The clock in the waggon

[Luigi Fortunati]

In my animation
<https://www.geogebra.org/m/vt22y2ww>
there are two interesting peculiarities.

The first is that the red clock (despite being inside the waggon)
belongs to the station reference system because it moves to the left at
the same speed v=0.866c with which the train moves to the right.

The second peculiarity is that the time of the red clock does not have
to be measured by others because it measures its time itself.

If someone reports any inaccuracies to me, I will make the appropriate
changes, otherwise I will proceed to complete the second part, the one
in the station reference.

[Luigi Fortunati]

[[Mod. note -- I'm sorry for the long delay in processing this article,
which arrived in my moderation system on 2022-08-04 and was unfortunately
misclassified as spam.
-- jt]]

Post by Luigi Fortunati
In my animation
<https://www.geogebra.org/m/vt22y2ww>
there are two interesting peculiarities.
The first is that the red clock (despite being inside the waggon)
belongs to the station reference system because it moves to the left at
the same speed v=0.866c with which the train moves to the right.
The second peculiarity is that the time of the red clock does not have
to be measured by others because it measures its time itself.
If someone reports any inaccuracies to me, I will make the appropriate
changes, otherwise I will proceed to complete the second part, the one
in the station reference.

In working on the second part, I encountered difficulties in managing
the contraction of space.

As you can see in the animation
<https://www.geogebra.org/m/a5gr8yr7>
I added the tracks with the sleepers (0 to 8) 0.866c apart from each
other.

But, in the station reference, this distance doubles, because the
tracks are not in motion and, therefore, are not contracted as in the
train reference (where they move).

And so, with the length of the waggon contracting by half (from 8 to 4)
and the length of the track sections increasing (from 1 to 2), in the
station reference the waggon is only as long as 2 sections of track and
no longer 8 as it was in the train reference.

It seems to me an excessive difference but, after having thought and
rethought it, it seems to me that it is just like that.

I just wanted to show you how my work is progressing and now I will go
on to implement the waggon motion in the station reference.

[Luigi Fortunati]

Post by Luigi Fortunati
In my animation
<https://www.geogebra.org/m/vt22y2ww>
there are two interesting peculiarities.
The first is that the red clock (despite being inside the waggon)
belongs to the station reference system because it moves to the left at
the same speed v=0.866c with which the train moves to the right.
The second peculiarity is that the time of the red clock does not have
to be measured by others because it measures its time itself.
If someone reports any inaccuracies to me, I will make the appropriate
changes, otherwise I will proceed to complete the second part, the one
in the station reference.

I have completed my animation
https://www.geogebra.org/m/j7qrdzdm

The proper length of the waggon is equal to 8 * 0.866 light-seconds.

The proper distance between one rail sleeper and another is equal to
0.866 light-seconds.

The speed of the train with respect to the tracks (and of the tracks
with respect to the train) is v=0.866c.

The length of the waggon is halved in the station reference.

The distance between one Rail sleeper and the other is halved in the
train reference.

The station time is double dilated in the train reference.

The train time is doubled dilate in the station reference.

It seems to me that nothing is missing.

Ps: Is it better vaggon or vagon?