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

  • In a way, distance is just a measure of how hard it is to get between two points.

  • The harder to get from here to there, the more distant "there" is.

  • Thinking about distance in multiple dimensions is easy now!

  • In two spatial dimensions, a point a mile north and a mile east is more distant than

  • one that's just a mile east - it's harder to get to.

  • What about one space and one time dimension?

  • Easy as well!

  • Getting to a point a mile east in 10 minutes is a lot harder than getting there in 10 hours

  • - so one mile east and 10 minutes in the future

  • is way more distant than 1 mile east and a day in the future.

  • And a point that's a mile east right now is impossible to get to - so it's super distant!

  • But hold on - that would mean that 10 minutes is farther away than 10 hours!

  • Doesn't that seem backwards?

  • It kind of is - but it's the way the universe works:

  • in special relativity, more time equals less distance!

  • So distance in time is negative!

  • And if you travel east and into the future in such a way that the negative time & positive

  • space distances cancel out, your total distance will be zero.

  • 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"?

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距離と特殊相対性理論。明日はどこまで遠いのか? (Distance and Special Relativity: How far away is tomorrow?)

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    林宜悉 に公開 2021 年 01 月 14 日
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