It is well known that the key to resolving the Twin Paradox is to realize that the situation between the twins is not symmetrical. In order to leave and come back home, the traveler needs to accelerate. Thus, a popular way to resolve the paradox is to assume that the traveler travels away from the Earth at constant speed, makes an instantaneous U-turn, then comes back at constant velocity. This leads to calculations that require only basic algebra, but the instantaneous U-turn results in a non-physical infinite acceleration and leads to objections from many people.
In order to solve this problem, I present in the tutorial below an exact and rigorous resolution of the paradox by considering a realistic acceleration of the traveler. The situation is analyzed from the points of view of both twins, who ultimately agree that it is the traveler who ends up younger.
Watch my tutorial here: https://youtu.be/QFWF90bch3c
If you like this tutorial, please share it!
There is no need for acceleration.
Instead of using the confusing antropocentric narratives you can use two pre-planned trajectories of two travelling clocks and stay home clock.
1 Clock one accelerated earlier arrives home and both clocks set their time to 0 and one continues unaccelerated motion.
2 clock one meets clock two on its path accelerated much earlier and programmed to fly a collision course with one and with home at the same time
3 At proximity clock two receives clock one time ands sets its own to zero.
4 upon return the total time of the round trip is the sum of the two.
5. Proper mathematical calculations of the twin piece wise trajectory confirms the sum of travelling clock time is less then home time.
Sure, but the twin paradox is originally about a twin going on a trip, then coming back to meet his brother again (therefore the traveler accelerated somewhere). Solving it the way you do won't satisfy anti-relativist people who will object that your example has no reality.
"Attempts to analyze the supposed twin paradox seem to always ignore the fact that acceleration involves transitioning through every intermediate velocity, which requires the integral of the Lorentz factor."
I'm not sure what you are complaining about. Integrating the Lorentz factor is precisely what I did in my tutorial.
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