Re: Query about simultaneous events..

From: Theo Wollenleben (alpha0x89_at_yahoo.de)
Date: 09/01/04 

Date: 1 Sep 2004 07:29:53 -0700

aweston@connectfree.co.uk (Tony Weston) wrote in message news:<55ec432f.0408250051.1edd657f@posting.google.com>...
> Hi There,.
>
> I've just been browsing through the Theory of Reletivity on Project
> Gutenberg,
>
> http://www.gutenberg.net/dirs/etext04/relat10.txt
>
> Now, the following two paragraphs, are an extract from the text, to
> which I have a query regarding:
>
>
> >When we say that the lightning strokes A and B are simultaneous with
> >respect to be 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 arrow B of the embankment. But the events
> >A and B also correspond to positions A and B on the train. Let M1 be
> >the mid-point of the distance A arrow B on the travelling train. Just
> >when the flashes (as judged from the embankment) of lightning occur,
> >this point M1 naturally coincides with the point M but it moves
> >towards the right in the diagram with the velocity v of the train. If
> >an observer sitting in the position M1 in the train did not possess
> >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.

That's the crucial point. From the above observation we know, that the
observer in the train doesn't see the flashes simultaneously. From
this observer's point of view there are two flashes starting at the
same distance, travelling with the same speed and arrive at different
times. Therefore:

> >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). Every reference-body (co-ordinate system) has its own
> >particular time ; unless we are told the reference-body to which the
> >statement of time refers, there is no meaning in a statement of the
> >time of an event.
>
>
> What I do not understand, is that when the lightning strikes point A,
> and point B, on the rails, at this moment, there will be the
> equivalent points A1 and B1 on the train. These points will be equally
> distace from M1.
>
> Now, according to what has already been said, relative to the observer
> on the train, the two light rays from A1, and B1 will travel towards
> M1. The speed of light is always c, so, the time taken to travel from
> A1 to M1, and A2 to M2, should be identicle. Therefore, I would have
> thought that the two beams should reach M1 concurrently,

Why? There is no reason to think so. Actually we know from the
observer on the embankment that the beams do not reach M1
concurrently. I suppose that you assume absolute simultaneity (i.e.
"at this moment" is frame independent). This of course leads to a
contradiction, since this gedanken experiment is designed to show that
simultaneity is relative. The important assumption is that the speed
of light has the same value for every inertial frame of reference.

> and so to the
> train Observer, both lightning strikes will indeed appear
> simultaneous.
>
> This seams at odds with what has been explained. Maybe I'm missing
> somthing?
>
> One thing that is noticed, is that, from an observer on the
> embankment, the two rays of light traveling from stationary points A
> and B, to M1 (note A and B are stationary, M1 is moving) Will appear
> to arrive at differn't times to M1,

Exactly.

> and likewise, if M1 is instead
> looking at what time the light rays hit M, he will see the light
> meeting M not simultainuously.

That's wrong. When the light flashes meet at M, this defines an event
(a point in space-time). The two events "light from flash A meets M"
and "light from flash B meets M" conincide, it's the same point in
space-time. And two events at the same point in space-time are always
simultaneous (trivially).

You can easily understand the situation when looking on Dirk's diagram
(http://users.pandora.be/vdmoortel/dirk/Stuff/BankTrain.gif): The
event LM (light beames arrive at M) is one point in space-time. In
contrast the events LA and LB (light beams arrive at M1) are different
points in space-time.

> Can anyone clarify what's realy going
> on.
>
> Thanks

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