The Fourth Spatial Dimension

This article is about the concept of fourth spatial dimension in addition of the three we know, length, breadth and height, don't confuse it with the four-dimensional spacetime in which time is taken as the fourth dimension. This article is about the concept of four dimensions of space itself in addition of the fifth time dimension, that is, a dimension in which mass can actually move in the regular sense.

So, why its important to think about an extra dimension in space? According to Einstein's General Theory of Relativity the spacetime is curved at points where mass is present, for example near stars and planets and this curve is the reason of gravity. It help explain why gravity is not really one of the four fundamental forces of nature because it is just due to the geometry of the spacetime rather than any exchange of particles like in other three forces. It also explains why there is no counter-force for gravity in regular sense (that is ignoring Casimir Effect) unlike other fundamental forces.

The arguement of existence of a fifth dimension in addition of the four dimensions of the spacetime is based on the perceived fact that for a n-dimensional thing to bend there need to exist a n+1-dimensional realm. So, the arguement says, there must exist a fifth dimension for the four dimensional spacetime to bend into. Its like a 2D bedsheet can bend in a 3D space but can't in a 2D surface, a shadow can't bend on itself means there can't be two layers of shadow at the same surface, a line can't bend if no 2D surface is present and so on. So, if you believe that gravity is due to curvature in spacetime, which you should as there is no better explanation then you should also believe in existence of a 5D realm we are living in.

Lets first straighten some terms to avoid confusion. A 2D environment is a surface, it can also be called plane but I prefer the term surface for easy understanding. A 3D environment is space, 4D is spacetime and for 5D there is no clear word dedicated so I use the general term "realm".

Lets see some examples of n-dimensional objects to better understand the concept:

A 0D thing can only be a point, it has no length, no breadth, no width, nothing, it is used just to locate a position in space assuming that the position is infinitely small. Also note that a 0D thing can have no shape as it has no dimensions. Infact it can be explained with zero information as there is nothing in it to explain. Also note that a point has no place to move.

A 1D object has only one direction forward-backward. It can have exactly one shape that is straight line. Since there is no second dimension to bend into a 1D object can have no other shape than straight line. Note that for the rest of this article I would be using the term "line" for straight lines and curves for any crooked kind of lines.

A 2D object knows two directions, forward-backward and right-left. It can be of an infinite number of shapes including square, rectangle, oval, circle, pentagon, hexagon etc. For our understanding of higher spatial dimensions its better to first understand a 2D Flatland and then use this understanding to imagine a 4D world. A 2D living being can only see things in 1D as we in our 3D world can only see in 2D. It is because when we see a thing from front we can only see its length and width but the width is hidden from us. Same way a 2D eye can only see a 1D object. Since all 1D objects have to be a line therefore all a 2D eye can see is lines, the only variety comes from the different lengths of the lines representing different objects in that world.

Now lets imagine a 4D world. A shadow in that realm would be 3D means like us. So, if a 4D object want to interact with us, the only way is to do so through shadows as it can't directly talk to us or hold anything of our world. Its like you being 3D can never hold in your hand your 2D shadow. Note that the other examples given of 2D objects in various books are technically incorrect, an image of you in a mirror is still 3D because the light forming the colors is 3D, the text appearing on computer screen in front of you is also 3D because the pixels of the screen are infact 3D. Infact you can't see any 2D thing because the light of our world that makes things visible to us is itself 3D. A shadow is the only 2D object but even that is not a real thing, its just an absence of light, not existence of anything. That is why I strongly criticize the story of books like FlatLand and SpaceLand because they talk about objects interacting with lower-dimensional objects which cannot happen. Infact its a very interesting point, if 2D worlds exist than an infinite number of them can be there one over another occupying no width therefore no existence in our 3D world.

A 4D living being would have a lots of superiorities over us 3D beings. For example it can see what is inside our stomach without having to do any surgeries in the same way that we can see what is inside a circle without breaking the boundaries of the circle. That is assuming if it can see, but since it cannot because for it we don't exist as we are not 4D, so it can't see.

What is this information useful for? Well, a way to travel long distance in spacetime is utilizing the curves making shortcuts. Its like a worm instead of travelling through the 2D surface of apple make a hole in the third dimension and travelling through it in short cut. Same way we can think of utilizing the naturally present curvatures in spacetime near massive celestial bodies, that may lead us to place far off in universe, say milions of light years in reasonable few tens of years. So, how to do that. One idea that come in my mind is discussed below.

Consider a room in which there is a window with a grill in it. A light source from outside cast a shadow of grill inside the room on the 2D floor of the room. The 2D shadow roll over the 2D floor as the light source moves. Then, by some special movement of the light source the shadow enter the third dimension, the wall of the room. Now think that we are this shadow but in 3D and the room is 4D. We roll over the 3D space of the room. If the room has an edge, that is, an end and we reach that end then like the shadow we ultimately enter the fourth spatial dimension, the wall. How would it feel like? Well first of all, during the transition time when part of our space ship would be in space and part curving 90 degrees in the extra dimension, the outside world for the front of ship which is in 4D would have fundamentally changed. Instead of seeing the regular things the back of the ship-mates are seeing from outside their windows the front ship-mates would be seeing a very different world. It is wrong to say that they would not be seeing anything. Like the shadow can see the 2D surface of the wall while climbing on it, the ship-mates in front of the ship too, just that it would be different than what they had ever seen before. The known 3D world at the floor of the room would ofcourse no longer be visible to the front ship-mates. The people at the back of ship still laying flat on the floor of the room would still be seeing the familiar world.

So, a 3D object can enter a 4D world by reaching the edge and continue travelling, but what the edge is? It not need be the end of universe because the 2D shadow not need to reach the end of 3D universe to climb the wall. The edge is local, limited to the room. If the shadow was laying in a flat field it would not enter the higher dimension. So, we have to find a 4D edge, it could be any 4D object, not need be a wall. If there was say a ball in the room, the object would climb on it to reach the third dimension, it not have to travel all the way to reach the wall of the room.

How would it feel to the ship while entering the extra dimension? At first the front of the ship would appear lost as the ship hit the wall, this would be a shock to the people at back of the ship and they might think they have reached the end of the world but if they continue travelling the entire ship would enter the new dimension. On their way back to the floor of the room they have to remember the co-ordinates of the point from where they entered assuming that the 4D object they climbed through would still be there. This would prove to be problematic as nothing in space can stay at one place, so when the ship go back to find the 4D object it would no longer be there.

Note that nothing in a 4D world can harm a 3D object, it would not even know about its presence, for it the 3D object do not exist. Only problematic thing would be shadows and its basically hard to imagine how a 3D void of light can affect a 3D object, may be it not affect at all because it is not anything real, just absence of a thing.

Now, the question is, why not the 2D object move under the 3D ball or wall instead of climbing on it. When a 3D object is put on another 3D object, like a wall put on ground or a ball on floor, there may still exist infinite number of 2D planes even if there is no physical 3D space between the two 3D objects. For a 2D plane or surface to exist no height is needed so the absence of space between the two 3D objects cannot stop the existence of 2D surfaces between the two 3D objects. Why then the shadow not just slip under the wall instead of laying on top of it? May be because the light source is 3D. If it would be a real 2D object it could no doubt go between the ball and floor even if no space exist between them. If that happen in our experiment then there is no other known way to enter a higher dimension.