764 lines
128 KiB
HTML
764 lines
128 KiB
HTML
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
|
||
<html>
|
||
<head>
|
||
<meta http-equiv="content-type" content="text/html; charset=utf-8">
|
||
<title>The Symmetry of the Lorentz Distortions in Pairs of Inertial Frames</title>
|
||
<meta name="generator" content="LibreOffice 4.2.8.2 (Linux)">
|
||
<meta name="author" content="Amr Gharbeia">
|
||
<meta name="created" content="20010831;10600000000000">
|
||
<meta name="changed" content="20150721;232948057731710">
|
||
<style type="text/css">
|
||
<!--
|
||
@page { margin-right: 1.2cm; margin-top: 1.2cm; margin-bottom: 1.25cm }
|
||
p { text-indent: 1.27cm; margin-bottom: 0.25cm; direction: ltr; color: #99ccff; line-height: 120%; text-align: left; widows: 2; orphans: 2 }
|
||
p.western { font-family: "Arial", sans-serif; font-size: 10pt; so-language: en-US }
|
||
p.cjk { font-family: "Times New Roman", serif; font-size: 10pt }
|
||
p.ctl { font-family: "Simplified Arabic"; font-size: 10pt; so-language: ar-EG }
|
||
p.sdendnote-western { margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; direction: ltr; color: #000000; font-family: "Times New Roman", serif; font-size: 10pt; so-language: en-US; line-height: 150%; text-align: left; widows: 0; orphans: 0 }
|
||
p.sdendnote-cjk { margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; direction: ltr; color: #000000; font-family: "Times New Roman", serif; font-size: 10pt; line-height: 150%; text-align: left; widows: 0; orphans: 0 }
|
||
p.sdendnote-ctl { margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; direction: ltr; color: #000000; font-family: "Times New Roman", serif; font-size: 12pt; so-language: ar-SA; line-height: 150%; text-align: left; widows: 0; orphans: 0 }
|
||
a:link { color: #0000ff }
|
||
a.sdendnoteanc { font-size: 57% }
|
||
-->
|
||
</style>
|
||
</head>
|
||
<body lang="en-GB" text="#99ccff" link="#0000ff" dir="ltr">
|
||
<p lang="en-US" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; text-indent: 0cm; 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,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" name="TtsOtkCLStr_13" align="right" hspace="5" width="300" height="29" border="0">he
|
||
Symmetry of the Lorentz Distortions in Pairs of Inertial Frames. </b></font></font>The
|
||
four Lorentz distortions make it impossible to detect absolute rest
|
||
(or absolute motion) by any local experiment, that is, by ordinary
|
||
interactions among material objects on moving inertial frames, such
|
||
as interferometers and comparing light clocks with dynamic clocks.
|
||
But as Einstein's argument emphasized, the empirical equivalence of
|
||
inertial frames implies that they are equivalent globally as well as
|
||
locally. It is also impossible to detect absolute motion by
|
||
experiments involving the relationships between inertial frames with
|
||
high relative velocity, for example by comparing how fast their
|
||
clocks are ticking or how long their measuring rods are. And as the
|
||
symmetry of the two sets of Lorentz transformation equations implies,
|
||
what makes it impossible to detect absolute motion by such global
|
||
experiments is that the Lorentz distortions <i>always </i>appear to
|
||
be occurring in the <i>other </i>inertial frame as a function of the
|
||
velocity of the two references <i>relative </i>to one another. Thus,
|
||
in order to explain the empirical equivalence of inertial frames
|
||
ontologically, we must explain this symmetry in the members of any
|
||
pair of inertial frames as an appearance. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; text-indent: 0cm; 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
|
||
first step in that explanation is to take note of how clocks on
|
||
inertial frames are mis-synchronized by using Einstein’s definition
|
||
of simultaneity at a distance, if the velocity of light is actually
|
||
due to an inherent motion in space itself. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; text-indent: 0cm; 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
|
||
second step is to show how that mis-synchronization of clocks on
|
||
inertial frames moving rapidly across space combines with the Lorentz
|
||
distortions that they are actually suffering as a result of their
|
||
absolute motion to make it appear that Lorentz distortions are always
|
||
in the other inertial frame (and that the rate seems to be a function
|
||
of their relative velocity). </font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; text-indent: 0cm; 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,iVBORw0KGgoAAAANSUhEUgAAALIAAAAPCAMAAAB3AGXxAAAASFBMVEUAAAANDAkcGBMzAAAqJR04MSZJAABGPjBmAAB2AAB+AABjV0NxY01/cFeOfGGciWqqlXS4on7HrojVu5Hjx5v8A/sAAAD///8Rn7hnAAAAFnRSTlP///////////////////////////8AAdLA5AAAAYdJREFUeJzVlQFuwyAMRdMOj60YMNj3P+u+Q5JqarW1qTYpVoucj4EX2yjTZTqcHRPZjmTPIHfdc4L0xWlXrd2NfNA2ZJk6/lZ+2I3lRkrf3HQzDy2tq+gq0p3Ah+2KnJIl8pyUgaaZe1VrTYTxHlC5wOmSpXtEKRlDZ2ZpnLWfWQqErDYW+A7FIHuWsRacLlhHsLuzthN5GsgcayZkMrNUn4lVBFSxc5JgOWHCHQm1BYlip8rZSAWCSI0apGM5Vwwe57mszJDRTo2EgeyChVoaKbUW5WVkOasjS0hSiCwH5Id68n6guZSzg7PHj8ZgqZgQzRHLMMeZbcrSUmMWizDilTWk3chLYzAuhR+nKKbPoMB4JBkEsZuuyC2h/iuyn0u60iIsbMjBehweGsJDXMBiUyqkahpvL8eTyCNDJdB8jVIgtGJYktugrsjo+agLspyISgnJq4K+anjakFGrNjwdZZgF7Nt8Pwm+yyvI963sq92f2m/I/4jyqE1H/WAfzS6fH+9vh7IvwNZ8I1ZzHDEAAAAASUVORK5CYII=" name="TtsOtkCLStr_14" align="right" hspace="5" width="350" height="29" border="0">he
|
||
mis-synchronization of moving clocks. </font>The strategy of
|
||
spatiomaterialism is to explain the truth of the principle of
|
||
relativity on the assumption that all forms of matter, including
|
||
light and material objects, coincide with parts of space. The
|
||
assumption that both matter and space are substances enduring through
|
||
time makes it possible to explain presentist change, but it also
|
||
entails that space and time are absolute. Thus, it must reject
|
||
Einstein’s definition of simultaneity at a distance. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; text-indent: 0cm; 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
|
||
stipulates that a local event is simultaneous with the moment of
|
||
reflection of a light signal from a distant mirror when that local
|
||
event occurs halfway through the total period required for the signal
|
||
to travel there and back. That is to assume that the velocity of
|
||
light is the same in both directions. This assumption is true on
|
||
inertial frames at absolute rest, but it is not true on objects
|
||
moving through absolute space. If light everywhere has a fixed
|
||
velocity relative to absolute space, the velocity of light relative
|
||
to a moving frame is slower traveling outward in the direction of
|
||
forward motion and faster in the opposite direction. Thus, clocks on
|
||
moving frames that are synchronized according to Einstein’s
|
||
definition of simultaneity at a distance will be actually
|
||
<i>mis</i>-synchronized. It is important to be clear about the nature
|
||
and amount of the error introduced, because mis-synchronization plays
|
||
a crucial role in causing the appearances that make absolute motion
|
||
undetectable by comparing inertial frames with one another, or the
|
||
symmetry of Lorentz distortions in pairs of inertial frames. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; text-indent: 0cm; 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
|
||
most revealing way to show the mis-synchronization is to use a
|
||
diagram to represent the spatial and temporal relations among the
|
||
relevant events. This is to use the Newtonian diagram of space and
|
||
time, which is the spatiomaterialist counterpart to Minkowski’s
|
||
“graphical method” of using spacetime diagrams for “visualizing”
|
||
what is going on, and it is both simpler and easier to understand.
|
||
Since spatiomaterialism assumes that space is a substance and, thus,
|
||
absolute, the argument may begin with the coordinate frame at rest in
|
||
absolute space. Nothing precludes representing time as an axis
|
||
perpendicular to spatial dimensions, as long as we do not assume that
|
||
anything exists but what is located on lines parallel to our absolute
|
||
space-axis (horizontal lines in the diagram) for each moment. We can
|
||
<i>refer </i>to events in the past and future, even though they do
|
||
not exist, because they can be interpreted as references to space and
|
||
matter which have, as substances, an existential aspect that entails
|
||
that they did exist and will exist. We can also represent the motion
|
||
of the other inertial frame as a timeline whose slope depends on its
|
||
velocity (<i>t = x/v</i>), as Minkowski did. Furthermore, we can take
|
||
this timeline to be the time-axis of the moving inertial frame,
|
||
because that involves only a simple Galilean coordinate
|
||
transformation of the kind used in Newtonian physics. So far, this is
|
||
equivalent to Minkowski’s spacetime diagram. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; text-indent: 0cm; 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">Spatiomaterialism
|
||
cannot, however, go on to assume that the moving frame has a
|
||
space-axis that is inclined relative to our absolute space-axis, as
|
||
Minkowski's spacetime diagram does. We must assume that moving
|
||
measuring rods always lie parallel to the absolute space-axis, since
|
||
all parts of moving rods are particular substances and must exist at
|
||
the same time. But spatiomaterialism does hold, following Lorentz,
|
||
that moving measuring rods lying in the direction of motion are
|
||
contracted, and so we must recognize that the moving measuring rod is
|
||
shorter than it would be if it were at absolute rest. Now, to see the
|
||
significance of Einstein’s definition of simultaneity at a
|
||
distance, we need only consider the geometry of synchronizing clocks
|
||
in absolute space and time, that is, from the point of view of the
|
||
absolute frame depicted below. (See the diagram below comparing the
|
||
synchronization of both forward and afterward clocks on the absolute
|
||
and moving inertial reference frames.) </font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; text-indent: -3.81cm; 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="StrSynchronization" align="bottom" width="702" height="287" border="0"></font></p>
|
||
<p lang="en-US" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; text-indent: 0cm; 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
|
||
foregoing diagram depicts the general nature of the
|
||
mis-synchronization, but we will need to know just how much clocks
|
||
are mis-synchronized. Thus, consider the following diagram in which
|
||
the moving measuring rod is depicted as <i>L'.</i> </font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; text-indent: 0cm; 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="StrMisSynch" align="bottom" width="406" height="449" border="0"></font></p>
|
||
<p lang="en-US" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; text-indent: 0cm; 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
|
||
length of the contracted moving measuring rod in absolute space is
|
||
<i>L'</i>. It is depicted at four locations that it occupies at
|
||
crucial moments during the process of synchronization. The thinner
|
||
inclined lines trace the path of each end of the rod where clocks are
|
||
located. The thin dotted-line represents the path of the light used
|
||
to synchronize the clocks at each end. Following Einstein’s
|
||
definition of simultaneity, (1) moving observers send a light signal
|
||
forward from the origin of their frame, (2) the light is reflected
|
||
from a mirror at the forward end of their measuring rod (and the
|
||
clock there is set at <i>0</i>), and (3) they record when it returns.
|
||
Einstein’s definition requires moving observers to set their clocks
|
||
on the assumption that the light was reflected halfway through the
|
||
total period required for its round trip. Since the light signal
|
||
reaches the mirror in the period <i>T</i><sub><font size="1" style="font-size: 8pt"><i>1</i></font></sub>
|
||
and returns to the observers in the period <i>T</i><sub><font size="1" style="font-size: 8pt"><i>2</i></font></sub>,
|
||
they assume it was reflected at <i>(T</i><sub><font size="1" style="font-size: 8pt"><i>1</i></font></sub><i>
|
||
+ T</i><sub><font size="1" style="font-size: 8pt"><i>2</i></font></sub><i>)/2</i>
|
||
after the light was sent. Thus, they set their nearest clock so that
|
||
it would have read <i>0</i> at that moment. But since the measuring
|
||
rod is actually in absolute motion, the light does not reach the
|
||
mirror at the far end until it has passed both the length of the
|
||
measuring rod and whatever distance the rod travels during the first
|
||
leg (<i>T</i><sub><font size="1" style="font-size: 8pt"><i>1</i></font></sub>).
|
||
And on the return leg (<i>T</i><sub><font size="1" style="font-size: 8pt"><i>2</i></font></sub>),
|
||
light does not have to travel the whole distance of the measuring
|
||
rod, since the other end is also moving toward the light. But since
|
||
moving observers assume that the reflection occurs halfway through
|
||
the period required for the round trip, they are, in effect, assuming
|
||
that the set of simultaneous events lies on the line that runs
|
||
through the halfway point on the timeline for the clock at the
|
||
observers’ end of the measuring rod and the point of reflection at
|
||
the mirror on the timeline for the clock at the forward end of the
|
||
measuring rod. That is what moving observers take to be their
|
||
space-line as seen by us from the frame at absolute rest.</font></font></font></p>
|
||
<p lang="en-US" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; text-indent: 0cm; 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 result
|
||
of mis-synchronizing clocks is precisely the same diagram for the
|
||
moving frame that Minkowski constructed from his hyperboloid curve,
|
||
representing the conclusion of Einstein’s special theory. (The same
|
||
results would also follow from the Lorentz transformation equations.)
|
||
However, we have derived the moving observers’ apparent space-axis
|
||
(or space-line), not from a mysterious equation, but in a perfectly
|
||
intelligible way. The moving space-line is rotated upward in the
|
||
diagram, <i>because </i>the moving clocks have been mis-synchronized.
|
||
And they have been mis-synchronized because the moving observers have
|
||
followed Einstein’s definition of simultaneity at a distance, which
|
||
assumes that the velocity of light is the same both ways in every
|
||
direction relative to any inertial frame.</font></font></p>
|
||
<p lang="en-US" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; text-indent: 0cm; 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
|
||
amount of the error introduced by mis-synchronization will be as
|
||
important as its cause in the next step of this argument, so bear
|
||
with me for one final point. The home clock reading <i>0 </i>is one
|
||
event in absolute space and time, and the forward clock reading<i> 0
|
||
</i>is another event. The separation between them in the absolute
|
||
frame has a curious value, both in space and in time. The moving
|
||
measuring rod has a length of <i>L'</i>, but the distance in absolute
|
||
space between these two events turns out to be <i>L'/(1 - v</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>)</i>,
|
||
which means that the mis-synchronization makes it seem that the
|
||
moving measuring rod is <i>expanded </i>at the <i>square </i>of the
|
||
usual rate (see above diagram). The length of time between the two
|
||
events can be derived from the slope of the moving space-line in the
|
||
diagram for absolute space and time (that is, <i>v/c</i><sup><i>2</i></sup>)<i>.</i><sup><a class="sdendnoteanc" name="sdendnote1anc" href="#sdendnote1sym"><sup>i</sup></a>[1]</sup>
|
||
This is the slope of the tangent to Minkowski’s mysterious curve at
|
||
the point of intersection with the timeline for the observers’
|
||
nearest clock,<sup><a class="sdendnoteanc" name="sdendnote2anc" href="#sdendnote2sym"><sup>ii</sup></a>[2]</sup>
|
||
and it occurs in the second expression in the numerator for the
|
||
Lorentz transformation for time.<sup><a class="sdendnoteanc" name="sdendnote3anc" href="#sdendnote3sym"><sup>iii</sup></a>[3]</sup>
|
||
But in this context, the slope means that the difference in time
|
||
between the events is <i>v/c</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup><i>[L'/(1
|
||
- v</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>)]</i>
|
||
(or the product of the slope of the moving space-line and the
|
||
distance between the points on it in absolute space). We will use
|
||
these values shortly.</font></font></font></p>
|
||
<p lang="en-US" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; text-indent: 0cm; 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,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" name="TtsOtkCLStr_15" align="right" hspace="5" width="350" height="29" border="0">he
|
||
Cause of the Apparent symmetry of Lorentz distortions. </font>Attempt
|
||
to detect absolute motion by measuring the rate of clocks and the
|
||
length of measuring rods on the other inertial frame are "global
|
||
experiments," and the reason that absolute motion cannot be
|
||
detected is that the Lorentz distortions appear to be symmetrical.
|
||
Since transformation equations must work both ways between any two
|
||
inertial reference frames, this symmetry is entailed by Einstein's
|
||
argument for the Lorentz transformation equations in his special
|
||
theory of relativity. And this symmetry is an essential part of the
|
||
empirical equivalence of inertial frames that Poincaré called the
|
||
"principle of relativity."</font></font></font></p>
|
||
<p lang="en-US" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; text-indent: 0cm; 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 the
|
||
clocks and measuring rods were material objects in absolute space,
|
||
this symmetry would imply that clocks on two inertial frames passing
|
||
one another in space are both going slower than the other and that
|
||
their longitudinally-oriented measuring rods are both shorter than
|
||
one another. It is one of the reasons that Einsteinians must give up
|
||
the belief in absolute space and time. By the same token,
|
||
spatiomaterialism must explain this symmetry about pairs of inertial
|
||
frames as a <i>mere appearance</i> of space and matter as substances
|
||
enduring through time, just as the local equivalence was. </font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; text-indent: 0cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">This is the
|
||
part of the explanation of the empirical equivalence of inertial
|
||
frames that Lorentz left out of his Newtonian theory. But it is
|
||
readily supplied by the geometry of events in absolute space and
|
||
time. The apparent symmetry of the distortions is a result of the
|
||
actual Lorentz distortions suffered by the moving frame, together
|
||
with the mis-synchronization of moving clocks, as we can see by
|
||
considering how the measurements of the others’ clocks and rods are
|
||
made. </font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; text-indent: 0cm; 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>Length
|
||
contraction.</i> Consider first the apparent symmetry of length
|
||
contraction. The most direct way to measure the others’ standard of
|
||
length is to make simultaneous marks from both ends of one’s own
|
||
measuring rod onto the other inertial frame as it passes by and
|
||
compare that distance with the others’ measuring rod. This works
|
||
fine for absolute observers; they mark off a distance longer than
|
||
moving measuring rods lying in the direction of motion, indicating
|
||
that the moving measuring rods are contracted. But it also <i>seems
|
||
</i>to moving observers that absolute rods are contracted in the
|
||
direction of motion, and we can see why by considering what takes
|
||
place in making the measurement. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; text-indent: 0cm; 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
|
||
is because (1) clocks on the moving frame have been mis-synchronized
|
||
and (2) moving measuring rods are contracted. We have just seen that
|
||
moving observers mis-synchronize their clocks when they accept
|
||
Einstein’s definition of simultaneity: the distance in absolute
|
||
space between the events at which moving clocks at both end of a
|
||
moving measuring rod read the same time is equal to an <i>expansion
|
||
</i>of the actually contracted measuring rod at the <i>square </i>of
|
||
the usual rate, that is, <i>(1 - v</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>)</i>.
|
||
Thus, when moving observers make what they think are simultaneous
|
||
marks on the absolute measuring rod that is passing by, they mark off
|
||
a distance on the absolute frame that is longer than their actually
|
||
contracted measuring rod by the square of the usual rate, and since
|
||
that distance is longer than the absolute measuring rod by the usual
|
||
rate, the absolute measuring rod seems to be contracted at the usual
|
||
rate.<sup><a class="sdendnoteanc" name="sdendnote4anc" href="#sdendnote4sym"><sup>iv</sup></a>[4]</sup>
|
||
</font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; text-indent: 0cm; 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, as the absolute inertial frame comes toward them, the
|
||
mis-synchronization of their clocks leads moving observers to make a
|
||
mark from the afterward end of their own measuring rod first and
|
||
then, after the moving frame has traveled some distance, they make a
|
||
second mark from the forward end, so that distance marked off on the
|
||
absolute frame includes both the length of the contracted moving
|
||
measuring rod and all the distance that the absolute frame travels
|
||
between making the two marks. That virtual expansion of the moving
|
||
measuring rod makes it appear that the absolute measuring rod is
|
||
contracted.<sup><a class="sdendnoteanc" name="sdendnote5anc" href="#sdendnote5sym"><sup>v</sup></a>[5]</sup>
|
||
</font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; text-indent: 0cm; 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
|
||
error introduced by mis-synchronization is, in short, a virtual
|
||
distortion at the square of the usual rate, but in the opposite
|
||
direction, so that when the method of measuring combines it with the
|
||
actual shrinkage of the moving measuring rod, the effect is to make
|
||
absolute measuring rods seem distorted at the usual rate relative to
|
||
the moving rod. This same “geometrical mechanism” is at work in
|
||
the measurement of how fast the other’s clocks are ticking. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; text-indent: 0cm; 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>Time
|
||
dilation.</i> The most direct way for us to measure the speed of
|
||
clocks on the other inertial frame is for us to move <i>in our
|
||
inertial frame </i>along with one of the others’ clocks that is
|
||
passing by and to compare it with the series of clocks on our own
|
||
frame by which we will be passing. (Observers cannot take a clock
|
||
with them as they move through their own frame, because that would
|
||
make it a clock on the other frame. But nothing precludes observers
|
||
from keeping up with the other inertial frame and using clocks
|
||
already located at various points on their frame for the comparison.)
|
||
When observers on the frame at absolute rest keep up with the moving
|
||
clock and compare it with a series of their absolute clocks, they
|
||
observe the real slowing down of the others’ clock caused by its
|
||
absolute motion. The symmetry of the distortions means, however, that
|
||
when observers on a frame in absolute motion keep up with an absolute
|
||
clock and compare it with the series of their own moving clocks by
|
||
which they pass, the absolute clock <i>seems </i>to be slowed down. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; text-indent: 0cm; 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
|
||
in the latter case, it is because (1) clocks on the moving frame have
|
||
been mis-synchronized, (2) the moving observers are moving backwards
|
||
on their own moving frame (<i>-v</i>) to keep up with the absolute
|
||
clock, and (3) clocks on the moving frame are slowed down. The amount
|
||
of deviation of a distant moving clock from absolute simultaneity
|
||
with a local moving clock is, as we saw, a function of the distance
|
||
in absolute space between the events at which two moving clocks have
|
||
the same readings, namely, <i>v/c</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup>
|
||
times the absolute distance (the slope of the rotated space line). In
|
||
this measurement, that distance depends on how long the moving
|
||
observer has been traveling at <i>-v</i>, that is, the distance <i>-vt'</i>.
|
||
Thus, the deviation of the next clock from absolute simultaneity will
|
||
be <i>VT</i> times <i>v/c</i><sup><i>2</i></sup><i>,</i><sup><font size="1" style="font-size: 8pt">
|
||
</font></sup>or <i>-t'(v</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>).</i>
|
||
That amount of time plus the time that elapses during the moving
|
||
observers trip from one clock to the next (that is, <i>t'</i>) yields
|
||
a total apparent time period of <i>t' - t'(v</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>)</i>,
|
||
or <i>t'(1 - v</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>)</i>,
|
||
<i>which is a virtual speeding up of moving clocks at the square of
|
||
the usual rate of distortions</i>. Thus, since (1), the
|
||
mis-synchronization of moving clocks, combines with (2), the moving
|
||
observers’ motion on the moving frame, to produce, in effect, a
|
||
virtual speeding up of moving clocks at the <i>square </i>of the
|
||
usual rate, the result, when combined with (3), the actual slowing
|
||
down of moving clocks at the usual rate, is that the absolute clock
|
||
being compared with them appears slowed down at the usual rate.<sup><a class="sdendnoteanc" name="sdendnote6anc" href="#sdendnote6sym"><sup>vi</sup></a>[6]</sup><sup>,
|
||
</sup><sup><a class="sdendnoteanc" name="sdendnote7anc" href="#sdendnote7sym"><sup>vii</sup></a>[7]</sup>
|
||
</font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; text-indent: 0cm; 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
|
||
sum, given how the measurements are made, the mis-synchronization of
|
||
moving clocks introduces a virtual distortion through which the
|
||
moving observers’ own distortions <i>are projected onto the
|
||
absolute inertial frame</i>. This can be seen in our diagram of
|
||
events happening to particular substances in absolute space and time,
|
||
for as we found, the mis-synchronization shows up as a rotation of
|
||
the moving space-line that involves both a virtual speeding up of
|
||
moving clocks and a virtual lengthening of moving measuring rods.
|
||
Thus, to see how it gives rise to the apparent symmetry of the
|
||
distortions, consider how the measurement of the others’ clock is
|
||
represented below. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; text-indent: 0cm; 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">When
|
||
absolute observers keep up with the moving clock and compare it with
|
||
a series of their own clocks, they follow the moving timeline. When
|
||
the moving clock says <i>t'=1</i>, they compare it with an absolute
|
||
clock (located on that absolute space-line) which reads
|
||
<i>t=1/</i><img src="data:image/png;base64,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" name="StrEqBeta" align="bottom" width="46" height="18" border="0">(represented
|
||
by the horizontal line labeled <b>I</b> in the diagram). And when
|
||
moving observers travel backwards on their own frame to keep up with
|
||
the absolute clock, they follow the absolute timeline (<i>x=0</i>).
|
||
When they pass by their own moving clock reading <i>t'=1</i>, they
|
||
compare it with the absolute clock which reads <i>t=</i><img src="data:image/png;base64,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" name="StrEqBeta" align="bottom" width="46" height="18" border="0">
|
||
(represented by the rotated moving space-line labeled II in the
|
||
diagram). The difference between these two measurements is obviously
|
||
due to the rotation of the moving space-line, which, as we have seen,
|
||
comes from mis-synchronizing moving clocks. Notice that the absolute
|
||
clock’s reading of <i>t=1</i> lies between these two comparisons.
|
||
Therein lies the power of mis-synchronization to cause the
|
||
appearance. Combining the slope induced in the moving space-line by
|
||
mis-synchronization (<i>v/c</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup>)
|
||
with the movement of the moving observers in making the measurement
|
||
(<i>x' = VT</i>, that is, keeping up with the absolute clock) is
|
||
equivalent to a temporal distortion on the moving frame at the square
|
||
of the rate of the actual distortion (<i>1-v</i><sup><i>2</i></sup><i>/c</i><sup><i>2</i></sup>),
|
||
but in the opposite direction. So, it combines with the actual
|
||
slowing down of moving clocks to make the absolute clock seem slowed
|
||
down relative to moving clocks. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; text-indent: 0cm; 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="StrAppDist" align="bottom" width="384" height="367" border="0"></font></p>
|
||
<p lang="en-US" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; text-indent: 0cm; 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
|
||
diagram also shows how the mis-synchronization is responsible for the
|
||
apparent symmetry of the contraction of measuring rods. But in this
|
||
case, it is the virtual expansion of the moving measuring rods
|
||
induced at the square of the usual rate by the mis-synchronization
|
||
that is relevant. When absolute observers make simultaneous marks on
|
||
the moving frame, they find that the moving measuring rod is
|
||
contracted at the usual rate (labeled III in the diagram). But when
|
||
moving observers make what they think are simultaneous marks on the
|
||
absolute frame, they actually mark off a distance that is expanded at
|
||
the square of the usual rate (labeled IV in the diagram). Once again,
|
||
the power of mis-synchronization can be seen in how the actual moving
|
||
measuring rod is contracted relative to the absolute measuring rod
|
||
and the virtual moving measuring rod is expanded relative to the
|
||
absolute rod, both at the usual rate. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; text-indent: 0cm; 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
|
||
symmetry of Lorentz distortions is, therefore, a symmetry betwen real
|
||
distortions in reference frames in absolute motion and apparent
|
||
distortions in the reference frame at absolute rest, and it is a
|
||
thoroughgoing symmetry, which holds for all the basic ways of
|
||
measuring the other frame's clocks and measuring rods. Indeed, any of
|
||
the standard measurements can made from either member of the pair of
|
||
inertial frames, though when they are considered from the point of
|
||
view of the other inertial observer, they reveal that the other's
|
||
clocks are speeded up and the other's measuring rods are expanded in
|
||
the direction of motion. This can be seen in the <font color="#0000ff"><u><a href="/F:/Philosophy/Existentialism/The%20Wholeness%20Of%20the%20World/www.twow.net/ObjText/"><font face="Arial, sans-serif"><font size="3" style="font-size: 12pt">table
|
||
of measurements</font></font></a></u></font>. </font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; text-indent: 0cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">This
|
||
explanation of the apparent symmetry of the kinematic distortions
|
||
also accounts for the apparent symmetry of the dynamic distortions
|
||
(though the longitudinal distortion in the force field is not always
|
||
recognized as such by Einsteinians), for the apparent increase in
|
||
absolute masses is implied by the false belief that absolute clocks
|
||
are slowed down and the assumption that Newton’s laws apply the
|
||
same way on all inertial frames (Einstein’s principle of
|
||
relativity). Likewise, the apparent decrease in longitudinal forces
|
||
is implied by Einstein’s principle of relativity and the false
|
||
belief that absolute measuring rods are contracted in the direction
|
||
of motion. </font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; text-indent: 0cm; 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
|
||
apparent symmetry of the four distortions has been explained for the
|
||
special case in which one of the inertial frames is at absolute rest,
|
||
but it can be generalized to explain the apparent symmetry between
|
||
any two objects moving in absolute space. In the general case, the
|
||
rate of the apparent distortions is a function of their (apparent)
|
||
relative velocity, and what is detected on both sides is partly a
|
||
result of real distortions and partly illusions caused in the way
|
||
described above.<sup><a class="sdendnoteanc" name="sdendnote8anc" href="#sdendnote8sym"><sup>viii</sup></a>[8]</sup>
|
||
</font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; text-indent: 0cm; 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
|
||
observers on any pair of inertial frames agree about their relative
|
||
velocity, it is worth noting that, on the spatiomaterialist
|
||
explanation of the empirical equivalence, their measurements of
|
||
relative velocity do not coincide with their real velocity relative
|
||
to one another in absolute space: the apparent relative velocity is
|
||
never more than the velocity of light, but the real velocity of
|
||
inertial frames relative to one another can approach twice the
|
||
velocity of light, because light moves at that velocity in opposite
|
||
directions from any given point in absolute space. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; text-indent: 0cm; 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><b>Conclusions.</b></i>
|
||
One part of the promise made in <font face="Arial, sans-serif">Spatiomaterialism</font>
|
||
in order to use this ontology as a foundation for demonstrating
|
||
necessary truths has been kept. We have seen that spatiomaterialism
|
||
can explain the truth of Einstein’s special theory of relativity,
|
||
and means that nothing established empirically by Einstein’s theory
|
||
forces us to give up spatiomaterialism. Thus, if spatiomaterialism
|
||
can also explain the truth of Einstein’s general theory of
|
||
relativity (and quantum mechanics), physics will provide no grounds
|
||
for doubting that spatiomaterialism is the best ontological
|
||
explanation of the world. But there are a few implications of this
|
||
ontological explanation of special relativity that should be noted in
|
||
conclusion. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; text-indent: 0cm; 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">First,
|
||
though we have discovered the power of absolute velocity to cause
|
||
changes in material objects by following in the footsteps of Lorentz,
|
||
that does not mean that we must postulate an ether in addition to
|
||
absolute space. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; text-indent: 0cm; 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 and
|
||
Poincaré both expected to explain time dilation and length
|
||
contraction as the result of an interaction between material objects
|
||
and an ether at rest in absolute space (as if material objects were
|
||
made of nothing but electrons that interact with the electromagnetic
|
||
ether as they move through it). Though material objects must also
|
||
have something to interact with on our explanation of the Lorentz
|
||
distortions, we can take it to be space itself. We have postulated
|
||
space as a substance that contains matter, and having already used
|
||
that relationship to explain the truth of the laws of classical
|
||
physics, we now use it to explain the Lorentz distortions. Indeed, I
|
||
have suggested reasons for expecting Lorentz distortions to occur
|
||
apart from what is necessary to make absolute motion undetectable. </font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; text-indent: 0cm; 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
|
||
there is no luminiferous ether, there is still a medium of light
|
||
propagation, and it still makes sense to hold that there is an
|
||
inertial frame in which light has the same one-way velocities in
|
||
every pair of opposite directions. That will be important in our
|
||
explanation of the truth of Einstein's general theory of relativity,
|
||
because we will not always assume that the light medium is at
|
||
absolute rest in space. The aspect of space by which it serves as the
|
||
medium of light propagation is more complex than it appears now,
|
||
because we shall have to assume that the velocity of light varies
|
||
with location in space in a way that can be seen as depending on the
|
||
velocity of the light medium relative to space. It is as if the ether
|
||
were being accelerated in space, but even though that may suggest
|
||
that the light medium is an ether after all, we will still not
|
||
postulate an ethereal substance coinciding with space to explain this
|
||
phenomenon. </font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; text-indent: 0cm; 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">Second,
|
||
the difference between the actual Lorentz distortions in material
|
||
objects with absolute velocity and the apparent symmetry of Lorentz
|
||
distortions in pairs of inertial frames revealed by this ontological
|
||
explanation shows that the mathematical representation of special
|
||
relativity is hiding an aspect of reality. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; text-indent: 0cm; 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
|
||
mathematical way of saying that inertial frames are all equivalent is
|
||
to say that the laws of physics are covariant, or Lorentz covariant.
|
||
That means that laws of physics that apply in one frame take the same
|
||
form in any other inertial frame, that is, when they are subjected to
|
||
the Lorentz transformation. (This equivalence is what is represented
|
||
by Minkowski’s equation for the absolute separation between any two
|
||
events and is the foundation for the equations of four-vector
|
||
physics, which do not mention any specific inertial frame.)
|
||
Einstein’s original article showed that covariance holds in the
|
||
case of electromagnetism, and imposing covariance as a requirement on
|
||
other physical theories has generated predictions that turn out to be
|
||
true. </font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; text-indent: 0cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Despite the
|
||
obvious simplicity, comprehensiveness, elegance, and fruitfulness of
|
||
this mathematical representation of special relativity, however, it
|
||
is a mistake to take covariance to be the deepest and most complete
|
||
truth about the real nature of the world. Our ontological explanation
|
||
of the truth of special relativity reveals that covariance actually
|
||
represents two different phenomena, with two different ontological
|
||
causes. There is the local equivalence of inertial frames, which is
|
||
caused by the actual Lorentz distortions, and there is the global
|
||
equivalence, which is caused by the mis-synchronization of clocks and
|
||
how that makes one’s own Lorentz distortions appear to be in the
|
||
other inertial frame. </font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; text-indent: 0cm; 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">Third,
|
||
this ontological interpretation of the mathematical representations
|
||
used in special relativity confirms that the method of physics is
|
||
implicitly skeptical about ontological causes that are not entailed
|
||
by realism about its efficient cause explanations. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; text-indent: 0cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">When
|
||
physics infers to the best efficient-cause explanation, it looks for
|
||
laws of nature that represent the quantitative aspects of the
|
||
regularities involved, because such mathematical representations can
|
||
often be used to predict surprising, precise measurements that
|
||
confirm their truth. The empirical method of science is so dependent
|
||
on mathematical representations that, once experiments have confirmed
|
||
their predictions, physicists are realists about their
|
||
efficient-cause explanations. They let scientific realism determine
|
||
their ontology. </font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; text-indent: 0cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Accordingly,
|
||
the belief in spacetime is simply realism about special relativity.
|
||
That is, substantivalism about spacetime is the ontology that results
|
||
from taking the simplest mathematical theory that can predict all the
|
||
relevant phenomena to correspond to what exists. Since the special
|
||
relativity holds that all inertial frames are empirically equivalent,
|
||
scientific realism takes the empirical equivalence among inertial
|
||
frames to be an ontological equivalence. That is to replace absolute
|
||
space and time with spacetime. But it is also the leave out an aspect
|
||
of reality, for it is to ignore the observable fact that only the
|
||
present exists. </font></font>
|
||
</p>
|
||
<p lang="en-US" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; text-indent: 0cm; 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">Finally,
|
||
the principle of relativity itself turns out to be merely a practical
|
||
principle, without ontological significance. Though as a practical
|
||
matter, the assignment of coordinates to events can be made only
|
||
relative to an inertial frame whose absolute motion cannot be known,
|
||
that does not mean that they do not have actual locations in absolute
|
||
space as time passes. There is an absolute truth about the dates and
|
||
places of events. Even though we can never know what they are, we can
|
||
know that there is a fact of the matter about when and where they
|
||
occur. That is what is implied by this ontological reduction of
|
||
special relativity. I have called it an explanation of empirical
|
||
equivalence, because by explaining the <i>apparent </i>truth of the
|
||
principle of relativity, it denies that this relativity is a basic
|
||
principle of physics.<sup><a class="sdendnoteanc" name="sdendnote9anc" href="#sdendnote9sym"><sup>ix</sup></a>[9]</sup>
|
||
</font></font></font>
|
||
</p>
|
||
<div id="sdendnote1">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm"><a class="sdendnotesym" name="sdendnote1sym" href="#sdendnote1anc">i</a><sup>[1]</sup>
|
||
The slope of the moving space-line is found in the Newtonian diagram
|
||
of space and time by calculating the difference between the absolute
|
||
time of reflection, <i>T</i><sub><font size="1" style="font-size: 8pt"><i>1</i></font></sub>,
|
||
and the time halfway during the round trip, <i>(T</i><sub><font size="1" style="font-size: 8pt"><i>1
|
||
</i></font></sub><i>+ T</i><sub><font size="1" style="font-size: 8pt"><i>2</i></font></sub><i>)/2,</i>
|
||
calculating the absolute distance between those events, and dividing
|
||
the latter into the former.
|
||
</p>
|
||
</div>
|
||
<div id="sdendnote2">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm"><a class="sdendnotesym" name="sdendnote2sym" href="#sdendnote2anc">ii</a><sup>[2]</sup>
|
||
In Minkowski’s derivation, the slope is the value of the first
|
||
derivative of his equation for the hyperbola when <i>t = x/v </i>(i.e.,
|
||
when
|
||
<img src="data:image/png;base64,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" name="StrEqXvsc" align="bottom" width="80" height="35" border="0">),
|
||
or <i>v/c</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup>.
|
||
And the length of the unit of distance on the moving space-line is
|
||
the distance required for light to have velocity <i>c</i>, that is,
|
||
the distance light actually travels in a unit of time according to
|
||
slowed-down clocks, which in terms of the length of the contracted
|
||
rod, <i>L'</i>, is also
|
||
<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADIAAAAfCAMAAACS025rAAADAFBMVEUAAAABAQECAgIDAwMEBAQFBQUGBgYHBwcICAgJCQkKCgoLCwsMDAwNDQ0ODg4PDw8QEBARERESEhITExMUFBQVFRUWFhYXFxcYGBgZGRkaGhobGxscHBwdHR0eHh4fHx8gICAhISEiIiIjIyMkJCQlJSUmJiYnJycoKCgpKSkqKiorKyssLCwtLS0uLi4vLy8wMDAxMTEyMjIzMzM0NDQ1NTU2NjY3Nzc4ODg5OTk6Ojo7Ozs8PDw9PT0+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////isF19AAAA7ElEQVR4nL1Uuw3DIBB9JVV6Vx7AJSN4hbRp3XuCkzKAe4bxBpSM4D2IwbH56ExEZPkVSNzjHY/jALYaKJFjjUQUSD66oFrSaTcS76Am0cUS1VRLfNDUSFy9zLk3lqEVQ52kjP8kWCFQxs7fauxCCQFxFxiBUn97aKtj1hVq+W0sY/shBHGi7Nwgsgxg0yVLjv7s4qgiTtHbZBNamL325PALwx5ymrRt3py9yBAsenLh0U9H3T5JRRLaXYbKtzNJSV6xPZ31PUyRROqvW9rOhCG5kOygbG+Gmj9cQswmu9PDz4FXOpVI/oF7OvkD1teCXJKS1HUAAAAASUVORK5CYII=" name="StrEqLPrime" align="bottom" width="50" height="31" border="0">,
|
||
or an effective expansion of the measuring rod at the square of the
|
||
usual rate.</p>
|
||
</div>
|
||
<div id="sdendnote3">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm"><a class="sdendnotesym" name="sdendnote3sym" href="#sdendnote3anc">iii</a><sup>[3]</sup>
|
||
The Lorentz transformation equations that Einstein derived also
|
||
imply that the others’ space-line at the point of coincidence of
|
||
origins is represented by the line, <i>t = vx/c</i><sup><font size="1" style="font-size: 8pt"><i>2</i></font></sup>.
|
||
Solve the moving observer's Lorentz transformation equations for
|
||
both time and space on the assumption that <i>t' = 0</i> (the moving
|
||
space-line through the absolute origin) and combine.</p>
|
||
</div>
|
||
<div id="sdendnote4">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm"><a class="sdendnotesym" name="sdendnote4sym" href="#sdendnote4anc">iv</a><sup>[4]</sup>
|
||
Mathematically, where <i>L</i> is the absolute measuring rod, <i>L'=L<img src="data:image/png;base64,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" name="StrEqBeta" align="bottom" width="46" height="18" border="0"></i>
|
||
is the actually contracted moving measuring rod and <i>L"=<img src="data:image/png;base64,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" name="StrEqLPrime" align="bottom" width="50" height="31" border="0">
|
||
</i>is the virtually expanded moving measuring rod, we know that
|
||
<i>L=L"<img src="data:image/png;base64,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" name="StrEqBeta" align="bottom" width="46" height="18" border="0"></i>,
|
||
and since moving observers mistakenly assume that <i>L</i>'<i>=L",
|
||
</i>that is the appearance that the absolute measuring rod is
|
||
contracted relative to the moving measuring rod.</p>
|
||
</div>
|
||
<div id="sdendnote5">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm"><a class="sdendnotesym" name="sdendnote5sym" href="#sdendnote5anc">v</a><sup>[5]</sup>
|
||
Measuring rods can also be measured with clocks, by timing how long
|
||
it takes for the others’ measuring rod to pass by traveling at <i>v</i>.
|
||
The absolute observers’ measurement is veridical, but the
|
||
appearance to moving observers that absolute measuring rods are
|
||
contracted results from using slowed down clocks.
|
||
Mis-synchronization is also implicated in this appearance, for it is
|
||
what gives moving observers the correct value for relative velocity,
|
||
despite having slowed-down clocks and contracted measuring rods.</p>
|
||
</div>
|
||
<div id="sdendnote6">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm"><a class="sdendnotesym" name="sdendnote6sym" href="#sdendnote6anc">vi</a><sup>[6]</sup>
|
||
Measuring rods can also be used to time the others’ clock, by
|
||
moving along with the other clock and comparing it with what clocks
|
||
should read after traveling at the relative velocity, <i>v</i>, for
|
||
a certain distance on our frame. Again, the absolute observers’
|
||
measurement is veridical, but the absolute clock seems slowed down
|
||
to moving observers because their measuring rods are contracted.
|
||
And mis-synchronizing clocks again plays a role in obtaining the
|
||
correct value for relative velocity.</p>
|
||
</div>
|
||
<div id="sdendnote7">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm"><a class="sdendnotesym" name="sdendnote7sym" href="#sdendnote7anc">vii</a><sup>[7]</sup>
|
||
This calculation of the effect of the mis-synchronization of moving
|
||
clocks on the moving observers measurements of the speed of absolute
|
||
clocks is also an interpretation of what is actually going on when
|
||
one derives a prediction from the Lorentz transformation equations
|
||
of what moving observers will find about absolute clocks. Assuming
|
||
that the primed variables, <i>t'</i> and <i>x'</i>, are those used
|
||
by the moving observers, then the Lorentz transformation equation by
|
||
which moving observers determine temporal coordinates in the
|
||
absolute frame for time is
|
||
<img src="data:image/png;base64,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" name="StrEqTimeDer" align="bottom" width="78" height="38" border="0">.
|
||
But since the observers’ motion is <i>x' = VT</i>, this equation
|
||
becomes
|
||
<img src="data:image/png;base64,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" name="StrEqTimeDil" align="bottom" width="79" height="38" border="0">.
|
||
The denominator represents the slowing down of moving clocks at the
|
||
usual rate; the numerator represents the result of moving backwards
|
||
past a series of mis-synchronized clocks, an effective speeding up
|
||
of clocks at the square of the usual rate; and so the partial
|
||
cancellation of the numerator by the denominator represents how they
|
||
give rise to the opposite appearance, an apparent slowing down of
|
||
the absolute clocks at the usual rate. This shows, at least, that
|
||
there are factors of the right size working in the right way to
|
||
produce the appearance.
|
||
</p>
|
||
<p lang="en-US" class="sdendnote-western"> In this case, the
|
||
deduction for moving observers happens to correspond to the cause of
|
||
the apparent distortion in the absolute frame, but the deduction
|
||
does not always corresponds to the cause of the observation. It
|
||
can’t because the deduction predicting time dilation is the same
|
||
on both sides of any pair of frames. But there is a more complete
|
||
symmetry among distortions involving opposite distortions on each
|
||
side, and one of the two kinds of deductions predicting them always
|
||
involves a mis-synchronization factor and the other does not,
|
||
suggesting there are always two ways that measurements of
|
||
distortions can be caused, namely, by real distortions and by the
|
||
appearance caused by mis-synchronization.
|
||
</p>
|
||
</div>
|
||
<div id="sdendnote8">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm"><a class="sdendnotesym" name="sdendnote8sym" href="#sdendnote8anc">viii</a><sup>[8]</sup>
|
||
The relative velocity of a third moving frame relative to the first
|
||
frame is given by Einstein’s formula for the addition of
|
||
velocities,
|
||
<img src="data:image/png;base64,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" name="StrEqRelVPlus" align="bottom" width="70" height="28" border="0">,
|
||
where <i>v</i> is the velocity of the second frame relative to the
|
||
first and <i>w</i> is the velocity of the third frame relative to
|
||
the second. This formula is derived by using the Lorentz equations
|
||
to transform the second frame’s description of the motion of the
|
||
third frame into a first frame’s description. But if the second
|
||
frame is at absolute rest, this formula yields the apparent relative
|
||
velocity of two frames as a function of their absolute velocities:
|
||
<img src="data:image/png;base64,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" name="StrEqRelVMinus" align="bottom" width="72" height="28" border="0">(since
|
||
<i>-v</i> is the absolute velocity of the first frame when <i>v</i>
|
||
is the velocity of the second frame relative to the first). This
|
||
formula for the “subtraction of velocities” describes how
|
||
observers on two frames moving through a third must appear to one
|
||
another. There is no reason for Newtonians not to use the Lorentz
|
||
transformation equations as an aid to calculation, since there is no
|
||
dispute about the predictions, only about the causes. The apparent
|
||
relative velocity is not, in general, the real relative velocity, <i>u
|
||
- w</i>, because the latter can approach twice the velocity of
|
||
light.</p>
|
||
</div>
|
||
<div id="sdendnote9">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm"><a class="sdendnotesym" name="sdendnote9sym" href="#sdendnote9anc">ix</a><sup>[9]</sup>
|
||
The equation derived from the special theory of relativity
|
||
describing the quantitative equivalence between energy and mass, <i>E
|
||
= mc</i><sup><i>2</i></sup>, is the foundation for the principle of
|
||
the conservation of mass and energy which was used as the working
|
||
hypothesis in the ontological explanation of classical physics.</p>
|
||
</div>
|
||
</body>
|
||
</html>
|