GOLD

#### Revealing Mysteries of the 4th Dimension

In my project, I proposed my ideas, backed up with research and investigation, related to the 4th spatial dimension. I covered topics like entropy, general relativity, multiverse etc. through demonstrations and real - world application scenarios.

### Problem

#1 Scenario

My first scenario is, Imagine you are starving. On the kitchen table, you see a jar of cookies. You are so tempted to open it, but the jar cannot open. You try harder and harder until your face turns red, but you simply cannot get the sealed cookie.

#1 Problem

How do you get the cookie out of a jar without opening it using the 4th dimension?

#2 Scenario

My second scenario is that you wake up on Monday morning and find out that school starts in just 5 minutes! After brushing your teeth swiftly, you sprint to school.

#2 Problem

So how can we prevent this problem? How can we scroll back through time using the 4th dimension?

#3 Problem

How can you travel faster between 2 locations without using more energy (increase in speed, decrease in energy) using the 4th dimension?

### Method

These are the concepts I have researched in order:

1. Understanding a dimension
2. Flatland
3. String Theory
4. Quantum Mechanics, Heisenberg Uncertainty Principle, Quantum Entanglement
5. General Relativity
6. Arrow of Time
7. Branes
8. Entropy
9. Determinism
10. 4D topology
11. 4D thought Experiments
12. Projections
13. Formation and destruction of the universe
14. Holographic Principle
15. Gravity in extra dimensions
16. Ekpyrotic Theory
17. E8 Lie Group
18. 4D quantum Hall Effect

### Research

My research includes the following concepts:

Flatland

General Relativity

Entropy

String Theory

Ekpyrotic Theory and Branes

Holographic Principle and Information Paradox

Quantum Physics - Heisenberg Uncertainty Principle and Quantum Entanglement

Hypertoruses

Studying 4D geometry and extracting 3 main geometric properties of 4D shapes:

- Visibility of all phases of a cube at once from the 4th dimension

- Hypercubes have 8 cells, I have also created a creative way of finding the number of cells in a 4D cube (tesseract)  by projecting a tesseract on a 3D surface and using a simple formula.

- 4D geometrical thought experiments such as drawing circles in squares, spheres in cubes, and hyperspheres in hypercubes in a specific way.

Stereographic projections

E8 Lie groups

### Data

Based on my research, I have come up with a solution to each problem. These solutions/results/data are recorded below:

#1 Solution

The cookie can be removed from a jar by transporting it through a 4th spatial dimension, because the cookie is not fully trapped, the jar is still open in the 4th dimension, even though we cannot perceive it. Notably, this process can be achieved by 3D humans as well, if that human is in the 4th dimension.

#2 Solution

Time can be controlled in the 4th dimension in two ways:

1. We can teleport to the future and experience different outcomes/ futures at our own will in the 4th dimension, according to superstring theory

2. We can teleport to the past because the forward arrow of time can be reversed in the 4th dimension. This is because entropy is constant, so isentropic or reversible processes can occur in extra dimensions. It would be equally likely for a time to go backward, as it would go forwards, in extra dimensions. Wormholes are theoretical holes in space-time, which link the past and future. By falling in a wormhole, a person can teleport to the past, faster than the speed of light. These wormholes require extra-dimensional elements called 'strings.' Therefore, extra dimensions can help teleport to the past, through constant entropy and theoretical wormholes in Einstein's general relativity.

#3 Solution

Traveling between two destinations in less time can occur by manipulating the geometry of Earth. Instead of the transportation equipment going faster, the distance itself, between two locations can be reduced. This can happen by curving the earth into a  hypertorus. If the Earth was curved around a 4D torus, then a trip from Rio to Tokyo would occur in a matter of minutes! The plane departing from Rio would have to fly up to the troposphere and continue going upwards. It would eventually reach Tokyo in roughly 5 minutes! Basically, Tokyo would be 36 km above Rio! A study, performed in 2015 demonstrated that the universe is shaped like a hypertorus because 3D torus patterns were not visible in the collected data, which proposed that these patterns might be encrypted in extra dimensions. Although there are arguments that prove that the 2015 data was wrong and the universe is actually flat, it does not totally disprove that we live in a hypertorus. Perhaps, the universe is vast than we thought, and only the observable part is flat, but the complete picture is yet to be unlocked.

### Conclusion

In conclusion, For the first hypothesis, I was incorrect due to the lack of perspective and visualization. For the second hypothesis, I was incorrect because I did not consider going past through time as well. And for the last hypothesis, I was partially correct, because the 4th dimension does allow a shortcut, but I was uninformed about the specific process.

From the 3 main points of my project, the first two can be achieved naturally in the 4th spatial dimension. However, the last point is arguably impractical, because it requires the bending of Earth. When we think of a " looping / curving the earth into hypertorus" we usually imagine a sphere stretching into a torus, which would distort the earth's geometry. This geometrical fluctuation can cause negative impacts on living beings. I would like to clear this misconception because the Earth would still remain a sphere from our 3D perspective, Earth's 3D geometry would not be disturbed if it is wrapped into a hyper torus in a proper way. But a question still arises:

Even though it will not geometrically harm 3D Earth, how can we exactly unfold and fold into a hypertorus?

The exact folding process is unknown, but I infer, that we can possibly fold and unfold extra-dimensional, compactified, vibrating, elements called strings and study how folding can occur between extra dimensions and our 3 Dimensions of space. This is possible because the  "Strings" in "String Theory " have contact to this and extra 10 - 11 dimensions.  These strings are extremely small, so a tool would have to be created which would break the rules of the "Heisenberg Uncertainty Principle" and enable us to practical contact with extra dimensions. I want to dive deep into this concept in the future, to unlock the doorways to extra dimensions.

Note:

None of the researches has been experimentally proven, so I want to apply them in real life. all three solutions can only be achieved in an extra-dimensional environment. Extra dimensions are required to implement the 3  points of my project, which is why I have studied theories that support the existence of higher dimensions. I persevered to summarize these studies into a report which is linked in the Attachments section. In the lab report, I have also proposed an idea that we may be living in a projection of a hyper-universe, and I  evaluated if this idea was correct. The link to the Lab report is here:

### Acknowledgement

I would have not be able to complete this project without the help of:

Parents, teachers, Physicist Brian Greene, Physicist Sean Carroll, Param Upadhyay