If a simple 3-dimensonal sphere were displaced in a 4th spacial dimension, even slightly, it would disappear from 3-space instantly, but it would still have a location in 3-space, right?


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

This sub doesn’t seem to make sense because posting a simple answer is apparently wrong, and my first answer got deleted.

To answer your question simply: yes, the sphere would look like it teleported and reappeared in a different spot.

You can do thought experiments like this using flat objects on a 2d plane, and imagining what a stick figure would be able to see if you pulled the object off the plane and had it reappear somewhere else on that plane

Yes, because a 3D object wouldn’t extend into the 4th dimension at all.

Imagine a drawing on a piece of paper, a 2D object in a 2D space. If you lift that drawing off the paper, it’s no longer on the paper, you removed it from that 2D space and put it in a different 2D space separated from the first by the 3rd dimension.

You would not, however, be able to describe its position in 3D space unless you were also shifted in the 4th dimension by the same amount. You would be able to say where it was and where it may reappear, but we aren’t sure how it would move in the 4th dimension or if it could still have influence in our 3 dimensions.

We are trying to figure out if it would have any effect on our 3D world, though. That’s one of the theories as to what dark matter is. Mass that’s been shifted in the 4th dimension, but still close enough that it can warp spacetime. This is unlikely because, as far as we can tell, the universe only has 3 spatial dimensions, so 4th dimensional shifts aren’t possible. We theorize about them because we would like to know what we are dealing with if we were to encounter one.

If you carry the 3D into 2D interaction through, a 4D object could, in 3D space, do things like appear and disappear inside a closed room and change its shape and size.

My ELI5 suggestion: Go read Flatland, by Edwin A Abbott.

Seriously, it dives into this conversation similar to some of the suggestions (think of how a 2d shape sees 3d movement, and one a 1d shape would experience 2d movement. It’s a fun thought exercise, and is something you can ready in an hour or two.

In any metric space there are symmetries like rotation and translation. You can imagine these symmetries in 2D and 3D euclidean space. My brain breaks trying to conceptualize symmetry transformations 4D euclidean space. However the concept of symmetric transformation of an n-dimensional shape is the same for all n-space.

I lose my mind trying to think about how what it *looks like* in 4D but I can keep my sanity thinking about w*hat is happening* 4D.

I can look at the math of a rotating tesseract and it makes intuitive sense. Then I see an animation of it and it breaks my brain. I’ve never been satisfied with any of these higher dimensional visualizations. I’m too locked into my own perspective (something akin to Minkowski space) for anything but the math to make sense.