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对爱因斯坦“双生子佯谬”的解释–安柏·斯特夫 – 译学馆
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对爱因斯坦“双生子佯谬”的解释--安柏·斯特夫

Einstein's twin paradox explained - Amber Stuver

“不管你多努力教你的猫学习广义相对论 你都会失败” -布赖恩·格林
On their 20th birthday
一对同卵双胞胎宇航员
identical twin astronauts volunteer for an experiment
在20岁生日之际 自愿参加了一项实验
Terra will remain on Earth
Terra将留在地球上
while Stella will board a spaceship
而Stella将登上一艘太空船
Stella’s ship will travel at
Stella的飞船将以
86.6% the speed of light
光速86·6%的速度
to visit a star that is 10 light-years away
前往距离我们10光年的恒星
then return to Earth at the same speed
然后以相同的速度返回地球
As they prepare to part ways
当准备分离之时
the twins wonder what will happen when they’re reunited
双胞胎不禁遐想再次相聚时会发生什么
Since a light year is exactly
由于光年是指
the distance light can travel in a year
光在一年中传播的距离
Stella’s journey should take 23 years
所以Stella的旅程应该需要23年
But from having studied special relativity
但是通过研究狭义相对论
the twins know it’s not that simple
她们知道事情没那么简单
First of all, the faster an object moves through space
首先 相对静止的观察者而言
the slower it moves through time
物体在空间中运动速度越快
compared to an unmoving observer
在时间上的运动速度就越慢
This relationship can be quantified with something called the Lorentz factor
这种关系可以用洛伦兹因子来量化
which is defined by this equation
该公式定义了洛伦兹因子
And secondly, the length of a moving object
其次 观察者在静止状态下
as measured by an observer at rest
测量的移动物体的长度
will contract by the same factor
也将收缩相同的因子
At 86.6% of the speed of light the Lorentz factor is 2
在86·6%的光速下 洛伦兹因子为2
meaning time will pass twice
这意味着在飞船上
as slowly aboard the spaceship
时间流逝速度会慢一倍
Of course
当然
Stella won’t notice time slowing down
Stella不会察觉到时间在变慢
That’s because all time-based processes in the ship
因为船上所有基于时间的流程
will slow down as well–
都会变慢 –
clocks and electrical devices
比如时钟 电子设备
Stella’s biological activities including her rate of aging
Stella的生物活性 包括衰老速度
and her perception of time itself
以及她对时间的感知
The only people who could notice
唯一能注意到
time on the moving spaceship
Stella在移动飞船上的
passing slower for Stella
时间会变慢的人
would be observers in an inertial, or non-accelerating, reference frame–
是处于惯性或非加速参考系中的观察者
like Terra back on Earth
例如地球上的Terra
Thus, Terra concludes that
因此Terra得出结论
when they meet back on Earth
当她们在地球上相遇时
she’ll be older than Stella
她将比Stella年龄大
But that’s just one way of looking at things
但这只是看事物的其中一面
Because all movement is relative
由于所有运动都是相对的
Stella argues it would be just as valid to say
所以Stella认为也可以这样说
her spaceship will stand still
宇宙飞船将静止不动

while the rest of the universe, including Terra
而包括Terra在内的整个宇宙
moves around her
都将围绕Stella运动
And in that case
在这种情况下
time will pass twice as slowly for Terra
Terra的时间将会慢一倍
making Stella the older twin in the end
最终Stella会成为年长的那一方
They can’t each be older than the other,
她们不可能互相都比对方年长
so which one of them is right?
所以哪个说法是对的呢?
This apparent contradiction is known as the ‘’Twin Paradox’’
这种明显的矛盾被称为“双生子佯谬”
But it’s not really a paradox–
但这不是一个真正的悖论
just an example of how special relativity
而是一个狭义相对论
can be easily misunderstood
很容易被误解的例子
To test their theories in real-time
为了实时检验她们的理论
each of the twins agrees to
两个人商定
send a burst of light to the other
在每过一年的时候
every time a year has passed for them
向对方发出一道光波
Unlike other objects
与其他物体不同
the speed of light is always constant
无论观察者处于哪种参考系
regardless of an observer’s reference frame
光速始终是恒定的
A light burst sent from Earth will
无论是在去程
be measured at the same speed as
还是回程中
a light burst sent from the spaceship
从地球发送的光的速度
regardless of whether it’s on its outbound or return trip
都将与从飞船发送的光的速度相同
So when one twin observes a burst of light
因此 当双胞胎中的其中一人
they’re measuring how long it took the other twin
观察到光波时 就可测量
to experience a year passing
另一人经历一年所需的时间
plus how long it took for light to travel between them
加上光在她们之间传播所需的时间
We can track what’s happening on a graph
我们可以用图表记录研究发生的事情
The X axis marks distance from Earth
X轴表示距地球的距离
and the Y axis tracks the passage of time
Y轴表示时间的流逝
From Terra’s perspective
从Terra的角度来看
her path will simply be a vertical line
她的路径只是简单地一条垂直线
with distance equal to zero
距离坐标为零
and each tick on the line
并且直线上的每个刻度
equivalent to a year as she perceives it
都等于她所感知的一年
Stella’s path will stretch from the same origin
Stella的路径将从同一原点出发
to a point 11.5 years in time
延伸到11·5年的时间坐标
and 10 light-years in distance from Terra
以及距离Terra10光年的距离坐标
before converging again at zero distance and 23 years’ time
然后以零距离和23年的时间坐标汇合
At her first one-year mark
在第一年
Terra will send a pulse of light from Earth
Terra将从地球向Stella的
towards Stella’s spaceship
飞船发送一道光波
Since light takes a year to travel one light-year
由于光需要一年才能传播一个光年
its path will be a 45-degree diagonal line
因此它的路径将是一条45度对角线
And because Stella is traveling away from it
由于Stella一直在远离光波
by the time the light catches up to her
所以当光波追上她时
over 7 total years will have passed for Terra
对于Terra已经过了7年多
and over 4 for Stella
对于Stella 则过了4年多
By the time Stella observes
等Stella观察到Terra
Terra’s second burst
发送的第二道光波时
she will already be on her return journey
她已经可以回程了
But now, since she’s moving towards the source of the light
但是现在 由于她正朝着光波前进
it will take less time to reach her
因此光追赶上她的时间将缩短
and she’ll observe the bursts more frequently
她会更频繁地观察到光波
This means that Stella observes Terra aging slowly
这意味着Stella在旅程的前半段
for the first half of her journey
会观察到Terra衰老在放缓
but aging rapidly during the return half
而在返程时会观测到Terra衰老在加速
Meanwhile for Stella, it seems as though
同时对于Stella来说
Terra the destination star
Terra和目的地
and the whole universe are moving around her
以及整个宇宙似乎都在围绕她移动
And because of length contraction
由于长度收缩
Stella observes the distance between them
Stella观察到她们之间的
shrinking by a factor of 2
距离缩小了一半
This means each leg of the trip
这意味着从Stella
will only take about six years
的角度来看 每段行程
from Stella’s perspective
需要大约六年的时间
When she sends the first signal to Earth
当她向地球发送第一个信号时
two years will have passed for Terra
对Terra而言 两年时间已经过去了
Stella will send four more light bursts during her outbound journey
Stella会在去程中发送超四次光波
each one from farther away
每一次都在更远的地方
By the time Terra observes the first pulse
等Terra观察到Stella
from Stella’s inbound journey
返程中发出的第一道光波时
over 21 years will have passed for her
已经过去了21年多
For the rest of Stella’s return home
对于Stella返程的剩余部分
Terra receives multiple light bursts each year
Terra每年都会收到多个光波
Thus, Terra observes Stella aging slowly
因此在这分开的23年间 Terra会在
for about 90% of their 23 years apart
90%的时间里观察到Stella缓慢衰老
and aging rapidly during the last 10%
而10%的时间则加速衰老
This asymmetry accounts for
这种不对称解释了
why the paradox isn’t really a paradox
为什么悖论并不是真正的悖论
Although each twin witnesses time
尽管双胞胎之间见证了
both speeding up and slowing down for the other
彼此的时间加速和减速
Stella sees an even split
但Stella看到Terra衰老加速和减速 各占了一半的时间
while Terra sees Stella aging slowly
而Terra则在分开的大部分时间里
for most of the time they’re apart
看到Stella的衰老是在减速
This is consistent with
这与双胞胎对
each twin’s measurement of the space voyage
太空航行的测量结果是一致的
which takes 23 Earth years
行程需要花23个地球年
but only 11.5 as experienced aboard the ship
但在飞船上的时间只有11·5年
When the twins are reunited
当双胞胎再次团聚时
Terra will be 43 years old
Terra将会43岁
while Stella will be 31
而Stella将会31岁
Where Stella went wrong
Stella不正确的地方
was her assumption that
是在于她假设了
she and Terra had equal claim to being inertial observers
她和Terra都看作成惯性观测者
To be an inertial observer
要成为惯性观测者
one has to maintain a constant speed and direction
必须相对于宇宙的其余部分
relative to the rest of the universe
保持恒定的速度和方向
Terra was at rest the entire time
Terra一直处于静止状态
so her velocity was a constant zero
因此她的速度恒定为零
But when Stella changed her direction for the return journey
但是当Stella改变回程的方向时
she entered a different reference frame from the one she’d started in
她就进入了一个和开始时不同的参考系
Terra and Stella now both have
Terra和Stella现在都
a better understanding of how spacetime works
更好的理解了时空的工作原理
And as twins who are eleven years apart in age
而且 作为一对相差十一岁的双胞胎
they’re a perfect example of special relativity
她们成为了狭义相对论的完美典范

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视频概述

当一对双胞胎,一个留在地球上,一个去往太空,23年后会发生什么呢?她们的年龄还会一样大吗?“双生子佯谬”的原理是什么,安柏·斯特夫将进行详细解说。

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翻译译者

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视频来源

https://www.youtube.com/watch?v=h8GqaAp3cGs

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