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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"?

B1 中級 中文 小時 到達 時空 難度 簡單 認知

# 距離與狹義相對論。明天有多遠？ (Distance and Special Relativity: How far away is tomorrow?)

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林宜悉 發佈於 2021 年 01 月 14 日