读者可能和我一样，都听说过一下内容，但都不太明白它们的来龙去脉，这章“不确定性原则”就讲了它们的故事（只提到薛定谔，没有讲猫）：
1, 薛定谔的猫。
2, 爱因斯坦说，上帝是不会掷骰子的（God does not play dice.）。
3，我们课本上学的，原子是带正电荷的原子核和围绕它旋转的带负电荷的电子构成。有没有人想到，带正副电荷的两个物体应该是互相吸引的，走到一起的，怎么就一个围绕另一个一直转呢？
4，量子力学。
下面大概介绍一下这一章和上面的这些故事。
继牛顿的各个定律，到爱因斯坦的相对论，让人们自信心大增。于是，就出现了“科学决定论（scientific determinism）”。就是认为，一切现象都可以由科学定路来预测。比如，使用牛顿的定律，我们可以预测到那些星球在任何时间的位置，整个太阳系的状态。不过，也有很多人反对它，他们认为，如果都能预测，那么上帝的自由就被侵犯了。
同时，根据我们当时认为的定律，高温物体应在所有频率上均等地释放电磁波。
According to the laws we believed at the time, a hot body ought to give off electromagnetic waves equally at all frequencies.
这意味着，这会使物体释放的能量是无限的。这是不可能的。
为了避免这一明显荒谬的结果，德国科学家马克斯·普朗克于1900年提出，光、X射线和其他波不能以任意速率发射，而只能以他称为量子的某些数据包发射。 而且，每个量子都有一定量的能量，波的频率越高，能量越大，因此，在足够高的频率下，单个量子的发射将需要更多的可用能量。 因此，高频辐射将减少，因此物体能量损失的速率将是有限的。
In order to avoid this obviously ridiculous result, the German scientist Max Planck suggested in 1900 that light, X rays, and other waves could not be emitted at an arbitrary rate, but only in certain packets that he called quanta. Moreover, each quantum had a certain amount of energy that was greater the higher the frequency of the waves, so at a high enough frequency the emission of a single quantum would require more energy that was available. Thus the radiation at high frequencies would be reduced, and so the rate at which the body lost energy would be finite.
之后，海森堡制定了他的著名的不确定性原则。比如，一个很小的粒子，如果要测它的位置和速度，需要用光，因为粒子很小，所以测它的光波就要足够短，光波波段越短能量越大，作用到粒子上就越能改变它的位置和速度。
海森堡指出，粒子位置的不确定性乘以其速度的不确定性乘以粒子的质量永远不能小于一定的量，这就是所谓的普朗克常数。
Heisenberg showed that the uncertainty in the position of the particle times the uncertainty in its velocity times the mass of the particle can never be smaller than a certain quantity, which is known as Planck’s constant.
这种方法导致海森堡、欧文·薛定谔和保罗·狄拉克在1920年代根据不确定性原理将力学重新构造为一种称为量子力学的新理论。
This approach led Heisenberg, Erwin Schrodinger, and Paul Dirac in the 1920s to reformulate mechanics into a new theory called quantum mechanics, based on the uncertainty principle.
通常，量子力学不会为观察预测单个确定的结果。 相反，它预测了许多不同的可能结果，并告诉我们每种结果的可能性。
In general, quantum mechanics does not predict a single definite result for an observation. Instead, it predicts a number of different possible outcomes and tells us how likely each of these it.
因此，量子力学将不可避免的不可预测性或随机性引入了科学。
Quantum mechanics therefore introduces an unavoidable element of unpredictability or randomness into science.
然而，爱因斯坦从未接受宇宙是偶然性控制的。 他著名的陈述“上帝不玩骰子”总结了他的感受。
Nevertheless, Einstein never accepted that the universe was governed by chance; his feelings were summed up in his famous statement “God does not play dice”.
尚未将量子力学适当的纳入的物理科学领域是重力和宇宙的大规模结构。
The only areas of physical science into which quantum mechanics has not yet been properly incorporated are gravity and the large-scale structure of the universe.
量子力学理论基于一种全新的数学形式，不再用粒子和波来描述现实世界。 仅仅是可以用这些术语描述对世界的观察。
The theory of quantum mechanics is based on an entirely new type of mathematics that no longer describes the real world in terms of particles and waves; it is only the observations of the world that may be described in those terms.
量子力学告诉我们，所有粒子实际上都是波，并且粒子的能量越高，相应波的波长越小。
quantum mechanics tells us that all particles are in fact waves, and that the higher the energy of a particle, the smaller the wavelength of the corresponding wave.
这里有个实验，用一个光子（photon）穿过墙上的两条狭缝，本来以为光子只会从其中一个狭缝穿过，结果发现这个光子从两条狭缝穿过，这里把这个光子看作波就好解释了。
我们课本学过的，带负电的电子围绕带正电的原子核旋转，组成了原子。
麻烦在于，在量子力学之前，力学定律和电定律预言电子将失去能量，因此向内旋转，直到电子与原子核碰撞。
The trouble with this was that the laws of mechanics and electricity, before quantum mechanics, predicted that the electrons would lose energy and so spiral inward until they collided with the nucleus.
新的量子力学理论解决了这一难题。 围绕原子核运行的电子可以看作是一种波，其波长取决于其速度。 对于某些轨道，轨道的长度是响应电子波长的整数（相对于分数）。 对于这些轨道，波峰每次都会位于相同的位置，因此波会累加； 这些轨道将与玻尔的允许轨道相对应。 但是，对于长度不是整数波长的轨道，随着电子的绕行，每个波峰最终都会被一个波谷抵消掉。 这些轨道是不允许的。
The new theory of quantum mechanics resolved this difficulty. It revealed that an electron orbiting around the nucleus could be thought of as a wave, with a wavelength that depended on its velocity. For certain orbits, the length of the orbit would respond to a whole number (as opposed to a fractional number) of wavelengths of the electron. For these orbits the wave crest would be in the same position each time round, so the waves would add up; these orbits would correspond to Bohr’s allowed orbits. However, for orbits whose lengths were not a whole number of wavelengths, each wave crest would eventually be canceled out by a trough as the electrons went round; these orbits would not be allowed.
感觉是把原子核的位置作为“电子”波的波源了。应了那句话，了解的越多，越发现自己的无知。
可视化波/粒子对偶性的一种好方法是美国科学家理查德·费曼（Richard Feynman）提出的所谓的历史总和。 在这种方法中，粒子不应该像经典的非量子理论那样在时空中具有单一的历史或路径。 相反，它应该通过所有可能的路径从A到B。 每条路径都有两个相关的数字：一个代表波浪的大小，另一个代表循环中的位置（即它是在波峰还是波谷）。 从A到B的可能性是通过将所有路径的波相加得出的，周期中的相位或位置将有很大的不同。 这意味着与这些路径关联的波将几乎完全相互抵消。 但是，对于某些组的相邻路径，路径之间的相位变化不会太大。 这些路径的波浪不会抵消。 这些路径与玻尔的允许轨道相对应。
A nice way of visualizing the wave/particle duality is the so-called sum over histories introduced by the American scientist Richard Feynman. In this approach the particle is not supposed to have a single history or path in the space-time, as it would in a classical, nonquantum theory. Instead it is supposed to go from A to B by every possible path. With each path there are associated a couple of numbers: one represents the size of a wave and the other represents the position in the cycle (i.e., whether it is at a crest or a trough). The probability of going from A to B is found by adding up the waves for all the paths, the phases or positions in the cycle will differ greatly. This means that the waves associated with these paths will almost exactly cancel each other out. However, for some sets of neighbouring paths the phase will not vary much between paths. The waves for these paths will not cancel out. Such paths correspond to Bohr’s allowed orbits.
《时间简史》第4章：不确定性原则 (The Uncertainty Principle)
《时间简史》第4章：不确定性原则 (The Uncertainty Principle)
上次由 Mia2014 在 周六 3月 27, 2021 3:41 pm，总共编辑 6 次。
