It is straight in reference to the distorted spacetime.
Conventionally, a straight line is defined as the shortest path between two points, but if you take a plane that is not flat, say the surface of a ball, the shortest path between two points will be curved. But from the perspective of the two-dimensional man who lives in surface, the line is straight because it moves perfectly along his world.
Is this 2D-3D comparison supposed to be like a human-understandable analogy for a 3D-4D relationship?
I saw an explanation once about how time is the 4th dimension. They drew a line on the edge of a book. From the perspective of a single page (2D) it just looks like a dot, but because we can see many instances of that 2D representation it appears to us as a line. An individual page represents how we experience time.
Is your ball example supposed to be kind of like that because I just can’t imagine how spacetime could be a 2D thing in a 3D universe.
Well, kind of. The time dimension is a bit tricky, though – in Minkowsky space, a common way to think about spacetime, it is hyperbolic in relation to the other dimensions. In a nutshell, this means that distance is not the square root of the sum of the squares of the distances in specific dimensions, but rather of the difference. This makes it especially tricky to visualise. (I do recommend you check out this series by minutephysics, he does a great job at making it intuitive)
My analogy, therefore, doesn’t translate directly to spacetime, but it does provide a very simple 2d explanation for why straight things can act curved (even in 4d).
It is straight in reference to the distorted spacetime.
Conventionally, a straight line is defined as the shortest path between two points, but if you take a plane that is not flat, say the surface of a ball, the shortest path between two points will be curved. But from the perspective of the two-dimensional man who lives in surface, the line is straight because it moves perfectly along his world.
Is this 2D-3D comparison supposed to be like a human-understandable analogy for a 3D-4D relationship?
I saw an explanation once about how time is the 4th dimension. They drew a line on the edge of a book. From the perspective of a single page (2D) it just looks like a dot, but because we can see many instances of that 2D representation it appears to us as a line. An individual page represents how we experience time.
Is your ball example supposed to be kind of like that because I just can’t imagine how spacetime could be a 2D thing in a 3D universe.
Well, kind of. The time dimension is a bit tricky, though – in Minkowsky space, a common way to think about spacetime, it is hyperbolic in relation to the other dimensions. In a nutshell, this means that distance is not the square root of the sum of the squares of the distances in specific dimensions, but rather of the difference. This makes it especially tricky to visualise. (I do recommend you check out this series by minutephysics, he does a great job at making it intuitive)
My analogy, therefore, doesn’t translate directly to spacetime, but it does provide a very simple 2d explanation for why straight things can act curved (even in 4d).
Here is an alternative Piped link(s):
this series
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