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相对同时性——狭义相对论第四讲

Relativity of Simultaneity | Special Relativity Ch. 4

在我们的宇宙中 当你
In our universe, when you change
在静止参考系与运动参考系相互转换
from a non-moving perspective to a moving one or vice versa
参考系的转换 是通过
that change of perspective is represented by
“洛伦兹变换”来表达的
what’s called a Lorentz transformation,
“洛伦兹变换”是一种时空的伸缩旋转
which is a kind of squeezed stretched rotation of space-time
这能通过机械 用时空坐标网格板呈现
that I’ve mechanically implemented with this space-time globe
简短回顾一下 时空坐标图
a quick reminder, space-time diagrams
横坐标表示位置 纵坐标表示时间
plot position on the horizontal axis and time on the vertical axis
那么随时间推移 物体位置
so something that moves as time passes
连续组成的路径
traces out a path through space-time
被称为世界线
called a world line.
关于洛伦兹变换你可能会注意到
one of the first things you might notice about Lorentz transformations is
变换前 事件发生位置不同而时间相同
that events that were at different places at the same time
那么变换后 事件的时间就会变得不同
before the transformation aren’t at the same time after the transformation.
从速度不同的人们看来
This means that from the perspectives of people going different speeds
对某个人来说是同时发生的事
simultaneous events for one person
对其他人来说却不同时 反之亦然
won’t be simultaneous for the other and vice versa.
比如 如果从我的视角
For example, if from my perspective
两个盒子同时自燃而你正
these two boxes spontaneously combust at the same time and you’re
向我右侧以1/3光速在移动
moving at 1/3 the speed of light to my right.
从你的视角来看
Then, from your perspective,
亦即你将自己视为静止的视角
that is from the perspective in which you’re not moving,
你的世界线会是完全垂直的
so your world line is purely vertical.
也就是右边的箱子会先烧起来
From your perspective, the box on the right will combust first,
而左边的箱子则后烧起来
and the box on the left will combust second.
这也就是说
The takeaway here is that
我们的世界既没有绝对的时间概念
our universe has neither an absolute notion of time
也没有绝对同时发生的事情
nor an absolute sense of simultaneous events, and that simultaneity
两个相距越远的事件它们的同时性就越差
breaks down more the farther away from each other two things are.
从我的视角来看更靠左的盒子和其它盒子
A box even farther to the left that from my perspective simultaneously
是同时自燃的 而从你移动中的视角看
spontaneously combusts with the others will, from your moving perspective,
它发生自燃的同时性会比它右边的更差
be even farther out of sync with the box on the right.
这是洛伦兹变换公式关于时间的描述
This is described by the time part of the Lorentz Transformation equations,
其表达式为:
The part that says:
tnew=γ(t – v*x/c²)
tnew equals gamma times t minus v over c squared times x.
当这个x 事件与你相距越远
Because of the x in there, the farther away an event
从新的视角来看 这个事件的时间
is from you, the more its time from the new perspective
就将会与你的时间越不同步
will be out of sync with events closer to you.
然而由于分母上c²
Though, because of the factor of c
这个因子数值非常大
squared in the denominator which is huge.
你很难注意到任何时间上的差异
It’s hard to notice anything being out of sync until
除非你的速度或待测物体的距离
either your speed or diatance to the object in question are
真的非常非常大 比如你必须
really really big. Like, you’d have to be going
达到一半的光速并且
half the speed of light and be comparing
比较距离远大于地月间距的事物
things farther apart than the earth and moon before things
这个时间差才会超过1秒
would become more than one second out of sync.
但在这种情况下 在我眼里同时发生的事
But in that case, events that were simultaneous from my perspective
在你看来真的会不同步
really would be out of sync for you.
就像看上去一样神奇
As surprising as this may seem,
你将会发现
it might feel more familiar and comfortable
当这种“不同时”的现象
when you remember that this “getting out of alignment” phenomenon
恰好发生在空间同一点时会更好理解
happens to points that are at the same point in space.
从我的视角来看
Too, from my perspective,
这个盒子在不同时刻
this box is at the same position
处于同一位置即它没有在移动
at different times that is it’s not moving.
但移动中的你所见是
But from your moving perspectives,
它在不同时刻处于不同位置
it’s at different positions at different times.
也就是它在移动即x坐标不相等
It is moving and it’s no longer in alignment.
同时性的相对性就是
Relativity of simultaneity is just the other side
事物的两面性 事实上
of the coin – the fact that events
同一时刻发生在
that happen at the same time
不同空间位置的事件 从移动者的视角
at different spatial positions happen at different times
来看 是不同时发生的
when viewed from a moving perspective.
总之 宇宙中
All together, in our universe,
结论就是:无论几个事件全都
the takeaway is this: events that were previously either
发生在同一地点或
all at the same place or all
都发生在同一刻 观测者是否移动
at the same time get out of alignment with each other when
都将影响它们发生的同步性
you change to a moving perspective.
非常感谢 Mark Rober
A big thanks again to Mark Rober
使得时空仪成为现实
for making the spacetime globe a reality,
想要了解更多关于同时性的相对性的细节
and to dive more into the details of relativity of simultaneity,
我强烈推荐Brilliant的
I highly recommend heading over to Brilliant.org’s course on
狭义相对论课程 它们和该系列视频同步
special relativity that they’ve been developing simultaneously with this vedio series.
(至少我觉得是同步的)
(well, at least, simultaneous from my perspective).
在那 你能探索自定义场景
There, you can explore custom scenarios and
并解决真正的难题来帮助你
do actual puzzles and problems that help you
巩固在本视频所学知识
build on what you learned in this video,
像相对论速度下激光射击游戏将如何运作
like figuring out how laser tag would work at relativistic speeds!
这些狭义相对论的问题是
The special relativity questions on Brilliant.org
专门为你们设计来帮助你们
are specifically designed to help you go deeper
深入了解这个系列
on the topics I’m including in this series,
通过该网址(见英文字幕)
and you can get 20% off of a Brilliant subscription
你将得到八折优惠 记住是
by going to Brilliant.org/minutephysics. Again,
该网址能够
that’s Brilliant.org/minutephysics which gets you 20 %
减去20%额外费用
off premium access to all
便享有相关课程与练习
of Brilliant’s courses and puzzles,
并让它知道你来自这里
and lets Brilliant know you came from here.

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狭义相对论的基本了解

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翻译译者

ID926783

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审核员 EM

视频来源

https://www.youtube.com/watch?v=SrNVsfkGW-0

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