字幕列表 影片播放 列印所有字幕 列印翻譯字幕 列印英文字幕 What do we really mean by "near" and "far"? 我們所指的"遠"跟"近"到底是指什麼? In a way, distance is just a measure of how hard it is to get between two points. 在某種程度上,距離不過是用來表示兩地之間通行的難度。 The harder to get from here to there, the more distant "there" is. 從A點到B點有多難距離就有多遠 Thinking about distance in multiple dimensions is easy now! 現在來簡單的想像在多維的情況下的距離 In two spatial dimensions, a point a mile north and a mile east is more distant than 在平面二維的情況下，向北一英里再向東一英里會比只向東一英里來的遠 one that's just a mile east - it's harder to get to. 兩英里比一英里更難到達 What about one space and one time dimension? 那如果是表達時空二維的距離？ Easy as well! 簡單！ Getting to a point a mile east in 10 minutes is a lot harder than getting there in 10 hours 十分鐘內往東一英里會比十小時內往東一英里來的難 - so one mile east and 10 minutes in the future 所以十分鐘內往東一英里會比十小時內往東一英里更"遠" is way more distant than 1 mile east and a day in the future. 現在在東邊一英里處有一個無法到達的點,所以它是"超級遠" And a point that's a mile east right now is impossible to get to - so it's super distant! 但等等,那表示十分鐘比十小時更遠對吧? But hold on - that would mean that 10 minutes is farther away than 10 hours! 聽起來似乎跟我們所認知的相反,但是宇宙就是這樣運作的 Doesn't that seem backwards? 狹義相對論說,越多的時間意味著越短的距離 It kind of is - but it's the way the universe works: 所以距離等於空間減去時間! in special relativity, more time equals less distance! 如果你往東旅行一英里且時間是倒退的 So distance in time is negative! 兩者將打消,也就是你的總距離為0 And if you travel east and into the future in such a way that the negative time & positive 那麼你將會以光速移動 space distances cancel out, your total distance will be zero. 所以明天有多遠? 比你想像的近 And you'll be traveling at the speed of light! So how far away is tomorrow? It's closer than you think.