BurtJordaan
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Why is relativity so hard to learn?[10X]
May 5th, 2017, 12:13 am

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This is a "whiteboard dump" for a post following on part [9] of a Philosophy of Science thread with the above name. I have thought to move things deemed too technical here for reference (As sort of Appendices).

BurtJordaan ยป 04 May 2017, 11:44 wrote:That said, in the next piece we will make Alice turn around en head home, and provided that her long-playing rocket has enough fuel left, make it little swifter.

As Mitchell has indicated above, there is a slight possibility that a future super-dooper technology could perhaps bring Alice back home with the amount of fuel that she has left. As we also discussed, if you have the technology, a higher acceleration would be better, so let us look at a one earth gravity (1g) setting on the rocket.

Say Alice rotates the coasting rocket through 180 degrees just as she gets to Alpha-C (AC for short) and fires the thing, still at 0.6c, but no pointing back to Bob. I have consulted my trusted old spreadsheet with the new acceleration and found that Alice will momentarily come to rest relative to Jim after 0.69 years on her clock. Then the rocket will accelerate her back towards Bob and reaches -0.6c relative to him just as it flies pas AC.

The whole turnaround rocket burn episode will take Alice 1.38 years, and use around 50% of her original load of fuel. So she has around 25% remaining and wisely decided there and then to cut the engine in order to save that fuel for her braking burn, needed to stop at Bob's location. The final rocket burn is identical to the one that brought Alice to a momentary 'stop' relative to Bob at the far side of AC, just in the opposite direction.

I know numerical figures are boring, but for closure, here are the return trip's values, as per the spreadsheet. Alice coasted for 4.9 years and then decelerated for 0.69 years. So it means Alice's total elapsed propertime was 10.7 to reach AC at the lower acceleration (as we discussed in part [9]) plus the 1.38 year stretch on the far side of AC, plus the coasting back of 4.9 years and then the final acceleration of 0.69 years. Added up, it amounts to 17.67 years of Alice's life.

For Bob, who lived a 'charmed inertial' life, the corresponding time accounting is: 11.8+1.5+6.9+0.75 = 20.95 years. Any accountants around who would care to validate these? OK, I know than you would want the spreadsheet and it's not quite in an auditable state - like most private spreadsheets. ;)

I fear the described process might be a bit too technical for a Philosophy of Science thread, and maybe is part of the problem rather than part of the solution. It is in dire need of more illustrations, a lot more than Epstein diagrams. However, it may yet play an important role in illustrating the difference between time dilation and "differential aging". There are two phases in the trip where relative time dilation could have been discussed, but I purposefully did not, because if the described scenario is difficult to wrap one's head around, bring in "relative aging" and it doubles the troubles.

I will try to come up with some graphics in the next part.

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