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
> So, while the sphere is still “outside 3-space” at W1
This is not true. If it has an X, Y and Z coordinate, it’s not outside of 3d space.
There is no “**the** 3d space” as your phrasing seems to imply. In the 4d space you describe, there is an entire continuum (collection) of 3d spaces. It’d disappear from one of those and appear in another. Think of moving across W as going to parallel dimensions/universes as depicted in popular media.
The best way I have found to think of this as slices. The same way you can make a 2d slice of, say, a 3d apple, you can make a 3d slice of a 4d object.
Similar, if any 2d object with no depth were moved even slightly out of the 2d space it exists it, it’d vanish entirely. If it had depth, an inhabitant of that 2d space would see it cycle through the various cross-sections until it vanished entirely.
A 4-sphere is a collection of many 3-spheres. So if you were to push a 4-sphere across the W direction and observe it from our point of view you would see a small sphere appear out of nowhere, grow in size, then shrink back down and vanish. These are all the 3d slices with increasing, then decreasing radii you see as it moves along the W direction.
As to your bonus question: I’m not sure you need a special intuition. You may conceptualize it as a distortion of space, but you may also think of it as a simple number attached to every point in space. Similar to the strength of the electric field.
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