A while ago there was a here thread about instant communications. . The thread evolved a.o. to the question of simultaneity and universal time in the universe. I think some of us remember...

At a certain point the following idea came into my mind , which I worked out a little and want the results have discussed here in order to check them if they're right...

The picture below might explain it .

Suppose we have a system of a central star orbited by two coorbital planets which are at 180° , so each being at the exact opposite site of the sun.

Suppose further that there is an inertial observer positioned highly above the ecliptic of the system . When he looks down he sees the planets evolve exactly at 180°.

Also an inertial observer located at the suns surface sees both sister planets at 180° ...

Suppose also that both planetes are tidally locked to the central star , so they both keep the same sides directed towards the sun .

For simplicity let the planets orbit the star without eccentricity . This means that at any given time an observer on each planet always sees the sun at the same point in the sky , all over the year ...

I can imagine the inertial observer highly above thinking : I'm a privileged guy . I can watch this small solar system for all time , but it must be really boring for the people living on these planets : they don't even know they have a sister planet as their sun blocks the light of their sister planet ....

Is this observer right ?

Depends . Depends upon the orbital speed of the planets and the distance towards the sun .

In case of the Sun-Earth system fi. the light of a (hypothetical) sister planet would take about 16 minutes to reach us . In this time our Earth moves by about 28000 km or 16/(24*60) arcdegrees . If the suns diameter would have been smaller or if our planet would rotate faster , it might even be possible that our sister planet becomes visible as at "moves" from behind the suns surface due to the time lag .

We would see the planet "lagging behind" .

Curiously the inhabitants of our sister planet would have the same perception : also our planet "lags behind" , instead of leading .

Consider the confusion if both societies were able to communicate : "you have lag " , "no, it's you having lag " .

While it makes common sense that if one leads the other must lag ...

Who is right ? The intertial observer above ? , the observer at the sun ?, the inhabitants of planet A ? , or those of planet B ?

So one might think about this : Is there such a thing as general truth in the universe ?

( This question had already been answerd ...)

I wrote down some simple equations to calculate the angle of lag ( or deviation from the zero angle ) as a function of v/c .

I expected that as v/c increases up to ~1, the formula would give a special value for the angle , but this doesn't seem to be so .

There's no special value or singularity , as the angle of deviation is about 42,. degrees at v/c~1., rather meaningless .

Even at higher v/c >1 , although fysically impossible, the deviation angle increases...