Re: The velocity of light going pass a moving train.


"Jeckyl" <noone@xxxxxxxxxxx> wrote in message
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"harry" <harald.vanlintelButNotThis@xxxxxxx> wrote in message
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"Jeckyl" <noone@xxxxxxxxxxx> wrote in message
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[...]

Here is what you see from the track (where the '^' represents the light
and the "===" the floor and roof of the train

------> motion of train
at t=0:
====


^
====

at t=1:
====

^

====

at t=2:
====
^


====
note the path of the light as seen from the track over time is

^
^
^

as seen from the train it is

====
^
^
^
====

Upto here, perfect and very clear. Well done! But next you seem to
misunderstand something,

Not at all

for your above design is the CORRECT design for the description in the
frame of the track as well as for the frame of the train.


If you reverse everything .. of course.. there is nothing special about
the train or the track .. they are just frames of reference.

In this special case it is irrelevant that the train is length contracted
in the frame of the track.

Yes .. as the light is travelling vertically, length contraction in the x
direction of the train doesn't matter

Note the when seen from the track, the light is moving diagonally in the
direction of the train.

Relativistic aberration would actually make what is observed from the
track ACTUALLY more like

^
^
^

ie further inclined in the direction of the train than classical physics
would tell us. This is sometimes called the headlight effect.

That "further inclination" is erroneous for this case, as the light beam
would miss the correct point on the ceiling in the train - I hope you now
spot the error.

Its not an error.

The first set of diagrams shows classical aberration. The second diagram
shows the difference in angle when you take SR into account .. the light
is more inclined and the train would have travelled further (otherwise, as
you noticed, the light wouldn't hit the roof directly above the source
within the train)

Eg. if the train was moving at 0.5c, classic aberation would put the angle
at 63deg = atan(2) because the train would have moved forward by a
distance equal to half the height of the train (because its only going at
half the speed). (ie you get a 1, 2, sqrt(5) triangle)
But with SR taken into about, the angle is 60deg (ie you get a 1, sqrt(3),
2 triangle)

I hop you understand now.

I certainly do.

Summary for a laserpointer inside a train that is pointing upwards:

For a speed v, the path of the light as seen from the track over time is:

^ x=v*t
^
^

as seen from the train it is

====
^ x'=0
^
^
====

As I pointed out, NO relativistic effects come into play in this particular
illustration, as the length contraction comes of the train doesn't matter at
90 degrees. But you replied by stating:
"when you take SR into account .. [...] the train would have travelled
further."

Further than what? Certainly NOT further than x=v*t ;-)

Aberration confuses many people, but with a consistent use of logic and math
there is no problem at all. If you want to illustrate relativistic
aberration, you can find it with the laser pointer pointing upwards on the
railway tracks, illuminating a spot on the electric wires. Then the length
contraction of the train can be seen as cause for the relativistic
aberration effect that is seen from the train when the train changes speed.

And this is where I abandon my efforts. Good luck!

Regards,
Harald



.

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