Can we build a four dimensional compass?

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Discussion Overview

The discussion revolves around the concept of navigating in four-dimensional space-time and the hypothetical need for a four-dimensional compass to track a spaceship's path. Participants explore analogies, instruments, and the implications of traveling in a universe that may be finite and closed.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant suggests that just as on Earth, where a compass is needed to maintain a straight path, a four-dimensional compass would be necessary to navigate in four-dimensional space-time.
  • Another participant counters that we are not "trapped" in three-dimensional space and argues that an accelerometer, rather than a compass, would be the appropriate tool to determine if a path is straight in space-time.
  • There is a reference to developments in using X-ray pulsars for navigation, which some participants mention as a potential method for pinpointing location in space.
  • Concerns are raised about the validity of certain analogies and statements made regarding the nature of the universe and cosmic radiation, with some participants challenging the relevance and accuracy of these claims.
  • One participant expresses difficulty in visualizing concepts related to seeing the back of one's head when looking far enough into space.

Areas of Agreement / Disagreement

Participants express differing views on the necessity and nature of a four-dimensional compass, with some arguing for its relevance while others assert that different instruments, like accelerometers, are more appropriate. The discussion remains unresolved with competing perspectives on the topic.

Contextual Notes

Participants highlight limitations in understanding and visualizing four-dimensional navigation, as well as the dependence on various analogies that may not accurately represent the complexities of space-time.

SleepDeprived
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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 spaceship takes off from earth, it will take off in a curved trajectory but even after that our spaceship 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 spaceship 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.
 
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SleepDeprived said:
we are trapped in a three dimension space in a supposedly four dimensional space time universe,
No we are not.

SleepDeprived said:
So the only way to know if our spaceship 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.
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.

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

SleepDeprived said:
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.
"Someone said" is not a valid reference.

SleepDeprived said:
But to do that we need a compass or some similar
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.
 
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SleepDeprived said:
So is this your final answer? :-)
Only if this is your final question. :-)
 
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