跌進黑洞沒那麽慢。。。。

戴榕菁

還記得科普作家們或甚至如霍金那樣的科學大咖給你講的如何跌進黑洞的故事嗎？他們告訴你說，那將是一個非常漫長的過程，甚至可以好似無限長，這是因為黑洞的巨大的引力會造成引力時間膨脹（Gravitational Time Dilation）【[1]】從而導致黑洞附近的時間變得非常地慢，直至無限慢。。。。非常童話，非常浪漫，嗬嗬。

而真相卻要骨感的多：黑洞的引力再大也無法改變時間的進度，所以如果誰要體驗一下跳進黑洞那漫長過程的話，遊戲會令他意外地很快就結束了。

事實上，1912年愛因斯坦在一篇題為“The speed of light and the statics of the gravitational field”【[2]】的文章中給出了下麵這個公式：

                                                 (1)

其中m和m’是兩個物體的質量，c是真空中的光速，k是引力常數（constant of gravitation），R是兩物體之間的距離，而ω則是當m’固定時m繞m’運動的角速度。假設m’是太陽，m是地球的話，那麽我們就可以將1/ω看成是記錄一年四季變化時間的記錄，ω越大時間過的越快，ω越小時間過的越慢。實際愛因斯坦直接將之稱為引力鍾（gravitational clock）。

由(1)可以看出，如果按今天的廣義相對論學者的說法光速c即便在重力場中也是不變量的話，那麽很顯然時間ω不但不會發生引力膨脹，而且會隨著引力的增加而迅速變的更快。

當然，1912年的愛因斯坦認為光速c在引力場中是變化的。但由(1)式可以看出，要想讓時間隨著引力增大而變慢的話，光速c必須以高於二次方的速度隨引力的增大而減小。這意味著從距離地球300公裏的太空站向地球發一束光到達地麵時它的速度已經減少了十分之一；或者說月球上的光速要比地球上快很多倍才能保證月球上的時間不會比地球慢。。。。假如這樣的天方夜譚是真的而地球科學們至今都沒有發現，那也太菜了吧！。。。。。。

隨著狹義相對論被推翻以及與之相關的相對論時間膨脹（time dilation）（注：雖然引力時間膨脹是廣義相對論的內容，但卻是由於其中的狹義相對論元素造成的）被否定，不但量子力學要麵臨極大的風暴，連作為現代宇宙學和天體物理學的核心內容的黑洞理論恐怕也會經曆一場雪崩。。。。。。

 

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[[1]] Rain, R. “Gravitational Time Dilation Calculator”. Reviewed by Dominik Czernia, PhD and Jack Bowater. Last updated: Nov 17, 2022. Retrieved from: https://www.omnicalculator.com/physics/gravitational-time-dilation

[[2]] Einstein, A. (1912). “The speed of light and the statics of the gravitational field”. Translated by D. H. Delphenich.“Lichtgeschwindigkeit und Statik des Gravitionsfeldes,” Ann. Phys. (Leipzig) 38 (1912), 355-369. Available at: http://neo-classical-physics.info/uploads/3/4/3/6/34363841/einstein_-_speed_of_light_and_grav.pdf

[慕容青草]

HARRISON在上麵的對話中沒有直接提到Shapiro,不過在他對話中提到的文章”Basics of Post Newtonian Gravity“中有Shapiro實驗：

Galileo and Tycho Brahe made extensive astronomical observationswhich led Kepler to formulate his laws of planetary motion. All theseobservations were of relative motion. This led Newton to propose his theory ofgravity, which could just as well have been expressed in a form that does notinvolve the concept of force. The approach in this paper extends the Newtoniantheory and the special theory of relativity by including relative velocity basedon the form of the measured data and also by comparison with electromagneticeffects. Application of the new single equation to the precession of the perihelion of Mercury, the gravitational deflection of light, the Shapiro timedelay, the Schwarzschild radius and the last stable orbit gives results whichagree with those of general relativity. Gravitational waves are also discussed.This approach could be used to determine non-Newtonian variations in thetrajectories of satellites

[慕容青草]

北航一位名叫Tony Yuan的人在academia.com貼出一篇題為“Exploring the Accelerating Expansion of the Universe”的討論文章：

https://www.academia.edu/s/1a5b08b8da#comment_1355327

我偶爾點進去看到有一人的評論提到那個所謂的證明重力時間膨脹的著名的Shapiro實驗，我就跟複的一貼指出時間從來不會膨脹，其中我就引用了本文中提到的愛因斯坦1912年的公式。

當時該討論顯示還有一個月才結束，想必北航人不缺錢。。。所以我還等著那位提到Shapiro實驗的人會回複我的跟帖，但隔天，該討論就結束了。。。

隻有兩方能提前結束一個討論：Tony Yuan本人，或academia.com



提前結束的動機可能有兩種：1）因為結束後之前沒有參與討論的人好像就不能再進去了，所以提前結束可能是為了不讓更多的人看到討論的內容；2）結束前，參與討論的人仍可以修改自己的發言，結束後誰也不能再做修改，所以提前結束可能是將已有的發言凍結。

上麵兩種可能代表著完全相反的態度。前者是害怕更多的人看到已有的討論，後者是將已有的發言凍結留著給已參與討論的人及可能的後人看。。。。

你們認為是哪種可能呢？下麵是那段對話：

H R HARRISON
7 days ago
Dear Tony Yuan,
My first responce to your paper is related to the mention of the speed of gravity. As shown in my Basics of Post Newtonian Gravity ( found in my profile) I initialy reagrd ti speed of gravity to be the same the speed of light in mass free space.. The first additional term in my equation is based on eletromagnetics and is normal to the relavive velocity. This gives the accepted results on the precession of orbits in the Solar system. But there are a few other measurable effects that are not predicted. Another term is added wich acts in the direction of the relative velocity. The new equation now predictes all the well verified phenomena. The equation now predicts that the speed of light is reduced when passing through a gravity field. The speed of gravity is still constant.
I have not found any way to test my ewuation when applied to dynamics outside the Solar system. Also I do not believe that your equations will work for the Solar system.
H Ron Harrison
Like1
Rongqing Dai
7 days ago
About the so-called Shapiro delay, delay is the observed fact but the so-called time-dilation is just the tale....

The delay could be most plausibly caused by the longer path when light grazing the Sun, and maybe arguably the slower speed of light as well as your theory claims, but definitely not the dilation of time.

Concerning the change of the speed of light in gravitational field, by Newtonian, we could expect that the speed of light would increase when approaching the massive object and decrease when departing the massive object instead of the opposite!

Einstein claims in his 1912 article that [A clock will run faster when we bring it to a location where c is greater] which is consistent to the famous GR claim that time runs slower in gravity if the speed of light decreases in gravity as your theory claims.....but Einstein also contradicted this with the following formula in the same 1912 article:

m ω^2 R = c^2 k mm’ /4πR^3 (1)

where m is the mass of the object circulating another mass m', R is the distance, and ω is the angular velocity of m circulating m'. Now if m is the Earth, m' is the Sun, then ω would be the clock of ancient people around world to count seasons and years!

From (1) we can conclude that the closer to a massive object, the faster the clock if the speed of light is constant, which contradicts the famous nowadays GR claim (which assumes a constant speed of light anywhere) that time goes slower in gravity.

Of course, now you can say that a decreased speed of light would make (1) not contradict to the famous GR claim......but obviously a linear decrease would not do the job, even quadratically decrease would not be enough since that would only make ω independent of R, not increase with R.

The problem is that if the speed of light would decrease faster than quadratically as gravity increases, we should have observed this effect in our earth environment, shouldn't we?