A four dimensional object spinning on it's axis.

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SUMMARY

The discussion centers on the concept of spinning objects across different dimensions, specifically focusing on a four-dimensional sphere. It establishes that a two-dimensional circle has a zero-dimensional point as its axis, while a three-dimensional sphere has a one-dimensional line as its axis. The inquiry extends to whether a four-dimensional sphere would have a two-dimensional plane as its axis and explores the implications of spinning in higher dimensions. Additionally, the conversation touches on the nature of point-like particles and their inability to spin due to lacking dimensions.

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  • Understanding of dimensionality in geometry
  • Familiarity with the concept of axes in different dimensions
  • Basic knowledge of topology and its relation to dimensional spaces
  • Concept of n-dimensional spheres and their properties
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This discussion is beneficial for mathematicians, physicists, and students interested in advanced geometry and the implications of dimensionality in theoretical physics.

Georgepowell
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If a two dimensional object (say a circle) spins, their is a zero dimensional 'point' that stays in the same place as it spins.

If a three dimensional object (sphere?) spins on its axis, there is a one dimensional 'line' (its axis) such that any part of that sphere that lies on that line would stay in the same position in space.

If you spun an 4d 'sphere', then would there be a 2d plane that you could call its 'axis'?

And further, if you spun an n dimensional sphere, would its axis be (n - 2) dimensional?

Any comments would be good, thanks.

edit: is this why a point like particle cannot spin? i.e. they have no dimensions to spin through?

Does a negative number of dimensions have any meaning?
 
Last edited:
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Maybe you can think about the revolving sphere spinning on a 2nd axis such that the original axis sweeps out a plane. Hmm...
 

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