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B Can we build a four dimensional compass?

  1. Nov 25, 2016 #1
    The reason I ask is that when we use the surface of the earth as an analogy, if we travel in one direction then eventually we will come back to where we started. But to do that we need a compass or some similar instruments to keep track of our path to make sure we are always in a "straight" line otherwise we may come back at some other place. Obviously the flat land people cannot use our GPS since they cannot have access to the satellites since the satellite would be somewhere above the flat land at some other dimension and that would be cheating.
    So like the people in the flat land, we are trapped in a three dimension space in a supposedly four dimensional space time universe, and if the theory is correct and if we travel in a "straight line" we will eventually come back to where we started (assuming the universe is close and finite). But a "straight line" in a four dimensional space time is not the same "straight line" like on the surface of the earth. I mean when our space ship takes off from earth, it will take off in a curved trajectory but even after that our space ship will be affected by gravity from other celestial bodies the path will not be straight in a three dimensional sense. But you get my point. So the only way to know if our space ship travels in a four dimensional straight line is the need of having a four dimensional compass to keep track of our path, but to visualize such a thing is a little bit foggy for my mind.
    The closest thing I can visualize is shining a light beam into space and wait for it to come back again assuming the universe is close and finite and not expanding faster than the speed of light. We will inevitably use the flat earth as an analogy, so when I look at the WMAP picture, I assume that any point in the universe, any observe will get the exactly the same picture of the cosmic radiation, just as any person on the earth flat land will see the same picture.
    Someone had said that if you can look far enough, you will eventually see the back of your head. I am still having a hard time able to visualize it though.
  2. jcsd
  3. Nov 25, 2016 #2


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  4. Nov 25, 2016 #3


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    No we are not.

    No, the way of doing this is not a compass, it is something that checks if a line curves or not. In space-time, this is an accelerometer.

    I do not see how this is relevant. It is also not true.

    "Someone said" is not a valid reference.

    No, a compass will not lead you on a great circle on the sphere. What you need is an instrument that can check if your path is straight.
  5. Nov 25, 2016 #4
  6. Nov 25, 2016 #5


    Staff: Mentor

    Only if this is your final question. :-)
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