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Hi Al,<br>
<br>
I do not see any conflict if the situation with synchronized clocks
is obeyed as I explained it in my last mail (see below). Those clock
assemblies show dilation, but do not present any logical conflict. <br>
<br>
When looking at a real situation one has to identify the observed
object on the one hand with a clock in the example, and on the other
hand the observer with another clock or a sequence of other clocks.
If we observe a moving particle (like a muon) in a laboratory, than
the muon is represented by one clock in the moving system. In this
case the observer is represented by a line of clocks positioned
along the path of the muon. Because, if we think in an idealized
way, we have first to note the time when the muon starts by looking
at the clock which is close to the muon at start time. When the muon
decays we have for the decay time to look to the clock which is
close to the muon at that moment. <br>
<br>
This may look ridiculous as for the observer in the lab all clocks
have the same indication. But from the "view" of the muon the clock
at rest at the start looks advanced and the clock at the end looks
retarded. So the muon has the impression that the time in the lab
was slowed down.<br>
<br>
As a reminder: The equation for time transformation is: t' = gamma*
(t - vx / c<sup>2</sup>) (i.e. the Lorentz transformation). Here is
x the position of that clock which is close to the moving object at
the time of observation. And that position is x = v*t if the
observer it at rest. So, for this observer there is t' = t/gamma.
For a co-moving observer there is v = 0, so the result is t' =
t*gamma. Both results are covered by this equation, and there is no
logical conflict.<br>
<br>
Best wishes<br>
Albrecht<br>
<br>
<br>
<br>
<blockquote
cite="mid:trinity-a44de491-0053-4643-b413-fc56bdaff69c-1444650152249@3capp-webde-bs01"
type="cite">
<div style="font-family: Verdana;font-size: 12.0px;">
<div>
<div>Hi Albrecht & Curious:</div>
<div> </div>
<div>Overlooked in my previous responce:</div>
<div> </div>
<div>If, as is done in virtually all text books on SR (I just
checked Rindler, for example) time dilation is discussed in
terms of the dialtion happening to a concrete objects (as it
must if the Muon story is to make sense) then there is an
obvious inconsitency and sever conflict with the relativity
principle. Two entities cannot at once be both be dialted
in the other's view and not their own. The real trick here
is explaing how this is not obvious to authors of text
books! Maybe, to paraphrase Weinburg: That stupid people
say dumb things is natural, to get smart people to say dumb
things, it takes physics!</div>
<div> </div>
<div>Your explantion (or my prefered version: perspctive)
renders the objection both mute and sterile wrt muons,
however. </div>
<div>
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<div style="margin:0 0 10px 0;"><b>Gesendet:</b> Sonntag,
11. Oktober 2015 um 22:55 Uhr<br>
<b>Von:</b> "Dr. Albrecht Giese"
<a class="moz-txt-link-rfc2396E" href="mailto:genmail@a-giese.de"><genmail@a-giese.de></a><br>
<b>An:</b> <a class="moz-txt-link-abbreviated" href="mailto:general@lists.natureoflightandparticles.org">general@lists.natureoflightandparticles.org</a>,
"A. F. Kracklauer" <a class="moz-txt-link-rfc2396E" href="mailto:af.kracklauer@web.de"><af.kracklauer@web.de></a><br>
<b>Betreff:</b> Re: [General] nature of light particles
& theories</div>
<div name="quoted-content">
<div style="background-color: rgb(255,255,255);">Hi Al,<br>
<br>
about time dilation.<br>
<br>
The problem is that time dilation looks inconsistent
at the first glance. But it is not. I shall try to
explain. It has to do with clock synchronization. (I
try to do it without graphics, which would be easier,
but a problem in an email.)<br>
<br>
Assume that there are two inertial systems, I call
them A and B. Both move in relation to each other at
some speed v. Now assume that there are clocks
distributed equally over both systems. And of course
in both systems the clocks are synchronized. Now there
comes a relativistic effect. If the observer in A
looks to the clocks in B, he finds them
desynchronized. The clocks which are in front with
respect to the direction of motion are retarded, the
ones in the rear advanced. Similar in the other
system. If an observer in B looks to the clocks in A,
he finds them also desynchronized in the way that the
clocks in the front are retarded and the clocks in the
rear advanced. Shall I explain why this happens? If
you want, I can do it. But next time to keep it short
here.<br>
<br>
Now, what is dilation in this case?<br>
<br>
If the observer in A takes one of the clocks in B and
compares it to those clocks in his own system, which
is just opposite in sequence, then the clock in B
looks slowed down. But if he takes one clock in his
own system, A, and compares it to the clocks in B
which are opposite in sequence, the clocks in B look
accelerated.<br>
<br>
Now it looks in a similar way for the observer in B.
If the observer in B does the equivalent to the
observer in A just described, he will make just the
same experience. No contradiction!<br>
<br>
In the case of the muons: The muon which will decay is
in the position of a clock in the muon-system, and
this clock is slowed down as seen from the observer at
rest as described above, and this is no violation of
symmetry between the systems. If an observer, who
moves with the muon, looks to the clocks of the system
at rest, he will find those clocks accelerated. No
contradiction. Correct?<br>
<br>
Albrecht <br>
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