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This episode of space time is brought to you from the information flowing through an impossibly complex network of quantum entanglement, 本期视频经过了无限复杂的量子纠缠网传输到你的电脑
that just happens to mutually agree that you and I exist inside it. 刚好你和我都在这个复杂的量子网中
Oh, and Schrodinger’s cat is in here too. 差点忘了 薛定谔的猫也在
In the quantum world things are routinely in multiple states at once - 在量子世界里 物质日常处于多种状态
what we call a “superposition” of states." 也就是所谓的“叠加态”
But in the classical world of large scales, things are either this or that. 但在经典的大尺度世界 物体不在这就在那
The famous thought experiment is Schrodinger’s cat - 对此最著名的思想实验就是薛定谔的猫
in which a cat is in an opaque box with a vial of deadly poison that’s released on the radioactive decay of an atom. 说的是一个暗盒里放着一只猫和一瓶毒药 毒药由原子的衰变控制释放
Quantum mechanics tells us that the atom’s wavefunction can be in a superposition of states - 量子力学告诉我们 原子的波函数可能处于叠加态
simultaneously decayed or not decayed. 原子同时处于衰变和未衰变状态
So is the cat’s wavefunction also in a superposition of both dead and alive? 那这只猫是不是也同时处于死亡和存活状态
That seems absurd - but quantum mechanics appears to allow this. 这听起来很荒谬 但量子力学似乎允许这种情况
In fact the idea of superposition is fundamental to quantum mechanics. 实际上 叠加态的思想是量子力学的根本
Pick any two valid quantum states - the sum of those states is also a valid state. 任意两个有效的量子态组合起来也是一个有效的量子态
In fact, at the quantum level, there isn’t a clear way to define what states are the most basic. 其实在量子世界 没有明确的方式来区分哪个状态是最基本的状态
Even very distinct-seeming properties can be expressed as superpositions - 甚至非常独特的属性也能由叠加态表达
for example a particle’s position can be expressed as a superposition of momentum states. 例如一个粒子的位置可以用多个动量叠加态来表达
I’ll come back to another example of this in a second. 马上还会讲另一个例子
But this raises the question: 那么问题来了
for Schroedinger’s cat, if alive AND dead are just as valid as alive OR dead, 既然薛定谔的猫可以处于生与死的叠加态
why do we only see the later in the real world? 那为什么在现实世界我们只能看到它非死即生？
The idea of decoherence seems to provide a partial answer - 退相干的思想似乎提供了部分解答
we talked about it last time - to observe a superposition there needs to be a knowable phase relation between two superposed states. 我们三个月前讲过退相干 要得到叠加态 两个叠加状态间的相位关系应该是可知的
But that doesn’t tell us why certain states that exist in the quantum world can survive this decoherence and become manifest in the classical world. 但退相干并没有解释 为什么量子世界中另一些特殊状态不能在退相干后表现在经典世界 （它只解释了为什么没有生死叠加态 没有解释为什么是生或死这两个状态）
To get the entire answer, we need to think about quantum entanglement. 要得到完整的答案 就需要考虑量子纠缠
In fact we’ll see that the properties we think of as fundamental - 实际上 那些我们认为的基本属性
for example the arrangement of atoms that define a living or dead cat - aren’t properties of the atoms. 比如描述活猫和死猫的这种原子排列并不是原子的属性
Rather, the information that defines these classical properties exists in the fantastically complex network of entanglement between those individual quantum system and their environment. 定义这些经典属性的信息 其实存在于这些量子系统与其环境间复杂的纠缠网中
The ideas I’m about to lay out are mostly due to Wojciech Zurek, who calls this framework quantum darwinism - 下面说的这个理论主要来自于W.楚雷克 他把这个观点称为量子达尔文主义
and you’ll see why. 一会你就知道这个名字的含义了
To get there we need to start by talking about quantum superposition. 要理解它 我们从量子叠加态开始讲起
Some quantum particles have a property called quantum spin. 一些量子粒子有一个属性叫自旋
That spin has an axis that points in some direction, analogous to the axis of a rotating ball. 这个自旋有一根轴指向某个方向 就像是一个旋转球的转轴
To measure that spin axis you have to choose what angle you want to measure it at - say, vertically or horizontally. 要测量这个自旋的轴向 必须先选择测量的方向 比如竖直方向或者水平方向
Measure vertically and you might see that the spin axis is pointing up or down, 在竖直方向进行测量 得到的轴向结果可能是向上或向下
measure horizontally and it’ll be pointing left or right. 水平方向测量得到的是向左或向右
Weirdly, if you measure vertically and see an up spin, 诡异的是 如果你先在竖直方向测得自旋轴向上
then measure horizontally you will NOT find that there’s zero spin in that direction, as you’d expect for a classical spinning object. 接着在水平方向测量 如果是常规物体的自旋 那水平方向的测量结果将是0
Instead the electron will randomly shift to having left or right spin. 但电子这类量子将变为随机拥有向左或向右的自旋
So the value for quantum spin depends on how you choose to measure it - 也就是说量子自旋取决于测量方式
it depends on your “measurement basis.” 取决于所选的测量基
And a well defined spin direction in one basis can be expressed as a superposition of two spin directions in another basis. 因此某个测量基下确定的自旋方向 可以用另一个测量基下两个自旋方向的叠加来表示
For example, spin-up is equivalently a particular combination of spin-left and spin-right. Same with spin-down. 例如 上旋可以等价于左旋和右旋的某种特殊组合 下旋也一样
Spin becomes defined in each new basis when you try to measure it in that way, 在每次测量时 自旋都会转变为该测量基下的一种确定组合
and in the process becomes undefined in any previous basis. 这个过程中 之前的测量基不再可知
This is an example of how seemingly-fundamental quantum states can be expressed as superpositions of other states. 这就是一个看似基本的量子态也能由其他状态叠加来表示的例子
So again - why are only certain quantum states observable on large scales? 既然这样 那为什么大尺度上观测到的都是几个特定的量子态
The answer lies in entanglement. 答案在于量子纠缠
The most famous entanglement experiment is the one that Einstein came up with to demonstrate an apparent absurdity predicted by pure quantum mechanics. 爱因斯坦构想了一个用来展示量子力学荒谬性的实验 那也是最著名的量子纠缠实验
This is the so-called Einstein-Podolsky-Rosen, or EPR paradox. 即所谓的EPR悖论
A high energy photon decays into an electron and a positron. 一个高能光子衰变为一个电子和一个正电子
These particles both have spin values of 1/2, but the original photon had spin 0. 它们的自旋值都是1/2 而原光子的自旋为0
So the axes of the new spins have to be in opposite directions in order to cancel out and conserve angular momentum. 因此它们的自旋轴必须相反 以满足角动量守恒
But besides being opposite to each other they can be aligned in any direction. 但除了方向相反以外 它们可以是任意方向
In fact each particle is in a superposition of states - 实际上每个粒子都处于叠加态
measured in the vertical basis, each particle starts in a state of both up AND down, while in the horizontal each is left AND right, etc. 如果在竖直方向上测量 那么两个粒子的自旋为上或下 水平方向则是左或右
The only thing we know is there’s this correlation - 我们唯一知道的是它们的相对关系
whatever spin direction gets measured for one particle, the other particle has to be opposite in the same basis. 只要其中一个粒子的自旋被测量 另一个粒子的旋向必定在同一个测量基下与之相反
We say that two particles with these sort of correlated properties are entangled. 我们称这种具有相互关联属性的粒子是纠缠的
The crazy thing is if I measure the spin of one particle - say the electron - 诡异之处在于 如果我测量其中一个粒子 比如电子的自旋
my choice of measurement basis defines the spin of the positron. 我对测量基的选择将影响正电子的自旋方向
If I measure the electron in the vertical basis and get, say, spin-up, 如果我在竖直方向测量电子的自旋 得到上旋
the positron will become defined in that basis and only that basis - in this case with spin-down. 正电子将在竖直方向 且只在该方向具有确定的自旋 下旋
There’s a sense that causal influence is transferred potentially faster than light. 看起来像是因果关系在超光速传递
This is what Einstein called spooky action at a distance, 这就是爱因斯坦所说的鬼魅般的超距作用
and we now know that this is a very real effect, even though you can’t actually transfer useful information this way. 目前已经证实这是一种真实存在的现象 只不过无法传递任何有用信息
But we’re not here to talk about this crazy result directly - in fact we already did it a long time ago. 但今天我们不是要讲量子纠缠 很早之前就讲过一次了
We’re here to talk about how entanglement is connected to measurement and the collapse of the wavefunction. 今天要讲的是量子纠缠对测量 以及波函数坍缩之间的关系
Let’s think about exactly what’s happening when I try to measure the spin of one of those entangled particles. 我们来看看在测量纠缠对中一个粒子时具体会发生什么
I’ll try to do that in the most subtle way possible. 我会以最微妙的方式测量
Here’s our measuring device - 下面介绍我们的测量装置
it’s a series of magnets designed to deflect the electron based on its up or down spin. 它是一系列基于旋向偏转电子的磁铁
Spin-up electrons are deflected upwards, spin-down electrons are deflected down. 上旋的电子将向上偏转 下旋的电子将向下偏转
Then both types are deflected back to their original straight path. 之后不管什么旋向都会再偏转回原位置
By itself this device isn’t useful - electrons passing through will still be in a superposition of spin states - both up and down, 单靠这个设备没什么用 穿过的电子仍然处于上旋和下旋的叠加态
as though they traveled both paths through the device. 就像是同时穿过了两条路径
But we can try to measure the spin state by placing a detection apparatus on one path. 但我们可以在一条路径上增加一个测量装置来测量自旋
This “apparatus” is as subtle as possible: just a single atom with a very special property. 这个装置的影响微乎其微 它就是一个拥有特殊属性的原子
If the electron passes close to the atom, the atom flips between two states. 如果电子近距离越过这个原子 它就会在两种状态间转换
The nature of those two states doesn’t matter as long as it doesn’t change the spin or sap energy from the electron. 这其中的原理无关紧要 只要这个装置不会改变电子的自旋和能量
One possibility would be that the spin of one of the electrons inside the atom gets flipped. 一种说法是原子中一个电子的自旋发生了变化
But for simplicity, we’ll call these two states off and on. 为了简洁起见 我们就把原子的这两种状态称为开和关状态
OK, so, we put this atom along the up path of our device, 那我们把这个原子放在设备上侧的路径中
and we start it out in the off state. 一开始是关态
If our electron takes the up path it flips the atom to the on state. 如果电子穿过上路 那么原子将转变为开态
If it takes the down path the atom remains in the off state. 如果电子走下路 那么原子仍处于关态
We should be able to just look at the atom to learn the electron’s path, and so learn its spin. 这样我们能通过原子的状态来获知电子走的路径 进而得知其自旋
But what happens after the electron passes through our device. 那电子穿过整个设备后会发生什么
Does its spin count as being measured? Does the positron’s spin immediately become defined? 其自旋算做被测量了吗 那与之纠缠的正电子的自旋也立刻被确定了吗
Well, actually no! 实际上还没有
After the electron passes through our device, we still have a superposition of states 在电子穿过整个设备后 电子仍然处于叠加态
- but now that superposition includes the atom. 只不过它跟那个用于测量的原子一同处于了叠加态
We have to think of the electron PLUS the atom as being in a joint superposed state of: electron up, atom on AND electron down, atom off. 我们只能认为电子与原子处于某种组合叠加态： 电子上旋原子开态 以及电子下旋原子关态
The atom’s state is now correlated with the electron’s state and the two are entangled. 原子的状态与电子的旋向关联了起来 它们发生了纠缠
Which means the atom’s state is also entangled with the positron’s state. 这就意味着原子的状态与正电子的状态也相关 它们也是纠缠的
We could prove that by measuring the spin of the positron, which would instantaneously influence the combine state of the atom and the electron. 要证明这一点只需要测量正电子的自旋 那将瞬间影响原子核电子的组合态
Or we could measure the atom’s state, which would influence the electron and positron. 或者测量原子的状态 也将瞬间影响电子和正电子的状态
The measurement hasn't actually happened yet. The wave function hasn't collapsed. 测量还没有发生 波函数也还未坍缩
Here’s more evidence, even with the vertically-aligned magnetic fields, which only affect the vertical component of the electron’s spin, 还有一点也能说明 虽然电磁场是竖直方向放置 但它只会影响电子旋向的竖直分量
we haven’t even defined the basis that the electron’s spin going to be measured in as up or down. It’s still undefined. 我们并没有确定电子自旋的测量基 因此它的总自旋方向还与水平方向的自旋有关
See, the entangled atom now holds information about the electron’s left-right spin. 所以纠缠的原子也隐含着电子的水平方向自旋
Whereas that information used to be expressible as a superposition of the electron’s up-down status, 这些信息原来是通过电子的上下旋叠加态来表达
now it’s hidden in a superposition of the atom’s on-off status. 现在它们隐藏在了原子的开关叠加态之中
Essentially, phase information got transferred from the electron to the atom. 本质上是相位信息从电子转移到了原子
I won’t go into the details here - suffice to say that it's possible to recover the horizontal spin information, 在这里就不深入讨论了 只要知道水平方向的自旋信息是可以复原的
even if it’s more straightforward to recover the vertical spin because of how we set up the device. 虽然从我们实验装置来看更需要的是复原竖直方向的自旋
OK, so our atomic measurement device doesn’t “collapse the wave-function.” 所以这个原子级实验装置并没有导致波函数坍缩
It doesn't settle measurement basis. So where does that happen? 它也没有设定测量基 所以坍缩发生在哪个地方？
In order for us to be aware of a measurement we look at a macroscopic indicator - say, the pointer on a dial of our instrument. 为了得知测量结果 我们会查看一个宏观的指示器 比如仪器刻度盘上的指针
There's a chain of quantum systems between that original atom and the pointer. 初始原子和指针间是一系列复杂的量子系统
Information spreads along this chain as these systems become entangled with each other. 信息沿着这些通路传播 并将它们纠缠在一起
In fact that growing web of entanglement always contains all of the information about the quantum system being tested. 实际上这个不断扩张的纠缠网 总是包含着被测量子系统的所有信息
The problem is, we never SEE all of that information. 问题在于 我们无从得知其中的信息
We only see the crude, macroscopic characteristics of the device - like the position of a pointer on a dial. 我们只能看到它表面宏观的特性 比如表盘指针的位置
So Zurek figured out why this might be the case. 楚雷克弄懂了其中的原因
It turns out that as more and more particles join our entanglement web, information about quantum states get spread amongst them. 研究发现随着越来越多的粒子加入纠缠网 量子系统的信息均布于每个粒子
It would be possible to extract this information if you could perfectly measure all particles in your measurement device. 除非测量装置能完美得知每个粒子的状态 才能从中提取出这些信息
But eventually this entanglement cascade reaches the surrounding environment - 但最终纠缠链触及了外界环境
it’s no longer bounded, and so the information about most quantum states can’t be recovered. 它们不再是受限的 于是大部分量子态的信息无法再被复原
But there are certain very special quantum states whose information does NOT get hopelessly mixed through this entanglement web. 但有一些非常特别的量子态 它们所携带的信息不会被卷入这个纠缠网
These are properties of the quantum system - measurement bases - whose information is relatively simply reflected throughout the surrounding environment. 它们是系统的某些属性 比如测量基 这些信息经过环境时不会被破坏
Now we call these pointer states. 我们称之为指示态
Pointer states are robustly copied and spread 指示态能够稳定地复制并传播
until the states of the surrounding macroscopic environment - for example our dial’s pointer - are strongly correlated with these states of our quantum system. 直到仪表盘指针这些外界宏观环境与量子系统的状态密切相关
So what determines whether a quantum state can be a pointer state? 那决定某个量子态成为指示态的因素是什么？
Well, to some extent the way you set up the experiment - 某种程度上 是实验的设置方式
whether you align your magnetic field vertically or horizontally. 磁场是竖直设置还是水平设置
But ultimately they are states that can survive contact with the environment. 但根本上说 是这个量子态能否在环境中“存活”
We say that the environment selects certain sets of states to propogate - 我们认为是环境选择了某些特定状态继续传播
Zurek uses the term einselection, for environmentally induced superselection. 楚雷克用的是“einselection”这个词 表示环境诱导超选择
And he coined the term quantum darwinism too, because we have these more “fit” states surviving and being replicated. 他还造了个词 量子达尔文主义 因为只有那些“适合”的量子态能生存并被复制
There’s no meaningful mutation and natural selection, so the link to evolution is dubious. 虽然其中并没有有意义的变种和自然选择 跟进化没太大关系
Still, makes for a great youtube video title. 但至少是个不错的视频标题
OK, so how does any of this explain Schrodinger’s Cat? 话说回来 这个量子达尔文主义要怎么解释薛定谔的猫
Well an important example of a pointer state is the position of a particle. 粒子的位置也是一个指示态
Most quantum interactions depend heavily on the relative location of interacting particles. 大部分量子反应与反应粒子的相对位置密切相关
Therefore information about relative particle locations is robustly shared and propagated through the entanglement network. 因此粒子相对位置信息能稳定地共享并传播至整个纠缠网
The individual particles do NOT have well-defined locations - they stay quantum-weird. 单个粒子没有确定的位置 它们都处于量子混沌中
But the entanglement network has this sort of collective consensus about those locations. 但整个纠缠网对其中粒子的相对位置有某种集体意识
The structure of macroscopic objects - including cats and dials - are strongly defined by the relative positions of their particles. 猫和指针等宏观物体的结构由其粒子的相对位置已经完全确定
Therefore the states of cats and dials will always appear well defined at least to us. 因此猫和指针的状态至少在我们看来是完全确定的
I should say none of this fully solves the measurement problem, 我想说所有的这些都没能解决测量问题
it only tells us why certain quantum states are observable on microscopic scales while Schroedinger Cat states - weird superpositions are not. 它只告诉我们为什么微观尺度中能观测到的叠加态 在薛定谔的猫上却观测不到
It still doesn't tell us why we observe one pointer state over another unless of course there are multiple of these entanglement networks aka worlds. 也仍然没有解释为什么只有一个特殊的指示态被观测到 除非有多个纠缠网 或者说多个世界
By the way - in case you missed it, I just told you how reality works. 提醒一下 我刚刚说的就是现实的运作方式
At least according to the framework of decoherence and these propagating pointer states. 至少在退相干和不断传播的指示态理论中
The observable qualities of reality - object positions, feline mortality statuses, even the results of quantum measurements - do NOT exist in the underlying quantum objects. 现实中可以观测的量 比如物体的位置 猫的生死 甚至量子测量的结果在组成它的量子物体中都是不存在的
Quantum objects remain in undefined and superposed states with no preferred basis for observation. 量子物体始终处于未知的叠加态 对其的观测不存在偏好基
No, the macroscopic observables only exist as a sort of mutual agreement across the network of entanglements that connect those quantum systems. 甚至宏观物体只是其量子系统纠缠网中约定俗成的产物
In a sense, WE exist in such a network. 某种意义上我们也处于这个纠缠网中
In this web of mutually consistent entanglement, even spooky-action-at-a-distance entangled particles maintain their correlations, 在这张相互纠缠的大网之中 甚至具有鬼魅般的超距作用的纠缠粒子间也存在关联
no matter how far separated in boring old space time. 不管它们在远古的时空中相隔多远
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Last week we talked about a thought experiment to test the many worlds interpretation of
quantum mechanics - quantum immortality, aka quantum suicide, in which a physicist will
survive a long chain of deadly quantum events ONLY if all possible histories - or worlds
- eventuate.
Some of you would like clarification on how this experiment actually proves many worlds.
After all, isn't the chance of finding yourself in the rare "survival" timeline the same between
many worlds and copenhagen. Well, that depends on your definition of "yourself". If by that
you mean any given version of you chosen randomly from all possible future timelines - then
yes, chances are that version will die. The difference between many worlds and copenhagen
is that in the former there's a version of you that survives - and that version actually
eventuates. In Copenhagen, its most likely that all of the very rare survival timelines don't happen.
Anonymous had an excellent insight. If every possible combination of quantum events exists
and if the increase of entropy is probabilistic, then is it inevitable that there are exceptionally
rare timelines where the universe gets to a state of low entropy to produce another
Big Bang? In other words - if all possible futures occur in Many Worlds, do some of those
lead to new Big Bangs. Well, the key phrase here is "possible future". Do the laws of physics
allow an entropy fluctuation large enough to produce a new big bang? Could a random
perfect alignment of all particle trajectories produce a big bang density? Maybe - some physicsts
think this may be how our big bang happened. If so, then the never-ending global wavefunction
of the Many worlds interpretation could indeed be a big-bang machine. On the other hand,
if the evolution of that wavefunction can't conceivable produce big bang conditions,
then no - only *possible* futures happen, as Seraphina explained in that same comment.
Ultimate Hair Dryer asks how the many world interpretation handles the probabilistic interpretation
of the wave function. And then goes on to correctly answer their own question - to paraphrase:
whereas the Copenhagen interpretation states that only one branch of the wavefunction survives
measurement, corresponding to one possible result of that measurement. And the wavefunction
itself defines the probability of a given branch "collapsing". The Many Worlds interpretation
states that all branches survive, and the measurement result that we observe depends
on which branch we find ourselves in. However not all measurement results are equal. You
can imagine the wavefunction as consisting of very many fine trajectories - possible
histories by which the system can evolve. Some final results are more probable because
more histories lead to that result. Most of the time you will naturally find yourself
in one of the more common histories - corresponding to more probable measurement results. It's
analogous to statistical mechanics, in which many different arrangements of air in the
room lead to the same measurement of temperature and pressure - so we'll almost always observe
those macroscopic measureables.
thatisjustgreat declines our offer of quantum immortality, saying "I'll stick with classical
immortality, thank you". thanks for commenting Keith Richards, I hope you enjoy watching
the heat death of the universe.