A completely different look at the 4th dimension

• pakmingki

pakmingki

I have an idea that completely renivents the idea of the 4th dimension that has absolutely nothing to do with time. BUt however, it will be easier to first think about the lower dimensions.

imagine a perfectly 2 dimensional universe which can be represented with a xy plane where -10 meters < x < 10 meters and -10 meters < y < 10 meters, and with the origin being at the center of this universe (0,0). So, we can say that this is a pretty finite universe.

There are only 3 living organisms, which are all perfect rectangular prisms with these characteristics: they all have equal length and height, which are 2 meters, and they all have an infinitely small depth, meaning they are infinitely thin.
An organism's location at any given time can be represented with a coordinate (x,y) of the prism's center, where x and y are any real numbers within the domain and range of the universe.

They have a very restricted motion; they can only traverse linearly, and they cannot rotate at all.

Since these organisms are in a perfectly 2 dimensional world, when they see each other, they just see a line equal to the length or height.

There is a very specific point i am trying to make by saying these are prisms with an infinitely small depth: i could say they are squares, but a square is a 2 dimensional figure. A prism is 3 dimensional, but in the 2 dimensional world, the organisms only have values for the 1st and 2nd dimension, and an infinitely small 3rd dimension (which is the depth of the prism in this case).

now, consider this situation. One of the organisms is just sitting in the upper most right corner of the universe. The other 2 are in a constant velocity. One has a velocity of (1i + 2j)m/s and the other has a velocity (2i - 3j)m/s. They both see each other moving. Suddenly, one of them changes their velociry to (i+j+z)m/s and vanishes out of the 2 dimensional universe. The one moving (2i - 3j)m/s has no idea what happened, the other organism literally just vanishes. They both stop moving. One is in the xy plane, while the other just entered the xyz plane. Since they are 2d beings,they can only see in 2 dimensional cross sections, and they cannot see each other. The one in the xyz plane starts moving again with a constantly velocity and stops some time later. The one in the xy plane has coordinates of (-3,4). When the one in the xyz plane stops, it has coordinates of (-3,4,3). They are directly above each other and completely unaware. The one in (-3,4,3) starts moving again with a velocity of (0i + 0j + kz)m/s, where k is a constant < 0. At some point in time, the two coexisted in the exact same location (-3,4) at the same time.

Some time later, the particle that entered the xyz plane finally finds its way to it's home, and sees the other particles. The one that learned how to move in the z direction realizes that even if it moves an infinite small value in the postive or negative z direction, it disapears off the plane.

So, apply that analogy to our world. What if we are just in a universe that can be represented with a xyz plane? And we can be seen as 4 dimensional shapes with an infinitely small 4th dimension. For our purpose, let's call the fourth dimension q. If 2 people are sitting right next to each other, and one of them moves even a nanometer in the q direction, he would completely vanish.

And let's go back to the 2d analogy. Let's say there is a line the organisms cannot cross; let's say it starts at (-1, 3) and ends at (1, 3). If one of the organisms went straight at it, it woudl just get stopped. However, if one fo the organiisms went even a micrometer in the z direction, then moved toward it, the organism would be completely unhindered by the line. You could say the line starts at (-1,3,0) and ends at (1,3,0) meaning it doest even exist in the 3rd dimension

If in our 3d universe we could traverse into the 4th dimension, then physical barriers would disappear completely, and wouldn't even exist in the 4th dimesion.

also, let's consider another interesting phenomena. Let's go back to the 2d analogy again. let's say there is a cone with a base radius of 5 meters and a height of 5 meters. Let' s say that the location of the center of the base is at (5,6,-20). So basically, the 2d organism sees nothing initially. let's say the cone now starts traversing with a velocity of (0i + 0j + 4z)m/s. Eventually the organism will see a point appear out of nowhere, and the organism will see the point basically continue to extend into a line which gets longer, until it completely disappears when the cone's center of the base has a z coordinate greater than 0.

what do you guys think about this? Do you think the 2d analogy could be aplpied to our 3d world?

Sounds like sequestration on Randall-Sundrum branes;
an attractive idea.
Nigel

It is probably the property of human mind to re-invent things. Ten years ago one of my friends secretly explained me his idea about what is now known as shutter glasses (for 3D computer vision). He was very excited saying that he is going to patent the device. And how much was he disappointed when the next day I found for him in internet that there were already international conferences discussing the possibility of standartizing the 3D-vision techniques he had just re-invented. But re-inventing something that was already described in 1884 is quite a case!