Distances with extra D

Well, I'm sure most of you have heard of the theory where the universe is a 4 dimensional circle/sphere (hyper shere?) so it has no end but no boundaries. (usually the example of a 2d world ona sphere is given).

Now, if we wanted to find if we were actually on this sphere, (think in 2d here) we'd get 3 people, they'd each start moving away from each other (120 degrees between each direction, perfect triangle). Then they'd stop... say 1000 miles away from the starting point. They then measure the distances between them (somehow)... If they're on a sphere the distances will seem too small won't they?:confused:

But then.. what if the sphere isn't a sphere, but jsut a 3 dimensional object? What if they're on a flat area, so the measurement seems to dispro-..


ugh, my head.

Isn't a sphere already a 3-d object?

How about the Kedaman theory? That the universe is the surface of a 4-D object...

Additionally, moving 1000 miles away from each other would consist of moving along a geodesic instead of a line, and then you'd have to take time into account when measuring the distance.

ugh... your head.

I reckon we can't directly observe the shape of the universe, because the instuments used to do so are IN that universe and thus are subject to its laws.

Which is why Gravitons (to my knowledge) have not yet been observed.

Quote:

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it has no end but no boundaries

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Wouldn't anything that has no end have no boundaries?

Mendhak: I was sortof jumping between 2-3-4Ds there.. I meant a 2d universe on a sphere.

Darkwraith: Woops, I meant it was FINITE but had no boundaries.

Wossname: The way I'm thinking, we COULD observe the shape of our universe. Think of it this way: You have a 2d universe, made up of flat surface, except for a depression in the center (let's say this depression is very deep). If your friend stood on one side of the depression, and you walked around it, when you looked at your friend he woudl appear very far away (because the light has to travel along the surface of the depression). Now if you had a mirror at 90 degrees, you were at 0, and your friend at 180.. he would appear close in the mirror but far in front of you.

Get what I'm saying?

So are you saying that if we were to use our line of sight (which I am assuming that follows the surface. If it didn't, then it wouldn't be like looking through another dimension) then he would look far away.

IF we were able to take our line of sight and direct it through another dimension, then he would look closer. If this is what you are inferring, then I understand.

That's exactly what I mean. The light has to travel down (which is straight for the 2d beings) then up, increasing the distance.

So (getting back to your original post) if you had three people that moved some distance away from a point equally, then according to their reality, they are all the same distance from that point.

However, now if you referenced it from the N+1 dimension (where N is the people's dimension), they might be closer than they think due to the distortions of the surface that they cannot observe

Here is a better way of looking at it. Take two points and put them on opposite sides of a piece of paper. Those points are at some distance. Now if you fold the paper, our way of distorting their surface, we could see that the distance between the points are shorter if we measure through our dimension.

They aren't just closer using our dimension, they are actually closer if they take different paths (the flat surface with depression comes to mind here. If you go around it's not as far as if you go through it).

The only way in which one path is shorter than the other is if one contains a distortion (its like trying to make a rectangular map of the world. You have to distort the map in order to make it fit.)

Are you saying that their world contains a distortion such that the measured distance at the distortion from the N+1 dimension is different from another portion of the world, and yet they are the same in the N dimension?

It's still 2 dimensional for them, their entire universe is curved so they wouldn't even realize it at first.

Then are you saying that there is a spot in their universe in which the distance covered is the same in their universe, but covers more in our universe?

Sorry if my last post was a bit short. Here, I'll draw a picture: (using MS Paint, of course)

http://www.vbforums.com/attachment.p...postid=1709710

It's sort of crude, but the general idea is that this represents a 2 dimensional universe (flat in this case, not on a sphere, for simplicity) with a depression in the center.

Let's say you exist in this universe and want to meausre the distance around and through the center of your universe (you don't know about the depression, since you have no concept of up or down).

First you start at the blue dot and go around the depression in a semicircle, and take a measurement. Then you go from the red dot to the blue one by passing through the center.

When you compare your measurements you notice that the direct path is NOT shorter than the semicircle (assume the depression is a bit deeper than it looks, ok?)

The problem is that in the 2-D environment, they will feel that the straight path is the fastest because the universe is distorted such that the unit distance between the points is the same (look at the universe head-on and the z-axis) but in a 3-D world, the distance traveled is different.

However, are we measuring the distance from the point to point in terms of (x,y) such that the distance is measured as sqrt(x^2 + y^2) (in which case the dimension in which we are referencing would matter) or are we measuring the distance in terms of sqrt(x^2 + y^2 + z^2) (in which case the dimension would not matter)

Sorry if this seems circular but at the time of this post, it is 1:12 AM. :)

I'm saying that the two dimensional universe exists on the surface of a three dimensional object. All things in this universe travel along the surface in straight paths. If you distort the 3d object it would have "weird" effects on how things happened in the universe.

The fact is, the people in the universe are not limited to moving left/right - up/down. They are limited to moving left/right - up/down relative to the surface of the object. So in a way they CAN move down, they are just completely unaware of it (except when they make the measurements and realize the distortion is there).

Another issue is scale. We currently live on a 3D sphere, but in most cases, we can assume that we live on a 2D plane when we consider the best path. The error in the 2D model only begins to apply over large distances. If the universe is any kind of object in 3 or 4D, at the very least, we can be very accurate by assuming a 3D space, unless you get into very large distances. Therefore, the distortion would only apply over distances such that communication between the three points would be subject to speed of light limitations. There would be a noticeable lag to any known communication medium. Maybe that's a part of the distortion in 4D.

I can just imagine scientists trying to "map" the 4d object our space (may) reside on.... hehe. They would have their work cut out for them.

The universe is constantly expanding so wouldn't the 4D object that we are on is constantly changing too?

Thus the work being cut out for them :lol: .

So could we asume that there are parts of our universe that time seems to be longer or shorter?

Furthermore, could the universe not be epanding but just becoming more distorted in 4-D space?

Time doesn't seem longer or shorter, only the distances (I'd assume... unless we had a 5d object on which space-time was placed). This could possibly be interpreted as a time distortion...

Ok, so if distortions cause the distances to change, could we say that our universe is not expanding indefinately but just becoming more distorted in 4-d space?