Edit: Sorry for “spacial” instead of “spatial”. I always get that spelling wrong.
Let’s call the four spatial dimensions W,X,Y, and Z, where X,Y, and Z are the 3 familiar directions, and W is our fourth orthogonal direction.
Suppose a simple 3 dimensional sphere of radius 1 (size 0 in W) has the positional coordinates W0, X0, Y0, Z0.
If the sphere is moved to any non-zero coordinate along W, it disappears from 3-space instantly, as it has no size in W. By analogy, if we picked up a 2D disk into Z, it would disappear from the plane of 2-space.
Now nudge the sphere over to W1. The sphere no longer intersects 3-space, but retains the coordinates X0, Y0, Z0. Right?
So, while the sphere is still “outside 3-space” at W1, it can be moved to a new location in 3-space, say X5 Y5, or whatever, and then moved back to W0 and “reappeared” at the new location.
Am I thinking about that correctly?
A 3-space object can be moved “away” in the 4th, moved to a new location in 3-space without collisions, and then moved back to zero in the 4th at the new 3-space location?
What does it even mean to move an object in 3-space while it has no intersection or presence with said 3-space?
What would this action “look like” from the perspective of the 3-space object? I can’t form a reasonable mental image from the perspective of a 2-space object being lifted off the plane either, other than there suddenly being “nothing” to see edge-on, a feeling of acceleration, then deceleration, and then everything goes back to normal but at a new location. Maybe there would be a perception of other same-dimensional objects at the new extra-dimensional offset, if any were present, but otherwise, I can’t “see” it.
Edit: I guess the flatlander would see an edge of any 3-space objects around it while it was lifted, if any were present. It wouldn’t necessarily be “nothing”. Still thinking what a 3D object would be able to perceive while displaced into 4-space.
Bonus question: If mass distorts space into the 4th spatial dimension… I have no intuition for that, other than that C is constant and “time dilation” is just a longer or shorter path through 4-space…. eli5
In: 296
You have to remember that, just like a 3D space is made of multiple “slices” of 2D planes, a 4D-hyperspace is made up of slices of infinite 3D spaces. So, instead of talking about the 3D space, you should talk about *a* 3D-space.
When the sphere is displaced along the W axis, even if so slightly, it would immediately leave the entire 3D-space it was familiar with. Just like when you lift 2D disk off the floor, it stops being part of the floor world.
So, if the rest of 4D-universe is empty, the sphere would instantly realize the disappearance of everything it was familiar with, and even though its 3 coordinates are the same, it’s still not in the same location at all (because all the 4 coordinates matter). It wouldn’t have a location in the 3D-space, but it would have a similar location in *a* 3D-space, just like the 2D-disk that quit the floor-world and joined the table-world do not have the same location anymore, and between these two worlds, the 2D-disk travelled through many new similar worlds (2D planes). As it is moving through the 4D-space and being put in a completely different location in its original 3D-world, the sphere would simply see the sudden disappearance of everything, then after a while of nothing, it sees itself immediately in another location in its own familiar world.
This is, of course, assuming that the rest of the 4D-universe is empty and all 4 coordinates are spatial coordinates.
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