The ultimate fate of black holes

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Are elementary particles ultimate fate of black holes?

From the “no hair theorem” we know that black holes have only 3 characteristic external observables, mass, electric charge and angular momentum (except the possible exceptions in the higher dimensional theories). These make them very similar to elementary particles. One question naively comes to mind. Is it possible that elementary particles are ultimate nuggets of the final stages of black holes after emitting all the Hawking radiation it could?

Yes, black holes are special kinds of elementary particles. That’s how they have to be represented in every consistent quantum theory of gravity. This representation of a black hole becomes especially useful and important for small black holes – whose mass is not much larger than the Planck mass.

And indeed, a black hole evaporates, which is just a form of a decay of a heavy elementary particle, and when it becomes very light, at the end of the Hawking evaporation process, it is literally indistinguishable from a heavy elementary particle that ultimately decays into a few stable elementary particles.

However, a difference that you seem to neglect is that black holes actually carry a large entropy

S = \frac{A}{4A_0} k_B

where A is the area of the black hole’s event horizon and ( A_0 ) is the Planck area ( A_0=\hbar G / c^3 ). The constant ( k_B ) is Boltzmann’s constant. This means that there actually exists a huge number of microstates

N = \exp(S / k_B)

and a single black hole, with a fixed value of mass, charges, and spin, is just a macroscopic description of the ensemble of N “microstates”. In reality, the black hole carries a huge information – the world distinguishes which of the N microstates is actually present.

It is these “microstates” that are really analogous to types of elementary particles. But the number of particle species that macroscopically look like the black hole of given mass, charges, and spin is not one: instead, it is huge, approximately N.

— Physics Stack Exchange

— user contributions licensed under cc by-sa 3.0 with attribution required

— answered Feb 27 ’11 at 16:45

— Lubos Motl

2014.07.18 Friday ACHK

I Am Legend

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Fair use rationale for I Am Legend

No free equivalent exists that would effectively identify the article’s subject.
The image does not in any way limit the ability of the copyright owners to market or sell their product.
The image is only used once and is rendered in low resolution to avoid piracy.

I Am Legend is a 2007 British-American post-apocalyptic science fiction horror film directed by Francis Lawrence and starring Will Smith. It is the third feature film adaptation of Richard Matheson’s 1954 novel of the same name, following 1964’s The Last Man on Earth and 1971’s The Omega Man. Smith plays virologist Robert Neville, who is immune to a man-made virus originally created to cure cancer. He works to create a remedy while defending himself against mutants created by the virus.

— Wikipedia on I Am Legend (film)

2014.07.16 Wednesday ACHK

受威脅招聘法

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大甲等人 5

這段改編自 2010 年 4 月 10 日的對話。

我看過一篇有關電腦界創業的文章。

大部人僱主，或者招聘部人員，也不敢聘請才華太出眾的應徵者，因為怕自己在公司的地位，受到威脅。而最高級的僱主，即是之前所講的「大甲等人」，就偏偏逆此趨勢而行。

「大甲等人」的招聘哲學是，凡是才智未高到，足以威脅到（招聘者）自己地位的應徵者，都不會考慮。換句話說，「大甲等人」只會聘請，有機會威脅到自己的應徵者。

後果是，公司越來越強大。

— Me@2014.07.16

2014.07.16 Wednesday (c) All rights reserved by ACHK

On Keeping Your Soul, 2

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Als 4 days ago

I’m happy to see that you still work on string theory. Do you intend to start publishing again?

Lubos Motl Als 3 days ago

No, I do not.

Kimmo Rouvari Lubos Motl 3 days ago

Why? (just curious) Obviously you have ideas and something to say.

Lubos Motl Kimmo Rouvari 3 days ago

I just virtually never had a real pleasure out of this process which has something like dozens of consumers in the world in average and which is laborious and demanding various formalities. This part of what I would be doing was always more or less just work and I was doing these things as a part of the package for the salary.

I am not getting the income for that, I am not a communist who would think it’s really right to do the expert work for free, so I won’t do these things. I think it’s common sense and it’s very simple.

I am sufficiently frustrated when I just report on someone’s excellent paper and the feedback is 100 times less excited than the feedback following some anti-science rant by a worthless sithead … And that’s something I may ignore because it’s just not my business.

— Lubos Motl

2014.07.15 Tuesday ACHK

Open Source MindOS, 2.3

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朋友同事 5.3 | 已婚單身 2.3 | Singles 2.3

這段改編自 2010 年 4 月 10 日的對話。

.

拍拖（談戀愛），是一個「互相改變」的過程。

無傷大雅的缺點，你可以選擇不改，因為更改太快太多，會十分煩厭。但對於事關重大的缺點，你不敢不改。

要發現和改正自己的缺點，往往需要一個，十分瞭解你的人，加以提醒和指導。而拍拖，就正正是那個「互相修正」和「互相創造」的過程。

M. C. Escher

Though this image is subject to copyright, its use is covered by the U.S. fair use laws because

1. It illustrates an educational article …
2. It is a low resolution image.
3. It is not replaceable with an uncopyrighted or freely copyrighted image of comparable educational value.

「不斷修正」和「不斷創造」的後果是，雙方各自也不斷重生成，新版本的自己。二人對於對方來說，也會不斷帶來新鮮感。那樣，愛情方能長久。

— Me@2014.07.14

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2014.07.14 Monday (c) All rights reserved by ACHK

天外救星 3C

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Deus ex machina 3C

「時間旅行」、「蟲洞」、「平行宇宙」、「奇蹟」等情節，都是「天外救星」。它們的出現往往代表，該故事有著，不可修補的漏洞。

故事凡是時間錯亂，就宣稱是「時間旅行」。

故事凡是地點有誤，就宣稱是「瞬間轉移」。

故事凡是自相矛盾，就宣稱是「平行宇宙」。

故事凡是有違常理，就宣稱有「奇蹟」。

— Me@2014-07-11 04:59:55 PM

2014.07.13 Sunday (c) All rights reserved by ACHK

Deus ex machina 3

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天外救星 3

Time travels, wormholes, parallel universes, miracles are all deus ex machina.

When a story’s author uses those deus ex machina, it means that the story broken, in the sense that the story has plot holes that the author cannot fix. 

With time travel, the story’s time logic is given up. With wormholes, the story’s space logic is given up. With parallel universes, the story’s internal consistency is given up. With miracles, the story’s scientific consistency is given up.

— Me@2014-07-12 01:15:25 PM

2014.07.13 Sunday (c) All rights reserved by ACHK

Deus ex machina 2

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天外救星 2

Towards the end of the 19th century, Friedrich Nietzsche criticized Euripides for making tragedy an optimistic genre via use of the device, and was highly skeptical of the “Greek cheerfulness”, prompting what he viewed as the plays’ “blissful delight in life”.

Nietzsche argues that the deus ex machina creates a false sense of consolation that ought not to be sought in phenomena.

— Wikipedia on Deus ex machina

2014.07.12 Saturday ACHK

Deus ex machina

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天外救星

Deus ex machina is a plot device whereby a seemingly unsolvable problem is suddenly and abruptly resolved by the contrived and unexpected intervention of some new event, character, ability or object. Depending on how it is done, it can be intended to move the story forward when the writer has “painted himself into a corner” and sees no other way out, to surprise the audience, to bring the tale to a happy ending, or as a comedic device.
  
Origin of the expression

The Latin phrase deus ex machina, from deus, meaning “a god”, ex, meaning “from”, and machina, meaning “a device, a scaffolding, an artifice”, is a calque from Greek ἀπὸ μηχανῆς θεός (apò mēkhanḗs theós), meaning “god from the machine”. Such a device was referred to by Horace in his Ars Poetica (lines 191–2), where he instructs poets that they should never resort to a “god from the machine” to resolve their plots “unless a difficulty worthy a god’s unraveling should happen”. He was referring to the conventions of Greek tragedy, where a machine is used to bring actors playing gods onto the stage. The machine could be either a crane (mechane) used to lower actors from above or a riser that brought actors up through a trapdoor.

Ancient usage

Aristotle criticized the device in his Poetics, where he argued that the resolution of a plot must arise internally, following from previous action of the play …

In modern literature

A deus ex machina is generally deemed undesirable in writing and often implies a lack of creativity on the part of the author. The reasons for this are that it does not pay due regard to the story’s internal logic (although it is sometimes deliberately used to do this) and is often so unlikely that it challenges suspension of disbelief, allowing the author to conclude the story with an unlikely, though perhaps more palatable, ending. Following Aristotle, Renaissance critics continued to view the deus ex machina as an inept plot device, …

— Wikipedia on Deus ex machina

2014.07.11 Friday ACHK

天外救星

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「天外救星」是意料外的、突然的、牽強的解圍角色、手段或事件，在虛構作品內，突然引入來為緊張情節或場面解圍。近似詞有「天降神兵」和「如有神助」等。

Deus ex machina

拉丁語片語Deus ex machina（英譯：God from the machine）翻譯自希臘語，意思是「機關跑出的神」，中文一般翻譯為「舞台機關送神」、「機械降神」、「機器神」、「解圍之神」等。

在古希臘戲劇，當劇情陷入膠着，困境難以解決時，突然出現擁有強大力量的神，將難題解決，令故事得以收拾。方法是利用起重機，或起升機的機關，將扮演神的演員，下降至舞台上。這種表演手法是人為的，製造出意料之外的劇情大逆轉。

現代批評

這種手法通常被評論家認為是，不高明的說書技巧，因為它破壞了故事的內在邏輯，縱使有時候會為了這個理由，而故意採用。繼亞里士多德之後，文藝復興時期評論家將其視為，一種迂拙的情節計策…

— 改編自維基百科

2014.07.10 Thursday ACHK

Open Source MindOS, 2.2

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朋友同事 5.2 | 已婚單身 2.2 | Singles 2.2

這段改編自 2010 年 4 月 10 日的對話。

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有重大壞處的「缺點」，如果可以改但不願意改，就是「人格問題」。

例如，「我太矮，不適合做籃球運動員」是我的「缺點」，但不是「人格問題」，因為這「缺點」不可能改。

又例如，「我烹飪欠佳，不適合做廚師」是我的「缺點」，但不是「人格問題」，因為這「缺點」並沒有重大壞處，只要我不以廚師作我的職業就可以。

再例如，「我烹飪欠佳，但選擇以廚師作職業」既我的「缺點」，又是「人格問題」，因為，這「缺點」既有重大壞處，卻又明顯「可改」—— 要麼我進修廚藝，要麼我轉換職業。兩步也不肯做的話，我的人格就明顯有問題。

換句話說，一個人如果「受教可改」，就自然沒有「人格問題」。所以，我的其中一個擇偶條件是，她的心靈作業系統，是 open source 的。

（安：但是，有時有些「缺點」，自己不單願意，甚至非常想改，但偏偏改不到。那樣，那個「缺點」，還算不算是「人格問題」？）

並不可能有這種情形發生。如果想改，但自己改不到，你自然會求教於人。如果自己改不到，但卻不肯求教，那就不算是「想改」。

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「缺點」有四大層次：

1. 你不知道自己有缺點；

2. 你知道自己有缺點，但不知道是什麼缺點；

3. 你知道自己有缺點，而且知道有什麼缺點，但偏偏不知道如何改正；

4. 你知道自己有缺點，而且知道有什麼缺點，再加上知道如何改正。

最後一種情形，很少會發生。而正正是因為大部分人，在大部分情況下，也不知如何改正，自己的缺點，「受教」才那麼重要。

拍拖（談戀愛），是一個「互相改變」的過程。

無傷大雅的缺點，你可以選擇不改，因為更改太快太多，會十分煩厭。但對於事關重大的缺點，你不敢不改。

要發現和改正自己的缺點，往往需要一個，十分瞭解你的人，加以提醒和指導。而拍拖，就正正是那個「互相修正」和「互相創造」的過程。

— Me@2014.06.30

 

M. C. Escher

Though this image is subject to copyright, its use is covered by the U.S. fair use laws because

1. It illustrates an educational article …
2. It is a low resolution image.
3. It is not replaceable with an uncopyrighted or freely copyrighted image of comparable educational value.

.

.

2014.07.08 Tuesday (c) All rights reserved by ACHK

望遠

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三十年前，初初學習駕駛非常膽怯，擔心車行駛時不是直綫，又擔心撞到旁邊，愈緊張就發現愈是難駕馭，往往把輪胎弄花。後來，有朋友教我駕車時，不要望近，只往遠處望。只要望遠的地方，車就自然會向前直綫行駛，也會駛到路的中間，不會撞到旁邊。

駕車跟做人一樣，愈望得近就會愈緊張，最後左右人生的大方向。越望得遠，就不會走了彎的路，不會浪費了人生的時間。

— 王維基

2014.07.04 Friday ACHK

Open Source MindOS, 2.1

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朋友同事 5.1 | 已婚單身 2.1 | Singles 2.1

這段改編自 2010 年 4 月 10 日的對話。

.

所以，我的其中一個擇偶條件是，她的心靈作業系統，是 open source 的。換句話說，即是「受教可改」。受教可改，就自然沒有「人格問題」。

「人格問題」不同於「缺點」。人不會「沒有缺點」，但可以「沒有人格問題」，即是「人格完整」。「人格問題」和「缺點」的分別，之前已經講過，所以，現在不再詳述。

簡單而言，個別不足之處，為之「缺點」，可以避開，因為其害處是局部的；思考或處事模式之誤，為之「人格問題」，必會碰釘，因為其害處無所不在。我之前講法是：

「

例如，我的其中一個缺點是『不懂烹飪』，但那不算是我的『人格缺失』。但是，如果我在既『烹飪欠佳』，又『不肯學習』的情況下，仍然要別人吃，我所煮的菜色的話，這性格就是我的『人格問題』。

又例如，『間中遲到五分鐘』不算是『人格缺失』。但是，如果『遲到五分鐘』後，竟然沒有任何歉意，亦沒有絲毫改正的意圖的話，這態度就是『人格缺失』。

又或者，你其實是有歉意的，但是『遲到五分鐘』已經成了你的習慣，再不是個別事件，這習慣就是『人格問題』。

」

比喻說，一個人的「一般缺點」，就好比一部電腦「個別應用程式」的問題。你可以把「個別應用程式」暫時關閉，甚至移除，然後安裝替代程式；而電腦中的其他程式，期間可以如常運作，不受影響。

一個人的「人格問題」，則有如「作業系統程式」的毛病，其害處你想避也避不到，直至你修改了，那「作業系統程式」的問題部分為止。

（安：「人格」其實即是「習慣」。「人格問題」，又即是「思考」或「處事」上的「壞習慣」，所以，其害處會如你所講，無所不在。）

差不多，不過要「同情地理解」才可以，因為「人格」和「習慣」，不算是百分百的同義詞。例如，我穿鞋時，每次都是先穿左邊的那一隻。那是我的「習慣」，但和我的「人格好壞」無關。

但是，如果我每次穿鞋都要花十分鐘，那就不只是我的「習慣」，而且是我的「人格問題」，因為那是有系統地浪費時間。

（安：無好壞處的「習慣」，就和「人格」無關。但是，有明顯壞處的的習慣，即是「壞習慣」，就是「人格缺失」。）

可以那樣說。

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人格

~ 性格

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格

~ 系統

~ 習慣

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人格

~ 性格系統

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— Me@2014.06.30

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2014.07.02 Wednesday (c) All rights reserved by ACHK

Mach principle, 2

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However, general relativity predicts and experiments confirm that gravitational waves do exist: the relevant observations were awarded by the 1993 physics Nobel prize, too. The waves are vibrations of the space itself. It means that the metric tensor remembers the information about the geometry – and curvature at each point, even in the empty space, something that Mach’s principle specifically wanted to prohibit.

…

Einstein had thought that Mach’s Principle was the way to go because it (also) made the universality encoded in the equivalence principle manifest. The equivalence principle says that all objects will be influenced equally – the same acceleration – by the whatever agent is causing gravity. Mach’s principle satisfies the criterion “totally” – it removes any field-like agent. Well, it’s going “too far” in this sense. Of course that Einstein was struggling for years to make Mach’s Principle compatible with the speed limit c – and GR is what eventually came out of it.

– Lubos Motl

2014.06.29 Sunday ACHK

Open Source MindOS

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這段改編自 2010 年 4 月 10 日的對話。

.

（安：我發覺我都有一個，大部人也沒有的優點。我這類性格的人，又真的很少。）

什麼優點？

（安：我比較容易受教。我舉一個例子：

有一次，我和朋友甲討論一個邏輯問題。我的心目中一直以為，因為「先決條件」和「充份條件」，是兩個不同的概念，所以沒有關係。但是，甲指出「充份條件」其實即是，「所有先決條件」的總和。

經過他的解釋，我發覺原本「兩者沒有關係」的想法是錯的。我就自然立刻承認。我不單不會因為發現自己錯，有絲毫不高興；我反而會十分開心，因為，「發現自己原本錯」，其實就即是「發現了真正的答案」。

換句話說，「發現自己錯」的那一刻，正正是我知識增長，和智力提升的那一刻。）

那就即是話，你腦中的作業系統，是 Open Source 的 —— 容許別人修改。

（安：但是，我發覺大部分人，也不是那樣的。他們不單不會因為，發現「真正答案」而高興，甚至會全盤否定它，為的只是要「自己不會錯」。

這是我不能理解的。直到學到你的「心靈作業系統」理論，加上哲學家羅素的那一句，我才開始理解到，為何大部地球人，無論在過去、現在、將來，也「不可能有錯」。）

— Me@2014.06.26

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A stupid man’s report of what a clever man says is never accurate, because he unconsciously translates what he hears into something that he can understand.

— A History of Western Philosophy

— Bertrand Russell

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2014.06.27 Friday (c) All rights reserved by ACHK

Craftsmanship

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mantrax5 2 hours ago | link

“You know, one of the things that really hurt Apple was after I left John Sculley got a very serious disease. It’s the disease of thinking that a really great idea is 90% of the work. And if you just tell all these other people “here’s this great idea,” then of course they can go off and make it happen.

And the problem with that is that there’s just a tremendous amount of craftsmanship in between a great idea and a great product. And as you evolve that great idea, it changes and grows. It never comes out like it starts because you learn a lot more as you get into the subtleties of it. And you also find there are tremendous tradeoffs that you have to make. There are just certain things you can’t make electrons do. There are certain things you can’t make plastic do. Or glass do. Or factories do. Or robots do.

Designing a product is keeping five thousand things in your brain and fitting them all together in new and different ways to get what you want. And every day you discover something new that is a new problem or a new opportunity to fit these things together a little differently.

And it’s that process that is the magic.”

~ Steve Jobs

This is why Apple doesn’t make “vision” videos now, and it didn’t during the Jobs years. During the period they did, they had serious problems in shipping any of the visions they have shown the world.

Microsoft is a bit like that. They know where the world is going, and Bill Gates himself knew from the very start where the world is going (short of a brief period where he conveniently ignored the Internet will happen). But they thought the fact they knew, that they had this cool idea and projection of how things will happen was giving them enough advantage. Nope.

It’s risk-free to ship vision videos. They’re like free T-shirts. There’s infinite demand. But when it comes to shipping products based on them, most people can’t live with the compromises and risk-taking a real product requires in order to ship.

With a new product you can’t just look at the competition and confirm that what you have will work. You’re on your own. Do you have the guts?

— Hacker News

2014.06.24 Tuesday ACHK