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In 1915, Albert Einstein published a very important equation - no, not that one - the one he published didn’t just relate mass and energy,
1915年，阿尔伯特·爱因斯坦发表了一个非常重要的方程，不，不是那个，他发表的方程不仅仅是关于质量和能量，
but mass, energy and gravity - this equation replaced the older “Newton’s law of Gravitation,”
而是质量、能量和引力——这个等式取代了老的“牛顿引力定律”，
which you may be familiar with, and it remains to this day our best description of how gravity works.
你们可能对它很熟悉，直到今天它仍然是我们对引力如何运作的最好描述。
Just like how F=ma is a mathematical description of how the acceleration of an object depends on the forces applied to it,
就像“F=ma”是一个数学描述，描述了物体的加速度如何取决于施加在它身上的力，
the Einstein Equation of general relativity relates the motion of mass and energy (the “T” on the right)
爱因斯坦的广义相对论方程把质量和能量的运动（右边的T）
to the curvature of spacetime (the “R’s” on the left).
时空曲率(左边的“R”)联系起来。
And Einstein didn’t just pull this equation out of thin air -
爱因斯坦并不是凭空提出这个方程的，
it was the natural consequence of a long and careful consideration of key principles of physics combined with the advanced mathematics of curved surfaces,
它是将物理学关键原理与曲面高等数学结合起来，经过长时间仔细研究的自然结果，
and of course, agreement with the experimental observations of the day.
当然，它也与当时的实验观察相符。
The equation, however, is deceptively simple.
然而，这个等式看起来很简单。
This one single line is in fact an incredibly fancy shorthand
这一行字实际上是一种非常花哨的速记法，
for what’s actually a system of ten second order partial differential equations relating mass and energy to the curvature of spacetime,
它实际上是一个由10个二阶偏微分方程组成的系统，它将质量和能量与时空曲率联系起来，
AND the R’s themselves are also a shorthand.
曲率R本身也是简写。
But the point is this: after figuring out that these equations matched up with Newton’s law of gravitation
但重点是：爱因斯坦发现，因为引力场弱，速度比光速慢得多，
for weak gravitational fields and speeds much slower than light speed,
所以这些方程符合牛顿引力定律，
AND after showing that the equations correctly predicted a previously “unexplained-by-Newton’s-law” anomaly in the orbit of Mercury,
并且他证明了这些方程正确地预测了水星轨道上先前“牛顿定律无法解释”的异常现象，
Einstein tried to figure out what the equations had to say about the universe as a whole.
然后他试图弄清楚这些方程对整个宇宙的影响。
Of course, all the matter and energy in the universe is too complicated to put into the equations and have any hope of solving them,
当然，宇宙中所有的物质和能量都太复杂了，无法放进方程中，也无法解决它们，
but if you zoom out enough, you can approximate the universe as having a roughly constant density everywhere, and in every direction.
但如果你把范围缩小到足够小，你就可以将宇宙近似为在任何地方、任何方向上都具有大致恒定的密度。
And Einstein was able to solve the equations for a very simplified universe with constant density everywhere -
在一个简化的密度恒定的宇宙中，爱因斯坦能够解释这些方程——
the ten complicated equations reduced to just two simple ones:
十个复杂方程减少到只有两个简单的：
this one says the curvature of space in the universe is proportional to the density,
这个方程表示宇宙空间的曲率宇宙密度成正比，
so more stuff in the universe means more curvature of space; and this one says that the density has to be zero.
所以宇宙中有更多的东西意味着更多的空间曲率；这个方程表示密度必须是零。
Which would mean there can’t be anything in the universe… Needless to say, this was a problem.
这就意味着宇宙中不可能有任何东西...不用说，这是个问题。
And it turns out that there are two solutions to the problem - the one Einstein took, and the one he didn’t.
结果是，这个问题有两种解决方法——爱因斯坦采用的一种，和他没有采用的一种。
Einstein’s solution was this: he knew (since he had dived deep into the math) that it was possible to slightly change his equations;
爱因斯坦的解答是这样的：他知道（因为他已经深入研究了数学）可以稍微改变他的方程式；
you can add a single very simple term without violating any key principles of physics.
你可以添加非常简单的一项而不违反任何物理的关键原则。
There wasn’t much other motivation for adding this term, but it doesn’t change anything about how well the equations match up with Newton’s law when gravity is weak,
加入这一项并没有什么其他的动机，但它并没有改变引力很弱时这些方程和牛顿定律的匹配程度，
or how well they predict the orbit of Mercury, or whatever, so maybe it was ok?
也没有改变它们能很好地预测水星的轨道，或者其他什么，
AND, crucially for Einstein, the new term changes the equation for the density of the universe:
所以也许它是可以的？而且，对爱因斯坦至关重要的是，新的这一项改变了宇宙密度的方程：
instead of saying “density equals zero,” it now says “density is proportional to the new term”.
它不再说“密度等于零”，而是说“密度与这个新术语成正比”。
So if the new term was non-zero, that meant the universe could have stuff in it! Voila - solution number one.
所以，如果新的一项是非零的，那就意味着宇宙中可能有东西！瞧，解决方案一。
The other solution to how the universe can have stuff in it was this: don’t assume (as Einstein had) that the universe is static and unchanging.
宇宙中如何存在物质的另一种解释是：不要假设（像爱因斯坦那样）宇宙是静止不变的。
The general understanding at the time was that the universe didn’t expand or contract,
当时的普遍理解是宇宙不会膨胀或收缩，
and Einstein had also made a small but unfortunate technical error in his calculations which appeared to prohibit the possibility of a changing universe,
而爱因斯坦在他的计算中也犯了一个小而不幸的技术错误，这似乎阻止了宇宙变化的可能性，
so it’s not surprising that Einstein didn’t see this solution.
所以爱因斯坦没有看到这个答案也就不足为奇了。
But it was there: if you don’t make the mathematical assumption that the universe is static,
但它确实存在：如果你不做宇宙是静态的数学假设，
and you don't make the technical error Einstein did, you can find a different valid solution to Einstein’s equations.
也不犯爱因斯坦犯过的技术错误，你就能找到爱因斯坦方程的另一个有效解。
Which physicist Alexander Friedmann did.
物理学家亚历山大·弗里德曼就是这么做的。
Actually he used the version of the equations with the new term, knowing he could always set that term to zero if it wasn’t real.
实际上他用的是包含新项的方程，他知道如果它不是实数，他总是可以将它设为0。
But the key part is he didn’t assume the universe was static.
但关键是他没有假设宇宙是静止的。
Friedmann found that the ten equations again reduced to two: the first equation now describes how the change in density of the universe relates to its change in size:
弗里德曼再次发现十个方程简化为两个：现在第一个方程描述了宇宙的密度的变化与大小的变化：
specifically, it says that if the universe gets bigger, then it gets less dense, which makes sense - stuff’s literally spreading out.
具体地说，它说，如果宇宙变大，密度较低，这是有道理的——物质的扩散。
The second equation says that the deceleration of the universe is proportional to its density minus Einstein’s constant;
第二个方程说宇宙的减速与它的密度减去爱因斯坦常数成正比；
that is, the stuff in the universe attracts itself gravitationally
也就是说，宇宙中的物质通过引力吸引自己，
so the universe would have a tendency to pull inwards on itself, slowing any expansion and possibly even contracting.
所以宇宙会倾向于向内拉，从而减缓膨胀甚至收缩。
Unless Einstein’s constant were real and had a value big enough to balance or overpower the gravitational attraction .
除非爱因斯坦常数是真实存在的，而且它的值大到足以平衡或压倒万有引力。
So that's the solution Einstein didn't see.
这就是爱因斯坦没有看到的解。
Later, once astronomers took sufficiently detailed measurements, it turned out that the universe WAS indeed expanding:
后来，天文学家进行了足够详细的测量，结果证明宇宙确实在膨胀：
So Einstein’s equations didn’t appear to have any need for the extra term he had added.
所以爱因斯坦的方程似乎不需要他添加的额外项。
Einstein was reported by physicist George Gamow to have called it “his biggest blunder” -
物理学家乔治·伽莫夫报道称其为“爱因斯坦最大的错误”——
and while there’s no known documentation that he ever actually said or wrote those words specifically,
虽然没有已知的文档表明他真的说过或写下这些话，
there’s plenty of record of him expressing disdain in other ways: “away with the cosmological term,”
有很多的记录显示他在其他方面表示的不屑：“去掉宇宙项，”
“I always had a bad conscience,” “I found it very ugly,” “such a constant appears…unjustified.”
“我的良心一直不好”，“我觉得它很丑，”“这样一个常数出现...不合理。而且，在爱因斯坦的一生中，这是肯定的——这个词似乎是不合理的。
And, during Einstein’s lifetime, that was certainly true - the term did appear unjustified.
而且，在爱因斯坦的一生中，这当然是正确的——这一项似乎是不合理的。
However, remember how Friedmann’s equations predicted that
但是，还记得弗里德曼的方程是如何预测的吗？
the universe should be attracting itself gravitationally and so the expansion should be slowing down, unless Einstein’s constant is real?
弗里德曼的方程预测，除非爱因斯坦常数是真实的，否则宇宙应该通过引力吸引自己，因此膨胀应该减速。
Well, in 1998 , decades after Einstein’s death,
1998年，在爱因斯坦去世几十年后，
astronomers made the surprising discovery that the universe’s rate of expansion isn’t constant, and it ISN’T slowing down - it’s getting faster.
天文学家们惊奇地发现，宇宙的膨胀速度并不是恒定的，它也不是在变慢，而是在变快。
And so in a great, ironic twist, Einstein’s constant does ultimately have a role in describing the universe…
因此，在一个伟大而又具有讽刺意味的转折中，爱因斯坦常数最终确实在描述宇宙中发挥了作用...
though it turns out to be a very different universe from what he had imagined.
尽管那是一个与他想象的完全不同的宇宙。
