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634 lines
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<title>What forced us to promise to explain how Einstein's special and general theories of relativity could be true in a world where </title>
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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">What
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forced us to promise to explain how Einstein's special and general
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theories of relativity could be true in a world where space and time
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are absolute was the commitment of contemporary physics to the belief
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in spacetime. We had to take out that "mortgage" on
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spatiomaterialism as the foundation for ontological philosophy,
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because spatiomaterialism is committed to absolute space and time.
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This section will pay it off by showing how how the special theory of
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relativity can be true in a spatiomaterial world.</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">Let
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us recall, first, our reason for believing that space and time are
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absolute. We were inferring to the best ontological explanation of
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the world. That is not the method of empirical science, because an
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ontological theory is a theory about the nature of what exists, not
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only about what happens to it. The first basic issue about the nature
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of what exists has to do with the nature of time, and we concluded
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that we had to prefer presentism to eternalism because it alone could
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explain our observations about how the present moment is different
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from the past and future. Presentism holds that only the present
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exists. The past and the future do not exist. <i>To be is to be in
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time.</i> </font></font></font>
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</p>
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<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">
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<font color="#000000"><font face="Times New Roman, serif">We know by
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reflecting on ourselves as agents that the future does not exist,
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because if it did, we would not be able to control what happens in
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the world. We act as we do in order to make the future different from
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what it would be otherwise, and that would simply not be possible, if
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the future already existed. Every event must aleady be determined, if
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eternalism is true, </font></font>
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</p>
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<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">
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<font color="#000000"><font face="Times New Roman, serif">Reflection
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should be considered relevant evidence about the nature of what
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exists in the world, since the beings who do the reflecting are
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clear;y parts of that world. But contemporary physicists cannot
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escape this empirical falisfication of the belief in spacetime. There
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is also plenty of evidence for those who insist that only peception
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can supply the empirical data for choosing among theories. It is
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found in our perception of change. To perceive change, for example,
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to see a book falling from a shelf, is the recognize that certain
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spatial relations are going out of existence and other spatial
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relations are comming into existence. Defined as properties coming
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into existence and going out of existence, change might be called
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"presentist change," in order to distinguish it from
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"eternalist change," or change defined merely as objects
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having different properties or relations at different times. Anyone
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who perceives presentist change has plenty of observational evidence
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that only the present exists because properties (and spatial
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relations) cannot go out of existence, if the past still exists. Nor
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can properties (or spatial relations) come into existence, if the
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future already exists. </font></font>
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</p>
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<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">
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<font color="#000000"><font face="Times New Roman, serif">If
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eternalism were true, the present would not be different from the
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past or the future in this basic way, and thus, eternalism cannot
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explain what we observe about the nature of existence in perceiving
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persentist change. </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">Presentism
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is an indispensible assumption for any ontology that hopes to be
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explanatory, for it allows one to hold that what exists are
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substances that endure through time and, thereby, to explain what is
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found in the world as being constituted by basic substances and the
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manner in which they exist together as a world. All truths about the
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world, including truths about the past and the future, are thereby
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reducible to facts about what exists now. </font></font></font>
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</p>
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<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">
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<font color="#000000"><font face="Times New Roman, serif">On the
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other hand, if eternalism were true, one would have to postulate many
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more basic entities in order to explain the world, because one would
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have to postulate distinct basic entities for every moment in the
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history of every material object found in the world. Though such
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basic entities would not be substances in our sense, they would serve
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as the basic ontological causes in an eternalist explanation of the
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world, because they would constitute substances in our sense. The
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spacetime events that make up the world-lines of ordinary objects in
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Minkowski spacetime diagrams would be basic entities in this sense. </font></font>
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</p>
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<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">
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<font color="#000000"><font face="Times New Roman, serif">Eternalism
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is what makes the belief in spacetime unacceptable to empirically
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minded thinkers who want to know the truth about the nature of what
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exists. Empirical ontology seeks to discover the theory that
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corresponds to the basic nature of what exists, and since we have
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observational evidence that existence is what makes present different
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from the past and the future, any ontological theory that denies that
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fact is not very likely to be true. Indeed, it is empirically
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falsified by our perception of presentist change and our reflection
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on ourselves as agents. </font></font>
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</p>
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<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">
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<font color="#000000"><font face="Times New Roman, serif">Though
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“change” may be defined in terms of the difference between events
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located earlier and those located later on a world line, that is not
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presentist change (since there is nothing coming into existence or
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going out of existence over time). It is eternalist change.
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Presentist change entials eternalist change (since propositions about
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the future and the past can be reduced to propositions about the
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substances that exist now), but eternalist change does not entail
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presentist change (since there is no way to distinguish the present
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from the past and the future). Thus, there are observational facts
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that a presentist ontology, like spatiomaterialism, can explan that
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cannot be explained by any eternalist ontology, such as the belief in
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spacetime. </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; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; 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">I<img src="data:image/png;base64,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" name="EpistCmt" align="right" hspace="5" width="202" height="20" border="0">t
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is not the case that this problem about the nature of time has gone
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entirely unnoticed in the literature. </span></font></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Putnama"><font color="#0000ff"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><u>Putnam</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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[1967] noticed that substantivalism about spacetime contradicts our
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ordinary assumption about time (that only the present exists). But he
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focused on the incompatibility between the future being already
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determined and our view of ourselves as agents. Since he does not
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recognize reflection as observational evidence about the nature of
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what exists, he simply accepts the belief in spaceime as another case
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of scientific discoveries correcting ordinary beliefs. Putnam's point
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was also made by </span></font></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Putnama"><font color="#0000ff"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><u>Rietdijk</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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[1966]. </span></font></font></font>
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</p>
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<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; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">Worries
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about having to hold that we are suffering a massive delusion in
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believing that the present is radically different from all the other
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moments in time are expressed by John </span></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Putnama"><font color="#0000ff"><font face="Times New Roman, serif"><span lang="en-US"><u>Post</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
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(1987, Chapter 3) and Roger </span></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Putnama"><font color="#0000ff"><font face="Times New Roman, serif"><span lang="en-US"><u>Penrose</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
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(1989, pp. 442ff). But it does not lead them to doubt that spacetime
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corresponds to the real nature of what exists. </span></font></font>
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</p>
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<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; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
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<a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Putnama"><font color="#0000ff"><font face="Times New Roman, serif"><span lang="en-US"><u>Maxwell</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
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[1985], pp. 23-43, stands out as the only philosopher who sees the
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incompatibility of substantivalism about spacetime with our
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observation of how the present is different from the past and the
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future as justifying our rejection of the belief in spacetime in
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favor of the belief in absolute time. His view has not gathered
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support in the literature.</span></font></font></p>
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<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; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">Others,
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like </span></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Putnama"><font color="#0000ff"><font face="Times New Roman, serif"><span lang="en-US"><u>Stein</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
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[1968, 1991], have tried to avoid having to choose between the belief
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in spacetime and the openness of the future by taking the truth of
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Einstein's special theory of relativity to be relative to the “here
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and now.” He uses the velocity-of-light limit on causal influences
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between distant events to distinguish between spacetime events with a
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time-like relationship to the here and now (with the past being those
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events that could affect us here and now and the future being those
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that we could affect) from spacetime events with as space-like
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relationship to the here and now (namely those spacetime events that
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we could not affect and that could not affect us without effects
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traveling faster than the velocity of light). That allows Stein to
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take spacetime events that are related in a space-like way to the
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here and now as neither determined nor undetermined, but
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“indeterminate.” However, if relativity to the here and now does
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abandon the requirement that theories in physics be true at the same
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time for observers located everywhere in the universe, it does give
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up ontology as a theory about the nature of the substances that
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constitute the existence of everything in the world, for there is no
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way to explain indeterminate spacetime events by taking spacetime
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events to be the basic entities that constitute the world (much less
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by taking substances enduring through time to constitute the world). </span></font></font>
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</p>
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<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; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">Similar
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objections hold for the attempt by </span></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Putnama"><font color="#0000ff"><font face="Times New Roman, serif"><span lang="en-US"><u>Smith</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
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([1993], p. 4) to solve these ontological issues by reducing
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existence to “being real to.” What exists cannot be relative to
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any particular subject without giving up naturalism and accepting an
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ontology that makes subjective minds basic and reduces objects in
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space to them in some way. </span></font></font>
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</p>
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<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; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">Mathematics
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also obscures this issue in the literature. A logical analysis of the
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difference between invariant and ontological temporal relations is
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offered by </span></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Putnama"><font color="#0000ff"><font face="Times New Roman, serif"><span lang="en-US"><u>Rakic</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
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[1997], but he apparently does not recognize that in introducing the
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ontological relation R, he is, in effect, adding Newtonian absolute
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time to STR. He does not see the ontological significance of his
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mathematical arugment. </span></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; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; 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">In
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the face of the prima facie difficulties with accepting the belief in
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spacetime, it is surprising that there has been so little interest in
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replacing Einstein's special theory of relativity with an explanation
|
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based on the belief in absolute space and time. And it is all the
|
||
more surprising, because the possibility of a “Newtonian” theory
|
||
the phenomena covered by special relativity is widely admitted. </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; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">For
|
||
example, it is admitted by </span></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Str"><font color="#0000ff"><font face="Times New Roman, serif"><span lang="en-US"><u>Zaher</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
|
||
[1989], </span></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Str"><font color="#0000ff"><font face="Times New Roman, serif"><span lang="en-US"><u>Sklar</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
|
||
[1992], and </span></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Str"><font color="#0000ff"><font face="Times New Roman, serif"><span lang="en-US"><u>Dorato</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
|
||
[1996], and it is even defended by </span></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Str"><font color="#0000ff"><font face="Times New Roman, serif"><span lang="en-US"><u>Maxwell</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
|
||
[1985], though for different reasons than will be given here. The
|
||
equivalence of such a “Newtonian” theory to Einstein’s special
|
||
theory is recognized by </span></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Str"><font color="#0000ff"><font face="Times New Roman, serif"><span lang="en-US"><u>Maxwell</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
|
||
[1985] and </span></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Str"><font color="#0000ff"><font face="Times New Roman, serif"><span lang="en-US"><u>Smith</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
|
||
[1993], shown mathematically by </span></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Str"><font color="#0000ff"><font face="Times New Roman, serif"><span lang="en-US"><u>Prokhovnik</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
|
||
[1985] and </span></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Str"><font color="#0000ff"><font face="Times New Roman, serif"><span lang="en-US"><u>Bell</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
|
||
[1987], and explained in a more intuitive way by </span></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Str"><font color="#0000ff"><font face="Times New Roman, serif"><span lang="en-US"><u>Scribner</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
|
||
[1989]. </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; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">But
|
||
commentators on Einstein’s special theory (such as </span></font></font><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Str"><font color="#0000ff"><font face="Times New Roman, serif"><span lang="en-US"><u>Sklar</u></span></font></font></a><font color="#000000"><font face="Times New Roman, serif"><span lang="en-US">
|
||
1992, pp. 27-30) often dismiss this possibility as a mere
|
||
“compensatory theory”, as if it were a crutch for those who feel
|
||
somehow psychologically crippled by the loss of an intuitively
|
||
intelligible explanation, whereas our reason for believing in
|
||
absolute space is that it is required by empirical ontology, given
|
||
the observational evidence for presentism.</span></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">Spacetime
|
||
is not, however, the only possible ontological explanation of the
|
||
phenomenon described by Einstein's special theory of relativity. It
|
||
is also possible to explain <i>all </i>those phenomena on the
|
||
assumption that space and matter are substances enduring through
|
||
time, even though that entails that space and time are absolute. We
|
||
need only assume that space and matter are so related as basic
|
||
substances constituting the world that the velocity of material
|
||
objects through substantival space causes distortions in them in
|
||
which clocks are slowed down, lengths are contracted in the direction
|
||
of absolute motion, masses increase and forcefields are flattend in
|
||
the direction of motion (all at the usual rate). These are the
|
||
distortions that are implicit in the conclusions of Einstein’s
|
||
argument, but in the following argument the order is reversed.
|
||
Instead of assuming the principle of relativity and deriving the
|
||
distortions as consequences, we shall assume the Lorentz distortions
|
||
as basic laws of physics and derive the principle of relativity—that
|
||
is, explain all aspects of the empirical equivalence of inertial
|
||
reference frames by the Lorentz distortions. </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; background: #cccccc; border-top: 6.75pt double #000000; border-bottom: 6.75pt double #808080; border-left: 6.75pt double #000000; border-right: 6.75pt double #808080; padding: 0.28cm 0.46cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">There is
|
||
probably an interesting story to be told about why Newtonian
|
||
physicists did not defend such a theory about the empirical
|
||
equivalence of inertial frames when it was still a live issue.
|
||
Lorentz did explain the negative result of the Michelson-Morley
|
||
experiment by the distortions he discovered, but he did even try to
|
||
explain the symmetry in the transformation equations he used to
|
||
describe them, because he thought of them as merely a convenient
|
||
mathematical device for describing the effects of absolute motion on
|
||
material objects. The reason that other physicists did not extend
|
||
Lorentz's basically physical approach to explain why comparisons
|
||
between inertial reference frames could not detect absolute rest and
|
||
motion may be the devastating effects of World War I on the talent of
|
||
that generation. An entire generation of potential physicists was
|
||
wiped out, and after the war, the relative ease of reaching
|
||
intersubjective agreement about mathematical arguments may have
|
||
driven out the more divisive Newtonian arguments. To explain special
|
||
relativity in terms of absolute space and absolute time requires
|
||
intutive understanding, and such physical explanations could not be
|
||
constructed without solving paradoxes about pairs of clocks both
|
||
going slower than the other and light having the same velocity in
|
||
different inertial frames. It also seemed ad hoc to postulate Lorentz
|
||
distortions, since their only role in physics seemed to be making it
|
||
impossible to detect absolute rest and motion. Einstein's elegant
|
||
mathematical argument may have seemed superior in the young, abstract
|
||
minds that picked up the discipline after the war untutored by the
|
||
lost generation of Newtonian physicists. Thus, most students may
|
||
simply have been taught Einsteinian equations from the beginning of
|
||
their graduate careers, and those who demanded a more intuitive
|
||
understanding of what they meant were weeded out as not being
|
||
intellectually fit to do 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">In
|
||
giving the spatiomaterialist explanation of the truth of the special
|
||
theory of relativity, I will start by following in the footsteps of
|
||
Lorentz. But the spatiomaterialist explanation disagrees with Lorentz
|
||
about what is required to explain special relativity, because it
|
||
recognizes that it is necessary to explain not only the negative
|
||
result of the Michelson-Morley experiment, but also why absolute
|
||
motion and rest cannot be detected by comparing inertial frames with
|
||
one another. </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">The
|
||
inability to determine the absolute velocity of a material object by
|
||
measuring the velocity of light relative to it is what Lorentz
|
||
explained by postulating the slowing down of clocks and the shrinking
|
||
of measuring rods in the measuring apparatus. Lorentz and Poincaré
|
||
attempted to explain these distortions by the interaction of material
|
||
objects with an ether, and I will suggest in the final section how
|
||
they might be explained ontologically (by the unit-like, or quantum,
|
||
electromagnetic interactions that constitute material objects in a
|
||
spatiomaterial world like ours). In order to explain not only the
|
||
kinematic phenomena on which Lorentz focused, but also the dynamic
|
||
phenomena that make the laws of physics apply the same way on all
|
||
inertial frames, it is necessary to recognize two additional
|
||
distortions: an increase in mass and a flattening of forcefields in
|
||
the direction of motion. But to focus on explaining the Lorentz
|
||
distortions, even including all four, is to fail to recognize that
|
||
there is another, quite puzzling aspect of the phenomena described by
|
||
Einstein’s special theory that needs to be explained.</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
|
||
puzzling aspect is the symmetry that holds between members of each
|
||
pair of inertial frames. It is implied by the Lorentz transformation
|
||
equations, and it is an essential part of the principle of relativity
|
||
as the empirical equivalence of all inertial reference frames, for it
|
||
implies that absolute rest and motion cannot be detected by
|
||
comparting inertial frames with one another. Explaining this symmetry
|
||
will require a two-step argument. The first step is to show that the
|
||
effect of following Einstein’s definition of simultaneity at a
|
||
distance in absolute space is to mis-synchronize clocks on a moving
|
||
inertial frame in a certain way. The resulting disagreement about the
|
||
simultaneity of events at a distance is widely recognized, but its
|
||
role in causing the symmetry between inertial frames is not. Hence,
|
||
the second step is to show how the mis-synchronization combines with
|
||
the Lorentz distortions themselves to make it appear that the Lorentz
|
||
distortions are always occurring symmetrically in the other inertial
|
||
frame.<sup><a class="sdfootnoteanc" name="sdfootnote1anc" href="#sdfootnote1sym"><sup>1</sup></a></sup></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 color="#993366"><font face="Verdana, sans-serif"><b>T<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJcAAAAPCAMAAADedK1lAAAAPFBMVEUAAAANDAkcGBMqJR04MSZGPjB+AABjV0NxY01/cFeOfGGciWqqlXS4on7HrojVu5Hjx5v8A/sAAAD///8O80d3AAAAEnRSTlP//////////////////////wDiv78SAAABaElEQVR4nO2T0XIDIQhFXcWCisr/f22vmnTbzDbJ9mkfykRnhSsehbiPa5r7t7Nm17PFpdOM68+gnkiEvb/La/8blwiRiNFD5mcP+ajFmg63DeHjhd/lMpCNFCnGhm/ith/QhaTjRXO2Gilby0LJmmdREclTqDF6NbHOxF0dvPCAR5oohJbb3VGIbeSRU1xsiQ15Cu1cWAqbeM4ttE6qvnbfekjaVMcpBkisFfKYTGtzGL7hZy5KhRBvdncUi9m2aukUl5qSbXgGt3O5OUY8odYkUMyijTrmxY/LjLUzjqXNHUOO4VZSjN2B2bO+argDLjf/Awdcwgi0b1zVr/QjOLks86avuXqK2wuwAy50j9WdazlHXAdGvXMV6+HWzqPss451lt11u4kmVxmfuwOZ6pSf5eoxhLiCRJQrprriOVAotxNKINlo9ZdxYD8OlUDUMaMfQ5B1MQiH/suBTDiA36zj1ezSXJe0TyIYWgFeEaHoAAAAAElFTkSuQmCC" name="TtsOtkCLStr_08" align="right" hspace="5" width="300" height="29" border="0">he
|
||
Lorentz Distortions</b></font></font><font color="#993366"><font face="Verdana, sans-serif">.
|
||
</font></font>To hold that space is a substance enduring though time
|
||
is to hold that space is absolute, and we have assumed that space is
|
||
the medium of light transmission. There is an inherent motion in
|
||
space that gives light a constant velocity relative to absolute
|
||
space. On that basis, the spatiomaterialist theory must explain why
|
||
inertial frames all appear to be alike, that is, why the velocity of
|
||
light seems to be the same and why the laws of physics all apply the
|
||
same way in every inertial frame. This "local equivalence"
|
||
among inertial frames must be explained as a mere appearance, because
|
||
motion across absolute space must change the velocity of light
|
||
relative to the moving object, as suggested by the analogy to the
|
||
boat moving through ripples in a pond. And the laws of physics
|
||
describing interactions among material objects (dynamic phenomena)
|
||
make different predictions for material objects with different
|
||
velocities. In order for it to be impossible to detect absolute
|
||
motion, moving material objects (that is, objects with with rest
|
||
mass) must be distorted in certain ways. </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">There
|
||
are four kinds of distortions in material objects with high absolute
|
||
velocity: a slowing down of clocks, a contraction of lengths in the
|
||
direction of motion, an increase in the mass of moving objects, and
|
||
an decrease in the strength of forces in the direction of motion.
|
||
These are what I will call the "Lorentz distortions." Only
|
||
the first two were actually discovered by Lorentz, but all of them
|
||
are required for the same kinds of reasons. Though I will not give a
|
||
formal mathematical argument, enough will be said about each to
|
||
explain their quantitative aspects. </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">The rate
|
||
involved in all these distortions is
|
||
<img src="data:image/png;base64,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" name="StrEqBeta" align="bottom" width="46" height="18" border="0">,
|
||
where <i>v</i> is absolute velocity. This is the rate of distortion
|
||
that is required to explain why Michelson and Morley were unable to
|
||
detect absolute motion by using an interferometer to measure the
|
||
velocity of light. This apparatus reflects light from two mirrors
|
||
lying in mutually perpendicular directions, and the velocity of light
|
||
in each direction is determined by measuring the period required for
|
||
each two-way trip (by the interference of the waves coming from the
|
||
two directions). </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">T<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFoAAAAPCAMAAABTNSh0AAAARVBMVEUAAAANDAkcGBMzAAAqJR04MSZJAABGPjBmAAB2AABjV0NxY01/cFeOfGGciWqqlXS4on7HrojVu5Hjx5v8A/sAAAD///+KU6y6AAAAFXRSTlP//////////////////////////wAr2X3qAAAAs0lEQVR4nNWQ2Q4DIQhFu0htQQaU///XXmd5aDKZZro8zA0qETwCp9NBFVtyrNo2U9a1oInOxK4rGRQcYqOr3m0vuiOiWh2KVsFzm2itFAoF2qW0IFarCGGZvP3jBQ1espwthbNRH0LWgRARMxtycHF4iDdhJO1ES28erEQXmy5nNFE/YMtGH6ILpt6rTgsaPcxohNi/QDcU2YepiSf06FhisZaJYx/65zow+oh63G/X/+gJQdE7CIFeCRoAAAAASUVORK5CYII=" name="TtsOtkCLStr_09" align="right" hspace="5" width="200" height="33" border="0">ime
|
||
dilation. </font>Assume that one mirror lies forward in the direction
|
||
of absolute motion with the other transverse to it. The need for
|
||
physical interactions to slow down on moving objects can be seen by
|
||
considering what happens on the transverse pathway as the apparatus
|
||
moves through absolute space. </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
|
||
transverse pathway of the interferometer is, in effect, a “light
|
||
clock”, using the velocity of light to measure time. Since the
|
||
velocity of light in absolute space is fixed, the light in a light
|
||
clock with absolute motion must travel farther than in a light clock
|
||
at rest, and that means that the moving light clock is slowed down.
|
||
It is slowed down at the same rate that all physical processes must
|
||
be slowed down in order to keep this effect from being detectable.
|
||
(See diagram of the path of light on the transverse light clock.) </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"><img src="data:image/png;base64,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" name="StrTranClk" align="bottom" width="437" height="218" border="0"></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">Light
|
||
traveling along the transverse pathway must go farther than it would,
|
||
were the apparatus at absolute rest, because to return to its
|
||
starting place, the light must also keep up with the apparatus, which
|
||
is also moving through space all the time that the light is
|
||
traveling. To observers on the moving object, light seems to travel
|
||
directly to the mirror and back, but its path in absolute space is
|
||
actually along the hypotenuse (<i>ct</i>) of the triangle formed by
|
||
the transverse pathway (<i>L</i>) and the motion of the starting
|
||
point in absolute space (<i>vt</i>). This increases the period
|
||
required for the two-way trip.</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">The period
|
||
is increased at the usual rate (except as a function of absolute,
|
||
rather than relative, velocity). The rate is obtained by Pythagoras’
|
||
theorem for the right triangle depicted in the diagram (<i>L</i><sup><font size="1" style="font-size: 8pt"><i>2
|
||
</i></font></sup><i>+ v</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>= 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>)
|
||
and solving for <i>t.</i> Since <i>L/c</i> is the period it would
|
||
take light to travel to the mirror at absolute rest, the period
|
||
required for <i>each leg </i>on the moving apparatus is
|
||
<img src="data:image/png;base64,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" name="StrEqLc" align="bottom" width="56" height="34" border="0"><i>.</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"><font face="Verdana, sans-serif">L<img src="data:image/png;base64,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" name="TtsOtkCLStr_10" align="right" hspace="5" width="200" height="35" border="0">ength
|
||
contraction. </font>The need for a contraction of the size of
|
||
material objects in the direction of motion can be seen by
|
||
considering what must happen to light clocks oriented in the
|
||
direction of motion in order for absolute motion to be undetectable.
|
||
Unless their lengths were also to shrink, it would still be possible
|
||
to detect absolute motion by comparing the longitudinal light clock
|
||
with the transverse light clock, because the former would be even
|
||
slower than the later. </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
|
||
addition to the distance back and forth along the longitudinal
|
||
pathway, the light on the longitudinal must also cover, as we have
|
||
seen, all the space that the apparatus itself travels during the
|
||
period of its two-way trip. But in the longitudinal direction, there
|
||
is a new factor at work, because the two legs of its trip are
|
||
unequal. Light must travel farther in absolute space on the outward
|
||
leg in the direction of the apparatus’ motion than on the return
|
||
leg, because of the motion of the apparatus in absolute space. </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">That
|
||
means that, relative to the apparatus, the effective velocity of
|
||
light toward the (forward) mirror is slower than when coming back. On
|
||
the outward leg, the velocity of light relative to the apparatus is <i>c
|
||
- v</i>, and on the return leg it is <i>c + v</i>. But light spends
|
||
<i>more time </i>traveling <i>slower </i>in the outward direction
|
||
than it does traveling <i>faster </i>on the return leg, and since the
|
||
effect on the total time of travel depends on how long it travels at
|
||
each velocity, it does not make up all the time lost during the
|
||
outward leg on the return leg. The whole period required would be
|
||
longer than the period required on the transverse pathway, because
|
||
with equal distances to cover to the forward mirror and back, it
|
||
spends a longer time going at the slower (at <i>c-v</i>) than it
|
||
spends going faster (at <i>c+v</i>). That would make absolute motion
|
||
detectable, unless the measuring rod were contracted. </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">If material
|
||
objects also shrink (at the usual rate), the measurements made by the
|
||
interferometer will be the same regardless of its absolute motion and
|
||
the principle of relativity will seem to be true. The required rate
|
||
is easy to calculate because the new length, <i>L'</i>, must be such
|
||
that the period for the two way trip, <i>L'/(c - v) + L'(c + v),</i>
|
||
is equal to the period for a two-way transverse trip derived in the
|
||
foregoing discussion of time dilation. Simply solve for <i>L'</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">The
|
||
two remaining distortions follow from the temporal and spatial (or
|
||
“kinematic”) distortions, for unless there were further
|
||
distortions, Newton’s laws of motion, notably his second law (<i>F
|
||
= ma</i>), would be false and the deviation from what it requires
|
||
would be a measure of absolute velocity. Time dilation and length
|
||
contraction are both relevant to dynamic phenomena, because both are
|
||
involved in the acceleration of material objects, which Newton’s
|
||
law says is proportional to the force exerted on them. Thus, there
|
||
are two dynamic distortions, an increase in mass and a decrease of
|
||
the force field in the direction of motion, corresponding to the
|
||
kinematic distortions.</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,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" name="TtsOtkCLStr_11" align="right" hspace="5" width="200" height="33" border="0">ass
|
||
increase. </font>The necessity of an increase in mass follows from
|
||
the temporal distortion, because unless the masses of material
|
||
objects increase at the usual rate with absolute motion, Newton’s
|
||
second law of motion (<i>F = ma</i>) will be false and physical
|
||
processes will not take place the same way in absolute motion as at
|
||
rest. </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">For
|
||
example, dynamic clocks, such as pendulum clocks and wind-up alarm
|
||
clocks, which depend on the acceleration of material objects to
|
||
measure time, would disagree with light clocks, and the difference
|
||
between the two kinds of clocks would be a measure of absolute
|
||
motion. </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 a
|
||
dynamic clock oriented in the transverse direction of the inertial
|
||
frame’s absolute motion. Since light clocks are slowed down, the
|
||
dynamic clock would seem to be speeded up, since the pendulum (or
|
||
whatever) would be accelerating over the whole distance just as
|
||
quickly as it does at rest. The only way the dynamic clock can be
|
||
slowed down to match the slowing down of the light clock is for the
|
||
mass being accelerated to be increased at the same rate the light
|
||
clock is slowed down. Thus, mass must increase at the rate as a
|
||
function of absolute velocity as time is slowed down. </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">L<img src="data:image/png;base64,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" name="TtsOtkCLStr_12" align="right" hspace="5" width="200" height="35" border="0">ongitudinal
|
||
decrease in the force field.</font> The necessity of a decrease in
|
||
forces exerted in the direction of motion follows from the spatial
|
||
distortion, the shrinkage of measuring rods in the direction of
|
||
motion, for unless the longitudinal force field decreases with
|
||
absolute motion at the usual rate, Newton’s second law of motion
|
||
will still be false and deviations from its predictions will be a
|
||
measure of absolute motion. </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">Consider
|
||
a dynamic clock oriented in the direction of the inertial frame’s
|
||
motion. Although the mass of the pendulum (or whatever) will be
|
||
increased at the usual rate and, thus, slowed down, it will still be
|
||
accelerating under the force at the same rate for the same period as
|
||
the transverse dynamic clock. But since measuring rods are contracted
|
||
in the direction of motion, the pendulum would still seem to be
|
||
accelerating faster, because it would seem to be going farther in the
|
||
same length of time. In order for absolute motion to be undetectable,
|
||
the pendulum in the longitudinal direction must accelerate more
|
||
slowly over space. But it is not possible for this acceleration to be
|
||
slowed down by a further increase in mass, since mass is a scalar
|
||
quantity, which does not depend on the direction of motion, and only
|
||
acceleration in the direction of motion has to be slowed down. The
|
||
only way the acceleration of the pendulum could be slowed down only
|
||
in the longitudinal direction is for the size of the force field in
|
||
that direction to be decreased at the usual rate as a function of
|
||
absolute velocity.<sup><a class="sdfootnoteanc" name="sdfootnote2anc" href="#sdfootnote2sym"><sup>2</sup></a></sup></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">Thus,
|
||
in order to explain the "local equivalence" of inertial
|
||
frames, that is, why absolute velocity cannot be detected by
|
||
measuring the velocity of light relative to the moving object and why
|
||
dynamic clocks do not disagree with light clocks, as if their
|
||
reference frames were at absolute rest in space, we need only assume
|
||
that the nature of matter is such that these four distortions occur
|
||
when material objects are in motion across absolute space. There are
|
||
two kinematic distortions and two dynamic distortions, all at the
|
||
same rate as a function of absolute velocity. The first two are the
|
||
distortions first described by Lorentz, and the latter two are
|
||
distortions that Einstein showed were entailed by the Lorentz
|
||
transformation equations when mass and force are also taken into
|
||
consideration. </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
|
||
order to show that spatiomaterialism can explain the truth of
|
||
Einstein’s special theory of relativity, therefore, I will assume
|
||
that matter has this nature. </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">I
|
||
have shown the necessity of these distortions here by following
|
||
Lorentz and arguing backwards from the Michelson-Morley experiment to
|
||
what is required for absolute velocity to be undetectable by
|
||
measurements of the velocity of light on any given inertial frame (or
|
||
from comparisons of dynamic clocks and light clocks), they are not as
|
||
ad hoc as that makes them seem. As I will argue in the final section,
|
||
they are the same distortions that would be caused by the nature of
|
||
ordinary material objects, if they were constituted by unit-like
|
||
electromagnetic interactions among its parts (among molecules, among
|
||
atoms within molecules, and between protons and electrons within
|
||
atoms). </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">What
|
||
made it possible for Einstein to infer the Lorentz distortions from
|
||
his principle of relativity (and his assumptions that light has the
|
||
same velocity relative to every inertial frame) is that these are the
|
||
only distortions in material objects that would make absolute
|
||
velocity undetectable by measurements of the velocity of light and
|
||
comparisons between light clocks and dynamic clocks. But since they
|
||
are merely implicit in the Lorentz transformation equations he
|
||
derived, they appear in the paradoxical form of symmetrical
|
||
distortions between any pair of inertial frames, and that is the
|
||
other aspect of these phenomena that needs to be explained. </font></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><span lang="en-US">
|
||
</span><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Prokovnik"><font color="#0000ff"><span lang="en-US"><u>Prokhovnik</u></span></font></a><span lang="en-US">
|
||
(1985, Chs. 5-6) develops a similar argument in a mathematically
|
||
general way, but the more intuitive approach used here brings out
|
||
the ontological significance.</span></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">
|
||
This distortion in longitudinal forces is not widely recognized. It
|
||
is suggested in a few obscure discussions of the difference between
|
||
“transverse mass” and “longitudinal mass” that follows from
|
||
Einstein’s special theory. See </span><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Prokovnik"><font color="#0000ff"><span lang="en-US"><u>Okun</u></span></font></a><span lang="en-US">
|
||
(1989). This complication in Einstein’s theory is not usually
|
||
acknowledged in textbooks in this field (and I thank Howard Reese
|
||
for bringing it to my attention). But since it makes no sense to
|
||
suppose that mass is different in different directions, the only
|
||
possible explanation of the principle of relativity (as opposed to
|
||
mathematical deduction) is a relativistic decrease in longitudinal
|
||
forces. </span><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/#Prokovnik"><font color="#0000ff"><span lang="en-US"><u>Prokhovnik</u></span></font></a><span lang="en-US">
|
||
(1985) recognizes it, and he explains it mathematically as a
|
||
retarded potential. (It is as if the force involved a two-way trip
|
||
at the velocity of light in order to act). </span>
|
||
</p>
|
||
</div>
|
||
</body>
|
||
</html> |