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When Galileo pointed his telescope at Jupiter in 1610, he was the first person to see the giant orbs attached to it by springs.
1610年，当伽利略将望远镜对准木星时，他是第一个看到由弹簧连接在木星上的巨大球体的人。
His actual drawings, compared night after night, show these bright spots moving back and forth past Jupiter, exactly the same as if they were balls hanging off of springs.
他夜复一夜画的图对比显示出，这些亮点穿过木星来回移动，就像是悬挂在弹簧上的球一样。
I mean, yeah Galileo was looking at the moons of Jupiter, but if you plot their motion back and forth and back and forth over time, it forms a sine wave.
我的意思是，虽然伽利略看到的只是木星的卫星，但如果你画出它们随着时间来回运动的轨迹，它会形成一个正弦波。
And that motion is mathematically identical to the motion of something bouncing up and down on a spring with a linear restoring force - also sine waves over time.
在数学上，这个运动和物体在具有线性恢复力的弹簧上上下弹跳的运动是一样的，也是关于时间的正弦波。
From a side-on perspective that projects two dimensions down to one, things in circular orbits look exactly like they’re springing back and forth on giant coils of wire.
从侧面的角度来看，从二维变成一维，那么圆形轨道上的物体看起来就像在巨大的弹簧线圈上来回弹跳。
Now, I’m not saying that we should think of the moons of Jupiter as being held on by giant invisible springs, but it’s a valid mathematical model when viewing them from a distance –
不过，我并不是说我们应该认为木星的卫星被巨大的无形的弹簧拉着，但从远处观测的时候，它是一个有根据的数学模型——
it’ll make the same predictions about the motions of the moons as the “orbiting in circles due to invisible gravity” model, and one can be mathematically transformed into the other.
它与”被看不见的引力牵着转圈”模型一样，都能够预测卫星的运动轨迹，这两者在数学上可以相互替换。
The moons of Jupiter aren’t alone in having multiple mathematical descriptions:
不是只有木星的卫星拥有多种数学描述：
projectiles and storms on earth experience a force (called the Coriolis effect) that causes them to turn,
炮弹和暴风雨在地球上运动时，会受“地转偏向力”的影响而转向，
but viewed from an external perspective, the projectiles and storms are what goes in a straight line while the earth turns beneath them.
但从外部角度看，炮弹和风暴是沿直线运动的，而地球在它们下方转动。
Both models, if you use them carefully, make correct predictions about reality.
如果你合理使用这两个模型，就能对现实做出正确的预测。
And quantum phenomena can be modeled in at least three different ways that all give the same predictions:
量子现象可以在至少三种不同的方法中都得出同样的预测结果：
as a particle being guided by a spread-out “pilot wave”, or as a spread out probability wave that collapses to a single point,
分散的“导航波”引导粒子，或分散的概率波坍缩在了同一个点，
or as a particle exploring all possible paths it could take and interfering with itself along the way.
又或者粒子在探索各种可行路径中进行自我干涉。
All three of these mathematical models suggest different ways of thinking about what’s “actually” going on in quantum mechanics,
这三种数学模型提出了思考量子力学中“实际”发生的事情的不同方法，而且它们都得出了相同的实验预测，
and the fact that all of them give the same experimental predictions suggests that perhaps none of them is the “right” way to picture what’s happening in quantum systems.
这一事实表明，也许没有一种方法是描绘量子系统中正在发生的事情的“正确”方法。
Mathematical models give us nice, easy-to-digest pictures of how the universe works:
数学模型为我们提供了宇宙运行的清晰、易于理解的图像：
moons orbit around planets, atoms bind together into molecules, electrons are clouds of probability, and so on.
卫星围绕行星旋转，原子结合形成分子，电子是概率云，等等。
But we need to be careful how much weight we give to the models in our heads (or on our blackboards, or computer screens).
但我们需要注意的是，我们给予头脑中（或黑板上，或电脑屏幕上）这些模型的权重是多少。
Do Jupiter’s moons move like they’re pulled back and forth by the invisible force of springs?
木星的卫星真的就像被无形的弹簧牵着那样来回移动吗?
Or held in orbits by the invisible force of gravity?
还是被看不见的引力牵着绕轨道旋转？
Or are they following helical paths which are actually straight lines in curved spacetime?
又或者它们遵循的螺旋路径其实是弯曲时空中的直线?
The way we describe the world influences the way we think the world is,
我们描述世界的方式会影响我们对世界的看法，
even when there are other, equally correct ways of describing the world that paint entirely different pictures from our own.
即使还有其他同样正确的描述世界的方式，也会描绘出与我们完全不同的画面。
That’s not to say we should accept wrong ideas, but we should be aware that sometimes a different correct picture, one we haven’t considered, is the one we need to see.
这并不是说我们应该接受错误的观点，但我们应该意识到，有时一种我们没有考虑过的观点，正是我们需要看到的。
