Time Travel and it’s myths

From the BBC TV programme “Doctor Who” to the recently released movie “Interstellar” we are inclined to believe that time travel is actually possible. I was so intrigued to find out, that I studied the subject myself and here are my conclusions:

Michelson and Morley with their experiment in 1887 in Cleveland Ohio have started the possibility of time travel.

http://en.wikipedia.org/wiki/Michelson–Morley_experiment

The experiment established conclusively that the speed of light is independent of the speed of it’s source. While, at first glance, this might not appear to be very significant, it has opened a new chapter in Physics with paradoxes that the human brain has trouble dealing with, it is beyond what we call logical.

 

In the following graph I try to demonstrate the dilemma. A bicycle rider, a stationary person and a sprinter all have a torch and a light receiver in their hand. They switch on their torches exactly at the same time at the blue starting line. The light will then travel towards a mirror where it is reflected and arrives back at the light receiver each persons holds in their hand. We can clearly see that as a result of the movement of the bicycle rider and the sprinter, their light beam will have to travel a much shorter distance than the light beam of the stationary person. The time, delta t, required for the light beam to travel the varying distances shown on the graph is the distance divided by the speed of light. Since the speed of light is constant, independent of the speed of it’s source, it is very obvious that only the time can change. That means if all three of them do wear a watch, they will all show a difference in time! This does not sound right, but it is!

 

the speed of light1

 

The Dutch physicist Hendrik Lorentz was one of the first to define what we call now “Time Dilation” with which we can calculate the time difference between objects that move relative to each other, with the “Lorentz Factor”(Gamma). Albert Einstein went further with his analyses and included mass in his equations which consequently resulted in the release of his “Special Theory of Relativity” in the same year 1905. http://en.wikipedia.org/wiki/Hendrik_Lorentz

 

●○「以英文為準, 中文翻譯只作參考」○●

從BBC電視劇“超時空博士”到最近發佈的電影“星際啟示錄”使到大家都傾向於認為時間旅行是實際可能的。我也因而很感好奇, 想找出答案來,於是我對這個課題作出了研究, 以下是我的結論:

於1887年, 在俄亥俄州的克里夫蘭, 邁克生和莫立就做了他們的實驗, 來實驗時間旅行的可能性。

http://en.wikipedia.org/wiki/Michelson–Morley_experiment

實驗確證了光速不單是一常數(光速是一常數, 早於此實驗前已被驗証了),並且, 並不依賴於光源的運動(即與光源運動無關)。當,乍看之下,這可能並不顯現出很重大意義,可是它卻揭開了物理學新的一篇並且是看似是對, 卻又互相矛盾的現象, 使得人的大腦出現處理障礙,這是超出了我們所說的邏輯。

在上圖中我嘗試指出這種窘境。

一個騎脚踏車的人,一個站牢的警員,一個短跑運動員等, 他們每個人都手拿有一個手電筒和一個光接收器。在藍色的起跑線上, 他們同一時間打開他們的手電筒。手電筒的光束也就立即射向前方的鏡子, 並且立即直線反射到每個人手持的光接收器之上。我們可以清楚地先看到,騎腳踏車的人和短跑運動員的結果,他倆反射的光束比起站牢的警員的距離是更短的。

時間,delta t (時間差,即由源點至終點的差別):

要計算上圖各人光接收器的時差就是距離除以光速(delta t =  距離 / 光速) 。可是由於光的速度是恆定的,並且是與光源運動無關, 這很明顯地,只有時間可以改變。這意味著,如果他們三個人都戴著同樣準確的手錶來計算, 由光源至光接收器接收到的時間, 他們將發現大家的手錶上的時間是一致(舉例, 如果騎腳踏車者的手錶顯示收到光反射來的光速是10秒, 其它兩人也會說, 他們的錶也是顯示出10秒)!這聽起來很不正確吧(因為我們明明就看到在上圖, 騎腳踏車者應該是最快接收到光的人!), ,但這卻是如此的發生著!

要去解釋 點解明明就是騎腳踏車者收到光先, 卻手錶上顯示出同其它兩人接收到光速的時間是一樣的, 唯一理由就只有他手錶是行得比其它兩人的要慢! 也就是, 當移動更快者, 他的時間相對於他人走得為慢!……….換句話來說, 唔郁的警察( 不動的警察) 也就是光反射路程最長的, 可是他的時間就要比其它兩人走得快了。 

 

荷蘭物理學家亨德里克·勞侖茲是第一個定義出現在我們稱為“時間膨脹”,由他的“勞侖茲因子”使我們可以計算出由物體彼此相對移動的時間差異。 1905年, 愛因斯坦更進一步分析,並將質量加入在他的方程,因而導致了他的“狹義相對論”於同年發佈.

 

 

Time Dilation 時間膨脹:

time dilation-1

 

In this picture we see a girl watching a light beam that travels from the source, on the bottom of a spacecraft, vertically up to a mirror on top of the spacecraft, at the distance D, and back down to a receiver on the bottom of the spacecraft.

If the spacecraft does not move as shown on the left, the time required, (delta t’), for the light to travel from the source to the mirror and back is clearly,

 

在這張圖,我們看到一個女孩觀看宇宙飛船上的光束從底部源頭垂直向上遊走至頂部上的反射鏡, 其距離為D,並回落到底部的接收器上。

如果如左邊所示的不移動的宇宙船,所需要的時間為(△T’),該光從光源到反射鏡再加回射回歸底部的接收器上, 顯然:

time9

 

where D is the distance between the source and the mirror, and c is the speed of light.

If, however, the spacecraft is moving at a speed v, the light will have to travel much further because the mirror and the receiver are moving away from the light source. This is causing the whole paradox, because we know that the speed of light is constant, independent of the movement of it’s source, but the distance it has to travel has significantly increased. So if the speed of the light is fixed and the distance is fixed, then only time can change as a result of it.

It is straight forward to calculate the time lapsed on the spacecraft for the light to travel from the source to the receiver. We draw the right angled triangle between the source and the mirror. The vertical cathetus is D, the horizontal cathetus is half the distance the spacecraft has travelled while the light travels from the source to the mirror, with v the speed of the spacecraft and delta t the time lapsed for the light to travel between the source and the receiver. The hypotenuse is the distance the light has travelled between the source and the mirror, at the same time, with c the speed of light.

 

其中,D是光源和反射鏡之間的距離,以及 c 是光速。

然而,如果宇宙飛船以v速度移動,光就必須比之前(宇宙飛船不動時)向前射前更多了,因為反射鏡和接收器都因宇宙飛船的移動而從光源移離更多。這是造成整個悖論,因為我們知道,光的速度是恆定的,與光源運動無關,但它卻因宇宙飛船的移動做成距離的(比前宇宙飛船不動時)顯著增加。所以,如果光的速度是固定的,該距離是固定的,那麼就只有時間可以改變,這就必然是其結果。

要明確計算當飛船移動後, 光束從底部源頭至頂部上的反射鏡, 再回落到底部的接收器上的時間差。我們繪製光源和反射鏡之間的直角三角形(即上圖左面的飛船飛行時, 光速與飛船移動所成距離的關系) 。垂直直角邊為D,水平線去到直角那一邊是宇宙飛船前行時光從光源到反射鏡再反射回到接收鏡, 整段距離的一半。 用v為飛船的速度, 和delta t 為由光源發射去到接收器的時間差距。斜邊是光在光源頭和反射鏡之間距離, 同時, c是光速。

(簡單地說: v = 飛船航行速度

                        c = 光的速度

                        delta t = 由光源發射去到接收器的時間差距)

 

time3

 

 

With the theory of Pythagoras we can now resolve the equation for delta t and get the following result. (It is a simple algebraic problem, I had not trouble resolving it)

由畢達哥拉斯的理論,我們現在可以解開三角方程式,找出delta t , 並得出以下結果。 (這是一個簡單的代數問題,所以很容易就計算到答案了.  計算過程列於本頁尾. )

 

time4

 

If we substitute 2D/c with delta t’ as we have defined it earlier, we get the time difference between a clock located on earth and a clock located in the moving spacecraft.

如果我們以2D / C 來替換 deltat t’  就如我們在之前已經做好的定義 ( clip_image001[1]),我們會得到了一個位於地上地球時鐘和一個位於移動飛船上的時鐘之間的時間差。

time5

 

clip_image001[5]

 

 

time8

 

 

 

 

Lorentz_factor1

 

Gamma (\gamma \,\!), referred to as the “Lorentz Factor”, is shown on the above graph as a function of v. As you can see on the graph, it does change very little between v = 0 and v = c/2, which is important to consider when we look at the potential of time travel with current space travel technologies. Gamma only increases significantly as the speed of the space craft approaches the speed of light. If the spacecraft reaches the speed of light then the time on the spacecraft stands still.

The twin paradox is commonly used to demonstrate the theoretical possibility of time travel, one twin enters a spacecraft and travels for 20 years at the speed of light while the other twin stays on earth. When the travelling twin returns after twenty years he has not grown older since he left earth, because time did stand still on the spacecraft, so he travelled forward in time when he meets his now twenty year older twin back on earth. Or the twin that stayed on earth has travelled back in time if he enters the spacecraft after it returns and meets his twenty year younger twin.

伽馬(\gamma \,\!),簡稱為“勞侖茲因子”(也即是我們之前計算所得, clip_image0015) 我們用圖來演示出出當v函數(飛船加速)的增加時, 它對\gamma \,\!所做成的變化。正如可以在圖中看到,從v= 0 和 v = C / 2之間, \gamma \,\!改變是極為之少。直至去到差不多90%左右的接近c,  \gamma \,\!突然急速增加, 並且愈接近c時, 即當飛船時速達至光速, \gamma \,\!會是無限. 也就是說, 飛船如果達到光的速度時, 那麼飛船上時間會靜止不動。然而在v= 0 和 v = C / 2之間, \gamma \,\!改變是極為之少。也即是說我們人類目前太空旅行技術來說,  我們宇宙飛船仍然是 v= 0 和 v = C / 2之間 的早期, 還有好一大段的距離先可看到明顯的轉變, 先可同光時速一樣快 。

孿生子悖論通常用來證明時間旅行理論的可能性,雙胞胎中的一個 (就當他是哥哥好了)進入飛船(就當他入飛船時是2000年好了) 以光的速度旅行了20年,而他的雙胞胎的弟弟(就叫他弟弟好了) 則留在地球上。可是當哥哥一踏入船艙飛行那一刻, 因為他以光速飛行, 他在船上的時鐘就開始靜止不動了,  當在20年後他回到地球(即2020年), 一踏出船艙, 他並沒有老了20年, 可是他見到的弟弟已經老了20年了。  因為是他在船上時間是靜止了, 所以哥哥可以停留在2000年, 回到地球卻已經是2020年, 他向前旅走20年, 再遇到老了20年弟弟, 可是弟弟一踏入船艙見到了年輕的哥哥, 他的時間就好像時光倒流回到20年前那個年輕的哥哥! 

 

time dilation33

 

While time travel is theoretically possible, I will now have a look at the time travel we can achieve with our current technologies.

The fastest spacecraft that we have ever built is Voyager 1 which is just leaving our solar system and is travelling right now at 61,380 km/h through outer space. The speed of light is approximately 1,080,000,000 km/h.

Voyager 1 is an unmanned spacecraft, much easier to accelerate than a manned spacecraft that would need to be much heavier to take all the amenities for a person to survive on board. So lets assume that we would be able to build a spacecraft that can take a person on board with supplies for a one year trip and travel at the extraordinary speed of 100,000 km/h, how much younger would the traveller be after a one year trip (assuming we don’t need much time to accelerate and slow down the spacecraft)

Using the above formula, gamma would be 1.0000000043 for this speed. One year with 365 days and 24 hours per day and 3600 seconds per hour has 31,536,000 seconds. If we multiply that by gamma and deduct one year we find that the space traveller would be only 0.14 seconds younger than his twin who stayed on earth.

So the reality is that time travel is not within the scope of our current technologies, and all the speculation about worm holes, gravity walls ect, is just pure science fiction. The “Tardis” of course is quite different, it does work, because that was developed by time lords not by humans.

 

既然時間旅行在理論上是可能的,現在我們可以用我們目前的技術來看時間旅行是否可以實現。

我們曾經建造的最快的飛船是航行者1號, 它是第一個離開我們的太陽系,並以每小時61380公里在外太空飛行的人造飛行器,而光速卻是近乎每小時10.8億公里。

航行者1號是無人飛船,它比起要載人的航天飛船(除了個人, 它需要負載個人在船上生存所須的設施)將更容易加速。所以,讓我們假設,我們將能夠製造一隻航天飛船,可以載一個人(如上例的雙胞胎的哥哥), 他並且可以擕帶一年的所須的維生用品以每小時10萬公里的速度進行外太空之旅究竟這位旅客經過這一年, 回到地球時將會比他留在地球上的胞胎弟弟年輕了多少呢?(為了較易於計算, 我們假設並不需要太多的時間來加速和減慢飛船,  亦即飛船起飛時所須的加速和飛船到達時的減速不計在內.)

使用上面的公式,我們計出, γ是1.0000000043這個速度。一年有365天,每天有24小時, 一小時有3,600秒, 所以一年就有31,536,000秒。如果我們乘上γ和扣除一年時間後, 我們發現太空旅行者(雙胞胎的哥哥)將會比他留在地球上的雙胞胎弟弟年輕只有0.14秒。

(也即是說拿我們現有的技術, 無人飛船的每小時61380公里, 改進成為有人的每小時10萬公里, 所得出來的結果是極少的0.14秒!)

 

因此,現實是,時間旅行將不是我們目前的技術可以做到的範圍之內,而所有關於蟲孔,重力牆等等的推測,只是純粹的科幻小說而已。而在“TARDIS”,當然是完全不同的了,它是可行的,因為這是由時間管主發明的, 而不是由人類發明的。

 

P.S.:  the calculation of clip_image017

 

Pythagorean theorem :

180px-Pythagorean

clip_image001

And

clip_image002

clip_image003

clip_image004

clip_image005

Then :

clip_image006

clip_image007

clip_image008

clip_image009

clip_image010

clip_image011

clip_image001[1]

 

clip_image002[1]

 

clip_image003[1]

 

clip_image015

 

clip_image017

 

P.S. :  This is the first part of Einstein’s special theory of relativity, I will cover the  theory of length contraction and the increase of mass later on, when I have time.

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