Thanks Zephir for making my diagrams accessable.


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What do the diagrams depict?

Both diagrams depict basically the same thing where we have planet A on the left and planet B on the right.
In both diagrams planet A is considered to be stationary and planet B is considered to be moving away (at half the speed of light just for ease of interpretation).
In both diagrams a photon is sent from one planet to the other.
Diagram 1 differs only in that a light photon is sent from planet A to planet B and in diagram 2 the light photon is sent instead from planet B to planet A.
Planet B is depicted as moving away from left to right from lightest depiction at closest to darkest depiction at furthest.
The lightest depiction is planet Bs place when the photon is emitted and its darkest depiction is planet Bs place when the photon arrives at the other planet.

What does Einstein tell us?

It is correct - as per Einstein's relativity - that both planet A and planet B see each other moving away rather then themselves.
In this respect what A sees from B will be exactly what B sees from A.
So a photon sent from A to B will travel exactly the same amount of time as a photon sent from B to A.
So if they are sent simultaneously both planets will receive the other's light photon simultaneously.


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What do the diagrams demonstrate?

Taking our base reference of planet A being the stationary planet in both diagrams you can see the following:
Planet B keeps moving away from planet A.
So for diagram 1:
A photon sent from planet A therefore chases planet B as it moves away.
The photon sent from planet A will eventually catch up with planet B.
And for diagram 2:
The photon is sent from planet B to planet A while planet A and planet B are at their closest.
It then travels to the stationary planet A without needing to chase it - from our perspective.

What can we then determine from the diagrams and Einstein?

You can see that relative to us (considering ourselves stationary at planet A) that a photon sent from our planet A to planet B travels twice the distance then a photon that is sent from planet B to us (where A & B are diverging at half light speed).
Yet we already know from Einstein's relativity that no matter which direction the photon travels between A and B that it will take the same amount of time.
If the photon travelling from B to A travels only half the distance as the photon travelling from A to B, and in the same amount of time, then you can only get the following conclusion:
The photon travelling from B to A is travelling at half the speed than the other photon that is travelling from A to B when considered relative to planet A.


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Explanation

As I mentioned already, planet B sees planet A moving away just as planet A sees planet B moving away.
In this respect you could reverse all that has been said above and apply exactly the same conclusions except oppositely.
How then can it be that a photon can travel, from planet A's perspective, only half the distance from B to A then it does from A to B; yet also oppositely, from planet B's perspective, only travel half the distance from A to B then from B to A.
This is where frames of reference and rulers come in.
If your frame of reference is planet A then your ruler begins from your planet A. If your frame of reference is planet B then your ruler begins from planet B.
If you were on planet A and you saw someone on planet B measuring the distance the photon travelled over time you would see their ruler moving.
You would say to them, "Hey! Your ruler is moving backwards; you are measuring wrong."
Correspondingly they would see and say the same to you.

So rulers are relative to the thing that is declared to be stationary.
In this respect, when the photon travels from B to A planet B will see it cover a distance of one light distance but A will see it cover only a distance of half a light distance.

What does this mean?

I think that this should show that light travels at different speeds to the receiver based upon the difference in speed between the emitter and receiver.
However, this does not matter. I'll explain why.

I am thinking that when we receive light that has travelled a long way from a far object that the following occurs:
We can determine the difference in speeds due to spectrum shifting against standards candles.
We see the star in appearance as it was; not as it is now.
However, against a standards candle we can work out where is now; not where it was back when it actually emitted the photon.
We can use the above to work out how much closer the star was when it first emitted the photon.
And we can do all this using a constant speed of light.

Of course the star or object may not be where we work it out to be because it could have changed existance, speed or direction and the light travelling to us could have changed speed and distance. But in the absence of being there this is as good as it gets except for some adjustments if we know what has occurred.

Now I have said that we can use a constant speed of light to work these things out despite having stated that light doesn't travel at only one speed relative to us.
Look again at the diagrams and you can see that although the photon from A to B travels twice the distance than the other photon travels from B to A - both relative to A - you can see that in both instances the planet A and planet B both end up the same distance apart by the time the photons reach the opposite planet.
So if we use the speed of light constant in the equation either way we will still end up with the final distance between A and B being the same for the same amount of time.

It is all a matter of perspective when it comes to measuring distances. This is the so called reference frames.

I hope that I have been able to clear this matter up for others here - as I have for myself.
But I also hope I have shown clearly that light actually travels at different speeds relative to the observer; though it can be considered to be travelling at one constant speed for purposes of calculation.
Obviously this may require further discourse so I'm happy to do so.