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
I’m not sure if this answers your question precisely.
If we dial down to 3D objects, for an observer in 2D space (which is one dimension less than our 3D world) we must first select the point of observation. Let’s say (0,0,0). Since the observer is in 2D, they can only “view” slices of the 3D object. Let’s say a sphere exists at (0,0,0) at time T0. This sphere now moves to (1,0,0) at time T2. For the observer who only sees 2D, he observes that there was a circle at time T0 and this circle becomes smaller. This is only when the observer is on a plane without the x coordinate, so necessarily the y-z plane. If the observer was on the x-y or x-z plane, they would observe a circle moving in the positive x direction.
Similarly, when this 4D object is at (w,x,y,z) of (0,0,0,0) and the observer is at (0,0,0) in the x,y,z dimension, if the object moves to (1,0,0,0), the observer will see a shrinking sphere. The velocity of the shrinkage depends on the velocity of the movement. If this observer was in any 3D space with “w” coordinates, they will observe a non-shrinking sphere move one unit in the positive “w” direction.
Now if we transport 3D objects in 4D space, with the same analogy, let’s move 2D objects in 3D space. A disc (in y-z plane) at (0,0,0) moving to (1,0,0). If the disc has NO thickness, it would seem to disappear at 0,0,0 for observer at 0,0,0 and appear to the observer instantly at (0.1,0,0) and then disappear again and so on until it reaches (1,0,0). But to the observers in x-y or x-z, they will see a straight line moving through their space. Depending on their position with respect to the disc they might observe different sizes this projected line.
Similarly, if we transported 3D objects in 4D space, a similar event takes place depending on which observing coordinates you pick.
I hope this helps.
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