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Negative distance? Can it be real?

  1. Mar 15, 2012 #1
    I started wondering about this after solving a problem on the exam. Here is the problem: 2 planes has a speed v1 and v2. They are flying from the airport at the same time. The difference between their landings on the same airport is t. Express the distance between the airports as functions of v1, v2 and t.

    This is what I got: distance= v1v2t/|v1-v2|

    If this formula for the distance between the airports allways applies and we have defined positive and negative velocities as oposite directions when the problem is 1 dimensional, we get a negative distance if the planes goes in oposite directions and lands on the same airport after a time t.

    So here is my question: May there be such a mystic thing as negative distance so that 2 planes can go in oposite directions and land on the same place after a finite amount of time? Could this be something physical, not observed in our universe, but still real in other strange universes and extremly hard for us to imagine?
     
  2. jcsd
  3. Mar 15, 2012 #2
    No need for weird alternate universes to have the two aircraft heading in opposite directions land in the same airport. If you map the coordinates to a sphere(like the Earth), that's exactly what you'll get.
     
  4. Mar 15, 2012 #3
    In relativity, the usual notion of distance is replaced by the invariant interval, which can be negative. The invariant interval between two events is (in +++- convention) the square root of
    [itex]ds^2=dx^2+dy^2+dz^2-c^2dt^2[/itex]
    This is just the usual notion of distance minus an extra term for the time difference between the two things you are measuring. If you are measuring the interval between two things at the same time, then ds is just the distance. A negative interval means that the interval is time-like, which means it's possible for a signal to travel from one endpoint to the other without going faster than c.
     
  5. Mar 15, 2012 #4
    Hey,

    You are thinking too hard.
    It has no physical significance what so ever
     
  6. Mar 16, 2012 #5
    http://www.datasea.info/avatar1.jpgNo need for weird alternate universes to have the two aircraft heading in opposite directions land in the same airport.
     
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