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  • 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.

What do we really mean by "near" and "far"?

我們所指的"遠"跟"近"到底是指什麼?

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