※ 引述《outlook2 (容)》之銘言： : ※ [本文轉錄自 StarTrek 看板] : 作者: outlook2 (容) 看板: StarTrek : 標題: 兩題物理問題 : 時間: Wed Jun 4 01:13:19 2008 : Modern Problems of Classical Electrodynamics : Special Relativity 以下都是個人直覺 : (1) : Data and the emperor of Ferengi are locked in a deadly battle of Wheel of : Fortune starring Vanna White, who has been travelling around the earth at : nearly the speed of light for centuries to stay young. Vanna is in an orbit : 100 light second from earth with Data and the Ferengi nearby, while the host, : Darth Vader, on loan from another studio, is on earth. When Vanna gives the : contestants the last question, the Ferengi emperor attempts to cheat by : speeding towards the Earth at a speed of 0.99c while he is thinking, so that : when he radios his answer to Darth Vadar, it will arrives first. However, he : forget that when travelling at nearly the speed of light, his thinking slows : down due to time dilation. Data takes 10 seconds and the Ferengi takes 12 : seconds to answer, each according to their own clock, so it takes, for : example, 110s for Data's answer to reach Darth Vadar. : Question: Does the cheating pay? That is, will the emperor's answer reach : earlier? Please present all the calculations and derivations. 時間的遲滯只發生在"""觀察者"""所看到相對運動中的"被觀察者"身上 現在,觀察者是Vadar.如果Data是跟著Vadar運行,那它們的相對運動是非常小的,也就是 10秒鐘沒有延時. Ferengi自己的計時是12秒,架設在沒有相對關係的空間中,他跑了12光秒,Vadar也繞行 軌道12光秒,非常小的軌道弧度,為方便計算,我假設Vadar幾乎沒有運動,只有Ferengi對 他做0.99c的相對運動. 不必考慮相對論,單是考慮Ferengi移動12秒,就已經話了12秒.之後Ferengi的答案也花 了近12秒才來到Vadar這邊.也就是至少24秒的做答時間... : (2) : A truce has been arranged between the Federation and the Romulans. According : to the treaty, the first captain to fire in an engagement is EXECUTED! The : evidence is as below. Captain Picard suddenly detects a Romulan ship as it : begins to uncloak itself, and realized that it is hostile! The strength of : the emmision shows that the Romulan ship is 1000 light second away so it must : have fired its photon torpedo (assume it travels at light speed). The : Enterprise immediately fired its own photon torpedo. 100 seconds later, : Enterprise is hit. Some time later (in the coordinate system of Enterprise), : the Romulan ship was also hit. Both ships travels at constant speed during : the engagement. Both ships were disabled, and a court of inquiry was : convented. The two captains agreed on the facts above, but each argued, : based on their e-logs, that the other fired first. Is it possible that both : are telling the truth, at least in their respective coordinate system? If : so, what is the minimum speed between them and what is the direction (either : toward each other or away from each other)? If not, who shall be executed? 依我的直覺, 假設他們同時在距離1000光秒,第0秒時發射 如果沒有相對運動,發射訊號在1000秒後到達,那他們不可能預先發射了 如果相對以光速靠近,訊號在500秒後到達,在這500秒內,他們會看到對方船上 負一千~0秒 所發生的事 如果以2倍光速靠近,訊號在1000/3=333秒後到達.這333秒,觀察對方船上 -1000~0秒事件 999倍光速,訊號在1000/(999+1)=1秒後..仍然不是在第0秒之前....orz ______________________________________________________________ 接下來和上面的問題無關. 我個人認為.以為光速運動就能讓時間無限延長,只是個天大的笑話,純屬個人信念 1st,當在'被觀察者'遠離時,'觀察者'看到發生在'被觀察者'身上的事件,例如一個呼吸 就是好久好久.但是要考慮'被觀察者'在準備返回時做減速運動,至反向的光速返回,這時 大部分的時間就會被補償回來(逆時間延長!).然後一直到回到出發點,就會全補償回來... 2nd,相對論既然自稱為相對論,說明的不只是時間空間的相對關係,也是要考慮到運動者的 相對關係,所以我一開始就說了'觀察者'和'被觀察者'.相對而言,兩者關係完全可以對調 那如果光速運動確實讓人不老化,就會有年輕的我看年老的你,說怎麼我變老了,你卻依然 年輕 相對論告訴我們的是,我們無法為光速運行的物體加速,因為它的相對質量是無限大 -- 以上是普物相對論章節考試趨近0分的傢伙的意見. 歡迎挑戰 XDD --

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