Upchurch:
In this specific case, the direction is the same for all frames of reference, but they could be different if moving in anything other than one dimension.
Say what?
Franko:
In other words from my perspective aren’t the two ships traveling away from each other at a rate Faster than the speed of light?
Upchurch:
The question you're asking is what is the relative speed between the east and west ships. You're trying to make it a three frame problem when speed is only applicable between two frames. with the three frames you've given, you can only talk about the speeds between each set of frames. However, given SR, we can from one frame, calculate the relative speeds between any other set of frames, given the relative speeds of each frame to the first frame.
Franko:
So if there are two photons being simultaneously emitted from the surface of the sun in opposite directions then you are claiming that they are moving apart from each other at less than 2xC?
Upchurch:
I just showed they are moving apart at half that speed above. Do you see an error in my math?
Franko:
Does that mean it takes photons longer than 8 minutes to go from the Sun to the Earth, because I am fairly certain the sun emits photons in ALL directions ALL the time?
Upchurch:
Well, I know that 8 minutes is an approximation, but no it doesn't take longer than that approximation. And I am also fairly certain that the sun emits photons in all directions at all times.
The Earth is approximately 93 million miles form the Sun. The speed of light (“C”) is about 186,000 miles per/sec. 93,000,000 divided by 186,000 = 500 seconds divided 60 = 8.333 minutes for light form the Sun to reach the Earth. Now, how can the light be reaching the Earth that quickly when there are also photons being emitted from the opposite side of the Sun and traveling in the opposite direction at the speed of light?
Look, imagine that there is another Planet the same distance from the Sun as Earth on the opposite side of the solar system. The Two planets would be approximately 186 million miles apart (93 million x 2), but light from the Sun reaches them both in 8.33 minutes. Obviously the photons headed off to the two different planets are moving apart from each other at twice the speed of light.
Are you still claiming something different Upchurch?
Franko:
So if the photons are traveling at 300,000 km/sec each, then in 10 seconds how far apart from the Sun will each photon be, and how far part from each other will each photon be?
I would say that in 10 seconds the two photons will each be 3,000,000 km from the Sun, and 6,000,000 km from each other. What EXACTLY are You claiming?
Upchurch:
Hm... Interesting question, which is actually beyond the scope of SR. Due to length contraction, one could approximate through limits that, from each photon's frame of reference, the relative velocity between the two photons is 1c. Special Relativity calculations of length contraction only work for velocities less than 1c. You can make an approximation using limits, however. So, from the photon's frame of reference, after "10 seconds" (I'm not sure that's valid to say), the photons would be 0 light seconds apart. Again, that's a tentative answer based on incomplete information.
I agree that they would be an amount of km greater than zero from the sun, but I can't say what they would be from each other, as per above.
So you are claiming that it takes Light Far longer than 8.333 minutes to reach the Earth from the Sun?