADoAAAAPCAMAAACC0iwEAAAAPFBMVEUAAAANDAkcGBMqJR04MSZGPjB+AABjV0NxY01/cFeOfGGciWqqlXS4on7HrojVu5Hjx5v8A/sAAAD///8O80d3AAAAEnRSTlP//////////////////////wDiv78SAAAAjUlEQVR4nMWS4Q7DIAiErdCC7qq8/9MOZ9I12dpsNtkuhJzAp/wwLMMKSxjWNdRGtKHQwxn5CC0KT0hwl70IXa1ERVFtnRO0EmYY6FaMITAVUCuWCi+eop56GCKTmr/E1sK3zm8WDk90FcvpYd1Z3aGv5A6NzNmE59pvEfJjRxMlTK17sPD3+if6+z98B9GgH4VRq7SWAAAAAElFTkSuQmCC" name="TtsOtkCLStr_04" align="right" hspace="5" width="125" height="32" border="0">orentz.</font>
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By 1887, some eighteen years before Einstein’s paper, Michelson and
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Morley had made experiments that showed that light has the same
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velocity relative to any object, regardless of its own motion. What
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made their result puzzling was the Newtonian assumption that the
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medium in which light propagates is a “luminiferous ether,” a
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very subtle kind of material substance that was supposed to be at
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rest in absolute space. Given that the velocity of light is
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everywhere the same <i>relative to absolute space</i>, they expected
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that the velocity of light, as measured from a material object, to
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vary with that object’s own velocity in absolute space—just as
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the velocity of ripples propagating in a pond arrive faster (or
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slower), when a boat is moving toward them (or away from them).</font></font></font></p>
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<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Michelson
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and Morley used an interferometer, which compares the two-way
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velocities of light in perpendicular directions; that is, light is
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reflected back from mirrors in perpendicular directions and the
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signals are compared to see if one is lagging behind the other. They
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made measurements at various points in the Earth’s orbit around the
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sun, where the Earth should have different velocities in absolute
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space. On a moving object, the time it takes for light to travel both
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to and from a distant mirror in the direction of absolute motion
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should be different from the time it takes to travel an equal
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distance in the transverse direction.<sup><a class="sdfootnoteanc" name="sdfootnote1anc" href="#sdfootnote1sym"><sup>1</sup></a></sup>
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The margins of error were small enough, given the velocity of light
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and the velocity of the Earth in its orbit around the sun, that it
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should have been possible for their interferometer to detect absolute
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velocity. But Michelson and Morley failed to detect any difference at
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all in the time it took light to travel the same distance in
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perpendicular directions. Absolute motion could not be detected.</font></font></font></p>
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<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><i><b>Length
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contraction.</b></i> The Michelson-Morley result was surprising, but
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even before Einstein published his special theory in 1905, Lorentz
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had proposed a Newtonian explanation of it. Lorentz showed, in 1895,
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that their result could be explained physically, if the motion of
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such an apparatus in absolute space caused its length to shrink in
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the direction of motion as a function of its velocity by a factor of
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<img src="data:image/png;base64,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" name="StrEqBeta" align="bottom" width="46" height="18" border="0">.
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Lorentz argued that this length contraction is a real physical change
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in the material object that depends on its motion relative to
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absolute space.</font></font></font></p>
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<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
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equation was <i>L=L</i><sub><i>o<img src="data:image/png;base64,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" name="StrEqBeta" align="bottom" width="46" height="18" border="0"></i></sub>,
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where <i>L</i><sub><i>o</i></sub> was the length at absolute rest.
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The shrinkage had been proposed independently by George F. Fitzgerald
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in 1889 and hence became known as the “Lorentz-Fitzgerald
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contraction”.<sup><a class="sdfootnoteanc" name="sdfootnote2anc" href="#sdfootnote2sym"><sup>2</sup></a></sup>
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</font></font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Lorentz
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tried to explain the length contraction physically, as an effect of
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motion through a stagnant ether on the electrostatic forces among its
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constituent, charged particles.<sup><a class="sdfootnoteanc" name="sdfootnote3anc" href="#sdfootnote3sym"><sup>3</sup></a></sup>
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But he could just as well have taken it to be a law of physics,
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making the Lorentz-Fitzgerald contraction the discovery of a new,
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basic physical law. (An ontological explanation of it will be
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suggested in the last section of this discussion of the special
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theory of relativity.)</font></font></font></p>
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<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Lorentz
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also described the length contraction as a mathematical
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transformation between the coordinates of a reference frame based on
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the moving material object and the coordinates of a reference frame
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at absolute rest. Lorentz started with the Galilean transformation by
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which Newtonians would obtain the spatial coordinates used on an
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object in uniform motion in the x-direction, <i>or x’ = x - vt</i>,
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and combining that with the length contraction he had discovered, he
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came up with the transformation equation,
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<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFQAAAAlCAMAAADryz6XAAAAD1BMVEUAAAD8A/v8A/sAAAD////nTSorAAAAAnRSTlP/AOW3MEoAAADcSURBVHic5ZXBDoQwCESn///TG+MubWGqQDEelngRyXOgBdAeMPwXVEMqoIYRgAI6+vAcD7Q/oohJwp7SXywg2k7tFdDJsws1Jf0WhP3Lz1xIoqWuN1y81UBtIhXQGma/e/Qg9qBD5sPd3obSjylj0DqlpFuymgV6e0gx5b5oHmWKBMk7DbUzu+1D1zPPDSWB5uZc3k/GXEOhHW4oG8WyU5QjBz236KRv6pecUuhCzkW/g0orow0dDFXI2N7vExHGnYZ2wGpFkOzd0Hlw6fqpseY4qPgYfAsat0egH+dmCyGOKLbbAAAAAElFTkSuQmCC" name="StrEqSpace" align="bottom" width="77" height="32" border="0">for
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obtaining the spatial coordinates on the moving material object.<sup><a class="sdfootnoteanc" name="sdfootnote4anc" href="#sdfootnote4sym"><sup>4</sup></a></sup>
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</font></font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><i><b>Time
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dilation.</b></i> There is, however, another distortion that material
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objects undergo as a function of their absolute motion. That is a
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slowing down of clocks (and physical processes generally) at the same
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rate as the length contractions, or the so-called "time
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dilation," which took somewhat longer for Lorentz to discover. </font></font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">The
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Galilean transformation for time in Newtonian physics is simply </span></font></font></font><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><i>t
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= t'</i></span></font></font></font><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">
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, because Newtonian physics assumes that time is the same everywhere.
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But by using transformation equations to describe the distortions in
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material objects, Lorentz found that he had to introduce a special
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equation for transforming time: </span></font></font></font><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><i>t’
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= t - vx/c</i></span></font></font></font><font color="#000000"><sup><font face="Times New Roman, serif"><font size="1" style="font-size: 8pt"><span lang="en-US"><i>2
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</i></span></font></font></sup></font><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">(</span></font></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Goldberg84"><font color="#0000ff"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><u>Goldberg</u></span></font></font></font></a><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">,
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p. 94). The new factor in the transformation equation, </span></font></font></font><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><i>vx/c</i></span></font></font></font><font color="#000000"><sup><font face="Times New Roman, serif"><font size="1" style="font-size: 8pt"><span lang="en-US"><i>2</i></span></font></font></sup></font><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">,
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implied that time on the moving frame varies with location in that
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frame. Lorentz called it "local time," but he did not
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attribute any physical significance to it. "Local time" is
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not compatible with the belief in absolute space and time, and
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Lorentz described it as “no more than an auxiliary mathematical
|
||
quantity” (</span></font></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Toretti83"><font color="#0000ff"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><u>Torretti</u></span></font></font></font></a><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">,
|
||
p. 45, 85), insisting that his transformation equations were merely
|
||
“an aid to calculation” (</span></font></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Goldberg84"><font color="#0000ff"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><u>Goldberg</u></span></font></font></font></a><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">,
|
||
p. 96). </span></font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">The
|
||
slowing down of physical processes is called “time dilation.”
|
||
Lorentz discovered this distortion by tinkering with various ways of
|
||
calculating the coordinates used on inertial reference frames in
|
||
relative motion. Thus, it is natural to describe time dilation as the
|
||
slowing down of clocks on the moving reference frame. It was included
|
||
in the final version of Lorentz's explanation, now called the
|
||
“Lorentz transformation equations.” (</span></font></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Lorentz04"><font color="#0000ff"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><u>Lorentz</u></span></font></font></font></a><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">
|
||
1904) Those equations contained not only the length contraction and
|
||
transformation for “local time”, but also the implication that
|
||
clocks on moving frames are slowed down at the same rate as lengths
|
||
are contracted (that is,
|
||
<img src="data:image/png;base64,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" name="StrEqBeta" align="bottom" width="46" height="18" border="0">).
|
||
The final Lorentz equation for time transformation included both the
|
||
variation in local time and time dilation:
|
||
<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFQAAAArCAMAAADRwV/nAAAAD1BMVEUAAAD8A/v8A/sAAAD////nTSorAAAAAnRSTlP/AOW3MEoAAADzSURBVHic5ZbbDsQgCETH///pTTetFxgpIk2zWZ4MxdNRRER5wPB/UHSkLCjKA9CSCYUauKBmBMjIAbUDmtCVRGGI/ib5cOBMDCQvphQXqTJpjAcKXJI7iRQYVLoPVd97vZPVOxLFJqA0qIpIrQP9Y6JpD1o3PRF6HpZc6Fi2kDWUAE0xQyliVqY1sa30fgsXhfpkrq7lNSiP0bcC7VdLUEh354grNW48H9S6iQnKAQU/dJijXFAWVetOOkJQQD/GZB+/42mlUCslERZzbEbXdSGErjY+kGnb0K4XN5faUYlxQcc8qLFqFcsvFI+9A43Y70A/AlMM9qECVTAAAAAASUVORK5CYII=" name="StrEqTime" align="bottom" width="79" height="37" border="0">.
|
||
</span></font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Though
|
||
Lorentz took the distortions that he discovered in fast-moving
|
||
material objects to be laws of nature, he did not think that they
|
||
were basic. He thought they were effects of motion on the
|
||
interactions between electrons and the ether which could be explained
|
||
by his electronic theory of matter, and he saw explaining this effect
|
||
as the the main challenge to Newtonian physics. The transformation
|
||
equations themselves never seemed puzzling to Lorentz, because he
|
||
never took them to more than just a mathematical aid to calculation.</font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Verdana, sans-serif"><font size="3" style="font-size: 12pt"><span lang="en-US">P<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADoAAAAQCAMAAABwUpxKAAAAQlBMVEUAAAANDAkcGBMzAAAqJR04MSZJAABmAAB2AAB+AABxY01/cFeOfGGciWqqlXS4on7HrojVu5Hjx5v8A/sAAAD///8HY0uoAAAAFHRSTlP/////////////////////////AE9P5xEAAACfSURBVHicxZLbDsMgDENZR3YJJID//2NnqNZpUvfQVlqtgAzkgB8Iz8f9dt2lcAQNu3UMxR4tqE8ibd4reSOqMEVLxKqjWrKxmdFUK5CLcupuFWWfmGq3Hl0KitBW8wiIOlIy+UbDOzDvlV4+aPaymEHkMg4gw62g2peRnR+U6RvU5gs5KtqPwFQW5lzQxndQokwzSidr6Hadif7/D78AE/wjPxtuiaIAAAAASUVORK5CYII=" name="TtsOtkCLStr_05" align="right" hspace="5" width="125" height="34" border="0">oincaré.</span></font></font></font><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">
|
||
H. Poincaré thought he saw more clearly what Lorentz had discovered
|
||
than Lorentz himself. As early as 1895, Poincaré had expressed
|
||
dissatisfaction with Lorentz’s piecemeal approach, introducing one
|
||
modification of the laws of Newtonian physics after another in order
|
||
to account for different aspects of the phenomenon discovered by
|
||
Michelson and Morley. Instead of such </span></font></font></font><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><i>ad
|
||
hoc</i></span></font></font></font><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">
|
||
modifications, he urged the recognition of what he called a
|
||
“principle of relativity” to cover all the phenomena involved in
|
||
fast-moving objects. As Poincaré put it in 1904, the principle of
|
||
relativity requires that “the laws of physical phenomena should be
|
||
the same for an observer at rest or for an observer carried along in
|
||
uniform movement of translation, so that we do not and cannot have
|
||
any means of determining whether we actually undergo a motion of this
|
||
kind” (from </span></font></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Toretti83a"><font color="#0000ff"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><u>Torretti</u></span></font></font></font></a><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">,
|
||
83). </span></font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">A principle
|
||
of relativity like this had, in effect, been affirmed by Newton
|
||
himself, when he admitted that his laws of motion depend, not on the
|
||
absolute velocities of material objects, but only on their relative
|
||
velocities. That is, Newton had already denied that absolute rest
|
||
could be detected by mechanical experiments. It seemed that absolute
|
||
motion could be detected only when Maxwell had discovered that light
|
||
could be explained as an electromagnetic wave. Thus, Poincaré saw
|
||
Lorentz's discovery of distortions in fast-moving material objects as
|
||
a way of extending Newton’s principle of relativity to cover
|
||
electromagnetic phenomena. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">Understanding
|
||
how the undetectability of absolute motion could be a result of the
|
||
distortions that Lorentz had discovered, he referred to Lorentz
|
||
theory as “Lorentz’s principle of relativity” even after
|
||
Einstein had published his special theory and Lorentz himself was
|
||
attributing the principle of relativity to Einstein (</span></font></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Toretti83b"><font color="#0000ff"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><u>Torretti</u></span></font></font></font></a><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">
|
||
85, </span></font></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Goldberg84b"><font color="#0000ff"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><u>Goldberg</u></span></font></font></font></a><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">
|
||
212, and </span></font></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Holton73"><font color="#0000ff"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><u>Holton</u></span></font></font></font></a><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">
|
||
178). Indeed, Poincaré joined Lorentz in the attempt to explain the
|
||
Lorentz distortions by the motion of material objects through
|
||
absolute space, also expecting to find their cause in the dynamics of
|
||
electrons; he also thought that motion through the ether caused
|
||
material objects to shrink in the direction of motion and natural
|
||
clocks to slow down by the exact amount required to mask their
|
||
motion, as implied by Lorentz’s transformation equations (</span></font></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Goldberg84b"><font color="#0000ff"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><u>Goldberg</u></span></font></font></font></a><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">
|
||
94-102, </span></font></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Toretti83b"><font color="#0000ff"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><u>Torretti</u></span></font></font></font></a><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">
|
||
38-47). Furthermore, Poincaré apparently thought that what Lorentz
|
||
said about those equations in his 1904 work answered his own demand
|
||
that it be a “demonstration of the principle of relativity with a
|
||
single thrust” (</span></font></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Goldber84b"><font color="#0000ff"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><u>Goldberg</u></span></font></font></font></a><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">
|
||
214-15).</span></font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Lorentz's
|
||
explanation of the distortions was not, however, a complete
|
||
explanation of the principle of relativity. There are really two
|
||
quite different aspects of the phenomenon described by the principle
|
||
of relativity, and Lorentz had explicitly explained only one of them.</font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">What
|
||
Lorentz’s electron theory of matter (and Poincaré’s own
|
||
refinements of it) explained physically were the Lorentz distortions
|
||
in material objects with absolute velocity. That explained the
|
||
negative outcome of the Michelson-Morley experiment: the contraction
|
||
of lengths in the direction of motion and the slowing down of clocks
|
||
as a function of motion through absolute space does make it
|
||
physically impossible to detect absolute motion on a moving object by
|
||
measuring the velocity of light relative to it. And that is one way
|
||
in which inertial reference frames are empirically equivalent,
|
||
because it holds of measurements made using any material object in
|
||
uniform motion as one's reference frame, regardless of its motion
|
||
through absolute space.</font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">But there
|
||
is more to the principle of relativity than explaining the null
|
||
result of the Michelson-Morley experiment. The transformation
|
||
equations that Lorentz constructed to describe the effects of
|
||
absolute motion on material objects predict the outcomes of other
|
||
experiments, such as attempts to measure directly the lengths of
|
||
high-velocity measuring rods and the rate at which high-velocity
|
||
clocks are ticking away. Though such experiments are more difficult
|
||
to perform, they are conceivable, and Lorentz's equations do make
|
||
predictions about them: moving measuring rods will be shrunken in the
|
||
direction of motion and moving clocks will be slowed down. That
|
||
suggests another way of detecting absolute motion. One might compare
|
||
measuring rods or clocks that are moving at a whole range different
|
||
velocities with one another and take the one with the longest
|
||
measuring rods and quickest clocks to be closest to absolute rest.
|
||
Hence, the principle of relativity would be false.</font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">It is not
|
||
possible, however, to detect absolute rest in this way, and as it
|
||
happens, its impossibility is also predicted by Lorentz's theory,
|
||
because he formulated his description of the Lorentz distortions in
|
||
terms of transformation equations. Transformation equations are
|
||
equations for transforming the coordinates obtained by using one
|
||
material objects as a frame of reference into the coordinates
|
||
obtained by using another material object as a frame of reference,
|
||
and to be consistent, they must work both ways. That is, it must be
|
||
possible to obtain the original coordinates by applying the
|
||
transformation equations to the transformed coordinates. Thus,
|
||
whatever distortions observers at absolute rest may find in material
|
||
objects with a high absolute velocity will also be found by observers
|
||
in absolute motion in material objects that are at absolute rest. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">The
|
||
recognition that Lorentz's theory, being formulated in terms of
|
||
transformation equations, implied that all such inertial reference
|
||
frames are empirically equivalent is presumably what led Poincaré to
|
||
proclaim that Lorentz had finally explained the truth of the
|
||
principle of relativity. Absolute rest and motion cannot be detected
|
||
from any inertial reference frame.</font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Lorentz's
|
||
theory was not, however, an adequate explanation of the principle of
|
||
relativity, for there is still something puzzling about the empirical
|
||
equivalence entailed by the symmetry of the Lorentz transformation
|
||
equations. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Lorentz
|
||
meant his transformation equations to be a way of describing the
|
||
length contraction and time dilation in material objects with
|
||
absolute motion, for that would explain the Michelson-Morley
|
||
experiment, that is, why absolute motion cannot be detected by
|
||
measuring the velocity of light in different directions. But since
|
||
the transformation equations describe a symmetry between the members
|
||
of any pair of inertial reference frames, they imply that observers
|
||
using a fast-moving material object as the basis of their reference
|
||
frame would observe a length contraction in measuring rods that were
|
||
at absolute rest and a time dilation in clocks at absolute rest. That
|
||
makes it impossible to detect absolute rest or motion by comparing
|
||
different inertial reference frames with one another. But it is
|
||
puzzling, because it is hard to see how both views could be true at
|
||
the same time, that is, how two measuring rods passing one another at
|
||
high velocity could both be shorter than the other and how two clocks
|
||
passing by one another could both be going slower than the other. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">In other
|
||
words, Lorentz's theory does not really give a physical explanation
|
||
of what Poincaré called the "principle of relativity."
|
||
What entails the truth of the principle of relativity is the
|
||
description of the Lorentz distortions in terms of transformation
|
||
equations; the inability to detect absolute rest and motion by
|
||
comparing inertial frames with one another comes from the symmetrical
|
||
relationship that transformation equations represent as holding
|
||
between the members of any pair of inertial reference frames. That
|
||
symmetry is not physically possible, at least, not in the sense of
|
||
"physical" that Lorentz had in mind when he tried to
|
||
explain the distortions as occurring to material objects because of
|
||
their motion in absolute space. If inertial frames are material
|
||
objects in absolute space, then their measuring rods cannot both be
|
||
shorter than the other and their clocks cannot both be slower. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">As we shall
|
||
see, what enables Lorentz's transformation equations to predict the
|
||
symmetry of distortions is the "local time" factor in the
|
||
time equation, <i>vx/c</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup>,
|
||
which Lorentz insisted was just an "aid to calculation." It
|
||
represents the readings that would be given by clocks on a moving
|
||
reference frame that have been synchronized by using light signals
|
||
between them as if they were all at absolute rest, that is, on the
|
||
assumption that the one-way velocity of light is the same both ways
|
||
along the pathway between any two clocks (as required by Einstein's
|
||
definition of simultaneity at a distance). That assumption is false,
|
||
as Lorentz understood these phenomena, and clocks on the moving
|
||
inertial frame would be mis-synchronized. It can be shown, as we
|
||
shall see, that this way of mis-synchronizing clocks on a moving
|
||
frame combines with the Lorentz distortions that the moving frame is
|
||
actually suffering to make it appear that its own Lorentz distortions
|
||
are occurring in the reference frame at absolute rest (or moving more
|
||
slowly). This is a physical explanation, given how the other frame's
|
||
measuring rods and clocks are measured. But it is an explanation of
|
||
the principle of relativity that reveals it to be the description of
|
||
a <i>mere appearance</i>. Though there is an <i>empirical equivalence
|
||
</i>among inertial frames, a physicist who accepted Lorentz's
|
||
Newtonian assumptions would insist that it has a <i>deeper physical
|
||
explanation</i>. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">It
|
||
was not Lorentz, however, but Poincaré who declared that Lorentz had
|
||
explained the truth of the principle of relativity, and Poincaré's
|
||
acceptance of Lorentz's explanation as adequate may have been colored
|
||
by his own philosophical commitment to conventionalism. Poincaré
|
||
viewed the choice between Euclidean or non-Euclidean geometry as
|
||
conventional, and he argued that convention is also what raised
|
||
inertia and the conservation of energy to the status of principles
|
||
that could not be empirically falsified. Poincaré's acceptance of
|
||
the principle of relativity should probably be understood in the
|
||
context of this more or less Kantian skepticism about knowing the
|
||
real nature of what exists. Considering how the standard of
|
||
simultaneity at a distance varies from one inertial reference frame
|
||
to another (depending on the "local time" factor in the
|
||
Lorentz transformation equations), the principle of relativity could
|
||
also be seen as a conventional truth. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Poincaré's
|
||
pronouncement that Lorentz's theory had explained the principle of
|
||
relativity could not have set well with Lorentz himself. Lorentz may
|
||
have continued to call it "Einstein's principle of relativity"
|
||
because he realized that it was not <i>explained </i>by his theory
|
||
about how spatial and temporal distortions are caused in material
|
||
objects by their absolute motion. What is responsible for the
|
||
principle of relativity is the symmetry in pairs of inertial frames
|
||
entailed by his equations being transformation equations. If the
|
||
distortions didn’t hold <i>symmetrically </i>in any pair inertial
|
||
frames, it would be possible to detect absolute rest and motion. But
|
||
to my knowledge, Lorentz never argued explicitly that what he called
|
||
"local time" on the moving material object (that is, <i>vx/c</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup>
|
||
in the time equation) represents a mis-synchronization of clocks on
|
||
the moving frame that causes the moving frame's own Lorentz
|
||
distortions to appear to be occurring in the other inertial reference
|
||
frame. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
|
||
Newtonian explanation of all the relevant phenomena did not,
|
||
therefore, have an adequate defender. Lorentz was more concerned to
|
||
find an adequate physical explanation of the distortions he had
|
||
discovered in material objects, and Poincaré was more interested in
|
||
defending conventionalism. That is the Newtonian context in which
|
||
Einstein's special theory of relativity won the day. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Verdana, sans-serif"><font size="3" style="font-size: 12pt"><span lang="en-US">E<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADoAAAARCAMAAAC7Dk/vAAAASFBMVEUAAAANDAkcGBMzAAAqJR04MSZJAABGPjBmAAB2AAB+AABjV0NxY01/cFeOfGGciWqqlXS4on7HrojVu5Hjx5v8A/sAAAD///8Rn7hnAAAAFnRSTlP///////////////////////////8AAdLA5AAAAJRJREFUeJzF09EOwiAMBVCmVNRSKOz+/7daiNFliVtkD7svtIGT8gDu+bjfrkNxR6gbzjGKkXyoXogSUllufjvepLG1WqEaTcwSK4iTeSvQ1iSbU6MisnogZFWwFIjkABAw5Shr6hZTG9V2ULwNsxJENHVK7yO7dIZSp6Fa/YuuL9wpe+vUM4on2qH/50x6xhse/nQvt8YoCx9RL4cAAAAASUVORK5CYII=" name="TtsOtkCLStr_06" align="right" hspace="5" width="125" height="36" border="0">instein.
|
||
</span></font></font></font><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">Einstein
|
||
took a dramatically different approach from both Lorentz and
|
||
Poincaré. Instead of taking the principle of relativity to be an
|
||
empirical hypothesis that could be explained physically by deeper,
|
||
Newtonian principles, or as a conventional truth, Einstein raised the
|
||
principle of relativity to the status of a </span></font></font></font><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><i>postulate</i></span></font></font></font><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">,
|
||
which was not to be explained at all, but rather accepted as basic
|
||
and used to explain other phenomena (</span></font></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Zaharb"><font color="#0000ff"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><u>Zahar</u></span></font></font></font></a><font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">
|
||
90-2). The mathematical elegance of Einstein's explanation of these
|
||
phenomena is stunning. From the premise that all inertial reference
|
||
frames are empirically equivalent, he derived a description of how
|
||
two different inertial reference frames would appear to each other;
|
||
that is, he deduced the Lorentz transformation equations. </span></font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Einstein's
|
||
new approach can be seen most clearly by considering the structure of
|
||
his argument. It is represented below in a diagrammatic form. </font></font></font>
|
||
</p>
|
||
<center>
|
||
<table width="431" cellpadding="0" cellspacing="0">
|
||
<col width="128">
|
||
<col width="152">
|
||
<col width="151">
|
||
<tr>
|
||
<td width="128" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="left"><font color="#000000"><b>Einstein's
|
||
<br>Premises:</b></font></p>
|
||
</td>
|
||
<td width="152" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="left"><font color="#000000"><i><b>The
|
||
Principle of Relativity</b></i></font></p>
|
||
</td>
|
||
<td width="151" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="left"><font color="#000000"><font size="1" style="font-size: 8pt">The
|
||
laws of nature apply the same way on all inertial frames.</font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="128" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="left"><font color="#000000"> </font></p>
|
||
</td>
|
||
<td width="152" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="left"><font color="#000000"><i><b>The
|
||
Light Postulate</b></i></font></p>
|
||
</td>
|
||
<td width="151" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="left"><font color="#000000"><font size="1" style="font-size: 8pt">The
|
||
velocity of light is the same on all inertial frames.</font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="128" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="left"><font color="#000000"> </font></p>
|
||
</td>
|
||
<td width="152" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="left"><font color="#000000"><i><b>The
|
||
Definition of Simultaneity at a Distance</b></i></font></p>
|
||
</td>
|
||
<td width="151" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="left"><font color="#000000"><font size="1" style="font-size: 8pt">The
|
||
local event halfway through the period required for light to
|
||
travel to the distant event and back is simultaneous with the
|
||
distant event.</font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="128" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="left"><font color="#000000"> </font></p>
|
||
</td>
|
||
<td width="152" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="left"><font color="#000000"> </font></p>
|
||
</td>
|
||
<td width="151" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="left"><font color="#000000"> </font></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="128" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="left"><font color="#000000"><b>Einstein's<br>Conclusions:</b></font></p>
|
||
</td>
|
||
<td width="152" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="left"><font color="#000000"><font size="1" style="font-size: 8pt">To
|
||
obtain the second frame's coordinates from the first frame:</font></font></p>
|
||
</td>
|
||
<td width="151" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="left"><font color="#000000"><font size="1" style="font-size: 8pt">To
|
||
obtain the first frame's coordinates from the second frame:</font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="128" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="left"><font color="#000000"><i>Lorentz
|
||
transformation equations </i></font><font color="#000000"> </font><font color="#000000"><font size="1" style="font-size: 7pt">(kinematic
|
||
phenomena)</font></font></p>
|
||
</td>
|
||
<td width="152" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="center"><font color="#000000"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFQAAAAlCAMAAADryz6XAAAAD1BMVEUAAAD8A/v8A/sAAAD////nTSorAAAAAnRSTlP/AOW3MEoAAADcSURBVHic5ZXBDoQwCESn///TG+MubWGqQDEelngRyXOgBdAeMPwXVEMqoIYRgAI6+vAcD7Q/oohJwp7SXywg2k7tFdDJsws1Jf0WhP3Lz1xIoqWuN1y81UBtIhXQGma/e/Qg9qBD5sPd3obSjylj0DqlpFuymgV6e0gx5b5oHmWKBMk7DbUzu+1D1zPPDSWB5uZc3k/GXEOhHW4oG8WyU5QjBz236KRv6pecUuhCzkW/g0orow0dDFXI2N7vExHGnYZ2wGpFkOzd0Hlw6fqpseY4qPgYfAsat0egH+dmCyGOKLbbAAAAAElFTkSuQmCC" name="image002" align="bottom" width="84" height="37" border="0"></font></p>
|
||
</td>
|
||
<td width="151" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="center"><font color="#000000"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFAAAAAlCAMAAADiIJ7tAAAAD1BMVEUAAAD8A/v8A/sAAAD////nTSorAAAAAnRSTlP/AOW3MEoAAADfSURBVHic5ZbbDsQgCETH///pbbf1giAZ0Kdd06SN4ukARYpyeOCHgKYl1BINhN7beDHgZY5uiD55XxiWaIWPAAm877A8poADGq+oImSngUJhGggziTp4LBDFBjZqWGFw/CcQOIn9Zr/VU/1sd4HGdHYI4CmFbgiD+l6aB0wo3FqPblgs60hDFHkUqKOOsgW05nmge+g5Dyug+WFqOTxwUUczhkzKXJiA0YTB9eXWO+ceBW3DAHuVP+fRWFhLB1yFAji9JwesvkigjiD/54Dq7crcSImf5dTZ6O45DsyMD7ZjCnnk54RFAAAAAElFTkSuQmCC" name="image004" align="bottom" width="80" height="37" border="0"></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="128" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="left"><font color="#000000"> </font></p>
|
||
</td>
|
||
<td width="152" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="center"><font color="#000000"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACEAAAAQCAMAAACvHOZVAAAAD1BMVEUAAAD8A/v8A/sAAAD////nTSorAAAAAnRSTlP/AOW3MEoAAABOSURBVHiclY9BEgAgCALp/5+ubCxLxYmjLQFolfBDJPA5oybylGGefkeYu3mGyLiViBOgfks8f2wiWwFdQFbcLWNAJpGaqxorQTq4MKIO+18B3KhV6LsAAAAASUVORK5CYII=" name="image006" align="bottom" width="33" height="16" border="0"></font></p>
|
||
</td>
|
||
<td width="151" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="center"><font color="#000000"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACEAAAAQCAMAAACvHOZVAAAAD1BMVEUAAAD8A/v8A/sAAAD////nTSorAAAAAnRSTlP/AOW3MEoAAABNSURBVHicpZBRCgAgCEPn/S8dUorGlh8NQRhPXcEm4ZvARGAmdsGLDCOIaG676rQFQW6l2Yi+oxIsbponB33FFUgB4kvQiGcIlUHcU1r7egHcdvVOgQAAAABJRU5ErkJggg==" name="image008" align="bottom" width="33" height="16" border="0"></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="128" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="left"><font color="#000000"> </font></p>
|
||
</td>
|
||
<td width="152" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="center"><font color="#000000"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAMCAMAAAA0yk+LAAAAD1BMVEUAAAD8A/v8A/sAAAD////nTSorAAAAAnRSTlP/AOW3MEoAAABASURBVHicY2AkABiIV4BDKVyYgaACnFYwgAAWBXBxFEkGqDDESAZGBMZpPZrhSCYwwgzCZj+yFUhasLmRcEgCAA21AVBW/R6MAAAAAElFTkSuQmCC" name="image010" align="bottom" width="32" height="12" border="0"></font></p>
|
||
</td>
|
||
<td width="151" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="center"><font color="#000000"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAMCAMAAAA0yk+LAAAAD1BMVEUAAAD8A/v8A/sAAAD////nTSorAAAAAnRSTlP/AOW3MEoAAABASURBVHicY2AkABgoVMBAQAEDQQVgM0AAUytYkAFqCQOSKANCK9yRWK1hQNBweSQTkARRlKC6DkMXhhtRjMIFAA3KAVBsBAX4AAAAAElFTkSuQmCC" name="image012" align="bottom" width="32" height="12" border="0"></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="128" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="left"><font color="#000000"> </font></p>
|
||
</td>
|
||
<td width="152" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="center"><font color="#000000"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFQAAAArCAMAAADRwV/nAAAAD1BMVEUAAAD8A/v8A/sAAAD////nTSorAAAAAnRSTlP/AOW3MEoAAADzSURBVHic5ZbbDsQgCETH///pTTetFxgpIk2zWZ4MxdNRRER5wPB/UHSkLCjKA9CSCYUauKBmBMjIAbUDmtCVRGGI/ib5cOBMDCQvphQXqTJpjAcKXJI7iRQYVLoPVd97vZPVOxLFJqA0qIpIrQP9Y6JpD1o3PRF6HpZc6Fi2kDWUAE0xQyliVqY1sa30fgsXhfpkrq7lNSiP0bcC7VdLUEh354grNW48H9S6iQnKAQU/dJijXFAWVetOOkJQQD/GZB+/42mlUCslERZzbEbXdSGErjY+kGnb0K4XN5faUYlxQcc8qLFqFcsvFI+9A43Y70A/AlMM9qECVTAAAAAASUVORK5CYII=" name="image014" align="bottom" width="84" height="43" border="0"></font></p>
|
||
</td>
|
||
<td width="151" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="center"><font color="#000000"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE0AAAAoCAMAAACM7odrAAAAD1BMVEUAAAD8A/v8A/sAAAD////nTSorAAAAAnRSTlP/AOW3MEoAAADpSURBVHiczZVJEsUgCAXb+1/6L/KNyBAnKhVXVoDmCUYomYsv0iCRRsmklRQaahPSGOVCmge0C/bghKTx3AWQ3hXKxaDqQpLG2pRThdD27oF92i3znx+bhCAqonXhezTfqVPoHDTugq9NxpsefPSvF7Q8IqnyKPSFPKSJ/t9gtlb+ST1tzbyirF3sONmatsceLNM2rLYeBzRdHcoJzX6fpzkezps8SfOapIfPPM3x0BOKuS7omUp/n+hIyzQ7oDD2mHTT2l/dS4t6a2G42vZoxafpqgWj0sPZoaRrpN+cIW1pJT4gWxHv0X5MgQrYZJSh4wAAAABJRU5ErkJggg==" name="image016" align="bottom" width="77" height="40" border="0"></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="128" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="left"><font color="#000000"><i>Relativistic
|
||
increase in mass </i></font><font color="#000000"> </font><font color="#000000"><font size="1" style="font-size: 7pt">(dynamic
|
||
phenomena)</font></font></p>
|
||
</td>
|
||
<td width="152" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="center"><font color="#000000"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF0AAAAlCAMAAAAX3hVdAAAAD1BMVEUAAAD8A/v8A/sAAAD////nTSorAAAAAnRSTlP/AOW3MEoAAAC8SURBVHic7dXRDoAgCAXQ6///dJvpQhIlkJpbziedJ9BEpMiGX99FB0oP0Ssfpde+n67HHXrUzjwKJPBTFFQla9dX4wnk6kXo/Ooht3W6+P/C1Ib62thVV88UOdHHvDEX3TLrRnl0nu89f4fOH5DOg6LWu38sM2y6cOpTXP8IvKbXslTyybN5zLwzvJiCTwoHP4HrwhIhzgGayQCZVYBE9WZ0gX5R0iM22hi1Di42ulSlFKfqqMaf644Wqx935gx0LITV2wAAAABJRU5ErkJggg==" name="image018" align="bottom" width="93" height="37" border="0"></font></p>
|
||
</td>
|
||
<td width="151" style="border: none; padding: 0cm">
|
||
<p lang="en-US" class="western" align="center"><font color="#000000"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFkAAAAlCAMAAAAeNbUnAAAAD1BMVEUAAAD8A/v8A/sAAAD////nTSorAAAAAnRSTlP/AOW3MEoAAADDSURBVHic7dbhDoMgDATg4/1f2qksyFHWcoPEZRL9AdIvtYKKtKrhr2QvUpYxWX555+EHjuac6RVyCrF3kuOwKK+oxlASj3yRy7aaLZdttXePNk221yiU1pen5uxuKy3lIvdp8RYCYfYUTqVJzZc7MI1zX5fbcUm2JoHi21UbkM2nCwqXZGtSXmKg/ogMmlS/Y2CrklzdA3ggKuN6vjcZqLjRtVNfg5nz93KyZa5yB3HqjFwIO+LD84vJWlv2r/qT3+4N/SYL4A2dV7IAAAAASUVORK5CYII=" name="image020" align="bottom" width="89" height="37" border="0"></font></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
</center>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">The
|
||
assumption that inertial frames are all empirically equivalent takes
|
||
the form of three premises in Einstein’s argument: the Principle of
|
||
Relativity, the Light Postulate, and Einstein's Definition of
|
||
Simultaneity at a Distance (see table). Einstein's principle of
|
||
relativity holds, with Poincaré, that the laws of nature hold in the
|
||
same way on every inertial reference frame. That allowed Einstein to
|
||
assume that Maxwell's laws of electromagnetism hold universally, and
|
||
he considered what would be true of two different inertial frames in
|
||
the same world. But in order to deduce the Lorentz transformation
|
||
equations, Einstein also had to assume that that the velocity of
|
||
light is the same relative to every inertial frame (the light
|
||
postulate) and, accordingly, that simultaneity at a distance is
|
||
defined on each reference frame as if the velocity of light is the
|
||
same both to and back from a distance object. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">What
|
||
Einstein deduced from these premises are the “Lorentz
|
||
transformation equations,” that is, equations for transforming the
|
||
coordinates of any given inertial reference frame into those of any
|
||
other. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">The Lorentz
|
||
transformation equations imply that any material object moving
|
||
relative to any other inertial frame at a velocity approaching that
|
||
of light will appear to suffer the Lorentz distortions: its clocks
|
||
(and all physical processes) will be slowed down, and its measuring
|
||
rods (and all material objects) will be shortened in the direction of
|
||
its motion—both by the same amount,
|
||
<img src="data:image/png;base64,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" name="StrEqBeta" align="bottom" width="46" height="18" border="0">,
|
||
which is a function of its velocity in the observer’s reference
|
||
frame. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Einstein
|
||
also inferred from these kinematic distortions and his principle of
|
||
relativity that the mass of objects moving in an inertial frame
|
||
increases at the same rate, making three distortions altogether. That
|
||
dynamical implication is the source of Einstein's most famous
|
||
equations, <i>E = mc</i><sup><i>2</i></sup>.</font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">It
|
||
should be emphasized that there are really two sets of transformation
|
||
equations. It may not seem that way, because Einstein's conclusion is
|
||
often stated as just one of the two sets of equations listed above,
|
||
making it look mathematically simpler. But that formulation overlooks
|
||
a mathematical detail and thereby obscures what Einstein's conclusion
|
||
is about.</font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Though the
|
||
Lorentz transformation is exactly the same both ways between the
|
||
members of any pair of inertial reference frames, it requires two,
|
||
non-identical sets of transformation equations, because their
|
||
relative velocity has the opposite sign for each observer. That is,
|
||
the two coordinate systems are set up so that their origins coincide
|
||
when <i>t = 0</i> and <i>t' = 0</i>, and since they are moving in
|
||
opposite directions, the relative velocity is <i>v</i> for one of
|
||
them and <i>-v</i> for the other. Thus, in order for the
|
||
transformation to be symmetrical, one set of transformation equations
|
||
has to have the opposite sign for the second factor in the numerator
|
||
of the equations for space and time. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Since this
|
||
seems to be a mere technicality, the conclusions of Einstein’s
|
||
argument are usually represented as a single set of Lorentz
|
||
transformation equations (the first set in the above table).
|
||
Duplication is avoided by introducing a special mathematical symbol
|
||
to make the single set of equations represent both transformations in
|
||
any pair of inertial frames. Thus, Einstein's conclusion seems more
|
||
like just another universal law of nature. But this is just homage to
|
||
the Pythagorean ideal of mathematical simplicity, which obscures the
|
||
fact that Einstein's theory is, in the first instance, about the
|
||
symmetry that holds between the members of every pair of inertial
|
||
frames. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">It
|
||
should also be emphasized that Einstein's theory is about how
|
||
<i>reference frames</i> are related, and only indirectly about the
|
||
material objects on which they are based. Though it does have
|
||
implications concerning the relationship between material objects
|
||
with a high relative velocity, that relationship is described by way
|
||
of a mathematical transformation that holds between the reference
|
||
frames based on them.</font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Inertial
|
||
reference frames are based on material objects that are not being
|
||
accelerated, and what makes the material object a reference frame is
|
||
that it is used as the basis for a coordinate system by which the
|
||
locations and times of events throughout the universe can be
|
||
measured. (For this purpose, it is useful to think of an inertial
|
||
reference frame as a grid of rigid bars extending wherever needed in
|
||
space with synchronized clocks located everywhere.) </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Notice that
|
||
Einstein's three premises are all about reference frames based on
|
||
material objects. Indeed, his definition of simultaneity prescribes
|
||
how clocks must be synchronized to set up such a reference frame. The
|
||
light postulate makes explicit the assumption about the velocity of
|
||
light on which his definition of simultaneity is based. And the
|
||
principle of relativity states that all the laws of physics will hold
|
||
the same way within that reference frame as every other one, that is,
|
||
will make correct predictions about what happens in that reference
|
||
frame. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Einstein
|
||
derives conclusions from his premises by assuming that there are two
|
||
different inertial reference frames in the world and figuring out how
|
||
they must appear to one another. Since his premises are about their
|
||
reference frames, it is hardly surprising that his conclusion is
|
||
about a mathematical transformation between their coordinates. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Indirectly,
|
||
however, Einstein's conclusion is a description of how material
|
||
objects with different constant velocities are related to one another
|
||
as parts of the same world, since the reference frames in question
|
||
are based on material objects. But to see Einstein's conclusion as a
|
||
description of how material objects are related in space is to take
|
||
Lorentz's approach. For Lorentz, these same transformation equations
|
||
were just a mathematically convenient way of describing <i>from the
|
||
absolute frame </i>the spatial and temporal distortions that occur in
|
||
material objects with a high velocity in absolute space. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">By calling
|
||
his argument a theory of <i>relativity</i>, Einstein emphasized that
|
||
his theory is about the empirical equivalence of all inertial
|
||
reference frames, not the relationship between the material objects
|
||
on which they are based. Observers on each inertial reference frame
|
||
have their own view of the relationship between the material objects
|
||
involved, but they are different views, and it is their views that
|
||
are related by the Lorentz transformation equations. The symmetry of
|
||
the relationship between their reference frames is what is crucial
|
||
for Einstein, because that is what rules out any way of detecting
|
||
absolute rest or motion by comparing inertial frames to one another
|
||
and ensures that there is nothing to distinguish one inertial frame
|
||
from another except their velocities relative to one another. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
|
||
Lorentz distortions in material objects are, however, a consequence
|
||
of the Lorentz transformation equations that Einstein deduced. And if
|
||
one does follow Lorentz, interpreting them as a way of describing the
|
||
material objects on which the inertial reference frames are based,
|
||
then the Lorentz transformation equations lead to paradoxes, as I
|
||
have already suggested. Those equations imply that observers using
|
||
any given inertial reference frame will find the Lorentz distortions
|
||
occurring in the material objects on which the <i>other </i>inertial
|
||
reference frame is based, and thus, the symmetry of the
|
||
transformation for any pair of inertial frames leads to paradoxes. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Consider
|
||
two inertial frames in motion relative to one another. From the first
|
||
frame it appears that clocks on the second frame are slowed down.
|
||
That would make sense, if from the second frame, it appeared that
|
||
first-frame clocks were speeded up. But special relativity implies
|
||
that it also appears from the second frame that clocks on the first
|
||
frame are slowed down. That is, the distortions are <i>symmetrical </i>on
|
||
Einstein’s theory, not the reverse of one another, as one might
|
||
expect. And if the Lorentz distortions are really symmetrical, it is
|
||
inconceivable that the two inertial frames are just material objects
|
||
moving relative to one another in absolute space, because in absolute
|
||
space, there can’t be two clocks next to one another both of which
|
||
are actually going slower than the other. If one assumes that
|
||
Einstein's theory is describing material objects, one must give up
|
||
the assumption that those objects are located in absolute space. They
|
||
are, of course, parts of the same world, but they must be related to
|
||
one another in some other way. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">The same
|
||
problem arises from the symmetry of the length contraction and
|
||
relativistic mass increase, for there cannot be two measuring rods
|
||
passing one another in space that are both shorter than the other.
|
||
Nor can there be two material objects both be more massive than the
|
||
other. It is simply not possible for material objects located in
|
||
absolute space.</font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">None of
|
||
this should be a surprise, however, because even the <i>Light
|
||
Postulate </i>itself is incompatible with absolute space (or at
|
||
least, with the assumption that light has a fixed velocity relative
|
||
to absolute space). Though Newtonian physics had taken absolute space
|
||
to contain the medium in which light propagates, Einstein assumed
|
||
that the velocity of light relative to every object is the same,
|
||
regardless of their own velocities relative to other objects in the
|
||
world. Thus, Einstein held that the velocity of light would be the
|
||
same in both members of any pair of inertial frames. This is not
|
||
possible, if electromagnetic waves propagate through (an ether in)
|
||
absolute space, like waves in water, for the motion of an object
|
||
through waves propagating in space would change the velocity of those
|
||
waves relative to the object—just as the motion of a row boat
|
||
through ripples propagating in a pond changes the velocity of those
|
||
ripples relative to the boat. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Taken
|
||
as a description of the relationship between material objects in
|
||
space, therefore, Einstein's special theory of relativity leads to
|
||
paradoxes. But Einstein was not discouraged by these paradoxes. He
|
||
was not thinking of inertial reference frames as material objects
|
||
that are related in space, that is, in absolute space, or a space
|
||
that is the same for both material objects. He was making a more
|
||
abstract, mathematical argument and, in the process, giving physics a
|
||
new standpoint from which to explain all physical processes. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">That
|
||
Einstein's basic approach is different from Lorentz's can be seen in
|
||
what made Einstein curious about these phenomena in the first place.
|
||
It was not the Michelson-Morley experiment, but rather something
|
||
peculiar about the connection between classical mechanics and
|
||
Maxwell’s theory of electromagnetism (</span></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Zaharb"><font color="#0000ff"><font face="Times New Roman, serif"><span lang="en-US"><u>Zahar</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
|
||
99-100). Einstein realized that even though Maxwell’s theory was
|
||
standardly interpreted as referring to absolute space, absolute space
|
||
was not needed in order to explain electromagnetic phenomena. For
|
||
example, a conductor moving through a magnetic field at absolute rest
|
||
moves electrons exactly the same way as if it were at absolute rest
|
||
and the magnetic field were moving. That is what suggested the
|
||
principle of relativity to Einstein, and though from it he derived
|
||
the same transformation equations that Lorentz had proposed in 1904,
|
||
Einstein claimed not to know about Lorentz's 1904 work.</span></font></font><font color="#000000"><sup><font face="Times New Roman, serif"><span lang="en-US"><a class="sdfootnoteanc" name="sdfootnote5anc" href="#sdfootnote5sym"><sup>5</sup></a></span></font></sup></font><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
|
||
</span></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">By raising
|
||
the principle of relativity to the status of a <i>postulate</i>,
|
||
Einstein was assuming, in effect, that the deepest truth that can be
|
||
known about the nature of space and time is that inertial frames are
|
||
all empirically equivalent. And by relying on the predictions of
|
||
measurements derived from that principle to justify his theory,
|
||
Einstein had the support of the positivists, who dominated philosophy
|
||
of science at that time. Indeed, Einstein admits to having been
|
||
influenced by Ernst Mach at the time of his first paper on special
|
||
relativity. To positivists, the paradoxes mentioned above about two
|
||
clocks both going slower than the other and two measuring rods both
|
||
shorter than the other are not real problems, but merely theoretical
|
||
problems. Theoretical propositions that could not be spelled out in
|
||
terms of observations were dismissed as "metaphysical," as
|
||
if theories were mere instruments for making predictions. That
|
||
attitude could be taken about the aforementioned paradoxes, because
|
||
there is never any occasion in which two clocks can be directly
|
||
observed both going slower than the other (or two measuring rods
|
||
observed both shorter than the other). Observations are made from one
|
||
inertial reference frame or another, and if both members of some pair
|
||
of inertial frames are observed from a third reference frame, their
|
||
clocks and measuring rods do not appear this way because of the
|
||
Lorentz distortions that are introduced by its own velocity relative
|
||
to them. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">Though
|
||
when taken as a description of material objects, the special theory
|
||
of relativity is incompatible with the existence of absolute space,
|
||
Einstein did not attempt to use its implications to show that
|
||
absolute space does not exist. He was making a mathematical argument
|
||
to show that accepted theories in Newtonian physics, which did assume
|
||
the existence of absolute space, could all be replaced by theories
|
||
that do not mention absolute rest or motion at all.</span></font></font><font color="#000000"><sup><font face="Times New Roman, serif"><span lang="en-US"><a class="sdfootnoteanc" name="sdfootnote6anc" href="#sdfootnote6sym"><sup>6</sup></a></span></font></sup></font><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
|
||
All he explicitly claimed was that physics does not require an
|
||
“absolutely stationary space” and that the notion of a
|
||
“‘luminiferous ether’ will prove to be superfluous” because
|
||
the “phenomena of electrodynamics as well as of mechanics possess
|
||
no properties corresponding to the ideas of absolute rest”
|
||
(</span></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/"><font color="#0000ff"><font face="Times New Roman, serif"><span lang="en-US"><u>Einstein</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">,
|
||
1923 p. 37). It could be argued, therefore, that Einstein was merely
|
||
imitating empiricist skepticism about theoretical entities generally
|
||
by casting doubt on the reality of absolute space. </span></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">As it
|
||
turned out, Einstein's theory proved to be remarkably successful in
|
||
making surprising predictions of new experiments. For example,
|
||
unstable particles have longer half-lives when moving at velocities
|
||
approaching that of light. Clocks flown around the earth are indeed
|
||
slowed down compared to clocks that stayed at home. The most famous
|
||
new prediction of special relativity, <i>E = mc</i><sup><i>2</i></sup>,
|
||
has been confirmed repeatedly. It is a consequence of the
|
||
relativistic increase in mass, which Einstein first pointed out, and
|
||
without it, high energy physics as we know it today would be
|
||
inconceivable. Finally, the equations of special relativity have
|
||
become (after Dirac) the foundation of quantum field theory as well
|
||
as Einstein’s theory of gravitation. The Lorentz transformation is
|
||
now so basic to physics that “covariance” (or “Lorentz
|
||
covariance”) is taken as a constraint on all possible laws of
|
||
physics. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">To be sure,
|
||
Newtonian physicists complained about the loss of intuitive
|
||
understanding that came with the acceptance of Einstein's way of
|
||
explaining these phenomena. It was no longer possible to construct in
|
||
ordinary spatial imagination a picture of the nature of the world.
|
||
But that objection did not detract from the predictive success of
|
||
Einstein's theory, and the Einsteinian revolution made the capacity
|
||
of mathematical arguments to make surprising predictions of precise
|
||
measurements the establishment criterion for accepting theories in
|
||
contemporary physics. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">But
|
||
physics is not just mathematics. A theory in physics is generally
|
||
thought to be true when it corresponds to what exists, and if the
|
||
special theory of relativity does not correspond to material objects
|
||
in absolute space, we want to know what it does correspond to. The
|
||
success in making surprising predictions of what happens by which
|
||
Einstein's theory has been confirmed means that it corresponds to
|
||
regularities that hold of change in the world, but it is natural to
|
||
want to know the nature of what exists that makes those regularities
|
||
true. The answer given by contemporary physics is spacetime, and it
|
||
was Minkowski that has made that answer possible.</font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><font face="Verdana, sans-serif">M<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADoAAAAQCAMAAABwUpxKAAAARVBMVEUAAAAcGBMzAAAqJR04MSZJAABGPjBmAAB2AAB+AABjV0NxY01/cFeOfGGciWqqlXS4on7HrojVu5Hjx5v8A/sAAAD///+jfPvlAAAAFXRSTlP//////////////////////////wAr2X3qAAAAvUlEQVR4nMWT3Q7CIAyFmVR0hVHoef93tWyySNyN82INNOXno6cE3Px83G+nzM3utP2H4sDK0SRQtUc7Kq5aB7iv0DEapXkeUGawbV+sSdSGarI4Kaogqy1oirWhqQ0+0RhyojUZpRzMKxXEmNe5yY5DyCKG8rJJ2spdUZn0jW4tyB6WxC2bb1lDxBdqFzOgCylChQdSqK0WhZDpMDEd7YKBEUXxWohMXvFoJbC3QRT1ZUR/tyvRK97w6U/3AqBKI3Ll7P5GAAAAAElFTkSuQmCC" name="TtsOtkCLStr_07" align="right" hspace="5" width="125" height="34" border="0">inkowski.
|
||
</font>In 1908, Minkowski offered a mathematically elegant way of
|
||
representing what is true from all inertial frames, according to
|
||
Einstein’s special theory of relativity, using only the coordinates
|
||
of any single inertial frame.<sup><a class="sdfootnoteanc" name="sdfootnote7anc" href="#sdfootnote7sym"><sup>7</sup></a></sup>
|
||
His was a “graphic method” which he said allows us to “visualize”
|
||
what is going on. The key to his diagram was to represent time in the
|
||
same way as space, and that is what has led to the belief that what
|
||
exists is not space and time, but rather spacetime. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">In
|
||
Minkowski’s “spacetime diagrams”, time is represented as a
|
||
fourth dimension perpendicular to the three dimensions of space
|
||
(though when comparing two inertial frames, the spatial dimensions
|
||
can be reduced to one by a suitable orientation of their coordinate
|
||
frames). A material object at rest in space is represented,
|
||
therefore, as a line running parallel to the time axis, and a
|
||
material object with a constant, non-zero velocity is represented by
|
||
a line inclined slightly in the direction of motion. Units for
|
||
measuring time and space are usually chosen so that the path of light
|
||
in spacetime (the “light-line”, <i>t = x/c</i>) bisects the time
|
||
and space axes, making the “basic unit” of distance how far light
|
||
travels in a unit of time. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Since the
|
||
second frame of reference is based on a moving object, we can think
|
||
of the tilted line representing its pathway as its time axis. From
|
||
such a moving reference frame, the location of an object at rest in
|
||
the first frame (such as one always located at its origin) would
|
||
change relative to the moving frame. So far, this diagram of space
|
||
and time would be acceptable in classical Newtonian physics, because
|
||
it represents a so-called Galilean transformation for the coordinates
|
||
of moving reference frames (in which distances in space would be
|
||
related as <i>x' = x – VT</i>, where <i>v</i> is their relative
|
||
velocity in the <i>x</i>-direction.) </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">What
|
||
Minkowski discovered was that the Lorentz transformation for moving
|
||
reference frames could be represented by tilting the space line of
|
||
the moving frame equally in the opposite direction and lengthening
|
||
the units of time and space. That is, the time-line and the
|
||
space-line of the moving frame are inclined symmetrically around the
|
||
pathway of light. (See the comparison of the Newtonian Diagram of
|
||
Space and Time and Minkowski's Spacetime Diagra</font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; text-indent: -2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><img 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" name="SpacetimeDgm" align="bottom" width="637" height="350" border="0"></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">In either
|
||
the Newtonian or Minkowski's diagram, every point represents the
|
||
location of a possible <i>event </i>in space and time (called a
|
||
“world-point”), and superimposing a second reference frame makes
|
||
it possible to give such coordinates in either reference frame. From
|
||
the coordinates for any event in the first reference frame, we can
|
||
simply read off the coordinates for the same event in the moving
|
||
reference frame, and <i>vice versa</i>. In the case of event <i>E</i>,
|
||
for example, the coordinates in the first frame are <i>(2,1)</i>, and
|
||
in Minkowski's diagram, they are <i>(1.3,0.3)</i>. All possible
|
||
reference frames can be represented in this way, each with a
|
||
different tilt to its time-axis representing its velocity relative to
|
||
the first. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">The two
|
||
reference frames in the Newtonian diagram have a very simple
|
||
relationship, because time coordinates are the same for both
|
||
reference frames and there is no change in the units of either time
|
||
or space. But Minkowski's spacetime diagram represents the Lorentz
|
||
transformation, and not only are the units of time and space
|
||
different, but the space-line of the moving reference frame is
|
||
inclined relative to the first reference frame. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Minkowski’s
|
||
spacetime diagram yields the same coordinates for the second
|
||
reference frame that are obtained from the Lorentz transformation
|
||
equations deduced by Einstein. Thus, it predicts that measurements of
|
||
the second inertial frame will reveal its clocks to be slowed down
|
||
and its measuring rods to be contracted in the x-direction. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">But since
|
||
the Lorentz transformation works both ways, it is possible to start
|
||
with the second (tilted) reference frame and obtain coordinates for
|
||
events in the first reference frame. Thus, it predicts that the
|
||
moving observers will detect Lorentz distortions occurring in the
|
||
first frame. This symmetry about the relationship between inertial
|
||
reference frames makes it impossible to single out any particular
|
||
frame as being at absolute rest by comparing reference frames with
|
||
one another. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Minkowski's
|
||
spacetime diagram may seem to mitigate the paradoxes resulting from
|
||
the symmetry of the relationship between members of any pair of
|
||
inertial reference frames, because it enables us to "picture"
|
||
two clocks both ticking away slower than the other and two measuring
|
||
rods both shorter than the other. It is just a result of how the
|
||
inertial reference frames are related to one another. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">But this
|
||
wonderful power of Minkowski's spacetime diagram to represent these
|
||
puzzling phenomena would not be possible, if the space-lines of
|
||
different reference frames had the same slope. The inclined
|
||
orientation of the space-line of the second inertial frame relative
|
||
to the first frame is crucial to representing the Lorentz
|
||
transformation, and it represents a disagreement between inertial
|
||
observers about simultaneity at a distance. That is, observers using
|
||
different inertial reference frames will disagree about which events
|
||
at a distance are simultaneous with the origins of their systems when
|
||
they pass by one another. That is the source of all the ontological
|
||
problems with the belief in spacetime. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Though
|
||
it is possible to interpret Minkowski's spacetime diagram as just a
|
||
useful mathematical device for predicting the measurements that would
|
||
be made on different inertial frames, that is what the Lorentz
|
||
transformation equations already do. The historical significance of
|
||
Minkowski's diagram is that it enables us to "picture" what
|
||
exists in a world where Einstein's special theory of relativity is
|
||
the deepest truth about the world. Thus, it leads to the belief in
|
||
spacetime (that is, "spatiotemporalism," as I called it in
|
||
<font face="Arial, sans-serif">Spatiomaterialism</font>, or
|
||
"substantivalism about spacetime," as it is called in the
|
||
literature.)</font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
|
||
belief in spacetime comes from realism about special relativity.
|
||
Scientific realism holds that theories in physics are true in the
|
||
sense of corresponding to what exists, and spacetime is what must
|
||
exist, if Einstein's special theory of relativity is the deepest
|
||
truth about the real nature of what exists as far as space and time
|
||
are concerned. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">With regard
|
||
to space and time, Newtonian realists would say that what their
|
||
theories correspond to is absolute space and absolute time, that is,
|
||
to a three dimensional space all of whose parts exists at the present
|
||
moment and endure simultaneously through time. But that is not what
|
||
Einstein's special theory of relativity corresponds to, because it
|
||
implies that observers on all possible inertial reference frames are
|
||
equally correct about the times and places of the events that occur
|
||
in the world, even though they disagree about the simultaneity of
|
||
events at a distance. What all the different inertial observers say
|
||
about the times and places of events can, however, be true at the
|
||
same time, only if what exists is represented by Minkowski's
|
||
spacetime diagram. Thus, spacetime is the natural answer to the
|
||
question about what corresponds to Einstein's special theory of
|
||
relativity. According to realists about special relativity, what
|
||
exists is spacetime, a four-dimensional entity that contains time as
|
||
a dimension and, thus, is not itself in time. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">Though
|
||
Einstein may merely have been arguing in the spirit of the empiricist
|
||
skepticism that prevailed in philosophy at that time, Minkowski made
|
||
it possible to give a realist interpretation of Einstein’s special
|
||
theory. His spacetime diagram showed how Einstein's theory could be
|
||
interpreted as a description of what really exists in the case of
|
||
space and time. Minkowski must have realized that he was giving a
|
||
realist interpretation of Einstein's special theory of relativity
|
||
when he introduced his spacetime diagrams; he said (</span></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Minkowski23"><font color="#0000ff"><font face="Times New Roman, serif"><span lang="en-US"><u>Minkowski</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
|
||
75) that “space by itself, and time by itself, are doomed to fade
|
||
away into mere shadows, and only a kind of union of the two will
|
||
preserve an independent reality”. In any case, later in the
|
||
twentieth century, when logical positivism gave way to scientific
|
||
realism, Einstein’s skepticism about absolute space, if that is
|
||
what it was, spawned the belief in the existence of spacetime.
|
||
Indeed, regardless what Einstein may have believed in 1905, he
|
||
apparently came to agree that what he had discovered was spacetime.
|
||
(See </span></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/Putnama.html"><font color="#0000ff"><font face="Times New Roman, serif"><span lang="en-US"><u>Einstein</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
|
||
1966, pp. 205-8). </span></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Scientific
|
||
realism is, however, a way of letting science determine one's
|
||
ontology. That is not the best way to decide which ontological theory
|
||
to accept, because the empirical method that science follows is to
|
||
infer to the best efficient-cause explanation, and that may not be
|
||
the best ontological-cause explanation. But we can see how realism
|
||
led to an ontology based on spacetime. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Einstein's
|
||
special theory of relativity was a better efficient-cause explanation
|
||
of the relevant phenomena than Lorentz's way of defending his
|
||
transformation equations, because it made all the same precise
|
||
predictions of measurements, but in a mathematically simpler way. As
|
||
an efficient-cause explanation, however, all that Einstein's special
|
||
theory requires is an <i>empirical equivalence</i> of inertial
|
||
reference frames. It assumes that inertial frames are experimentally
|
||
indistinguishable from one another, and it derives a description
|
||
about how they must appear to one another as parts of the same world
|
||
(where Maxwell's laws of electromagnetism hold). That relationship is
|
||
described by the Lorentz equations for transforming their coordinates
|
||
into one another, and it is represented by Minkowski's spacetime
|
||
diagram. But Einstein's was a mathematical argument, and no mechanism
|
||
or cause of the empirical equivalence was given. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">A realist
|
||
interpretation of special relativity goes beyond mere <i>empirical
|
||
equivalence </i>and holds that inertial frames are all <i>ontologically
|
||
equivalent</i>. If special relativity is the literal and deepest
|
||
truth about the world, then what observers on all possible inertial
|
||
reference frames believe must be true at the same time. That is to
|
||
hold, not merely that no experiment can distinguish any one inertial
|
||
frame from all the others as the absolute frame, but that there is
|
||
nothing about the nature of any inertial frame that makes it stand
|
||
out from all the others. That means, among other things, that no
|
||
assertion made by observers on one inertial frame can be true unless
|
||
the same kind of assertion made by observers on every other inertial
|
||
frame is also true. (Nor can any assertion made on one inertial frame
|
||
be false unless the same kind of assertion made on every other
|
||
inertial frame is also false.) </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">The virtue
|
||
of Minkowski's spacetime diagram is that it enables us to "picture"
|
||
what exists in a world where inertial reference frames are all
|
||
<i>ontologically equivalent</i>. Though it may still be unclear what
|
||
spacetime is, Minkowski's diagram does allow us to believe that all
|
||
possible reference frames are related to what exists in the same way,
|
||
for it accommodates all possible standards of simultaneity at a
|
||
distance. But they can all correspond to what exists only if the
|
||
world is a four-dimensional entity all of whose parts in both space
|
||
and time exist in the same way. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">It is clear
|
||
that this <i>ontological equivalence </i>of inertial frames is
|
||
incompatible with absolute space and time, because if space and time
|
||
were absolute, one inertial frame would be singled out ontologically
|
||
from all possible inertial frames. Only one of all possible inertial
|
||
frames would have the correct standard of simultaneity. Its location
|
||
in space and time could be shared by observers on many other inertial
|
||
frames, but none of their claims about which distant events are
|
||
simultaneous with their shared here and how would correspond to what
|
||
exists. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Einsteinians
|
||
do not use the term "ontological equivalence" to describe
|
||
the relationship between different inertial reference frames, but
|
||
that is what the belief in spacetime comes to. Most philosophers of
|
||
space and time simply take it for granted that they must accept
|
||
"substantivalism" about spacetime in order to interpret the
|
||
special theory as a description of the real nature of what exists. <sup><a class="sdfootnoteanc" name="sdfootnote8anc" href="#sdfootnote8sym"><sup>8</sup></a></sup></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">To
|
||
believe in spacetime is to accept an ontology that is fundamentally
|
||
different from Lorentz's Newtonian view, and the difference can be
|
||
seen in what each implies about the nature of material objects. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Newtonian
|
||
physicists assumed that material objects are substances that endure
|
||
through time. They had to believe in absolute time, because the
|
||
endurance theory of substances presupposes that only the present
|
||
exists, or "presentism." (If the world is everything that
|
||
exists, then objects that exist at only one moment in their histories
|
||
must exist at the same time, for otherwise they would not be parts of
|
||
the same world.) And since Newtonian physicists believed that
|
||
material objects are all related to one another by (consistent)
|
||
spatial relations, they were also forced to believe in absolute
|
||
space. In a natural world, absolute time entails absolute space.
|
||
Hence, the Newtonian world was made up of material objects in three
|
||
dimensional space that endured through time. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Spacetime,
|
||
on the other hand, is a four-dimensional entity. What exists is
|
||
spacetime and all the events that are located in spacetime. Since
|
||
time is an aspect of its essential structure, a spacetime world
|
||
cannot endure through time. Thus, spacetime points and spacetime
|
||
events must all exist in the same way independently of one another,
|
||
if they exist at all. There are no material objects in a spacetime
|
||
world, at least, not in the way that Lorentz believed. There are only
|
||
the spacetime events that seem to make up the histories of so-called
|
||
material objects. Thus, what is ordinarily called a "material
|
||
object" is just a continuous series of spacetime events in
|
||
spacetime. Its real nature is represented accurately by a “world
|
||
line” in a spacetime diagram, because each spacetime event making
|
||
up the history of a "material object" has an existence that
|
||
is distinct from all the others, just as one point on a line exists
|
||
distinctly from every other point on the line. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">In short,
|
||
whereas a material object in a Newtonian world exists only at each
|
||
moment as it is present, but is identical across time, a so-called
|
||
material object in a spacetime world is a continuous series of
|
||
spacetime events, each of which exists eternally as a distinct part
|
||
of the world. This is the difference between the endurance and
|
||
perdurance theory of substances, and between the presentist and
|
||
eternalist theory about time and existence. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Scientific
|
||
realists sometimes assume that they can believe that Einstein's
|
||
special theory of relativity corresponds to what exists without
|
||
denying that they are themselves substances that endure through time
|
||
by holding that only objects at a distance from themselves must exist
|
||
the same way at all different moments in their histories. But that is
|
||
not possible, if they believe that the truth of Einstein's special
|
||
theory means that it corresponds to what exists for every observer.
|
||
If Einstein's theory is universally true, then it must be true for
|
||
inertial observers located elsewhere in the universe, and the only
|
||
way that different inertial observes at a distance from us can all be
|
||
correct about which moment in our local history is simultaneous with
|
||
their passing by one another is if the moments in our local history
|
||
all exist in the same way. We must perdure, rather than endure,
|
||
because we are material objects at a distance for inertial observers
|
||
elsewhere in the universe. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">What
|
||
Minkowski's “union” of space and time means ontologically is,
|
||
therefore, that presentism is false. The denial of presentism is such
|
||
a serious obstacle to an ontological explanation of the world that,
|
||
in <font face="Arial, sans-serif">Spatiomaterialism</font>, we were
|
||
led to reject spacetime substantivalism (or "spatiotemporalism"),
|
||
promising to justify it later by showing how it is possible for space
|
||
and time to be absolute, despite the Einsteinian revolution. That is
|
||
the argument we take up in the next section. But first, let us
|
||
consider briefly why physics has ignored the ontological problems
|
||
with eternalism. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">What
|
||
explains the ascendancy of the belief in spacetime is, once again,
|
||
the empirical method of science and the physicists' addiction to
|
||
mathematics as a means of practicing it. Behind Minkowski's spacetime
|
||
diagram lies an elegant equation that has proved to be irresistibly
|
||
attractive. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Minkowski
|
||
provided a method of constructing in our own spacetime coordinate
|
||
frame the spacetime coordinate frame that would be used by observers
|
||
on an object moving relative to us. We may call their world-line the
|
||
“moving timeline” (<i>t = x/v</i>), because it will be the time
|
||
axis that moving observers use for their spacetime coordinate frame. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><img 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" name="Minkowski" align="bottom" width="420" height="330" border="0"></font></p>
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<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Minkowski
|
||
formulated the conclusion of Einstein’s special theory as an
|
||
equation that describes a hyperboloid in four dimensional spacetime:
|
||
<i>1</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup> <i>= c</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup><i>t</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup>
|
||
<i>- x</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup>
|
||
<i>- y</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup>
|
||
<i>- z</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup><font face="Uncial, Times New Roman, serif"><font size="1" style="font-size: 8pt"><i>.
|
||
</i></font></font>(When we orient our x-axis in the direction of the
|
||
others’ motion, we can ignore the other two dimensions and it
|
||
reduces to <i>1</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup>
|
||
<i>= c</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup><i>t</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup>
|
||
<i>- x</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup>.)
|
||
(It is the red curve in the diagram depicting how Minkowski's
|
||
spacetime diagram is constructed.) The intersection of Minkowski’s
|
||
hyperboloid curve with our time-axis is the unit of time in our frame
|
||
(<i>t = 1</i>), and the unit of distance (in “basic units”) is
|
||
the distance in our frame that light travels during that period of
|
||
time (<i>x = 1</i>). The moving timeline (the time-axis of the moving
|
||
spacetime frame) also intersects the curve described by Minkowski’s
|
||
equation, and the distance of that point along our time-axis is the
|
||
length of a unit of time on the moving coordinate frame according to
|
||
our clocks. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">As the
|
||
diagram shows, moving clocks are slowed down in our frame. The other
|
||
axis of the moving spacetime frame, the “moving space-line”, is
|
||
also deduced from Minkowski’s equation. Moving space-lines all have
|
||
the same slope as the tangent to Minkowski’s curve at the point of
|
||
the moving timeline’s intersection with his curve. (Its slope is
|
||
<i>v/c</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup>;
|
||
the points on any line with this slope are simultaneous in the moving
|
||
spacetime frame.) Finally, the unit of distance on the moving
|
||
space-line is how far light travels in the moving frame during a unit
|
||
of time on the moving frame. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Inertial
|
||
frames are all equivalent on Minkowski’s theory, as on Einstein’s,
|
||
since Minkowski’s equation determines precisely the same hyperbola
|
||
in every moving inertial frame constructed this way in our own
|
||
spacetime coordinate frame. That is, their hyperbolas all coincide.
|
||
In particular, the same procedure <i>on the moving coordinate </i>frame,
|
||
using the same equation (and taking the velocity to be <i>-v</i>
|
||
along the x'-axis), produces the original coordinate frame. Or more
|
||
abstractly, Minkowski’s equation can be generalized as a measure,
|
||
<i>s</i>, of the separation between any two events that is the same
|
||
in every inertial frame, despite variations in their coordinates for
|
||
particular events: <i>s</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup>
|
||
<i>= c</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup><i>t</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup>
|
||
<i>- x</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup>
|
||
<i>- y</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup>
|
||
<i>- z</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup>.
|
||
</font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">In
|
||
Minkowski’s equation, the parallel between the representation of
|
||
space and time is remarkable. Time would be just another spatial
|
||
dimension, except that it lacks a minus sign (and needs the velocity
|
||
of light, <i>c</i>, to make units of time commensurable with
|
||
distance). Indeed, that is how Minkowski includes relativistic mass
|
||
increase. His equations’s form can be used to state the <i>laws of
|
||
nature </i>that hold true in every inertial frame. In “four vector
|
||
physics”, or “covariant” formulations of laws of physics, the
|
||
energy of an object, <i>E</i>, takes the place of time and the three
|
||
dimensions of momentum, <i>p</i>, take the place of the three spatial
|
||
dimensions, so that the objects’ rest mass, <i>m</i><sub><i>0</i></sub>,
|
||
rather than the separation, is what is the same about the object in
|
||
all inertial frames: <i>m</i><sub><font size="1" style="font-size: 8pt"><i>o</i></font></sub><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup><i>c</i><sup><font size="1" style="font-size: 8pt"><i>4 </i></font></sup><i>= E</i><sup><font size="1" style="font-size: 8pt"><i>2 </i></font></sup><i>- p</i><sub><font size="1" style="font-size: 8pt"><i>x</i></font></sub><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup><i>c</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup>
|
||
<i>- p</i><sub><font size="1" style="font-size: 8pt"><i>y</i></font></sub><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup><i>c</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup>
|
||
<i>- p</i><sub><font size="1" style="font-size: 8pt"><i>z</i></font></sub><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup><i>c</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup>.
|
||
The mathematics of four vector physics is so elegant and suggestive
|
||
about the relationship of energy and momentum that it is not
|
||
surprising that physicists now find themselves committed to the
|
||
belief in spacetime. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">By
|
||
comparison with Lorentz’s ad hoc attempts to patch up classical
|
||
physics in the wake of the Michelson-Morley experiment, Einstein’s
|
||
argument was astonishingly simple and elegant, making it seem that
|
||
Einstein had a deeper insight into these phenomena. And since
|
||
Minkowski provided a diagram that made it possible to represent what
|
||
special relativity implies about the world independently of
|
||
particular reference frames, it is hardly surprising that the belief
|
||
in spacetime has become the orthodox ontology in physics and the
|
||
philosophy of science. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
|
||
acceptance of Einstein’s special theory of relativity involved,
|
||
however, a remarkable change in the empirical method of physics, for
|
||
it involved the abandonment of the requirement that explanations in
|
||
physics be intuitively intelligible. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">To follow
|
||
the empirical method is to infer to the best efficient-cause
|
||
explanation. Even in classical physics, theories were highly
|
||
mathematical and confirmation was most convincing when they predicted
|
||
surprising, quantitatively precise measurements. But since classical
|
||
physicists still believed in absolute space and time, they also
|
||
expected the best scientific theories to be intuitively intelligible,
|
||
in the sense that it was possible to think coherently about what was
|
||
happening in spatial imagination. But intuitive intelligibility was
|
||
no longer possible when the best scientific theory required giving up
|
||
the belief in absolute space and time. That was undeniably a loss,
|
||
but physicists felt that they had to grow up and recognize that their
|
||
deepest commitment was to judging the best theory by which is the
|
||
simplest and most complete prediction of measurements. Since this
|
||
came from mathematical theories, abandoning the requirement that
|
||
physical explanations be intuitively intelligible left them addicted
|
||
to mathematics. </font></font>
|
||
</p>
|
||
<div id="sdfootnote1">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm; margin-bottom: 0.25cm">
|
||
<a class="sdfootnotesym" name="sdfootnote1sym" href="#sdfootnote1anc">1</a>
|
||
This is because the velocity of light relative to the object in
|
||
motion is different in opposite directions, and going one way the
|
||
whole distance at the lower (relative) velocity takes more extra
|
||
time than it can make up coming back over the same distance at the
|
||
higher (relative) velocity. Though the path back and forth is
|
||
spatially symmetric, the effect of the velocity of light relative to
|
||
the frame on the time of travel accumulates per unit time, and so
|
||
the signal loses more time than it gains.</p>
|
||
</div>
|
||
<div id="sdfootnote2">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm; margin-bottom: 0.25cm">
|
||
<a class="sdfootnotesym" name="sdfootnote2sym" href="#sdfootnote2anc">2</a><span lang="en-US">
|
||
The equation was </span><span lang="en-US"><i>L=L</i></span><sub><span lang="en-US"><i>o<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC4AAAASCAMAAAAT3xzTAAADAFBMVEUAAAABAQECAgIDAwMEBAQFBQUGBgYHBwcICAgJCQkKCgoLCwsMDAwNDQ0ODg4PDw8QEBARERESEhITExMUFBQVFRUWFhYXFxcYGBgZGRkaGhobGxscHBwdHR0eHh4fHx8gICAhISEiIiIjIyMkJCQlJSUmJiYnJycoKCgpKSkqKiorKyssLCwtLS0uLi4vLy8wMDAxMTEyMjIzMzM0NDQ1NTU2NjY3Nzc4ODg5OTk6Ojo7Ozs8PDw9PT0+Pj4/Pz9AQEBBQUFCQkJDQ0NERERFRUVGRkZHR0dISEhJSUlKSkpLS0tMTExNTU1OTk5PT09QUFBRUVFSUlJTU1NUVFRVVVVWVlZXV1dYWFhZWVlaWlpbW1tcXFxdXV1eXl5fX19gYGBhYWFiYmJjY2NkZGRlZWVmZmZnZ2doaGhpaWlqampra2tsbGxtbW1ubm5vb29wcHBxcXFycnJzc3N0dHR1dXV2dnZ3d3d4eHh5eXl6enp7e3t8fHx9fX1+fn5/f3+AgICBgYGCgoKDg4OEhISFhYWGhoaHh4eIiIiJiYmKioqLi4uMjIyNjY2Ojo6Pj4+QkJCRkZGSkpKTk5OUlJSVlZWWlpaXl5eYmJiZmZmampqbm5ucnJydnZ2enp6fn5+goKChoaGioqKjo6OkpKSlpaWmpqanp6eoqKipqamqqqqrq6usrKytra2urq6vr6+wsLCxsbGysrKzs7O0tLS1tbW2tra3t7e4uLi5ubm6urq7u7u8vLy9vb2+vr6/v7/AwMDBwcHCwsLDw8PExMTFxcXGxsbHx8fIyMjJycnKysrLy8vMzMzNzc3Ozs7Pz8/Q0NDR0dHS0tLT09PU1NTV1dXW1tbX19fY2NjZ2dna2trb29vc3Nzd3d3e3t7f39/g4ODh4eHi4uLj4+Pk5OTl5eXm5ubn5+fo6Ojp6enq6urr6+vs7Ozt7e3u7u7v7+/w8PDx8fHy8vLz8/P09PT19fX29vb39/f4+Pj5+fn6+vr7+/v8/Pz9/f3+/v7////isF19AAAAvUlEQVR4nJWRvRHDIAyFVbKDmwxAxwYZIwNoCdcMwQJZghUomYE1FH6EwRhythrd0/t44gDoUUHtd8o2/FG6XeN2gmO4YAF0ahJZbR2ulpthpmJTONA+9Lj3Z1zrATcJkJLVlwbcNPBFG+GO1VfAinF/TneC6tnkC0LXZNypt4znv/jkKW818S7GHTnJgGL2d4f6UvEjOfFINwU3sg/hEknAO/QG7Ks/xdHIOKxw8OOgbFvh0wG4K3nz/P/6AWEGw/I19lI/AAAAAElFTkSuQmCC" name="StrEqBeta" align="bottom" width="46" height="18" border="0"></i></span></sub><span lang="en-US">,
|
||
where </span><span lang="en-US"><i>L</i></span><sub><span lang="en-US"><i>o</i></span></sub><span lang="en-US">
|
||
was the length at absolute rest. The shrinkage had been proposed
|
||
independently by George F. Fitzgerald in 1889 and hence became known
|
||
as the “Lorentz-Fitzgerald contraction”. Relevant portions of
|
||
Lorentz’s 1985 monograph and 1904 theory are reprinted in </span><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Lorentza"><font color="#0000ff"><span lang="en-US"><u>Lorentz</u></span></font></a><span lang="en-US">,
|
||
</span><span lang="en-US"><i>et al</i></span><span lang="en-US">,
|
||
(1923, pp. 3-84).</span></p>
|
||
</div>
|
||
<div id="sdfootnote3">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm; margin-bottom: 0.25cm">
|
||
<a class="sdfootnotesym" name="sdfootnote3sym" href="#sdfootnote3anc">3</a><span lang="en-US">
|
||
See Stanley </span><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Goldbergc"><font color="#0000ff"><span lang="en-US"><u>Goldberg</u></span></font></a><span lang="en-US">
|
||
(1984, p. 98) and Roberto </span><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Torettic"><font color="#0000ff"><span lang="en-US"><u>Torretti</u></span></font></a><span lang="en-US">
|
||
(1983, pp. 45-6). Hereafter, these works are referred to as
|
||
“Goldberg” or “Torretti”, with page numbers. “Holton”
|
||
refers to </span><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Goldbergc"><font color="#0000ff"><span lang="en-US"><u>Holton</u></span></font></a><span lang="en-US">
|
||
(1973). “Zahar” refers to </span><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Goldbergc"><font color="#0000ff"><span lang="en-US"><u>Zahar</u></span></font></a><span lang="en-US">
|
||
(1989). </span>
|
||
</p>
|
||
</div>
|
||
<div id="sdfootnote4">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm; margin-bottom: 0.25cm">
|
||
<a class="sdfootnotesym" name="sdfootnote4sym" href="#sdfootnote4anc">4</a><span lang="en-US">
|
||
The discovery of the Lorentz distortions was complicated by the fact
|
||
that there are other effects of absolute motion on material objects,
|
||
besides those that are directly related to the Michelson-Morley
|
||
experiment. These are the “first-order” effects of motion in
|
||
space (which vary as </span><span lang="en-US"><i>v/c</i></span><span lang="en-US">,
|
||
rather than as </span><span lang="en-US"><i>v</i></span><sup><font size="1" style="font-size: 8pt"><span lang="en-US"><i>2</i></span></font></sup><span lang="en-US"><i>/c</i></span><sup><font size="1" style="font-size: 8pt"><span lang="en-US"><i>2</i></span></font></sup><span lang="en-US">,
|
||
or “second order” effects), such as the way telescopes must be
|
||
inclined slightly in the direction of motion in order to intercept
|
||
light from overhead stars (much as umbrellas must be inclined
|
||
slightly forward in walking through rain to keep raindrops from
|
||
hitting one’s body). First order effects (including the effects on
|
||
the index of refraction) had previously been explained by the “ether
|
||
drag” hypothesis (that the motion of material objects drags the
|
||
ether along with them), but Lorentz abandoned it . Lorentz’s
|
||
explanation of length contraction assumed that the ether is totally
|
||
unaffected by the motion of material objects through it, and he had
|
||
no explanation of such first order effects except to state
|
||
transformation equations by which one could obtain the coordinates
|
||
used on the moving object from those used at absolute rest.
|
||
</span><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Goldberc"><font color="#0000ff"><span lang="en-US"><u>Goldberg</u></span></font></a><span lang="en-US">,
|
||
pp. 88-92; </span><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Goldbergc"><font color="#0000ff"><span lang="en-US"><u>Torretti</u></span></font></a><span lang="en-US">,
|
||
pp. 41-45</span></p>
|
||
</div>
|
||
<div id="sdfootnote5">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm; margin-bottom: 0.25cm">
|
||
<a class="sdfootnotesym" name="sdfootnote5sym" href="#sdfootnote5anc">5</a><span lang="en-US">
|
||
</span><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Goldbergc"><font color="#0000ff"><span lang="en-US"><u>Zahar</u></span></font></a><span lang="en-US">
|
||
(1989), p. 99; </span><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Goldbergc"><font color="#0000ff"><span lang="en-US"><u>Holton</u></span></font></a><span lang="en-US">
|
||
(1973, pp. 175-178).</span></p>
|
||
</div>
|
||
<div id="sdfootnote6">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm; margin-bottom: 0.25cm">
|
||
<a class="sdfootnotesym" name="sdfootnote6sym" href="#sdfootnote6anc">6</a><span lang="en-US">
|
||
</span><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Goldbergc"><font color="#0000ff"><span lang="en-US"><u>Prokhovnik</u></span></font></a><span lang="en-US">
|
||
(1985, Appendix 2) argues that in the original formulation of his
|
||
argument, Einstein was actually assuming the existence of a
|
||
stationary coordinate frame.</span></p>
|
||
</div>
|
||
<div id="sdfootnote7">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm; margin-bottom: 0.25cm">
|
||
<a class="sdfootnotesym" name="sdfootnote7sym" href="#sdfootnote7anc">7</a><span lang="en-US">
|
||
H. </span><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Goldbergc"><font color="#0000ff"><span lang="en-US"><u>Minkowski</u></span></font></a><span lang="en-US">,
|
||
“Space and Time”, reprinted in Lorentz, </span><span lang="en-US"><i>et
|
||
al,</i></span><span lang="en-US"> </span><span lang="en-US"><i>The
|
||
Principle of Relativity</i></span><span lang="en-US">, pp. 75-91. </span>
|
||
</p>
|
||
</div>
|
||
<div id="sdfootnote8">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm; margin-bottom: 0.25cm">
|
||
<a class="sdfootnotesym" name="sdfootnote8sym" href="#sdfootnote8anc">8</a><sup><span lang="en-US">
|
||
</span></sup><span lang="en-US">See, for example, M. </span><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Putnama"><font color="#0000ff"><span lang="en-US"><u>Friedman</u></span></font></a><span lang="en-US">
|
||
(1983), J. </span><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Putnama"><font color="#0000ff"><span lang="en-US"><u>Earman</u></span></font></a><span lang="en-US">
|
||
(1989), and </span><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Putnama"><font color="#0000ff"><span lang="en-US"><u>J.
|
||
R. Lucas and P. E. Hodgson</u></span></font></a><span lang="en-US">
|
||
(1990). </span>
|
||
</p>
|
||
</div>
|
||
</body>
|
||
</html> |