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传送门悖论

The Portal Paradox

The video game Portal is built around a sci-fi device
电子游戏《传送门》是基于一种
that can create a portal connecting one place on the wall
能创造出一个将墙壁 天花板或地板的一处
or ceiling or floor to another,
连接到另一处的传送门的科幻设备
and objects in the game, or the player themselves
游戏中的物体 或是玩家本身
can pass essentially instantaneously from one end of the portal to the other.
可以瞬间从传送门的一端传送至另一端
In particular, an object entering one end of a portal with a certain speed
特别的是 一个物体以一定速度进入传送门的一端
leaves the other end with the same speed,
会以相同速度从另一端穿出
though if the portals aren’t oriented in the same direction,
即使传送门的朝向不同
then the object will exit in the new direction.
物体也还是会从新的方向穿出
But the speed will be the same.
但是速度还是跟原来一样
And this leads to an apparent paradox:
这就产生了一个明显的悖论
what happens if one of the ends of the portal is itself moving?
如果运动的是传送门的一端 会发生什么?
Does a stationary object plop out the other end of the portal with zero speed,
一个静止的物体是否会因为它在进入之前没有速度
since it had no speed before entering?
而以速度为零的状态从传送门另一端掉出?
Or if the orange portal moves quickly downwards,
或者假如橙色的传送门快速下降
does the cube shoot out of the blue portal
那小方块是否会以相应的相对速度
with the corresponding relative speed?
从蓝色的传送门射出?
It’s easy to argue in favor of either case,
支持这两种情况都有道理
which I suspect is why this puzzle is so popular on the internet!
我觉得这就是这个谜题在网上如此流行的原因
Of course, as far as we know such portals don’t exist,
当然 我们都知道这种传送门并不存在
but supposing they did, and obeyed the laws of physics,
但假设它们存在 而且遵守物理定律
then the question really boils down to this:
那么问题就可以归结为
if objects have to enter and exit the portals with the same speed,
如果物体必须以相同的速度进出传送门
then what’s that speed being measured relative to?
那么这个速度是相对于什么参照物测得的?
Because in our universe there’s no absolute reference frame
因为在我们的宇宙中
from which to measure speeds and velocities on their own.
并不存在能以自身为参考测得速度的绝对参考系
Velocities can only be determined relative to another object.
速度只能由另一个参照物决定
So here are a few options:
这里有几个选项:
perhaps when passing through a portal,
可能当物体穿过传送门时
the object maintains the same speed relative to the environment,
仍保持着相对于环境的0速度
This one’s option A.
这是A选项
Or perhaps objects maintain the same speed
又或是物体穿过传送门时
relative to the average position of the portals themselves.
其相对于传送门的平均位置速度为0
Except that’s mathematically the same as measuring relative to the environment,
尽管从数学上来说 当传送门匀速运动时
as long as the portals aren’t accelerating – so option A.
这跟以环境为参考系结果一样 即与A选项相同
Or perhaps the speed of an object has relative to the portal it enters
或者物体相对于传送门入口的速度
is the same as the speed it has relative to the portal it exits.
与其相对于传送门出口的速度一致
This one is option B.
这是B选项
Or perhaps objects enter and exit at a constant speed
又或者物体以一相对于还没用到的
relative to the end of the portal they’re NOT using at the moment.
传送门出口的恒定速度进出传送门
It’s a valid possibility, although it’s kind of weird.
尽管有点荒唐 但确实有可能
The thing is, all of these options are consistent with what you see in the video game,
问题是 这些选项都与你在电子游戏中看到的一致
Because in the game the portals pretty much never move
因为在游戏中
relative to the environment.
传送门相对于环境几乎从未移动过
My personal opinion is that the most physically natural option is B,
我个人认为 B选项是最符合物理常识的
where the velocity is locally measured relative to the individual ends of the portals,
B选项中 速度是相对于传送门各个进出端所测得的
and so the cube shoots out of the blue portal.
所以小方块会从传送门蓝色端射出
This would be roughly what you’d expect
这大概就是你想要的答案
if the portals were wormholes bending spacetime,
如果传送门是扭曲时空的虫洞
because the objects then would obey conservation of momentum in a curved spacetime,
因为物体在扭曲的时空中也遵守动量守恒
or if the portals were more of a teleportation device
或者说传送门更像是一个瞬间移动设备
that scans the matter coming in one end and reconstructs it,
它就像3D打印机一样 扫描一端进入的物体
kind of like a 3D printer, at the other end.
然后在另一端重构
So I think B is more natural.
所以我认为B选项更现实
It’s also tempting to think
很容易想到
that there’s simply no way it can be option A,
选项A是根本不可能的
the one where objects keep their same speed relative to the environment.
即物体始终保持相对于环境的恒定速度
Because how could a stationary object exit a stationary portal while remaining stationary?
因为静止物体怎么可能在静止状态下通过静止的传送门?
The object would have to move, right?
物体必须得移动起来 对吧?
However, there is a way for option A to work.
然而 还有一个方法能实现A选项
Precisely because the cube doesn’t enter the orange portal all at once.
正是因为小方块并非一下子完全进入橙色传送门
It goes in bit by bit.
而是一点一点地进入
And if those bits come out of the blue portal not moving,
假如这些点穿出蓝色传送门却不移动
then they all appear exactly in the plane of the portal stationary,
那么它们都会静止且精确地出现在传送门的平面上
and they would keep on piling up against each other,
它们会不断地彼此堆积在一起
squishing the cube into a flat square which is not moving.
把方块压扁成了一个静止的正方形
Or, if the cube were rigid and couldn’t be squished,
又或者 假如小方块是刚性的 无法被压扁
then it simply couldn’t enter the orange portal in the first place,
那么它根本无法进入橙色传送门
The blue end of the portal will act like a wall
蓝色传送门会像一堵墙一样阻止小方块进入
and the orange portal would bounce off of it!
而橙色传送门会弹起
And I suspect option A is actually
我怀疑选项A正是
how the portals are programmed in the video game itself,
这款电子游戏中传送门的编程逻辑
both because measuring speeds relative to the global environment
因为相比于计算与特定物体的相对速度
as opposed to relative to a particular object
计算与环境的相对速度
is typically the easiest thing to program.
通常是最容易编程实现的
And because people who’ve done experiments within the game engine
而且 一些在游戏引擎中做实验
to try to see what happens have discovered that the game glitches
想看看结果的玩家却发现游戏出故障了
and doesn’t let solid objects pass through a portal moving towards them.
固体无法穿过朝它们移动的传送门
Which is perhaps unsatisfying answer to a paradox,
这可能并不是一个令人满意的答案
and not how you think the portals should work.
也并非你所认为的传送门的工作方式
But that’s ok!
但是这也不错
We don’t have to agree with the game designers.
我们并不一定要和游戏设计者想法一致
To me, the moral is that the portal paradox is not a paradox.
对于我来说 传送门悖论并不是悖论
The answer depends on how the portals themselves actually work,
答案取决于传送门本身是如何工作的
which, since they’re fictional, is up to you to decide.
但因为它们是虚拟的 所以也取决于你
What you think should happen says more about you:
你所选择的更多是反映你自己
and whether you think more like a programmer,
你的思维方式更像程序员
or more like a physicist!
还是更像物理学家
And so, I leave you with a final portal puzzle to ponder:
所以 我给你们留了一个终极传送门谜题来思考
what if instead of moving down towards the cube,
假如橙色传送门并非向下移动靠近小方块
the orange portal is moving sideways on the ground
而是在地面上横移
and you drop the cube through it.
然后你把小方块扔进去
Does the cube shoot straight up through the blue portal?
那么小方块会直接从蓝色传送门射出吗?
Does it bounce off the orange portal?
还是会从橙色传送门弹出?
Or does it shoot out of the blue portal at an angle?
又或是以一定角度从蓝色传送门射出?
This MinutePhysics video was supported by CuriosityStream,
《分钟物理》频道由一项经济的订阅流媒体服务
an affordable subscription streaming service
“CuriosityStream”赞助播出
that’s all about science, documentaries and non-fiction.
“CuriosityStream”都是关于科学 纪录片和纪实作品
Look, I’m not going to beat around the bush
听着 我就直截了当告诉你吧
CuriosityStream has in their collection what in my opinion
在我看来 “CuriosityStream”收集了
is the best documentary about physics I’ve ever seen,
我见过的最好的一部物理记录片《Particle Fever》
“Particle Fever”, and you can watch it right now by heading to curiositystream.com/minutephysics
你现在就能通过网址curiositystream.com/minutephysics看到这个节目
and signing up with the promo code “minutephysics”,
同时在注册的时候输入优惠码“minutephysics”
which gets you the first 30-days completely free.
就能享受首次30天的免费特权
After that, a subscription to CuriosityStream is
之后 你只需要每月花2.99美元
just $ 2.99 a month for you to have unlimited access to
订阅“CuriosityStream” 就能无限制地访问
over 2400 other documentaries and nonfiction programs,
超过2400部其他纪录片和纪实项目
including some from people you might recognize.
包括一些你可能见过的大佬视频
But seriously, just go watch Particle Fever
言归正传 快上curiositystream.com/minutephysics
by heading to curiositystream.com/minutephysics
去看《Particle Fever》吧
and using the promo code ‘minutephysics’.
别忘了用优惠码“minutephysics”
Particle Fever is so good!
《Particle Fever》真的很棒!

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