http://www.askamathematician.com/201...s-take-you-to-other-universes/

 What’s the difference between  black holes and worm holes? Could  black holes take you to other universes?


Posted on October 18, 2011 by The Physicist



Physicist: The short answer is: A worm hole is a “tube made of spacetime” that connects two different regions.  If it’s set up right, you could enter one side of the tube and exit the other end somewhere else, or even somewhen else.  In contrast, a black hole destroys the hell out of things, and doesn’t “go anywhere”.

A worm hole is a funnel (what’s shown here is only a two dimensional funnel) that tapers down to a “throat” (which although thinner never pinches off entirely) which connects to another funnel that opens up somewhere else.  A black hole is a funnel that pinches off at a singularity.  A traversable worm hole needs to be large and “mellow” enough that it doesn’t have an event horizon (a black hole’s “point of no return”), or any fatal tidal forces.



[圖]
 


 worm holes (left)                     vs.                      black holes (right).

There’s a long history of the two being mixed up.  For example, there are a number of stunningly bad movies that make the connection between  black holes and worm holes explicit.  But even in legitimate (non-Holywood) physics circles you’ll sometimes find people talking about “going through”  black holes, as opposed to (or in addition to) “being destroyed a lot” by  black holes.

Over the years physicists have gotten a little gun shy about ignoring solutions.  For example, one of the clearly impossible solutions to the Schrodinger equation (which describes the wave nature of things) involves particles crossing through impossible boundaries.  Turns out they can, and it’s now called “quantum tunneling“.  In fact, you probably even own some electronic devices that take advantage of this “impossible” solution!

Another example is when Dirac took the Schrodinger equation and re-wrote it in a relativistic form to create the Dirac equation (the original equation isn’t compatible with relativity).  He found that he suddenly had a second set of solutions which imply the existence of anti-particles.  At the time the idea of an anti-particle was ridiculous, but a few years later positrons (anti-electrons) were discovered and Dirac was shown to be right.

So, given the history, physicists today are a little hesitant about chucking out solutions, even when they’re silly.  And  black holes are a bottomless pit of math with solutions that seem impossible.

The singularity at the center of a black hole is usually described as a point.  However, this is a symptom of our paltry computational power back when  black holes were first being theoretically researched.  A singularity can actually take a number of forms.  According to a variety of (modern/powerful) computer models, as a star collapses to form a black hole it often finds itself forming “singularity sheets” in areas where its density becomes large enough.  All of it ends up in the same tiny singularity moments later, but it’s still interesting.  In a spinning black hole (which is all of them, to some extent or another) the singularity takes the form of a “ring singularity”, which is exactly what it sounds like.

One of the wild things about ring singularities is that they make the topology of spacetime qualitatively different, in a way not entirely dissimilar to the way that the surface of a sphere is qualitatively different from the surface of a dohnut (or, for our New York readers, a bagel).

In normal, everyday space, if you travel in a big loop you come back to the same place.  If you were a mathematician you would prove this using a “continuous deformation”.


In ordinary space moving in a loop has the same net effect as not moving. But if your loop takes you through a ring singularity, that may not be the case.

A big loop is nearly the same as a slightly smaller loop, is nearly the same as a slightly smaller loop, is nearly the same… is nearly the same as a point.  If there’s a singularity in the way the loop that goes around it can’t be smoothly deformed into a loop that doesn’t.  As a result, travelling on a path that takes you through a ring singularity doesn’t necessarily need to bring you back to where you expected to be.

As hand wavy and weird as this idea sounds, it has a lot of mathematical relevance.  It shows up all the time in complex integrals and branch cuts, and just a hell of a lot in algebraic topology.  But, to be fair, nobody’s ever seen a physical “doorway through space and time” kind of example.

Beyond just the singularity, there are a lot of weird problems involving picturing how  black holes work.  For example, they screw up spacetime so much that at their surface (the “event horizon”) time literally points downward.  Not only do you have to contend with the fact that spacetime is four dimensional (3 space directions plus 1 time direction), but the time direction is very different, so it’s four dimensional in a really weird way.  Now add to that that  black holes royally mess things up and you’ll find yourself in dire need of a better coordinate system to make things easier to picture.


A black hole in K-S coordinates. Light travels at a 45° angle everywhere in this diagram, which physicists like, but everything else is weird.

Enter Kruskal–Szekeres coordinates.  Although the situatuion is still a little weird, time points more or less up (the standard set up for space/time diagrams), and light travels diagonally (again: standard).  In these cooridinates all of our universe is on the right side, including all of the past and future, the event horizon of the blackhole is the upper diagonal (and, oddly enough, the infinite future), and the singularity is a sweeping curve in the top area.  Keep in mind that this coordinate system is more than a lttle bit weird.  For example, they assume that the blackhole exists forever (into the past and future) at the same size.  So the bottom diagonal is an un-ashamed representation of the infinite past.  Any finite time in the past (say, the beginning of the universe) would be slightly above the lower diagonal.

Now the point: you can write down a lot of the physics of general relativity in these coordinates and they look pretty good, so it feels like there’s something to them.  However, they include a left side.  General relativity treats the stuff on the left the same way it treats everything on the right (our universe).  So, if the left is something more than just a mathematical artifact, then it’s another space and time completely independent from our own.  Since nothing travels faster than light, which in these coordinates travels along diagonals, it’s impossible to get from any point in our universe to the other universe.  However, if you fall into the black hole you can see someone from the other universe that’s also fallen into the balck hole, and have a nice chat before you’re both destroyed at the singularity.


Although you'd need to travel faster than light to get from one universe to the next (if the next exists), you can meet other doomed travelers from the next universe without traveling faster than light. The upside is making new friends. The downside is being destroyed in a black hole.

If faster than light travel were possible, and if there were another spacetime on the other side of the black hole that wasn’t just a mathematical convenience or ring singularities behave exactly like we want them too, and if you could make it into and out of the black hole without being destroyed a lot or taking forever doing it (it takes literally forever to fall past the event horizon), then  black holes are certainly doorways to other universes, or different parts of our own.

So, to the point, there’s a history of people confusing or blurring the distinction between  black holes and worm holes, and not completely without reason, but in general:  black holes mean stop and worm holes mean go.











按照恆星演化理論,黑洞是恆星演化的最後階段,即是「死亡」了的恆星。
   由於黑洞不會放射出物質或輻射,我們不能直接觀察到黑洞。但是黑洞可以
   與鄰近的恆星構成雙星系統,從地球上看來,那可見的恆星 (伴星)
   便好像是與一個看不見的天體不停地大跳華爾滋

	
	
	
[圖]


圖一   黑洞與一顆巨型的恒星組成一雙星系統,伴星的氣體物質以螺旋軌道衝進黑洞,產生高熱及高能輻射。
 


   (見圖),從它運動的程度可推算出那看不見天體的質量,如果那天體的質量
   非常龐大,便很有可能是一個黑洞。此外,黑洞的巨大引力使伴星的氣體物
   質以螺旋軌道衝進黑洞,由於被急速壓縮,物質的溫度變得很高,Χ射線和
   伽瑪射線從而產生,在地球上觀察這些射線,便可找到黑洞存在的證據。



[圖]
 



   是一類密度極高的星體。由於它周圍存在巨大的引力場,所有經過附近
   的物質均被吸進去,即使光也不能逃脫,同樣,處於黑洞裡的物體也不能逃
   出黑洞。我們知道,地球上的物體若獲得很大的初始速度,便可脫離地球的
   引力而飛到太空,如果初始速度足夠大,還可以脫離太陽的引力而逃出太陽
   系,而人類用火箭發射衛星或太空船便是利用了此原理。

	
	
	
	
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作者 xgcj     看板: ott
標題
 Re: [新聞] 「宇宙最大黑洞」曝光! 將成銀河黑洞新

時間 2012年12月01日 Sat. AM 07:53:03

 
說到黑洞

什麼是黑洞呢?


現在意義上的黑洞,是廣義相對論的愛因斯坦場方程一種解

                    1
         R    - ── g    R = κ T         --------愛因斯坦場方程
            μν   2     μν             μν

[圖]
 


 


[圖]
 

 

一 黑洞的性質


一般來說 我們根據黑洞的性質 可以分成以下幾種黑洞
╔══════════             ══╦═   ═╦═    ═╦════       ══╦
║黑洞種類                                ║質量║電荷  ║角動量(旋轉) ║
╠════════════             ╬═   ═╬═    ═╬════        ══╬
║1.Schwarzchild 黑洞          ║ 有    ║沒有 ║    沒有             ║
╠═══════════             ═╬═   ═╬═    ═╬════        ══╬
║2.Reissner-Nordströ黑洞║ 有    ║ 有    ║    沒有             ║
╠═══════════             ═╬═    ═╬══   ╬════        ══╬
║3.Kerr 黑洞                            ║ 有     ║沒有║     有                ║
╠═══════════              ═╬═    ═╬═  ═╬════        ══╬
║4.Kerr-Newman 黑洞        ║ 有     ║ 有    ║     有               ║
╚═══════════              ═╩══    ╩═    ═╩════      ══╩

因為我們目前認為黑洞可以被這三種性質唯一決定 這也叫無毛定理

二 黑洞的結構

我們就拿Schwarzschild黑洞來說好了



[圖]
 


[圖]
 



[圖]
 




[圖]
 

 




[圖]
 




[圖]
 






愛因斯坦方程的解 會是一個叫作度規的東西

他刻化了時空中的每一的附近的微小線段的長度

也就是他決定了時空的結構

它是長這樣的
 2  2     2GM     2      2GM   -1  2  2   2    2     2
ds=c (1- ═══)dt -(1- ═══)  dr -r (dθ+sin(θ)dφ)
          rc^2           rc^2


G:重力常數 c:光速 M:黑洞質量 r:在r>2GM/c^2 時候是以黑洞當中心座標半徑

我們可以看到在r=2GM/c^2 上面 這一個地方有很奇怪的事情發生

那就是會有一個好像是發散的情形發生

這種發散 其實是有物理意義的 他其實就是一般我們會說的黑洞的"表面"

他叫做event hozizon 我們在很遠的地方看黑洞的時候

我們會看不到 event hozizon內部的東西

Schwarzschild黑洞的event hozizon是一個面

而其他種類的黑洞 可能會是一個環 或者可能是雙層的event hozizon


三 黑洞的熱力學

這是比較近代才出現的理論

我們把熱力學的概念運用到黑洞當中

這其中也融合了 熱力學 量子力學 廣義相對論的很多概念進來

既然熱力學有四種定律

那黑洞熱力學有什麼定律呢?

黑洞熱力學第零定律:黑洞在event horizon上面的重力都相同

黑洞熱力學第一定律:黑洞的質量的增加將當於重力乘上面積增加加上

                    event horizon的自旋角速度乘上增加的角動量(對黑洞作功)

                            κ
                     δM= ═══δA+ΩδJ
                           8πG      H

    熱力學第一定律    dU=TdS+PdV



黑洞熱力學第二定律:獨立系統的黑洞event horizon的面積不會變小

黑洞熱力學第三定律:黑洞表面重力不會是0


在這邊 我們可以看到熱力學跟黑洞熱力學的相似性

溫度 相當於重力
熵   相當於event horizon面積
還有互相對應的一些公式

四 量子效應

改天再打好了 太冷想念棉被中

--
  -1       μν ╴   μ
L=─ F    F    +Ψ(iγ (∂ +ieA  )-m)Ψ
   4  μν               μ    μ




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※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 220.132.98.155
e314520:恩恩  跟我想的一樣11/30 22:19
proman614:原來如此11/30 22:19
zzoe09:嗯嗯這樣啊 我覺得最大的黑洞還是被窩呢11/30 22:19
被發現了
L2N:嗯嗯 略懂11/30 22:19
Kay731:這篇元文在哪阿11/30 22:19
vchenkoshe:跟我想的一樣11/30 22:19
vchenkoshe:原文被黑洞吃了
bugmens:我想說的就是這些,只是讓你先寫出來而已11/30 22:20
cybergenie:是這樣的沒錯                 快推不然會被以為看不懂11/30 22:20
RolfP:別富姦!11/30 22:20
globekjller:內容有錯誤...拿回去修改...明天再PO上來11/30 22:20
minicess:是的 沒錯 恩恩11/30 22:20
taco20:雖然跟我想得不太同 但整體上是沒錯的11/30 22:20
wyvernlee:寫篇八卦也富監 ?11/30 22:21
johnny3:恩恩我本來想講的都被你講完了11/30 22:21
Zeroyeu:推 zzoe09:嗯嗯這樣啊 我覺得最大的黑洞還是被窩呢...XDDD11/30 22:21
MSNboy:你能推導一下正妹的黑洞嗎?11/30 22:21
netsc:有黑洞裡面有什麼的八卦嗎?11/30 22:22
黑洞裡面時間空間會互換 我們的奇異點會變成時間的終結點
KTR5566:原PO對教育部關心學生健康有什麼看法呢?11/30 22:22
呼呼 KTR抱一個
monismile:zzoe09:嗯嗯這樣啊 我覺得最大的黑洞還是被窩呢11/30 22:23
SRNOB:一顆沙的體積卻有太陽的重量  所以很會吸 裡面都是暗物質11/30 22:23
Kevin1103:是的寶傑!!11/30 22:25
playerst:黑洞中心是時間的終結點 那是不是表示宇宙最初也是黑洞形11/30 22:27
potter1529:真好看~~~~~~~~~~~~~~~多說一點11/30 22:27
其實黑洞會有溫度 是因為在horizon附近的真空量子效應造成的
真空中產生的虛粒子因為horizon實化 被創造出來 產生霍金輻射
而他的頻譜 就像黑體輻射一樣 因而有了溫度
playerst:式呢? 那是否自旋是取決於奇異點是否有選轉嗎??11/30 22:28
jaw109:我記得好像離黑洞夠近的話 望著黑洞可以看到自己後腦勺11/30 22:29
在旋轉的黑洞會這樣
chogosu:看不懂11/30 22:29
cacasi:略懂11/30 22:29
jaw109:忘記是誰說的了11/30 22:29
j0958322080:那物理版的黑洞呢??11/30 22:31
Refauth:嗯  跟我算的一樣11/30 22:34
事實上在一個加速作標系中運動的物體 也會因為量子效應而感覺到溫度
kimimskimi:就像小便斗一樣吧11/30 22:34
MoseHas:event horizon是一部知名的電影…很好看(?)11/30 22:35
chinhan1216:乾 看不懂啦11/30 22:36
xpu:N.Young11/30 22:36
GOLxDxROGER:多說一點啦  我想知道時姦停止到底會怎樣11/30 22:36
GOLxDxROGER:真的像SOD演那樣嗎
playerst:可是這麼冷的天氣 騎車只會越騎越冷 是因為速度不夠快的11/30 22:37
playerst:關係嗎XDDD
因為加速度不夠快 另外 這邊的"加速度"也跟一般認知的加速度不太一樣
這邊是相對論中的加速度 不是牛頓體系的加速度
hu610346:宇宙之於黑洞是不是就像水之於漩渦一樣???11/30 22:37
jaceda:.....11/30 22:37
DarkFog:那.....進入黑洞到底會發生甚麼事?11/30 22:38
nice123:霍金很多預測還有跟人對賭都失敗 他是不是有點被過度高估11/30 22:38
nice123:你寫的equation有點錯 應該是這樣Guv=8(pi)Tuv
nice123:還有如果有人進黑洞還沒死 那他自己的時間還是正常的
我是用κ來代替8π的
進入黑洞之後 在他本身的Local座標系 基本上還是自由落體的慣性座標系
所以如果沒有什麼潮汐力的話 他會活得好好的
nice123:只是對外面的人是停止的11/30 22:42
Loxodanta:我只知道無毛定理叫做白虎11/30 22:43
nice123:黑洞最中心(跟第心一樣)是零重力 時間是很正常的11/30 22:47
不 應該是說 看你運動的軌跡的四維加速度大小 如果沒有的話
那就是沿著測地線走的 那你將不會感覺到任何力量拉你
gn02239542:可不可以說明一下在這邊代號的意義呀?11/30 22:48
gn02239542:G? M? r? c?
Qoofate:哩A工殺誨    = =11/30 22:48
krauserq:看無..11/30 22:48
wjuiahb:趕快推,不然人家會笑我們看不懂11/30 22:49
nice123:如果不了解就po,不就是 copy wiki的,copy wiki我也會11/30 22:49
當然 這邊有些資料是直接從WIKI上面弄的 但是我是了解才會打這篇文章的
喔!對了 觀念有錯的話歡迎指正根討論^^
※ 編輯: xgcj            來自: 220.132.98.155       (11/30 23:01)
jerry50411:有些人不知道在酸甚麼1F 11/30 23:01






 














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