Are tesseracts and hyperspheres ‘time’? Or is it completely different?
In: 0
Time is not quite the same as a fourth spatial dimension.
The most common way to think about time being a fourth dimension is through the mechanism of something called *Minkowski space*, a mechanism first invented to help describe Lorentz contraction, a phenomenon that got folded into Special Relativity.
In Minkowski space, there are three “real” dimensions, being the three spatial dimensions, and an “imaginary” dimension, time. It’s called that because when you calculate distances, you sum the squares of the three spatial dimensions (like usual), but you actually **subtract** the time component. This means that in a Minkowski space, if two events are 1 light-second away from each other in space, and one second away from each other in time, the “distance” between them is zero!
Here, one interpretation of “distance” is as a sort of a measure of how easily light can pass between things – if the distance between objects is zero or negative, then light can pass between them such that one of these things can affect the other; distance being greater than zero means that they’re too far apart for light to pass between them in time.
Because of this “negative dimension”, hypercubes don’t work the way you’d want them to, and “hyperspheres” actually take the form of hyperboloids.
I’ll address your other specific questions.
>You can lift up something out of a 2D drawing in the third dimension. Can something in our world be moved to the past/future?
Yes, this is called “the passage of time”, whereby all objects tend to exist across an entire interval of time, even as they are often located in only a single point in space at any moment, so that an object’s “trajectory” in Minkowski space tends to be a 1 dimensional-object (called a “world line”).
>A dot on a circle can move in one dimension, and if it does so far enough, it comes back to the starting point because the space is curved. On earth you can move in two dimensions curved, move far enough and you come back to the starting point. In 3D space, does time allow you to go back to the starting point?
No, because time doesn’t curve that way.
What you’re describing is how things move on a surface of *positive curvature*; it is not a requirement that a space work that way. In fact, if you neglect the time component, 3D space by itself does not seem to work that way; instead, if you keep going, you’ll just…keep going. Space-time, as it happens, actually has *negative* curvature, so this will tend not to happen.
Latest Answers