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Is for example a tesseract the same thing as cube over time? If not, is there a 3-d object that in some sense is a tesseract over time?

EDIT: What I mean is, are 3 dimensional objects in time "real-life" 4-d objects? If so, is it a cube that is a tesseract or some object that is not a cube that nonetheless viewed over time is a tesseract? Or is time not useful since in 4-d geometry they really mean 4 spatial dimensions?

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    $\begingroup$ I'm not exactly sure what you're asking here, but yes, you can visualize a 4-dimensional shape by seeing slices of it as it passes through a three-dimensional hyperplane over time. See here $\endgroup$ Commented Apr 25, 2017 at 3:57

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As often, we can answer a question like this by reducing the dimension by $1$. We could define $\Bbb R^3$ with one axis time. In that case we would see a sphere as a circle that started from a point, expanded to maximum radius, then shrank to a point. If that is useful to you, go for it. In special relativity and a particular reference frame, we can find a three space perpendicular to the local time axis and look at shapes as they transit that subspace. In general relativity it is messier.

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