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
> 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?
> Am I thinking about that correctly?
Yes, you do.
> What does it even mean to move an object in 3-space while it has no intersection or presence with said 3-space?
Technically it isn’t in the same 3-space during that move, but a parallel copy. You shift the sphere into a parallel 3-space, move it there as usual, then shift it back to its original (hyper)plane of existence.
> What would this action “look like” from the perspective of the 3-space object?
The rest of 3-space sees it popping out of existence and then back into it at another location. The sphere itself sees kind of the reverse: everything else pops out of existence, and if the parallel 3-spaces it moves through and to are not empty, it sees their content pop into and out of existence. The middle “lateral” movement will look just as usual.
You mention feelings of acceleration, but that is unlikely: we and no other purely 3D things do not have any receptors to sense motion in the 4th direction of space. Our ears for example feel motion by inertia, things lacking behind and needing a little bit of time to reach speed and keep up; but there is zero width in the new direction, whatever small distance anything would lack behind means it just vanishes for all that matters, like part of your ear being replaced by vacuum (sounds painful).
> 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
I am not entirely sure if this speaks about the typical image of masses bending spacetime “into” another dimension, as if lying on a sheet. If so, that’s a simplification only. The actual bending happens within spacetime itself; it takes no extra dimensions, instead it rather figuratively stretches and thins the fabric without any “bumps” into a new direction. That however doesn’t make a good analogy for why it would cause what we call _gravity_.
If anything, it might need more than one extra dimension to even properly draw the bent shape of space(time) into it. Mathematics of what we call _embeddings_ says we need about as many extra dimensions as we already have normal ones, so 3 or 4 more, not just one. You can try to imagine it as one dimension not being enough to accommodate all the potential ways things can be bent: think of a knot, where a line (1D) uses all of 3 dimensions, while it is completely impossible to make any knots in 2D alone.
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