Re: SR length contraction - the train example reworked.

On Sep 20, 5:41 pm, Mathal <mathmusi...@xxxxxxxxx> wrote:
The observer on the embankment measuring the distance travelled by the
light and dividing this distance by the time the light took to travel
this distance comes up with the speed of light.

No more than a shadow seen racing across the surface of the
moon has any relevance to the speed of light.

On the train time is
running slower than in the embankment rest frame.

Not to a physicist.

The distance the
light travels WRT the frame the light is measured in is less than the
distance measured in the rest frame. There is no space contraction in
the path of the light WRT the frame on the train. There is contraction
WRT the path of the train but in the example this is irrelevant. The
measurement of the distance by the time on the train will again be the
speed of light.

Ahhh.... No.

   The one and only thing two frames of reference with different
velocities can agree upon is the speed of light. SR translates the
measuring rods and clocks in one frame so they are in accord with the
measuring rods and clocks in the other frame.
  That is what the translations are for. Neither measuring rod or
clock is "right" but with SR there is an understanding of what eack
frame measures WRT the other.
   Mathal- Hide quoted text -

- Show quoted text -

You are on the right track but don't have it quite right. Let's set
things up the same way Einstein did with A, B and M on the tracks and
A', B' and M' on the train.

A' M' B' >>
A M B

At t=t'=0 a flash is emitted from M/M' at x=x'=0

At t'=1 the light reaches B'

A' M' B'
A M B

If M and B are the same distance apart as M' and B' then the light
must have gotten to B at t=1. And for light to be traveling at the
same speed on the train it must have gotten to B' at t'=1. But when
it arrived at B' it had gone beyond B, so it arrived at B' some time
later than t=1 in track coordinates. IOW if B' looks at a track clock
he will see that its reading doesn't agree with his.

You can see this by looking at the LT for converting from t to t'. It
contains an x in it which means t' not only depends on t, but where
you are on the x axis. The further you go from x=0 the greater the
difference. The clocks being out of sync this way is called Relative
Simultaneity.

When you measure a length you record where the end points are at the
same time. If you look at the first diagram the distance between M'
and B' is the same as the distace between M and B as measured in the
track frame at t=0. But as far as the track frame is concerned it is
not yet t'=0 at B', so that is not where B' will be when the
measurement is recorded. He will be a bit further down the tracks
when his clock reads t'=0, so as far as the train can tell the tracks
measured the length short.

Hope this helps.

Bruce
.

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