How fast are you moving right now? That seems like an easy question. The first tempting answer is, "I'm not moving." Upon further reflection, you realize that maybe the Earth's motion counts. So, a second tempting answer is, "19 miles/second around the Sun." But then you recall learning that the Sun moves around the center of the Milky Way galaxy, and the Milky Way moves within the Local Group of galaxies, and the Local Group moves within the Virgo Cluster, and the Virgo Cluster moves within... "How fast are you moving?" is not an easy question. When Mission Control tells astronauts how fast they're going, there's always an assumed standard of rest. At the start of the voyage, speeds are given relative to the launchpad. But later, when the launchpad is just one more arbritrary place down there on Earth's spinning surface, speeds are given relative to the idealized, non-spinning pinpoint center of Earth. On their way to the Moon, Apollo astronauts had a hard time answering the question, "How fast are you moving?" Speed away from Earth was one thing, and speed toward the Moon was quite another. That's because the Earth and the Moon move relative to one another. Ah, of course! Speed is a relative quantity. When Captain Kirk ask Lieutenant Sulu if the Starship Enterprise has reached a speed of warp 7, Sulu should reply, "Relative to what, Captain?" Such a sassy reply may get subordinate Starfleet officers in trouble, but it is the only good answer to the question, "How fast are you moving?" This is basic relatively talking. Not fancy Einsteinian relativity, but good old fashioned (and still correct) Galilean relativity. Galileo seems to have been the first person to realize that there is no such thing as an absolute speed. Speeds are relative. This means that speeds only have meaning when they are referred to a reference frame. Presumably that reference frame is itself at rest. But then we have to ask again, "At rest relative to what?" Because even the concept of rest has lost any hint of absolute meaning. Speed is relative, and rest is relative. Earth's speed is 19 miles/second relative to the Sun. The Enterprise's speed is warp 7 relative to the center of the Milky Way galaxy. Your speed is zero relative to your easy chair. But depending on where you sit, it is hundreds of miles/hour relative to Earth's center. When we furrow a brow and ask, "But how fast is Earth really moving?" we imagine Spaceship Earth plowing through the ocean of space as it orbits the Sun. But space is not an ocean. It has no substance as water does. Space is not a thing; space is nothing. Space is no thing. You can move between two points in space, say between Earth and Mars, but you can't move through space. There's nothing to move through. It's like trying to say how much a hole weighs. A hole weighs exactly nothing because a hole is nothing. It's a void, and so is space. To move relative to nothing is meaningless. The concepts of speed and of rest have only relative meaning. They are absolutely meaningless. They mean something only with respect to arbitrarily chosen, artificial frames of reference. If, someday, you are buckled into your spaceship, and you see from the side window, say, a space station whizz by at constant speed, there is no way to know which of you is really moving. Neither of you is really moving because there is no deep reality about constant speed. Constant speed in a straight line has only relative meaning, a kind of relative reality. Does this mean that all motion is relative? No! Some motions have only relative meaning, but some motions have absolute meaning, are absolutely real. For example, constant speed is relative, but change in speed is absolute. Calling something absolute in science means that arbitrary standards are not used in its measurement. It is unambiguously measurable. When your spaceship fires its engines, your change in speed is beyond doubt. You feel it in your stomach, and your ship's sensors can measure it. Outside your window, the passing space station may seem to be changing speed, but the beings inside the station will not feel it. And no sensors can measure it. You are really changing speed, and they are really are not. There's something absolutely real about changes in speed. The same goes for rotation. If your spaceship is spinning, you can feel it, and your ship's sensors can measure it. The space station outside may seem to be going around you, but it is you who feels queasy, not the folks in the space station. You are really spinning, and they really are not. There's something absolutely real about rotation. So, some motions are relative, and some are not. There is no deep reality about constant speed, but changes in speed are deeply real, and so are rotations. We have to be thoughtful in our analysis of everyday experience in order to identify what is deeply real. Since we can be fooled by perceptions as basic as speed, maybe every perception deserves careful scrutiny. This is what inspired Einstein to his incredible insights about the speed of light and forward time travel. Knowing how to identify what is deeply real is tough and important work. If a police officer ever pulls you over for speeding and asks, "Do you know how fast you were going?" an insightful, though perhaps unwise, reply would be, "Relative to what?" And then, as you sit in the backseat of the police car and feel it accelerate toward jail, you can add, "But some things are absolute!"
「現在你的時速多快?」 你以為這問題很單純吧。 對於使用個人電腦看影片的你, 首先閃過的念頭應該是: 我沒移動啊。(除非你在通勤中) 更細深思, 你意會到,說不定 地球的運轉也得考慮進來。 因此,再試一次你答道: 平均每秒 29.79 公里繞著太陽轉,對吧 (一月地球通過近日點,高於均速。 七月遠日點則相反) 但不想則已,一想你又發覺太陽 正繞著銀河系中心運轉, 而銀河系正在本星系群中運轉, 本星系群又是室女座星系團的一部分, 室女座星系團又是室女座超星系團...... 於是「你正以多快速度運動?」 不是個好回答的問題。 當太空任務控制中心告訴太空人 他們火箭的飛行時速 總有個默認的「靜止」參考點。 在發射之初, 火箭速度根據的基準點是發射平台。 然而不久之後, 發射平台就退居 地球快速運轉的表面上 一個無關緊要的地點,此時 飛行速度的參考基準點是一個 理想化的:地球本體的旋轉、質量中心。 在登月任務中, 阿波羅太空人瞭解到 即使問題簡單如 「你們現在飛行得多快?」 都很難回答。 遠離地球的速度是一回事, 朝向月球的速度 並不見得與前者相同。 理由是地球與月球 事實上是互相繞轉的系統 (地月系統的質量,也是旋轉中心位在地球當中,但距離地心長達地球半徑的3/4,也就是地月的花式溜冰中地球也會相對於此中心搖擺。另外,太陽對月球的引力事實上比地球對月球大兩倍。想想看為何月球沒被太陽吸走。) 啊,你恍然大悟。 這影片想要彈 「速度是相對概念」這老調,對吧? 當《星艦迷航記》的寇克鑑長對蘇魯上尉提問 (注:星艦當用海空軍軍階) 「星艦企業號是否已達曲速因子7 」 (Star Trek的科幻空想單位, 對應幾倍光速設定很亂, 總之皆為超光速) 假如蘇魯是物理魂,應該回答: 「艦長,你問多快是相對於什麼?」 即使如此有性格的答案 八成會讓這位艦隊部屬惹上麻煩, 這卻是唯一有格調的答案, 因為「現在多快?」本身條件並不充足。 這是基本的相對性思考。 不是愛因斯坦那種高級的相對性, 而是老忠實,仍然可靠的 加利略式的相對性(運動相對性) 加利略大概是史上第一人做出 「世上無絕對的速度」的洞見 「世上無絕對的速度」的洞見 速度,如前所述,皆相對 亦即在沒有給予參考系 (reference frame)之下 速度是無法定義的。 一開始你似乎能假定這個參考點靜止。 然而追究起來, 「你說靜止是對於什麼靜止?」 (這裡忘了提,沒有絕對速度也代表 沒有絕對空間、或者絕對座標) 因為,即使靜止(也就是速度為零) 也是速度,因此 也不能獨立於系統定義出來。 速度是相對的,靜止也是相對的。 地球的每秒29.79公里是相對於太陽。 企業號的曲速 7 是相對於銀河系中心。 你的速度是零,相對於你的椅子。 但取決於你所在地的緯度, 你與地心的相對速度可以介於每秒 463 公尺,和 0 公尺之間(各強國的衛星發射站首選低緯地區,為什麼?) 當我們皺眉尋思: 「那地球本身究竟是以什麼速度移動呢?」 我們想像中的宇宙太空船「地球號」 正在宇宙廣袤的空間中一面破浪而進 一面繞行太陽。 但空間可不是海洋, 空間不存在水那樣靜止的介質(沒有以太) 空間本身不是物質 (Michelson-Morley 實驗說明以太不存在) 空間什麼都沒有。 空間是空無一物。 你從空間中的一點運動到另一點, 例如從地球到火星, 然而實際上你不能「穿過空間」, 空間就像影子一樣無物可穿。 就好像問「洞有多重」一樣。 (譯:倘若 Vsauce 有這標題的影片我也不會驚訝XD) 洞的重量什麼的根本沒有, 因為洞是一個概念,不是實體。 洞只是「空無一物」的概念,而空間也一樣。 相對於「什麼都沒有」而動, 不是什麼有用的概念。 速度,或靜止,如同加利略的灼見 天生就得有外在的參考物, 一個巴掌拍不響。 宇宙也不懂你說的速度是怎麼一回事。 因為速度總是附帶著隱藏前提, 一個自由設置 全然是人為概念的參考框架(參考系)。 設想,有一天,你在 你的太空座椅上繫著安全帶 望向窗外看到,舉例而言, 一個等速移動的太空站, 你和對方,在荒涼的宇宙中沒有任何實驗能證明誰真的在動,或者兩者都在動。 又,某種程度來說你們的移動都沒有意義 因為等速本身的實在性完全無法確認, 等速運動永遠有可能只是種表象 永遠需要藉由外在現象而定義 (注:這傢伙台詞文采差,還跳針,翻譯火大) 某種相對現實。 所以,你已被我說服 「所有運動都是相對」了嗎? (是啊,感謝你的洗腦) 哈,事情不是憨人所想得那麼簡單。 有些動作只有純粹相對下的意義, 然而確實存在絕對意義的運動 (感謝你的拖拖拉拉現在才說) 擁有非常真實的效應。 簡言之,常速是相對的, 但【加速度是絕對的】。 科學上,說某物是絕對的, 代表測量的基準 無法任意選擇。 而且對於實驗觀測只有唯一解讀方式。 當你的太空船引擎點火, 加速度的效應無庸置疑, 你會被 G 力壓到椅子裡。 連你的內臟都測量得到, 當然,飛船上的力學儀器也能輕鬆分辨。 看出你的窗口, 現在太空站與你的相對速度, 似乎也在改變加速, 然而在太空站裡的人 會繼續飄浮毫無感覺, 並且他們的儀器並不會感到加速。 真正的在改變速度的是你, 而非你觀察的太空站。 與恆速運動(慣性運動)不同的是, 變速運動(加速運動) 是貨真價實測量得到的。 同樣的理由,旋轉運動也是絕對的。 若你的太空船正在旋轉, 你絕對感覺得到 你飛船的感應器也可以。 (加速座標必有假力,旋轉座標中 是離性力、柯氏力) 在你看來你窗外的太空站, 也在用與你一樣的角速度旋轉, 但唯一會暈得亂七八糟的是你, 他們不會(繼續飄浮)。 你在轉而對方沒在轉, 可以透過扎實的實驗分辨出來。 旋轉,很神奇的,具有一個獨立的實在性。 總結本集,有純粹相對的運動, 也有純粹絕對的運動。 慣性/恆速運動永遠不能 以實驗確定為實在, 總是有只是表象的可能 但加速度本身是實在的, 旋轉也是。 在平凡的日常經驗中, 你得要萬分謹慎,並且「想太多」 才能分辨實在與否。 因為即使簡單如速度的概念 都會為我們的感官所混淆, 那或許所有感覺都值得審慎檢驗。 這個思想實驗啟發了愛因斯坦 去寫下不朽的真知灼見 關於光速,與加速座標系的時間膨脹 --向未來的時間旅行。 對於鑑別各種 「究竟真實」 是重要而艱難的工作。 下次若被警察路邊攔檢,說, 「這位先生,你知道剛才你開多快嗎?」 你可以報以一個深刻,也許有點不智,的回答: 「那要看相對於什麼而言啊。」 於是乎,你就可以在警車的後座 感受那朝向拘留所的加速度, 並且補充說 「啊,但還是有些運動是絕對的啊。」