Once again, the earth measures time for the twins as going slower, but the twins measure time for the earth as going slower. This is different than what you said.Polymath is too afraid to answer these questions because he knows where I am leading him.
So we know Polymath will refuse to answer the simple questions, therefore I will just explain what I was leading him into.
1. three brothers are on Earth in the same rest frame
2. two of the brothers hop on a ship and accelerate to 0.5*c away form Earth (as Polymath has admitted, according to Einstein's relativity their proper time must always begin to tick slower than time on Earth)
yes, which is different than the rest frame of the earth.3. the two brother on the ship still share the same rest frame
Each will measure the clock of the other as going the same rate. But the clocks will no longer be synchronized. The ship measures time for both the earth and shuttle as going slower than its own.4. one brother on the ship hops into a shuttle and accelerates to 0.5*c towards Earth
5. the shuttle has entered into Earth's rest frame and is stationary relative to Earth, therefore the shuttle must now observe the same proper as observed on Earth
Here is where you are assuming an absolute time frame. The ships time slows down *with respect to the earth*. But the earths' time slows down *with respect to the ship*.6. acceleration of the ship caused the ship's proper time rate to slow down
No, it did not. The ship sees time for both the earth and the shuttle as going slower. Both the earth and the shuttle see time for the ship as going slower. This is not a contradiction because the time measurements are for different positions each way.7. acceleration of the shuttle caused the shuttle's proper time rate to speed up
No, you simply don't understand what it is predicting.8. Einstein's theory of relativity is shown to be false
Do you want me to run the numbers for you? Do you mind if I use .6*c rather than .5*c since the time dilation factor is easier for .6*c?