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爱因斯坦的最大失误

Einstein's Biggest Blunder, Explained

《分钟物理》
In 1915, Albert Einstein published
1915年 阿尔伯特•爱因斯坦发表了
a very important equation
一个非常重要的方程
no, not that one,
不 不是这个
the one he published didn’t just relate mass and energy
他发表的方程不只是将质量和能量联系起来
but mass, energy and gravity
而是把质量 能量和重力联系起来
this equation replaced the older “Newton’s law of Gravitation,”
它取代了早期的 “牛顿万有引力定律”
which you may be familiar with
那个你或许熟悉的
and it remains to this day our best description of how gravity works.
至今仍是对重力作用的最佳描述的定律
Just like how F=ma is a mathematical description
它用数学描述了加速度取决于物体的受力
of how the acceleration of an object depends on the forces applied to it.
就像F = ma一样
The Einstein Equation of general relativity relates
爱因斯坦的广义相对论
the motion of mass and energy (the “T” on the right)
将质量 能量的运动(右侧的“ T”)
to the curvature of spacetime (the “R’s” on the left).
与时空的曲率(左侧的“ R”)联系起来
And Einstein didn’t just pull this equation out of thin air.
这并不是爱因斯坦凭空得来的
it was the natural consequence
这是自然而然的结果
of a long and careful consideration of key principles of physics
来源于长期对物理关键原理
combined with the advanced mathematics of curved surfaces
与曲面高等数学相结合的思考
and of course , agreement with the experimental observations of the day.
当然 与当时的实验观察也是相符的
The equation, however, is deceptively simple.
然而 该方程只是看似简单
This one single line is in fact an incredibly fancy shorthand
实际上这短短一行
for what’s actually a system
是对十个二阶偏微分方程系统的
of ten second order partial differential equations
一种难以置信的奇妙简写
relating mass and energy to the curvature of spacetime
将质量 能量和时空曲率相联系
and the R’s themselves are also a shorthand
并且R本身也是一种简写
But the point is this:
但关键问题是
after figuring out that these equations matched up with
在弄清楚这些方程
Newton’s law of gravitation for weak gravitational fields
与弱引力场的牛顿万有引力定律相一致
and after showing that the equations correctly predicted
并且证明了这些方程正确预测了
a previously unexplained anomaly in the orbit of Mercury
先前无法解释的水星轨道异常之后
Einstein tried to figure out what the equations had to say about the universe as a whole.
爱因斯坦想弄清楚这些方程对整个宇宙的意义
Of course, all the matter and energy in the universe is much too complicated
当然 宇宙中的物质和能量都太复杂了
to put into the equations and have any hope of solving them,
既无法列入方程中也无望求解
but if you zoom out enough,
但如果把宇宙充分缩小
you can approximate the universe as
就能将宇宙任一方向方位的密度
having a roughly constant density everywhere and in every direction.
近似为一个大致的恒定值
And Einstein was able to solve the equations
有了极度简化且密度恒定的宇宙
for a very simplified universe with constant density everywhere
爱因斯坦就能够解出方程了
the ten complicated equations reduced to just two simple ones:
十个复杂的方程被削减至两个简单方程
this one says the curvature of space in the universe is proportional to the density
这一个表示宇宙的空间曲率与密度成正比
so more stuff in the universe means more curvature of space
因此宇宙中物质越多 空间曲率越大
and this one says that the density has to be zero.
而这个表示密度必为0
which would mean there can’t be anything in the universe…
意味着宇宙中不可能存在任何事物
Needless to say, this was a problem.
不用说 这是个问题
And it turns out that there are two solutions to the problem
事实证明 这个问题有两种解决方法
the one Einstein took and the one he didn’t.
爱因斯坦采取的 和他未采取的
Einstein’s solution was this:
爱因斯坦采取的办法是
he knew (since he had dived deep into the math) that it was
他明白(因为他深入钻研数学)
possible to slightly change his original equations
可以对原方程进行微调
you can just add on a very simple term
可以在不违反任何物理的关键原则下
without violating any key principles of physics.
添加一个简单量
There wasn’t much other motivation for adding this term but it doesn’t change anything
这没什么其他理由 但不会引起任何变化
about how well the equations match up with Newton’s law when gravity is weak,
无论是引力较弱时 方程与牛顿定律的匹配度
or how well they predict the orbit of Mercury or whatever
还是预测水星轨道的准确性等
so maybe it was ok?
所以应该没问题吧
And crucially for Einstein,
对爱因斯坦而言
the new term changes the equation for the density of the universe:
关键在于新增项改变了宇宙密度方程式
instead of saying “density equals zero,”
它不再表示“密度等于零”
it now says “density is proportional to the new term”.
而是“密度与新增项成正比”
So if the new term was non-zero,
因此 如果新增项非零
that meant the universe could have stuff in it!
就表示宇宙中可以存在物质
Voila – solution number one
瞧 这就是一号解决方法
The other solution to how the universe can have stuff in it was this:
另一种解释宇宙中存在物质的方法是
don’t assume (as Einstein had) that the universe is static and unchanging.
不要像爱因斯坦那样 假设宇宙是静止不变的
The general understanding at the time was that the universe didn’t expand or contract
那时普遍的观点是 宇宙不会膨胀或收缩
and Einstein had also made a small but unfortunate technical error in his calculations
而爱因斯坦计算时 不巧犯了技术性小错误
which appeared to prohibit the possibility of a changing universe
这似乎就排除了动态宇宙的可能性
so it’s not surprising that Einstein didn’t see this solution.
所以爱因斯坦没有想到这个方法并不奇怪
But it was there: if you don’t make the mathematical assumption that the universe is static
但它是存在的:如果你不作宇宙是静态的数学假设
and you don’t make the technical error Einstein did,
也不犯爱因斯坦的技术错误
you can find a different valid solution to Einstein’s equations
你就能发现爱因斯坦方程的另一种有效解法
which physicist Alexander Friedmann did.
物理学家亚历山大 •弗里德曼就找到了
Actually he used the version of the equations with the new term
实际上 他用的是带有新增项的方程
knowing he could always set that term to zero if it wasn’t real.
如果不对 他就会把新增量设为0
But the key part is he didn’t assume the universe was static.
但最关键的是 他没有假设宇宙是静态的
Friedmann found that the ten equations again reduced to two:
弗里德曼同样发现 十个方程可以简化为两个
the first equation now describes
第一方程现在描述的是
how the change in density of the universe
宇宙密度的变化与其大小的变化
relates to its change in size:
是如何相互联系的
specifically, it says that if the universe gets bigger, then it gets less dense
具体来说 如果宇宙变大 密度就会减小
which makes sense – stuff’s literally spreading out.
这说得通 因为物质确实在扩散
The second equation says that the deceleration of the universe is
第二个方程表示 宇宙的减速度
proportional to its density minus Einstein’s constant
与其密度减去爱因斯坦常数的值成正比
in other words, the stuff in the universe attracts itself gravitationally
换言之 宇宙中的物质因万有引力 而自我吸引
so the universe would have a tendency to pull inwards on itself
因此 宇宙有内拉的趋势
slowing any expansion and possibly even contracting.
这会减缓扩张速度 从而可能导致收缩
Unless Einstein’s constant were real and had a value big enough
除非爱因斯坦常数存在且值够大
to balance or overpower the gravitational attraction
大到足以平衡或克服引力
So that’s the solution Einstein didn’t see.
这就是爱因斯坦没有发现的方法
Later, once astronomers took sufficiently detailed measurements
之后 天文学家们做了充分细致的观测
it turned out that the universe was indeed expanding:
事实证明宇宙确实在扩张
So Einstein’s equations didn’t appear to have any need for the extra term he had added.
所以爱因斯坦方程似乎并不需要那个新增项
Einstein was reported by physicist George Gamow
据物理学家乔治•伽莫夫称
to have called it “his biggest blunder”
爱因斯坦说这是“他最大的错误”
and while there’s no known documentation
虽然没有已知文献记载
that he ever actually said or wrote those words specifically
他确实说过或写过这些话
there’s plenty of record of him expressing
但是有大量记录显示
disdain in other ways:
他以其他方式表达了轻蔑:
“away with the cosmological term” ,“I always had a bad conscience”
“远离宇宙项” “我一直很愧疚”
“I found it very ugly,”
“我觉得它很丑陋”
“such a constant appears…unjustified.”
“这个常数看起来…不合理”
And, during Einstein’s lifetime, that was certainly true
而且爱因斯坦在世时 那确实是正确的
– the term did appear unjustified.
新增项确实显得不太合理
However, remember how Friedmann’s equations predicted
但请记住 弗里德曼方程是如何预测
that the universe should be attracting itself gravitationally
宇宙因万有引力而自我吸引
and so the expansion should be slowing down,
因而膨胀应该减缓
unless Einstein’s constant is real?
除非爱因斯坦常数是真的?
Well, in 1998 , decades after Einstein’s death
然而爱因斯坦去世几十年后
astronomers made the surprising discovery
天文学家于1998年有了惊人发现
that the universe’s rate of expansion isn’t constant,
宇宙的膨胀率不是恒定的
and it isn’t slowing down – it’s getting faster.
而且它不是在放缓 而是在变快
And so in a great, ironic twist,
所以在这讽刺的大反转下
Einstein’s constant does ultimately have a role in describing the universe
爱因斯坦常数确实在描述宇宙发挥了作用
though it turns out to be a very different universe from what he had imagined.
尽管那是个和他想象中截然不同的宇宙
If you don’t want to make silly math mistakes like Einstein,
要是你不想像爱因斯坦一样 犯不明就里的数学错误
then you should probably head to Brilliant.org, this video’s sponsor
那么你应该访问Brilliant.org(本视频赞助方)
to sharpen and hone your math and science skills.
打磨你的数学和科学技能
In fact, Brilliant has a whole interactive course on cosmology
Brilliant上有一套完整的宇宙学互动课程
and within it, a quiz specifically titled “The fate of the Universe”
在课程中 还有题为“宇宙命运”的测验
that was tailor-made for giving you a deeper and longer lasting understanding
这是为了帮你加深巩固理解而量身定做的
than you can possibly gain from simply watching a video
比起光看视频 你能获得更多
Brilliant also has fun daily challenges,
Brilliant 还有趣味日常挑战
which are bite-sized math and science-puzzles
包括微数学知识和科学谜题
– like this one about what happens to a thermometer
比如把温度计放在太空并旋转后
if you put it in space, and then rotate it.
它将会发生什么
Does it still read the same temperature? Or hotter or colder?
还会显示一样的温度吗? 或是变冷或是变热吗?
Brilliant is offering 20% off of a premium subscription
Brilliant会为前200名分钟物理的观众
to the first 200 MinutePhysics viewers to
提供8折订阅优惠
go to brilliant.org/slash minutephysics
请登录brilliant.org/slash MinutePhysics
– that lets Brilliant know you came from here,
这让Brilliant知道你来自本视频
and gets you full access to all of Brilliant’s courses, puzzles, and daily challenges.
并获得你在Brilliant所有课程 谜题和日常挑战的全部权限
Again, that’s brilliant.org/minutephysics
最后 有了Brilliant/ Minutephysics
so that you don’t mess up like Einstein.
你就不会像爱因斯坦那样犯错了

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视频概述

爱因斯坦著名的方程与他一生中的最大“失误”。

听录译者

收集自网络

翻译译者

路痴

审核员

审核员MS

视频来源

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

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