The orbital speed v of the planet Earth is about 30km per second to the east.
The ratio v/c against the speed of light is 1/10000. As the light propagates independently from it's source there is enough space and time for aberration:
Light signals from a source in the north or south direction at a distance of .. are offset by:
- 0.5m (Eye to screen distance): 0.05mm=1 hair width
- 1m (1000 mm): 0.1mm=2hw
- 1.6m (Distance to your feet) : 0.16mm=3.2hw
- 11m (Michelson interferometer): 1.1mm
- 3000m (Virgo North arm, 70°): 28cm
- 4000m (Ligo H1 South arm, 288°): 38cm
According to Aleksandar Gjurchinovski in Am. J. Phys. 72, 1316 (2004); http://dx.doi.org/10.1119/1.1778390
"the moving mirror is contracted along the direction of its motion by the usual Lorentz factor."
"The result emphasizes the reality of Lorentz contraction by showing that the contraction is a direct consequence of the first and second postulates of special relativity, and is not a consequence of the relativistic measurement of the length."
This is the explanation given to the students all around the world. Is this something to believe or does it make any sense? For the upward motion a shortened angle of mirror S may turn the ray to the right, maybe matching the target position. But, on downward motion the same right turn of the target would take place! Failure!
The right answer is:
There will be no shift on screen E because the aperture moving with v which is necessary to cut a narrow part of the light beam removes all but the rays of angle sin(α)=v/c.
Sometimes it's too easy to see the solution. Therefore the most educated scientists may have trouble to realize reality.
``The orbital speed v of the planet Earth is about 30km per second to the east.''
Whatever that means. To the east or west, I can agree that we have a velocity of 30 km/s
On the other hand, there is no aberration simply because both source and observer share this motion.
Sometimes it is too easy to see the solution.
F.Leyvraz: "On the other hand, there is no aberration simply because both source and observer share this motion."
What does it mean "share this motion". Is "sharing" enough to fix some argument?
And what does the light? Does it share this motion too?
If not, the light would have to take a different path to E.
Both source and observer have the same rectilinear uniform motion, which we can therefore transform away.
To some extent, of course, the motion is not exactly rectilinear uniform: in the time necessary for light to cover, say 4 km, the Earth turns a bit around its axis and the orientation of the path is affected. This does give an effect, but one too small to measure.
But even your language is a bit strange : you say the light would have to take a ``different'' path. Different from what?
GLG: The orbital speed v of the planet Earth is about 30km per second to the east.
It is to the east at midnight but to the west at noon, however that is irrelevant.
The problem is that you seem to be assuming that the speed of light is defined relative to the Sun. The speed is c in any inertial frame. The surface of the Earth is inertial apart from its rotation about its own axis and its small acceleration towards the Sun due to it orbital motion. Neither of these would cause aberration.
We don'r have to discuss any postulates here.
This is a fully empirical question:
Please mark in the template picture below the path of of light according to your ideas/concepts/postulates/principles/theories etc.
(Any pixel graphic app may be applied)
The simple empirical answer is that, if you position your laser at L pointing at D, then the light beam will be a horizontal line from L to D as long as the box is moving inertially regardless of the speed of the box as measured by someone outside.
What you need to think about is what location you are using within the box as the origin for measuring distances x and y.
P.S. I missed your previous diagram that notes you have a mirror at S. The light path will be exactly horizontal until it hits the mirror, thereafter exactly vertical to E.
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