Subject:      A Rebuttal of the Relativity of Simultaneity
From:         cj@totcon.com (C.J. Luke)
Date:         1997/02/27
Message-Id:   <5f30od$k9c@usenet81.supernews.com>
Organization: Totally Connected
Reply-To:     cj@totcon.com
Newsgroups:   sci.physics.relativity

Chapter IX of "Relativity the Special and the General Theory" gives
the now famous railway embankment and railway carriage  scenario that
goes like this:
Two lightning bolts strike the rails at A and B.  Observer M is
situated at the embankment such that he is located equidistant from
points A and B.  The railway carriage is moving along the rails with
constant velocity v with respect to the embankment. 
What follows is a quote from the chapter IX:

"When we say that lightning strokes A and B are simultaneous with
respect to the embankment, we mean: the rays of light emitted at the
places A and B, where the lightning occurs, meet each other at the
mid-point M of the length  A -> B of the embankment.  But the events
also correspond to positions A and B on the train.  Let M'  be the
mid-point Aà B on the traveling train.  Just when the flashes (as
judged from the embankment) of lightning occur, this point M'
naturally coincides with the point M, but it moves towards the right
in the diagram with velocity v of the train.  If an observer sitting
in the position of M' in the train did not posses this velocity, then
he would remain permanently at M, and the light rays emitted by the
flashes of lightning A and B would reach him simultaneously, i.e. they
would meet just where he is situated.  Now in reality (considered with
reference to the railway embankment) he is hastening towards the beam
of light coming from B, whilst he is riding on ahead of the beam of
light coming from A.  Hence the observer will see the beam of light
emitted from B earlier than he will see that emitted from A.
Observers who take the railway train as their reference-body must
therefore come to the conclusion that the lightning flash B took place
earlier than the lightning flash A.  We thus arrive at the important
result:
        Events which are simultaneous with reference to the embankment are not
simultaneous with respect to the train, and vice versa (relativity of
simultaneity)."

By this point in the book, Einstein has stated the Principal of
Relativity (in the restricted sense),  he has defined simultaneity as
follows:

"There is only one demand to be made of the definition of
simultaneity, namely, that in every real case it must supply us with
an empirical decision as to whether of not the conception that has to
be defined is fulfilled.   That my definition satisfies this demand is
indisputable.  That light requires the same time to traverse the path
AàM as for the path BàM is in reality neither a supposition nor a
hypothesis about the physical nature of light, but a stipulation which
I can make of my own freewill in order to arrive at a definition of
simultaneity."

The Diagram

v-->       A                M'              B        v-->

___________|________________|_______________|____________/  Train
___________|________________|_______________|________________Embankment

                            M
Now for a closer look

Considering the railway embankment and observer M, how can he know the
event of the lightning strikes were simultaneous?  There is only one
answer that is consistent with what has been set forth in text so far,
i.e. the observer at M must know that the distance A-->M is equal to
the distance M-->B and that light has a uniform velocity c in his
reference frame.  In other words, he must be at a point that is
equidistant from A and B when the light from A and B arrives and light
must have a uniform velocity c with respect to his reference frame.

I believe that the above is consistent with the Theory of Relativity.

Consider the event from the reference frame of the observer at M',
i.e. the railway train.  If light travels at velocity c with respect
to his frame of reference, then how can he be "hastening towards the
beam of light coming from B, whilst he is riding on ahead of the beam
of light coming from A".  This statement requires that  the ray of
light from B have a velocity c (with respect to him) while he has a
velocity v with respect to the ray of light coming from A, thus the
light B would reach M' with velocity v + c and for the same reason the
light from A will reach M' with velocity c - v.  This is not
consistent with the Principle of Relativity.

When we consider this from the observer at M' frame of reference, A
and B have no motion with respect to M'.  To quote from above, "the
events also correspond to positions A and B on the train" , so we can
ignore the embankment  and all references to it and just consider the
frame of reference of the observer at M'.  Lightning strikes A and B
on the train which are equidistant from the observer at M'.  The light
travels the distance A-->M' and M'-->B at velocity c with respect to
the frame of reference of the observer at M', therefore the observer
will record that the events are simultaneous.  This is consistent with
the Principle of Relativity.

Now we add two clocks that were synchronized in the frame of reference
of the embankment at time t.  The observer on the train gets one of
the clocks and the observer on the embankment gets the other.  For the
moment let us say that time is absolute, that 1 second on the train is
equal to 1 second on the embankment.  The question to answer is; `when
did the event occur?'  Both observers can agree that the event was one
of simultaneity but do they agree as to when it occurred?  By the
original description we remember that according to the frame of
reference of the observer at M, points A and B on the embankment and
the train were coincidental and equidistant from M and M' which were
coincidental.  The observer at M is in complete agreement with the
Principal of Relativity and analyzes the event from that perspective
using his frame of reference.  He records the event at time t + 100and
notes the simultaneity.  It took the train time t + 100 to arrive at
the point where the coincidence of M and M' occurred.  Looking at it
from the frame of reference of the train we arrive at the same result,
i.e. the train took time t + 100 to arrive at the point of coincidence
of M and M', and the event was recorded as being simultaneous.  We
also recognize that  because A and B on the embankment are coincident
with A and B on the train and that M and M' are coincident, there is
no mysterious change in the physical length of the train or
embankment.

The two observers  are discussing the results of the test and the
observer  M makes the following statement while speaking to the
observer at M':

From my frame of reference, you had velocity v towards point B and
according to Maxwell, Morely and Michaleson  et. al. The velocity of
light in my frame of reference is c.  That means that you had velocity
v + c with respect to the ray of light coming from B and c - v with
respect to the ray of light coming from A with respect to my frame of
reference.  In other words from my frame of reference I don't see how
you could record the same time or see the event as simultaneous.
The observer at M' pauses for a moment and replies:   But I can say
the same of you based on my frame of reference, you were the one in
motion with respect to me and as a consequence you had velocity v with
respect to light in my frame of reference.  That means that you were
approaching the ray of light from A at velocity v + c and the ray of
light from B was approaching you at velocity c - v, therefor you could
not have recorded the event as simultaneous nor could you have
recorded the same time as I.  The observer at M thinks for a while and
says:  As an observer I am limited to my perception of what is true by
the velocity of light.  In other words when I see that point M' on the
train is coincident with point M on the embankment, this in fact is
not true.  The train has velocity v with respect to my frame of
reference and light propagates at velocity c with respect to my frame
of reference, so when I `see' that a condition of coincidence exist,
in fact point M' has moved beyond coincidence towards B at velocity v.
The distance of this `offset' can be defined by v * ( d/c ) where d is
the distance that separates M from M'.  Conversely, you have the same
limitation and can calculate my `offset' as v * ( d/c ) also with the
difference being that with respect to M, the `offset' of M' is towards
B and with respect to M' the `offset' of M is towards A.

Because of this new understanding they both realize that they could
only have recorded the event as happening at the same time if M and M'
were the end points of a line of length d that intersected a line that
intersected A and B and that the line M-->M' was bisected by and
perpendicular to the line A-->B. 

What is wrong with the above analysis???


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