Einstein's Twin Paradox explained: Find out why one who remains on Earth would be elder?: Tech Flecks

EINSTEIN'S TWIN PARADOX: Terra and Stella's story, one who remains on Earth would be elder. Find out why? 

[EINSTEIN'S SPECIAL THEORY OF RELATIVITY]

Topics covered:

Einstein's Twin Paradox explained. Twin paradox explanation. All about Twin Paradox given by Albert Einstein.Simple and visual explanation of Einstein's Twin Paradox. Twin paradox images. Terra and stella story. TechFlecks

The Twin Paradox is indeed a special relativity conceptual hypothesis about identical twins, including the one who takes a high-speed spacecraft voyage into space and comes home to discover that twin who remains on Earth would be elder(more aged than that in space actually, after same time).

Two twin explorers apply for an experiment on their twentieth birthday. Terra decided to stay on Earth, and Stella will take a spaceship on board. At about 90% of the velocity of light, Stella's ship will fly to reach a star which is ten light-years far and return to Earth with same velocity. The twins wonder what will happen when they're reunited. They're preparing to cross paths. Since the distance light can travel in a year is precisely a light year, the voyage of Stella would take 23 years. But the twins know that it's not that easy, having studied special relativity. Firstly, relative to an unmoving observer, the quicker an object moves through space, the slower it moves through duration. 

Spectators in an inertial or non-accelerating frame of reference, like Terra returned to Earth, would be the only people who could detect time on Stella's travelling spacecraft passing slower. Thus, Terra believes that she'll be old than Stella when they settle returned to Earth. But that is just one way to look at it. Stella claims that since all movement is subjective, it would be just as true to say that her space ship would remain still while the rest of the world shifts around her, including Terra. So in that case, time of Terra would pass twice as slowly, ultimately making Stella the elder sibling. Both of them can't be older than another, which one is right?

Thus they compare how long it took the other twin to witness a year passing, and how long it would take for light to move between them, when one twin observes a burst of light. On a chart, we can watch what's occurring. Distance from Planet is marked by the X axis and the Y axis measures the passage of time. Her direction would simply be a vertical line from Terra's viewpoint, with a distance equal to zero and every tick on the line equivalent to a year as she recognises it. The path of Stella extends from the same source to 11.5 years in time and 10 light-years away from Terra before merging also at zero and 23 years.

Terra would transmit a pulse of light from Earth to Stella's spacecraft at her first one-year mark. As light travels a year to move one light-year, a 45-degree diagonal line will be its direction. And since Stella is moving away from it, more than seven cumulative years would have passed for Terra, and more than four for Stella by the time the light catches up to her. She will already be on her trip home by the time Stella watches Terra's second blast. But now, as she's heading toward the source of the light, it's going to take less time to hit her, and she's going to watch the flashes more often.

This means for the first part of her voyage, Stella experiences Terra ageing gradually, but ageing rapidly during the return half. Meanwhile for Stella, it seems as though Terra, the target star, and the entire universe are shifting around her. But Stella notices the gap within them reducing by a factor of 2 because of the restriction in time. This means that each leg of the journey, from Stella's viewpoint, will only take about 6 years. Two years would have gone by for Terra when she sends the first signal to Earth. On her outbound ride, Stella will give 4 further light flashes, each one from further away.

Even by time its first echo from Stella's incoming journey is detected by Terra, more than 21 years would have passed. Terra experiences several light bursts annually for the remainder of Stella's return home. Thus, for around 90% of their 23 years apart, Terra observes Stella ageing slowly, and ageing quickly in the last 10%. This imbalance explains how the paradox is not a paradox really. Although each twin experiences time both running up and slowing down for the other, Stella sees even and separation, while Terra sees Stella ageing steadily for much of the time both are separated.

That's also compatible with calculation of the space journey taken by each twin, which takes 23 Earth days, but just 11.5 as experienced onboard the ship. Terra will be 43 years of age whenever the twins get met, while Stella will be 31. Her presumption that she and Terra had fair claim of becoming inertial spectators is what Stella went wrong. One has to maintain a steady speed and position relative to the rest of the universe in order to be an inertial viewer. The whole time, Terra was at rest, so her speed was a steady zero. But when Stella changed her course for the return ride, she reached a different frame of reference from one in which she had begun. Now both Terra and Stella have such a full idea of how spacetime acts. So they're a very nice example of special relativity, as the twins were 11 years age difference. Thus, the twin who remained on Earth was more aged when compared to that in space indeed, after same time.