Thread:User talk:WaitingforGodot/Brian Cox/reply (6)

Think of a place, which is actually in 4 dimensions so it also has a time too. It has its X, Y and Z position (say, my house) but it also has its time dimension (which is a little awkward but call it 12:00 GMT, Janurary 8th). "Near" and "far" are basically a measure of "how difficult it is to get there" - as he puts it in the minute-physics video. So if you try to get to my house from your house (and it's X Y and Z) now, that is, 15:15 GMT December 30th, it would be relatively easy. If you left it until 11:55 GMT, January 8th to leave, it would be considerably difficult. You have to work much harder in that latter case - and if you left it until 12:00 GMT to get here at 12:00 GMT it would be impossible, you'd have to expend infinite energy to do that. I.e., go at the speed of light (and that's where we come back to the whole "now" thing from above).

In four dimensions, and the four dimensions is the key, the distance between my house at 12:00 GMT on January 8th and your house today is less than the distance between my house at 12:00 GMT on January 8th and your house with 5 minutes to get here.

Often, when working in relativity and 4D the terminology changes a little bit to avoid a conceptual roadblock and to force you to think of what it means - just like how Minute Phyiscs tries to describe distance as "how hard it is to get somewhere" rather than in metres or yards. So instead of a "location" (which implies just X, Y and Z) it's an "event" (which has X, Y, Z and T) - and of course we're used to "events" having a time associated with them, right? And instead of "distance" (which again implies only X, Y, and Z) it's called an "interval", and we're used to intervals consisting of time.

So suppose you set off and drove across town; the interval between your start and finish might be 4 miles and 10 minutes, or if you're briskly walking it might be 4 miles and a full hour. If you need to move faster, you have to plow more energy into doing so - and as walking is slower than driving, it's "easier" get across town in an hour than in 10 minutes. The interval is smaller, even thought the time is longer.