The concept of dimensions beyond three has long been a subject of debate. While some view the idea of higher dimensions as purely theoretical, others believe they may hold the key to understanding the fundamental nature of reality. So, I did this topic to explore theories that propose the existence of additional dimensions. From this project, I hope to shed light on the scientific and controversial side of higher dimensions.

I'll start by doing basic background research from my cited sources. Then, I'll add them to my research section, slowly piecing it together. Once I've finished my main topic, I can start on my data and final conclusive thoughts. After that, I'll ask my coordinator or another trusted adult to review my work, before editing it completely, potentially adding more specific information. In general, this is what my science fair journey will look like:

1. Finish the Research section first
2. Work on Data and Conclusion
3. Get feedback and edit
4. Finishing touches I might want to add (eg. Logbook, additional files, citations)

After the fact, I can begin working on my trifold to make it physically appealing and deciding what information to put on it. Believe it or not, I also have a specific method I want to follow through on that!

1. Obtain the trifold
2. Search online for aesthetic visuals/formats I could use
3. Implement the one I find suits best
4. Decide the placement of information
5. Print things out
6. Glue them onto the trifold

And then... success!

Before we delve into higher dimensions and the theorems and conceptions around them, we must first define a dimension. Formally defined as “a measurable extent of some kind, such as length, breadth, depth, or height.” A dimension is the minimum number of coordinates needed to specify any point. It's a direction of movement, perpendicular to other directions from a fixed point in the origin (which can vary based on the scientific field). In the world we live in, our spatial world is composed of three dimensions and three directions: up/down, left/right, and forward/backward. Despite being 3 dimensional, we can only see in 2D. Our eyes individually see 2D images, and our brain combines these images to give a 3D perception of what we’re looking at. This is referred to as stereoscopic vision. Because our eyes are separated, each retina has a slightly different image than the other. When those two objects are perceived in our brain, that creates depth. Likewise, in 2D, you are not able to see you are in 2D because of that lack of the third direction.

So, with that logic, 3D people won't be able to see 4D objects. This may be confusing because we can't see 4D, so we can infer that it is hard to prove its existence. However, there does exist an object which resides in the 4th dimension, the tesseract or a hypercube as shown below. Obviously, we can't physically see it, but consider the following example. When you draw a cube on a flat piece of paper, you aren't making the cube 3D on a 2D plane, you're simply projecting the image's shadow to represent the shape. So, we can think of the tesseract as viewing a 4D object in 3D space, like the cube example we just discussed.

However, this is just one interpretation of the fourth dimension. Generally, there is a consensus that there are two different iterations of the fourth dimension: spatial and non-spatial. The spatial one usually represents the 4th dimension as a hypercube (as shown above) while the non-spatial version mainly delves into how time is the 4th, temporal dimension. The former is primarily used in discussions about higher spatial dimensions. This, well, is the main topic of the matter.

More on higher dimensions being controversial-- many people disagree to this idea simply because we have 3 spatial dimensions and one temporal one, so where would the extra dimensions be? Well, when delving into this world, the answer varies based on the theories but mainly stays the same. The idea is that they're either really big or really small. So, thus, we can't see them on a macroscopic level of the world. There are many different ideas of how many dimensions there truly are, so we'll go over some of the many theories.

One of these theories is the Kaluza-Klein theory, which suggests five dimensions.

Kaluza-Klein theory

The Kaluza-Klein theory is an idea in physics that tries to bring together gravity and electromagnetism into one framework. It’s named after two scientists, Theodor Kaluza and Oskar Klein, who developed the concept in the 1920s. Kaluza-Klein starts with the idea that gravity (which we experience as the curvature of spacetime) and electromagnetism (the force behind electric and magnetic fields) might actually be connected. Kaluza suggested that if you add an extra, hidden dimension to space—so instead of just three spatial dimensions (up/down, left/right, and forward/back), there’s a fourth one that’s "curled up" and very small—then both gravity and electromagnetism could be described by the same equations. Klein took it further by suggesting that this extra dimension is "compactified," meaning it’s so tiny and curled up on itself that we can't see or experience it in our everyday lives. Think of it like a tiny, rolled-up sheet of paper; it’s still a dimension, but it’s too small to notice. The extra dimension causes certain properties, like the electric charge, to emerge naturally from the geometry of this higher-dimensional space. Essentially, the theory shows how electromagnetism might be a result of the geometry of a higher-dimensional universe. 

String theory

Quantum mechanics describes the physics of the small, while general relativity describes the physics of the very large. However, there is a problem, those two theories can't really coincide. This is because of gravity based on general relativity and quantum mechanics. In general relativity, time is flexible—it can speed up, slow down, or even stop depending on gravity. But in quantum mechanics, time is treated as a constant, ticking forward like a universal clock. When scientists try to merge these two theories, they run into a problem: time doesn’t behave the same way in both. String theory attempts to solve this problem by proposing that, at the smallest scales, everything is made up of tiny, vibrating strings rather than point-like particles. These strings can stretch, vibrate, and interact in ways that naturally include gravity. One of the vibrations of these strings corresponds to a particle called the graviton, that transfers the gravitational force from its field. String theory is unfortunately a very complex system and isn't one singular thing per say, rather multiple related things at once. It varies based on the version you follow. In the superstring theory, we are left with 10 dimensions. In the bosonic string theory, spactime is 26 dimensions. Finally, in M-Theory, we have 11 dimensions.

Despite the fact these concepts seem like they could be plausible based on the inconsistencies they solve, there are plenty of inconsistent ideas in the two theories I mentioned. Here, we'll bring up concepts that make the theories plausible, to slightly questionable. Keep in mind, these counter arguments do not automatically disprove the theories, but bring up an interesting discussion topic as to how things work. As mentioned numerous times before, there is no experimental evidence surrounding either of the two theories which begs the question of if they're real or not.

For example, with string theory. It lacks a complete and consistent definition in all situations. Another problem is that it suggests a vast number of possible universes, making it harder to develop clear predictions for particle physics. Because of these issues, some scientists criticize string theory and question whether it is worth pursuing as a way to unify physics. 

The debate over higher dimensions ultimately comes down to a struggle between what works in theory and what we can actually prove. In physics, ideas like string theory suggest that extra dimensions must exist for the universe to make sense at the deepest level, helping to explain how gravity and quantum mechanics might fit together. These theories are mathematically solid, but the problem is that we have no direct way of seeing or measuring these dimensions. Science is built on evidence, and without any proof, some argue that higher dimensions might just be a useful idea rather than something real. Researchers have tried to test for them by looking at gravity on tiny scales or searching for signs in particle physics, but so far, nothing has confirmed their existence. Another challenge is that as humans, we experience the world in three spatial dimensions, which could mean we're simply unable to perceive anything beyond that. This raises a big question—if something can never be observed, even in theory, does it really exist? Because of this, the reality of higher dimensions remains uncertain, stuck between being a necessary part of our best models and something we may never be able to confirm.

• Andrew J. Parker, Ifan Betina Ip (2017). Stereoscopic Vision -  https://www.sciencedirect.com/topics/biochemistry-genetics-and-molecular-biology/stereoscopic-vision
• Statewide California Earthquake Center (2002). How do I see Depth?http://scecinfo.usc.edu/geowall/stereohow.html#:~:text=We%20are%203D%20creatures%2C%20living,and%20try%20to%20play%20tennis
• Alex Bogomolny (March 2000). The Tesseract, Cut the Knot! - https://www.cut-the-knot.org/ctk/Tesseract.shtml
• Edwin A. Abbott, Flatland (1884)
• Physics 101: Intro to Physics, Study.com -  https://study.com/learn/lesson/fourth-dimension-overview-examples.html#:~:text=The%20fourth%20dimension%20remains%20a,time%20as%20the%20fourth%20dimension.
• Gunnar Nordström (1914).  About the Possibility of Uniting the Electromagnetic Field and the Gravitational Field https://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/17520
• New Scientist. String Theory - https://www.newscientist.com/definition/string-theory/#:~:text=In%20simple%20terms%2C%20it%20does,as%20atoms%2C%20electrons%20and%20quarks.
• Samantha Statter (2020). Senior Theses: String Theory - https://digitalcommons.bard.edu/sr-theses/1470/.
• David Berman (October 10, 2012). Kaluza, Klein, and Their Story of the Fifth Dimension - https://plus.maths.org/content/kaluza-klein-and-their-story-fifth-dimension.
• YouTube (August 12, 2024). The Fourth Dimension Explained - https://www.youtube.com/watch?v=WC1JvpCemlw. Popular Mechanics.
• Tim Newcomb (January 30, 2023). What the Fourth Dimension Looks Like - https://www.popularmechanics.com/science/environment/a42709141/what-the-fourth-dimension-looks-like/.
• Folger, T. (December 20, 2007).  Newsflash: Time May Not Exist - https://www.discovermagazine.com/the-sciences/newsflash-time-may-not-exist.
• NASA (March 19, 2020). Chandra Data Tests Theory of Everything - https://www.nasa.gov/image-article/chandra-data-tests-theory-of-everything/#:~:text=Astronomers%20used%20Chandra%20to%20perform,be%20connected%20in%20one%20framework.
• Cosmoknowledge (March 15, 2023) No, Time Is Not The 4th Dimension - https://www.youtube.com/watch?v=bUYfFCpaDUI

I would like to thank my science fair coordinator, Mr. Hagen, for allowing me this chance. I will also use this chance to thank my supportive parents whose advice helped my project advance. As an honourable mention, I thank all of my peers who have been with me since the start of my project, encouraging me to continue despite their conflicting thoughts about my topic. And finally, thank you for considering my project for judging.