# Can we build a four dimensional compass?

• B
• SleepDeprived
In summary, the conversation discusses the concept of traveling in a straight line in a four-dimensional space-time universe, and the need for specialized instruments, such as an accelerometer, to track this path. The analogy of the flat Earth is used to explain this concept, and the possibility of using X-ray pulsars for navigation is mentioned. The conversation also touches on the idea of seeing the back of one's head by looking far enough, but this is not a valid reference.
SleepDeprived
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.

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.

PeterDonis
SleepDeprived said:
Only if this is your final question. :-)

stoomart

## 1. Can we physically build a four-dimensional compass?

Technically, yes. However, it would not function in the same way as a traditional compass that we use to navigate on Earth. A four-dimensional compass would require a different set of principles and mechanisms to work.

## 2. What would a four-dimensional compass be used for?

A four-dimensional compass would be used to navigate in a four-dimensional space, which is a theoretical concept in physics. It would be relevant for studying and understanding higher dimensions and could have potential applications in advanced technologies.

## 3. How would a four-dimensional compass differ from a regular compass?

A regular compass uses a magnetic needle to align itself with Earth's magnetic field, while a four-dimensional compass would need to utilize a different type of alignment mechanism to navigate in four-dimensional space. It would also require additional dimensions to be displayed, making it more complex than a traditional compass.

## 4. Is it possible to visualize a four-dimensional compass?

It may be challenging for us to visualize a four-dimensional compass as our brains are not accustomed to understanding higher dimensions. However, scientists and mathematicians have developed mathematical models and visualizations to help understand four-dimensional concepts.

## 5. Are there any real-life examples of a four-dimensional compass being used?

Currently, there are no physical four-dimensional compasses being used in real life as the concept of four-dimensional space is still being studied and explored. However, theoretical models and simulations have been created to help understand and potentially utilize four-dimensional navigation in the future.

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