 Twin paradox

The twin paradox compares proper time along the different world lines of a travelling observer and a stay-at-home observer who reunite. Reciprocal inertial time dilation produces an apparent contradiction only if the traveller's change of inertial frame is ignored.

The decisive experiment is local: put two clocks together at departure, separate them, then compare their readings together at reunion. Everyone agrees on those two spacetime events and on the final difference. The twin paradox asks why two clocks can accumulate different proper times between the same spacetime events, despite reciprocal time dilation during uniform motion. Its answer is the geometry of their complete world lines, together with the relativity of simultaneity when comparing distant clocks.

The Twin Paradox is a thought experiment in the realm of special relativity, famously introduced by Albert Einstein. It involves two twins, one of whom makes a journey into space in a high-speed rocket and then returns home, while the other twin remains on Earth. Due to the effects of time dilation predicted by Einstein's theory of relativity, the traveling twin will age more slowly compared to the twin who stayed on Earth.

The key question is: why is this not symmetrical?

One answer is: because one of the twin accelerates, and therefore changes inertial frames.

But the better answer is: understand what happens when the stationary twin sends light signals at constant time intervals to each other. When does the travelling twin receives them?

By doing that, we see that "all the extra aging happens immediately when the twin turns around":

Another way of understanding it is: you have to make all calculations on a single inertial frame for the entire trip.

Supposing the sibling quickly accelerates out (or magically starts moving at constant speed), travels at constant speed, and quickly accelerates back, and travels at constant speed setup, there are three frames that seem reasonable:

If you do that, all three calculations give the exact same result, which is reassuring.

Another way to understand it is to do explicit integrations of the acceleration: physics.stackexchange.com/questions/242043/what-is-the-proper-way-to-explain-the-twin-paradox/242044#242044 This is the least insightful however :-)

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