Einstein's twin paradox explained - Amber Stuver
-
0:06 - 0:11On their 20th birthday, identical twin
astronauts volunteer for an experiment. -
0:11 - 0:15Terra will remain on Earth, while Stella
will board a spaceship. -
0:15 - 0:19Stella’s ship will travel at 86.6% the
speed of light -
0:19 - 0:22to visit a star that is 10
light-years away, -
0:22 - 0:24then return to Earth at the same speed.
-
0:24 - 0:26As they prepare to part ways,
-
0:26 - 0:29the twins wonder what will happen
when they’re reunited. -
0:29 - 0:32Since a light year is exactly the distance
light can travel in a year, -
0:32 - 0:35Stella’s journey should take 23 years.
-
0:35 - 0:38But from having studied
special relativity, -
0:38 - 0:41the twins know it’s not that simple.
-
0:41 - 0:44First of all, the faster an object moves
through space, -
0:44 - 0:49the slower it moves through time
compared to an unmoving observer. -
0:49 - 0:52This relationship can be quantified with
something called the Lorentz factor, -
0:52 - 0:55which is defined by this equation.
-
0:55 - 0:59And secondly, the length of a moving
object as measured by an observer at rest -
0:59 - 1:01will contract by the same factor.
-
1:01 - 1:05At 86.6% of the speed of light
the Lorentz factor is 2, -
1:05 - 1:09meaning time will pass twice as slowly
aboard the spaceship. -
1:09 - 1:12Of course, Stella won’t notice
time slowing down. -
1:12 - 1:16That’s because all time-based processes
in the ship will slow down as well– -
1:16 - 1:18clocks and electrical devices;
-
1:18 - 1:22Stella’s biological activities including
her rate of aging -
1:22 - 1:24and her perception of time itself.
-
1:24 - 1:28The only people who could notice time
on the moving spaceship -
1:28 - 1:29passing slower for Stella
-
1:29 - 1:34would be observers in an inertial,
or non-accelerating, reference frame– -
1:34 - 1:36like Terra back on Earth.
-
1:36 - 1:39Thus, Terra concludes that when they meet
back on Earth, -
1:39 - 1:41she’ll be older than Stella.
-
1:41 - 1:44But that’s just one way of
looking at things. -
1:44 - 1:46Because all movement is relative,
-
1:46 - 1:51Stella argues it would be just as valid to
say her spaceship will stand still -
1:51 - 1:55while the rest of the universe,
including Terra, moves around her. -
1:55 - 1:59And in that case, time will pass twice as
slowly for Terra, -
1:59 - 2:02making Stella the older twin in the end.
-
2:02 - 2:06They can’t each be older than the other,
so which one of them is right? -
2:06 - 2:10This apparent contradiction is known as
the “Twin Paradox.” -
2:10 - 2:12But it’s not really a paradox–
-
2:12 - 2:17just an example of how special relativity
can be easily misunderstood. -
2:17 - 2:19To test their theories in real-time,
-
2:19 - 2:22each of the twins agrees to send
a burst of light to the other -
2:22 - 2:25every time a year has passed for them.
-
2:25 - 2:28Unlike other objects, the speed of light
is always constant -
2:28 - 2:31regardless of an observer’s
reference frame. -
2:31 - 2:34A light burst sent from Earth will be
measured at the same speed -
2:34 - 2:36as a light burst sent from the spaceship,
-
2:36 - 2:40regardless of whether it’s on its
outbound or return trip. -
2:40 - 2:42So when one twin observes
a burst of light, -
2:42 - 2:47they’re measuring how long it took the
other twin to experience a year passing, -
2:47 - 2:50plus how long it took for light
to travel between them. -
2:50 - 2:52We can track what’s happening on a graph.
-
2:52 - 2:58The X axis marks distance from Earth,
and the Y axis tracks the passage of time. -
2:58 - 3:02From Terra’s perspective, her path will
simply be a vertical line, -
3:02 - 3:03with distance equal to zero
-
3:03 - 3:08and each tick on the line equivalent
to a year as she perceives it. -
3:08 - 3:13Stella’s path will stretch from the same
origin to a point 11.5 years in time -
3:13 - 3:16and 10 light-years in distance from Terra…
-
3:16 - 3:20before converging again at zero
distance and 23 years’ time. -
3:20 - 3:22At her first one-year mark,
-
3:22 - 3:26Terra will send a pulse of light from
Earth towards Stella’s spaceship. -
3:26 - 3:29Since light takes a year to travel
one light-year, -
3:29 - 3:32its path will be a 45-degree
diagonal line. -
3:32 - 3:35And because Stella is
traveling away from it, -
3:35 - 3:37by the time the light catches up to her,
-
3:37 - 3:42over 7 total years will have passed for
Terra, and over 4 for Stella. -
3:42 - 3:45By the time Stella observes
Terra’s second burst, -
3:45 - 3:47she will already be on her return journey.
-
3:47 - 3:51But now, since she’s moving towards the
source of the light, -
3:51 - 3:53it will take less time to reach her,
-
3:53 - 3:55and she’ll observe the bursts
more frequently. -
3:55 - 3:58This means that Stella observes Terra
aging slowly -
3:58 - 4:00for the first half of her journey,
-
4:00 - 4:03but aging rapidly during the return half.
-
4:03 - 4:06Meanwhile for Stella, it seems as though
Terra, the destination star, -
4:06 - 4:09and the whole universe are
moving around her. -
4:09 - 4:11And because of length contraction,
-
4:11 - 4:15Stella observes the distance between
them shrinking by a factor of 2. -
4:15 - 4:19This means each leg of the trip will only
take about six years -
4:19 - 4:21from Stella’s perspective.
-
4:21 - 4:25When she sends the first signal to Earth,
two years will have passed for Terra. -
4:25 - 4:29Stella will send four more light bursts
during her outbound journey, -
4:29 - 4:31each one from farther away.
-
4:31 - 4:35By the time Terra observes the first pulse
from Stella's inbound journey, -
4:35 - 4:38over 21 years will have passed for her.
-
4:38 - 4:40For the rest of Stella's return home,
-
4:40 - 4:44Terra receives multiple light
bursts each year. -
4:44 - 4:50Thus, Terra observes Stella aging slowly
for about 90% of their 23 years apart, -
4:50 - 4:53and aging rapidly during the last 10%.
-
4:53 - 4:57This asymmetry accounts for why the
paradox isn’t really a paradox. -
4:57 - 4:59Although each twin witnesses time
-
4:59 - 5:02both speeding up and slowing
down for the other, -
5:02 - 5:04Stella sees an even split,
-
5:04 - 5:08while Terra sees Stella aging slowly for
most of the time they’re apart. -
5:08 - 5:12This is consistent with each twin’s
measurement of the space voyage, -
5:12 - 5:17which takes 23 Earth years, but only
11.5 as experienced aboard the ship. -
5:17 - 5:23When the twins are reunited, Terra will be
43 years old, while Stella will be 31. -
5:23 - 5:24Where Stella went wrong
-
5:24 - 5:29was her assumption that she and Terra had
equal claim to being inertial observers. -
5:29 - 5:34To be an inertial observer, one has to
maintain a constant speed and direction -
5:34 - 5:37relative to the rest of the universe.
-
5:37 - 5:41Terra was at rest the entire time,
so her velocity was a constant zero. -
5:41 - 5:44But when Stella changed her direction
for the return journey, -
5:44 - 5:48she entered a different reference frame
from the one she’d started in. -
5:48 - 5:52Terra and Stella now both have a better
understanding of how spacetime works. -
5:52 - 5:55And as twins who are eleven
years apart in age, -
5:55 - 5:59they’re a perfect example
of special relativity.
- Title:
- Einstein's twin paradox explained - Amber Stuver
- Speaker:
- Amber Stuver
- Description:
-
View full lesson: https://ed.ted.com/lessons/einstein-s-twin-paradox-explained-amber-l-stuver
On their 20th birthday, identical twin astronauts volunteer for an experiment. Terra will remain on Earth, while Stella will board a spaceship. Stella’s ship will travel to visit a star that is 10 light-years away, then return to Earth. As they prepare to part ways, the twins wonder what will happen when they’re reunited. Who will be older? Amber Stuver investigates the “Twin Paradox.”
Lesson by Amber L. Stuver, directed by Aim Creative Studios.
- Video Language:
- English
- Team:
- closed TED
- Project:
- TED-Ed
- Duration:
- 06:00
lauren mcalpine edited English subtitles for Einstein's twin paradox explained | ||
lauren mcalpine edited English subtitles for Einstein's twin paradox explained | ||
lauren mcalpine approved English subtitles for Einstein's twin paradox explained | ||
lauren mcalpine accepted English subtitles for Einstein's twin paradox explained | ||
lauren mcalpine edited English subtitles for Einstein's twin paradox explained | ||
Tara Ahmadinejad edited English subtitles for Einstein's twin paradox explained | ||
Tara Ahmadinejad edited English subtitles for Einstein's twin paradox explained | ||
Tara Ahmadinejad edited English subtitles for Einstein's twin paradox explained |