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
During the course of his series Cosmos, Carl Sagan discussed this very topic. It blew my mind 40 years ago and is absolutely an explain it like I am five
This sounds similar to how Ender’s AI Jane could make a ship in Children of the Mind (Enders game saga) perform instantaneous moves. Moving outside of 3-space and re-entering at a chosen location and velocity, they called it Detouring I believe and was abstracted a bit but still pretty similar and an interesting concept.
If you take a 2d circle and manipulate it in 3d, two things can happen.
If it’s still intersecting with its original plane, inhabitants of that plane would see a cross-section of it, which would be a single line segment. It would seem to be an impossible object with no area, and if viewed from the correct angle it would disappear into a single point. If it’s not intersecting with its original plane, it would look like it’s disappearing from existence.
It works much the same in 3d, just with an extra dimension at each step. The intersection between a sphere and the 3d space it came from would be a circle, flat and massless. It would disappear if it was moved far enough on the 4th dimensional axis to no longer intersect with its home space.
I think an interesting aspect of this would be what would happen with the gravitational force that had affected the three-dimensional space if a a three-dimensional object was “pulled” into the fourth dimension. Would the gravity also instantly disappear? Does gravity continue to affect nearby three-dimensional planes even if they aren’t in the plane? Could this be what dark matter is, gravity from objects just outside of our three-dimensional plane but not actually in our plane? To use a two dimensional example, if we were in flatland and a baseball started to pass through our plane, we would see a point and then a circle would get bigger and bigger and then it would get smaller and smaller and vanish. But would that circle exert gravity like anything else in our world? I would think so, but the question I’m asking is would we have been able to detect some gravity pull just before it entered our plane?
3-dimensional sphere is a ball on your table. 4th dimension is time. If you move the ball in time, say to tomorrow, the ball would disappear for one day and reappear tomorrow, in the same place on the table (that is, with the same 3D coordinates, but with a different T)
A sphere of radius 1 that was continuously moved from (0, 0, 0, 0) to (1, 0, 0, 0), using your (w, x, y, z) coordinate system, would gradually shrink to a point. It would not “disappear from 3-space instantly”, and it wouldn’t disappear until it no longer intersected the space of (w, 0, 0, 0). If you moved the sphere of radius 1 further than 1 unit away from (w, 0, 0, 0), it would no longer intersect at all, and it would disappear at that moment.
>Edit: Sorry for “spacial” instead of “spatial”. I always get that spelling wrong.
Both are actually acceptable spellings
I think the radius of the sphere matters.
If the amount translated along the Z axis was less than the radius, it would just appear to be a smaller sphere.
Well, tbh you seem to understand the concept pretty well so there isn’t much to add, yes you can move a 3d object in W then move in xyz and return it to w=0 and from 3-space perspective it would seem to disappear and the reappear on a different location, about what would be “perceived” by the flat lander he would see edges rapidly appearing, disappearing, growing and shrinking, say he was on a table and you pick him up he suddenly would perceive the edge of a glass and it would be constant but the one of the apple would change size weirdly as he goes up and down and then some edges would vanish once he is above them, for a 3d being it would be something like seeing objects warping weirdly while moving through W and the everything goes back to normal once you are returned to your normal “plane”/3-space
Is a sheet of paper a two dimensional object? We perceive it as a three dimensional object with a really thin dimension. Similarly, your sphere would also be 4-dimensional if it exists in 4 dimensions. Any thought experiment you do with yourself and 4 dimensions, you can do with 3 dimensions and someone living on 2 dimensions.
Latest Answers