Einstein's twin paradox explained - Amber Stuver

翻译人员: Carol Wang 校对人员: Lipeng Chen

On their 20th birthday, identical twin astronauts volunteer for an experiment.

一对同卵双胞胎宇航员 20 岁生日时， 自愿参加了一项实验。

Terra will remain on Earth, while Stella will board a spaceship.

特拉将留在地球上， 而史黛拉将登上一艘太空船。

Stella’s ship will travel at 86.6% the speed of light

史黛拉的飞船将去拜访 距我们 10 光年的一颗恒星，

to visit a star that is 10 light-years away,

飞船速度是光速的 86.6％，

then return to Earth at the same speed.

然后再以同样速度返回地球。

As they prepare to part ways,

当他们准备分别时，

the twins wonder what will happen when they’re reunited.

这对双胞胎也想知道， 她们再相聚时会发生什么。

Since a light year is exactly the distance light can travel in a year,

1 光年指光在一年中传播的距离，

Stella’s journey should take 23 years.

所以史黛拉的旅程应该是 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.

她俩知道事情没那么简单。

First of all, the faster an object moves through space,

首先，与静止的观察者相比，

the slower it moves through time compared to an unmoving observer.

物体在空间运动的速度越快， 时间就会过得越慢。

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.

这是洛伦兹因子的定义公式。

And secondly, the length of a moving object as measured by an observer at rest

其次，观察者在静止状态下

will contract by the same factor.

测量的移动物体的长度 将收缩相同的因子。

At 86.6% of the speed of light the Lorentz factor is 2,

当速度为光速的 86.6％ 时， 洛伦兹因子为 2，

meaning time will pass twice as slowly aboard the spaceship.

意味着飞船上的时间 慢为原来时间的一半。

Of course, Stella won’t notice time slowing down.

当然，史黛拉觉察不到时间在变慢，

That’s because all time-based processes in the ship will slow down as well–

因为飞船上所有基于时间的 进程也都会变慢——

clocks and electrical devices;

时钟和电子设备、

Stella’s biological activities including her rate of aging

包括史黛拉衰老速度在内的生理活动、

and her perception of time itself.

以及她对时间的感知。

The only people who could notice time on the moving spaceship

移动飞船上史黛拉的时间变慢了，

passing slower for Stella

唯一能觉察到这一点的人

would be observers in an inertial, or non-accelerating, reference frame–

是在惯性或非加速参考系中的观察者,

like Terra back on Earth.

譬如在地球上的特拉。

Thus, Terra concludes that when they meet back on Earth,

因此，特拉得出结论，

当她俩在地球上再次相遇时， 她将比史黛拉年龄大，

she’ll be older than Stella.

But that’s just one way of looking at things.

但这只是看待这件事的一面。

Because all movement is relative,

因为所有运动都是相对的，

Stella argues it would be just as valid to say her spaceship will stand still

史黛拉认为太空船静止不动，

while the rest of the universe, including Terra, moves around her.

而是包括特拉在内的整个宇宙 都围绕她运动的说法同样有效。

And in that case, time will pass twice as slowly for Terra,

在这种情况下，特拉的时间 将慢为原来的二分之一，

making Stella the older twin in the end.

而最后年龄更大的是史黛拉。

They can’t each be older than the other, so which one of them is right?

而她俩不可能都比对方年长， 那么，哪种说法正确呢？

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–

但这并非一个真正的悖论，

just an example of how special relativity can be easily misunderstood.

只是狭义相对论易被误解的一个例子。

To test their theories in real-time,

为了实时检验他们的理论，

each of the twins agrees to send a burst of light to the other

两个双胞胎商定，

每一年过去的时候 都向对方发出光脉冲。

every time a year has passed for them.

Unlike other objects, the speed of light is always constant

与其他物体不同，

无论观察者的参考系如何， 光速始终是恒定的。

regardless of an observer’s reference frame.

A light burst sent from Earth will be measured at the same speed

无论是发出去的光还是收到的光，

as a light burst sent from the spaceship,

从地球发出光脉冲的测速

regardless of whether it’s on its outbound or return trip.

与从飞船发出光脉冲的测速相同。

So when one twin observes a burst of light,

因此，当双胞胎中的一人 观察到光脉冲的时候，

they’re measuring how long it took the other twin to experience a year passing,

即可测得另一人的一年的时间

plus how long it took for light to travel between them.

加上两点间传播所需的时间。

We can track what’s happening on a graph.

我们可从图表上观察所发生的事情：

The X axis marks distance from Earth, and the Y axis tracks the passage of time.

X 轴表示距地球的距离， Y 轴表示所用的时间。

From Terra’s perspective, her path will simply be a vertical line,

从特拉的角度看，

她的轨迹是一条垂直线，距离为零，

with distance equal to zero

and each tick on the line equivalent to a year as she perceives it.

并且直线上的每个刻度 相当于她所感知的一年。

Stella’s path will stretch from the same origin to a point 11.5 years in time

史黛拉的轨迹首先从相同原点出发，

and 10 light-years in distance from Terra…

延伸到一点，其时间坐标 11.5 年， 距离坐标是特拉的距离 10 光年；

before converging again at zero distance and 23 years’ time.

然后再汇合到零距离和 23 年的时间点。

At her first one-year mark,

在特拉的第一年，

Terra will send a pulse of light from Earth towards Stella’s spaceship.

她将从地球发出光脉冲， 射向史黛拉的飞船。

Since light takes a year to travel one light-year,

由于光需要一年才能传播一光年，

its path will be a 45-degree diagonal line.

因此其轨迹将是一条 45 度对角线。

And because Stella is traveling away from it,

而且由于史黛拉正驶离光线，

by the time the light catches up to her,

等光线追上她的时候，

over 7 total years will have passed for Terra, and over 4 for Stella.

特拉已过了 7 年多， 史黛拉过了 4 年以上。

By the time Stella observes Terra’s second burst,

等到史黛拉观察到 特拉的第二次光脉冲时，

she will already be on her return journey.

已是在返程途中。

But now, since she’s moving towards the source of the light,

但此时的她正朝着光源前进，

it will take less time to reach her,

光到达她的时间会缩短，

and she’ll observe the bursts more frequently.

而且她会更频繁地观察到光脉冲。

This means that Stella observes Terra aging slowly

这意味着，在旅程的前半段，

for the first half of her journey,

史黛拉会观察到特拉衰老减缓，

but aging rapidly during the return half.

而返程时，她则观察到特拉加速衰老。

Meanwhile for Stella, it seems as though Terra, the destination star,

同时，对于史黛拉来说，

特拉、目的地和整个宇宙 似乎都在围绕她移动。

and the whole universe are moving around her.

And because of length contraction,

由于长度的收缩，

Stella observes the distance between them shrinking by a factor of 2.

史黛拉观察到 她俩的间距离缩小了一半。

This means each leg of the trip will only take about six years

这意味着，从史黛拉的角度来看，

每段行程仅需约 6 年的时间。

from Stella’s perspective.

When she sends the first signal to Earth, two years will have passed for Terra.

当她向地球发送第一个信号时， 对于特拉来说已经过去了两年。

Stella will send four more light bursts during her outbound journey,

史黛拉在前往恒星的旅程中 将再发出四次光脉冲，

each one from farther away.

一次比一次离地球远。

By the time Terra observes the first pulse from Stella's inbound journey,

等特拉观察到史黛拉返程中 发出的第一个光脉冲时，

over 21 years will have passed for her.

时间已过了 21 年多。

For the rest of Stella's return home,

对于史黛拉返回地球的剩余旅程，

Terra receives multiple light bursts each year.

特拉每年都会收到多个光脉冲。

Thus, Terra observes Stella aging slowly for about 90% of their 23 years apart,

因此，在分开的 23 年里， 特拉观察到：

在 90% 的时间里， 史黛拉减缓衰老， 而在最后的 10％ 时间，她则加速衰老。

and aging rapidly during the last 10%.

This asymmetry accounts for why the paradox isn’t really a paradox.

这种不对称解释了 为何该悖论并非真正的悖论。

Although each twin witnesses time

尽管双胞胎二人

both speeding up and slowing down for the other,

都见证了彼此的时间加速和减速，

Stella sees an even split,

但史黛拉看到的是 时间均等的加速和减速，

while Terra sees Stella aging slowly for most of the time they’re apart.

而特拉在大部分时间里 看到的是史黛拉减缓衰老。

This is consistent with each twin’s measurement of the space voyage,

这与每个双胞胎所测量的 对太空航行的结果是一致的，

which takes 23 Earth years, but only 11.5 as experienced aboard the ship.

该过程需要 23 个地球年， 但飞船上只有 11.5 年。

When the twins are reunited, Terra will be 43 years old, while Stella will be 31.

当双胞胎团聚时，特拉 43 岁， 而史黛拉将会是 31 岁。

Where Stella went wrong

史黛拉出错是因为她的假设错了，

was her assumption that she and Terra had equal claim to being inertial observers.

即假设她和特拉都是惯性观测者。

To be an inertial observer, one has to maintain a constant speed and direction

作为惯性观测者，

必须相对于宇宙的其余部分 保持恒定的速度和方向。

relative to the rest of the universe.

Terra was at rest the entire time, so her velocity was a constant zero.

特拉一直处于静止状态， 因此她的速度恒定为零。

But when Stella changed her direction for the return journey,

但当史黛拉改变方向返程时，

she entered a different reference frame from the one she’d started in.

她输入的参考系 与开始时的参考系不同。

Terra and Stella now both have a better understanding of how spacetime works.

特拉和史黛拉现在 对时空工作原理有了更深了解，

And as twins who are eleven years apart in age,

而且，作为一对相差 11 岁的双胞胎，

they’re a perfect example of special relativity.

她俩是狭义相对论的完美典范。