一早上被两条信息给惊醒了。

我最近订购了一本平生最贵的书，一本讲阿拉伯史前文字的书，国内没有，在国外托朋友网络购买，大概加上税什么的1300元RMB。十多天了，本来以为很顺利，朋友这2天就到北京，等着看书心情喜悦。结果，朋友来信说，他马上要出发可书还没有到，所以只能等到后让爱人给寄到国内。这可麻烦了，那邮费估计得又一千也打不住吧？ 我寄一本平常的中国小书也三百多块邮费呢，这1000多块的大书寄来那邮费是多少钱啊！可不寄又怎么办？我事先为了让人免除对买书费用的困扰，怕被人给顺手好意给“资助”了，撒了一white谎，说这书是可以报销的公费，人家可能想这邮费也报销了吧。我得赶紧去声明一下。花费这样的钱太冤，这可怎么办？要么让退掉，要么转让其他同城美国同胞捎一回。怎么办怎么办？

二是关于我的第七本书出版的。责编是位孕妇，本来上帝安排的时间是，我的书先出，孩子后出，看来上帝突然改变了计划，孩子早产先出生了，好在母子平安，祝他们端午愉快！本来这几天等着热乎乎的书出来呢，看来我得先凉快凉快呵呵，这事好办。

这几天读语言学方面的书籍读得愉快，所以上面两个小“挫折”不算什么。

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按部就班回到英语课堂继续上课吧，这一课预定的主题是"黑能" "加速的宇宙" "大撕裂".

首先回顾了"暗物质"的神秘特性,它占据了宇宙70%的成分. 讨论了不同模型下宇宙的曲线。讨论了超新星的性质\频率\和存续时间. 再一次谈到"黑能".大撕裂(The Big Rip)作为宇宙的命运之一得到论述。

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世界上充满着黑能，一种反重力使宇宙分离的东西 .图示与解说，略，有兴趣的建议按照上面的网址自己去看video。  黑能、超新星、白矮星、氢氦、氧、碳......热核爆炸thermonuclear explosions

..... And so, you pile up all this hydrogen and you wait some amount of time, somewhere between 10 days and 10⁵ years, depending on the object. You pile up all this hydrogen and helium and finally it gets dense and hot enough to explode, and then it explodes all at once. Huge hydrogen bomb on the surface of this white dwarf. And that makes the system much, much brighter, because there's all this stuff exploding. This is the phenomenon we call a nova, because it looked to the ancients as if a new star had appeared, because the thing had gotten so much brighter. 

So, stuff piles up. Novae occur. More stuff piles up. More novae occur. And one of the things that's happening while this is going on is that the white dwarf is gradually getting more massive, because it's piling up all this extra material.

新星的产生就是，所有的氢与氦融为碳、氧、氮、氖等. 然后，它就看起来象其余的白矮星一样,被白矮星吸附 assimilated into the white dwarf, except the white dwarf is bigger now.

这样白矮星就越来越大，越来越重 massive. 但会有一个临界限制点， Chandrasekhar Limit, 不能大于太阳的1.4 倍. 到了临界点由于无法抗拒吸引力而收拢不住，就会马上崩溃. 崩溃时会很热，密度提升。碳啊什么的就融化，生成能量.他们熔合到一起构成重元素如铁啊什么的. 所以，这等于是一颗标准的原子弹，一到临界就马上爆炸。

这就引起一个结果，他们爆炸时的亮度一定是同样的。所以它们成为标准光。

知道亮光可以测量距离. 当他们爆炸的时候测试他们的红移，然后就知道他们的距离。他们会惊人地亮， -19.5. 在一两个星期内会亮过整个星系 . 以此也可以探测宇宙。

in the early 1990s, 有2个关键的发展. 一是哈伯太空望远镜测量了Cepheids（天仙座）和其他一些星体、新星, Type Ia Supernovae. 这并不经常发生，一个星系里两百年会有那么一次. 太空望远镜建立以来没发生过在我们星系，我们晚了。我们星系假如能有一次超新星爆炸就太棒了.

不过历史上我们是有过观察超新星的记录的 Kepler and Tycho第谷就都看到过。十一世纪时the Chinese and Arab 的天文学家也都看到过 . The Europeans were, in barbarity at the time and didn't even notice. 现在我们看到的the Crab Nebula蟹状星云, 就是正在大爆发.那些东西成为天空中最亮的东西.甚至白天都可以看到，不过在我们的星系，至少400年以内没发生过了.

Student: How long did you say they lasted?

Professor Charles Bailyn: They last--well, I'll show you in a minute what the light curve looks like. They take a couple weeks to rise to their maximum brightness, and then they decay over a few months. So, you can see them for a little while.

So, it just--measured Cepheids（仙王座内的“造父变星”）. This meant that we could 校准calibrate them. Remember the distance ladder? So, you could calibrate these things – calibration. 

   ......

    So -19.5 is a typical magnitude--absolute magnitude. And each color is a different supernova.  顶峰 -18.8, the orange one on the top gets up to about -20. That's almost a factor of 3 in difference of peak brightness.......the maximum brightness of these things is always the same at around -19.5. So, you have to make this correction in order to be able to use these things effectively as standard candles.

 .......

 So, this means that you can discover supernovae in the--so, there are thousands of galaxies, here. And if supernovae occur once per every 100 years per galaxy, there ought to be about ten or twenty supernovae going off in this tiny piece of space right now. Or any other such tiny piece of space. And so, if you're looking for high redshift supernovae, you don't care where you point. They're everywhere. And so, you just pick out some nice blank piece of space, take really deep pictures of them, and wait for the supernovae to start showing up. And this is what people have done.

 ......

So, if you want to come up with some kind of explanation for this that does not involve dark energy, you've got to get around both of these points; namely, the fact that we expect them to look like each other, and the fact that they do look like each other. Now, it's possible to do that and, in fact, one of the problems on the problem set addresses just this issue. If you can invent some way that all of the supernovae at a redshift of .8, high redshifts like that, are all systematically fainter than otherwise identical-looking supernovae in the nearby Universe, then you can get around this problem. But they have to be identical-looking in the sense that they have the same color and decay rate, but are fainter.

We don't see that in the local Universe. We don't see a category of things, which have the same color and decay rate, but one is fainter than the other.  The Universe was, you know, half its size back then. All sorts of things were different. Maybe there's some way that supernovae then were systematically different from how they are now, except that they don't show it in these particular ways. They only show it in the overall brightness. That's tough. That's tough, theoretically. It's tough empirically. You know, you would expect that if that were true, then there would be intermediate cases that we could see, and we don't see them.

But, you know, shortly after this result was announced, I used to--when I was at conferences and stuff, I would try and take the supernovae people off in a corner and give them beer and stuff, until they would, you know--and then, after you give them four beers, you ask the question, what could be going wrong? Do you really believe in dark energy? And then, they start mumbling stuff about all the different weirdnesses that supernovae have. And, of course, these are people who have devoted their life to studying the weirdness of supernovae, and so, they have many things that they will tell you under cover of darkness. Which, of course, then, everybody went out to try and check. And none of these things have turned out to be able to provide a satisfactory explanation for the data, except the idea that there's something very significant, cosmologically, going on.

许多人为此感到困惑。  in 1998, when this was first announced, it was not announced by one group, 而是2个. There were two groups trying to do the same thing, they were sort of spying on each other, because this was an important result. And they both found out, at a certain point, that the other guys had been spending a year driving themselves crazy because they didn't believe their results其中一组早已花费了一年的时间，但他们没有公布结论因为他们不相信自己的发现.   But then, they spied on each other and they found out that the other guys were having the exact same problem, having taken their data and dealt with it in quite a different way.

非常奇怪地说，他们几乎同时递交了报告And so, then, miraculously enough, they kind of submitted their papers within twenty-four hours of each other, so they both got credit. And so, the two groups doing the same things, but doing them differently. Different approaches, in some ways, got the same result.

 one group were a bunch of particle physicists led by Saul Perlmutter, who had gotten depressed by the fact that the Super Collider大碰撞 was cancelled in the early 1990s, and had decided--somebody described this as "adult onset cosmology," where you used to be interested in particle physics, but then, they didn't build your machine, so now you're interested in astrophysics. And those guys took a very particle physics approach to it. They had a big team, with a team leader and a whole hierarchy. The other guys were a bunch of supernova--and they were very expert in the cosmology side of things, and in the dark energy explanations, and stuff like that.

 another group,  was totally differently organized. It was kind of a loose confederation of small research groups here and there. They had done this interesting work with the correction factors on supernovae some years before, and they approached it as, you know, my group will do this little piece. My group will do this other little piece. We'll get together over lunch and we'll figure out what's going on, kind of thing. And they both got the same kinds of answers. They both basically got the same answers.

And so, this is one of the fables. So, fable: 发现黑能discovery of dark energy. And I would say that the moral here is that replicating important results is one of the things that leads people to actually believe what you're saying--leads to greater acceptance.

And it was particularly nice in this particular case, because neither of them were replicating the others. They both made the discovery independently, at the same time, using a very different kind of organizational structure and a very different approach to their data. So, this was kind of compelling.

....... 

And, as you will recall, the explanation for this--or, the first explanation that was offered was the fact that Einstein had this figured out eighty years before, except he decided he was wrong. And so, the first explanation of this was Einstein's Cosmological Constant--that's this symbol, lambda [λ], that I keep writing down.

And so, once people believed this result, you had to start worrying about what the heck this actually is in real life. And it has some very peculiar properties. In particular, there is the issue of what is constant about Einstein's Cosmological Constant爱因斯坦的宇宙常数?

 The energy density – remember, that's the crucial quantity--of λ is constant as the Universe expands. So, if you take 1 cubic meter of space, and you say, how much dark energy is there in this cubic meter of space? We take an average cubic meter of space. You figure that out by how fast the Universe is being pushed apart. And then, you know, you wait 10 billion years, or something like that, until the Universe is very much bigger. And then, you take a cubic meter of space, and you ask yourself how much dark energy is in this cubic meter, and you get the same answer, 10 billion years later. And you got the same answer now, and you would have gotten the same answer 10 billion years ago.

You know, the Universe also has a bunch of matter in it. All right, so I measure the average density of the Universe in the way we've discussed, and you get some answer. So, for matter, you can get some density to the Universe宇宙的密度 now. And then, supposing you imagine in your mind, you go back in time when--to the time when the scale factor of the Universe, when a was half its present size, its present amount. But, of course, you have the same amount of matter in the Universe. Matter doesn't--you know, in general, it doesn't get created. Or, at least, you have the same amount of matter plus energy. So, you go back to when you have the same amount of matter, but it's in half the size, by which I mean, 1/8 the volume, right? Half squared--half cubed is 1/8. And so, if I reduce the linear scale of the Universe by a factor of two, I have 1/8 the volume, but same amount of matter.

....

We've talked about this before, right? The whole deal with the Big Bang is that if you go back into the past, things were denser than they were today. Also hotter, which is a by-product of the density. You take a big balloon full of stuff. You make it smaller. The same amount of stuff is in there. It's got to be denser inside the balloon after you've squashed it down. You take a balloon and you stretch it out. If you don't let stuff come in or out, then it has to be less dense--the stuff inside, after you've stretched it out. And then, you get into all these nice little thermodynamics problems where you have, pressure is equal to density times temperature, and things like that. So, all of familiar gas physics comes into play.

And so, you expect that the density of the Universe is constantly getting smaller, because the Universe is getting bigger. And, in fact, there's extremely good empirical evidence of that, because you look back in time by looking at distant things. Sure enough, it's denser back then.

But not the dark energy. Dark energy density, at least in Einstein's conception, is constant. So, a cubic meter of the Universe has the same amount of dark energy in it now as a cubic meter of the Universe did when the Universe was only a cubic meter across, right? Where the whole observable Universe was packed down into a cubic meter, that cubic meter had only as much dark energy in it as, you know, this part of the Universe does now. Very odd behavior, but this is what Einstein's equations predict.

Now, the thing is, we don't know that Einstein really was right. We don't, because we don't have a clue what the dark energy actually is. So let me--so, λ, the Cosmological Constant, suggests that dark energy has constant density. But, since we don't know what the heck this stuff is, maybe that's wrong.

Or maybe not. If it's not, we don't call it λ anymore. But if you allow for changes in the density, you can get very interesting potential effects. And let me--we'll talk about this more next time, but let me just describe one of the very strange things that could happen.

Suppose it is true--and this is not ruled out by the data we have so far. Suppose the dark energy density increases as the Universe gets bigger. And since we don't have any idea what this stuff is, it might do that, and we can't rule it out by observations just yet. And so, the Universe gets bigger and bigger. The density of the matter is going down, because you have the same amount of matter in a bigger space.

But, supposing we invent some kind of dark energy where the density actually gets bigger as the Universe increases in size. Then, a cubic meter of volume has increasing dark energy as time goes along. That, of course, pushes the Universe out faster, so the acceleration increases. That makes the size increase and you get a feedback as the Universe exponentially expands. You get an exponential expansion. And as that exponential expansion increases, the amount of dark energy in any particular cubic meter gets bigger too.

And so, what happens? After a while, the dark energy in any cubic galaxy has become so much that it blows the galaxy apart. Gravity can't hold the galaxy together. And then, the expansion continues. And then, after a while, the amount of dark energy in one cubic star, if I can use that term, in one star becomes so great that it overcomes the gravity of the star and it blows the star apart. And then, the expansion continues even faster. And after a while, the amount of dark energy in a cubic meter--that would be a human being. Remember, human beings are exactly a cubic meter and exactly 100 kilograms in mass. The amount of dark energy in a human being overcomes the chemical bonds that hold your body together and human beings get blown apart. And eventually, you have so much dark matter that whole atoms--that atoms get blown to bits, and even the sub-atomic particles that are within them eventually get blown to bits. And so, dark energy conquers all.

大撕裂This is described as the Big Rip, and it is kind of an alternative hypothesis of what might happen to the Universe, that stems from an alternative hypothesis of what the dark energy is, that there's no particular reason to believe, but that hasn't been disproved. And since there's no particular reason to believe anything else, you can amuse your students by talking about it.不用一定信，但当然也没有被证伪，它也是解释黑能的一种方式。

本课总结--it's all a question of the scale factor versus time. Here is now. Here is 1. Here is an empty Universe. We thought that what would happen is that it would look like this, and either collapse, or not. What actually happened is, it turns out, things look like this. We only really observe it in the past, so there's a whole bunch of supernovae proving that that's true. And you can extrapolate a kind of gentle expansion that looks like this. This is the standard model with a Cosmological Constant. But if you assume that things get even bigger--that the dark energy increases per volume with time, then you asymptotically go to infinity at some time in the future and you blow everything apart.

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