Mobius Strip

Mobius Strip.

Mobius strip is a twisted strip. The strip is twisted 180 degrees and the ends are glued together.

Paper Mobius Strip.

Mobius strip has some remarkable properties like, if you walk around the strip you find that it is only one sided! Moreover if  a flat-lander walks around it then all his internal organs will be reversed. He will be transformed into his mirror image without his knowledge.

Flat-lander on Mobius strip.

So if at all our universe is also a 3D Mobius strip then, even we will be transformed into our mirror images by going around it. All our internal organs would be reversed. It would be a medical miracle!

Seeing Higher Dimensions

There is no way of seeing the higher dimensions directly. It is because of the error in evolution that we can interpret only 3 dimensional objects. It is impossible for us to visualize a fourth dimensional object. But there are indirect methods of observing a 4th dimensional object.

The following are the different methods :

• Unraveling higher dimensional objects
• Observing the cross-section
• Observing the shadows  

Dissecting the Demon

Observing the cross-section of higher dimensional objects is the most important and direct way to recognize any higher dimensional object. This method is easy to understand when we consider a flat-lander looking at a 3D object.

The flat-lander can see only the plane on which he is situated. That's his universe. So if a 3D object passes through his universe, then he will be able to see only the part that is passing through his universe. He can see only the cross-section of the 3D object. Take an example of a sphere passing through his universe ( plane ) as shown in the figure. As the sphere passes through the plane, the flat-lander sees a series of circles changing shapes automatically. He will see a circle appear out of nowhere and grow bigger and bigger. Then it starts growing smaller and eventually disappears from his universe.

Passage of a sphere though a plane.

Similarly if we ( 3D humans ) pass through the universe of a flat-lander, then the flat-lander will see 2 black circles of cloth appear in his universe ( our pants ) which will join together ( our hip ) and then change color ( from pant to shirt ) and then change to smaller circle of flesh ( our neck and face ) and will disappear in a black mess ( our hair ). So by observing how these circles change for different humans the flat-lander can tell us apart.

Similarly we can see and interpret the 4D objects by looking at their 3D cross-sections. So when a 4D sphere passes through our universe we first see a small sphere appear out of nowhere and then grow bigger and the become smaller and disappear from our universe. Similarly the cross-section of other objects can be studied and using this information we can tell apart the hyper objects. This is a direct method of recognizing higher dimensional objects.

Shadow of the Colossus

Shadow ( basically projection ) of higher dimensional objects in lower dimension is another method of 'seeing' these higher dimensional objects. The shadow of 3D cube on a 2D plane is a square inside a square with all the corners connected as shown in the figure.

Shadow of 3D cube

Extending this logic to 4D cube we can conclude that the shadow of a 4D cube on 3D space should be a cube inside another cube with all the edges connected as shown in figure.

Shadow of 4D cube

Tesseract

Tesseract is an analog of cube in higher dimensions. A fourth dimensional cube is called Hinton's cube or hypercube.

Imagine the formation of a 3D cube. It can be done by folding 6 squares (2D cross) in 3rd dimension as shown in the figure.

A 3D cross can be formed by keeping 8 cubes as shown in figure.

By folding this 3D cross in 4th dimension we can get a 4D hypercube. By doing the exact opposite ie. by unraveling a 4D hypercube u get a 3D cross. So this is one of the methods to interpret a 4D object.

But we cannot visualize the folding of the 3D cross. To understand why, we have to take the analog of flat-lander (2D being) living on a plane. He can see the 2D cross. But when the 2D cross is folded, a square moves up into 3rd dimension and out of the plane. So the square would disappear from his world. With each folding the squares keeps on disappearing. Finally only one square would be left in his plane. This one square would depict a 3D cube for the flat-lander.

Similarly when the 3D cross is folded, each cube will start disappearing from our world. Finally only one cube would be left depicting a 4D tesseract.

Shortcut through the universe

The concept of hyperspace ( multi dimensions ) can be used to travel a long distances in the universe by curving the 4 dimensional space-time. The space-time separating the two points in universe is curved in a higher dimension so that the 2 points come close to one another. Thus making the travel in our universe less time consuming

This concept can be better understood by considering a flatlander ( 2 dimensional being ) living on a rectangular paper. This flatlander can move only along the 2 dimensional paper ( front, back, left, right ) and cannot visualize the 3rd dimension ( up, down ). He has to travel from one corner of the paper to another. He has to travel along the diagonal for this. But if he can find some technology to curve the paper ( in 3rd dimension- upwards ) and bring the 2 corners close to one another, then he can walk off from one corner to another directly and avoid traveling along the diagonal. Thus his journey becomes shorter.

This concept when extended to our 4 dimensional universe requires the space-time to be bent in a higher dimension. The energy required to do this is enormous. We have not yet developed the technology required. This curving of space-time is similar to the opening of worm holes and like teleporting seen in the movies. But in reality we are far away from achieving this.

Need for dimensions more than 4

We all know about the 3 space dimensions ( length, breadth, width) and also about the 4th time dimension. These are the dimensions we can feel and see. So we know that they exist.

Now by adding some new dimensions we are able to unify the different fundamental forces in nature. Fundamental forces like the strong nuclear force, weak nuclear force, electromagnetic force and the gravitational forces can be unified by the use of multi-dimensions. String theory predicts that atleast 11 dimensions are needed to unify all the fundamental forces. So our universe is thought to be made up of 11 dimensions. These new extra dimensions are used as mathematical tools for unifying the forces.