Why is the “Fourth Dimensional” representation of a cube a tesseract? If time is a dimension shouldn’t the higher dimensional representation of an object be it’s worldline/timeline?
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There is nothing that says time is *the* fourth dimension.
Ultimately, a cube evolved into a shape with *four spatial dimensions* is a tesseract.
When people refer to a tesseract they’re talking about a hypercube, the extension of a cube into four *spatial* dimensions, in the same way that a cube is the extension of a square into three spatial dimensions. The fourth dimension being referred to isn’t time.
The problem I think you are having is determining the difference between a 3+1 dimensional and a 4 dimensional situation. The former is a physical description of the universe and the latter a mathematical construction with no proven relevance to the physical universe.
A cube in our world, if we treat time as a fourth spatial dimension, is not a 4d cube. It would be more like a long, wiggly extrusion with a square cross section.
A true 4d cube would appear from nothingness, exist stationary for its side length, and then disappear just as suddenly. This requires a unit conversion between length and distance, which cannot be properly done because time is not a spacial dimension.
While time is considered a dimension, it’s not quite the same thing as dimensions regarding physical objects. Where a tesseract, or an object constructed with sides of 3-dimensional sides, is a physical, interactive thing; time (while technically interactive), is more of an “observable” dimension.
A tesseract is an an answer to the hypothetical question “What kind of shapes could exist if there were more than three *spatial* dimensions?” It’s not something that exists within 3+1 dimensional space (three spatial dimensions plus time).
It’s a geometrical thing. Extend an *n*-dimensional object into *n*+1 dimensions:
* 0 dim: 1 point
* 1 dim: 2 points connected by 1 line
* 2 dim: 4 points connected by 4 lines forming 1 surface
* 3 dim: 8 points, 12 lines, 6 faces, forming 1 cube
* 4 dim: 16 points, 32 lines, 18 faces, 6 cubes, forming 1 hypercube
* 5 dim: …
When people say time is the fourth dimension, they mean that time is the fourth dimension of space-time, where we have three spatial dimensions and 1 temporal dimension.
What people generally mean with “fourth dimensional” cube is a 4th spatial dimension, so not time (since time is not a spatial dimension, it’s a temporal one and behaves differently).
It’s just a visual illustration of an object with 4 geometrical dimensions.
Time is not a dimension.
Time is a dimension but when people talk about “fourth dimensional” shapes like hypercubes or klein bottles they’re referring to a fourth dimension of space (basically if we had length, width, height, and “another one”).
Any random real-world object is going to be affected by time, but we still think of them as 3D for the same reason.
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