The 4th special dimension

Scientists have been pondering whether there exists a dimension beyond the third dimension-The fourth dimension. Some scientists think that the fourth dimension does exist and it is possible to find it while others think that the fourth dimension is merely a mathematical wonder. Recently, an international team of researchers from Penn State, ETH, and Holon Institute of technology has found the "four-dimension version" of quantum Hall effect. A behavior of particles which is theorized that it can only exist in four dimensions. In their experiment, they built an array of light tubes and observed how the light pass through those tubes. In the two dimensional system they set up, scientists observed that light behaved as there are two extra dimensions. After observing the phenomena that are theorized to only exist in four dimensions, researchers assume that there is a fourth dimension involved. The next step for the researchers is figuring how the higher-dimensional physics is relevant to three-dimensional physics.

At this point you may wonder, what is that fourth dimension anyway? How can we visualize it? Thinking about the higher dimension is very tricky but interesting in a way. Before scientists demonstrated the physics in four dimensions, the fourth dimension can only be proved mathematically.  To prove that the fourth dimension can exist mathematically, we can use the concept of projection. Assume that there is a two dimensional plane in front of you and you want to make a projection of this plane on one-dimensional space. You will simply shine a light directly on the edge of this plane and what you will see is a straight line, a one-dimensional object (Note that there's no left and right in one dimension, only forward and backward). Now, there is a box (a three-dimensional object) in front of you and you want to project it on the two-dimensional space. This time, you can shine the light at any angle. What you will see is the shadow of this box on a two-dimensional plane. At this point, we can see some patterns already. In fact, there is a description in math states that an n-dimensional space R^n is the projection of the higher dimension R^(n+1). Based on this description, we can say that the three-dimensional space that we live in is the projection of the four-dimensional space. Therefore, the existence of the fourth dimension is proven mathematically. An implication of this description is that there is no limit for the numbers of dimensions. In other words, you can have an infinite amount of dimensions based on the description. Since an n-dimensional space is the projection of (n+1) dimensional space, we can always move on to a higher dimension and n will go to infinity.

You may argue that thinking higher dimension mathematically does not help anything because it doesn't help you "see" it. Let me tell you something, it is perfectly normal and logical that you can not "see", "fell", or "experience" it. I dare say that there's no one who lives in three-dimensional space can show me where the fourth dimension is. Don't believe me? Let's try! If I ask you to demonstrate one dimension, you will point to either your front or back. If I ask you to add another dimension, you will point to your left or right. When I ask you to add the third dimension, you will point up or down. However, the big problem is what would you do if I ask you to show me the fourth dimension? You may point 45 degrees upward. Ha Ha. Nice try! But you are still demonstrating three dimensions by doing that. None of us three-dimensional creatures can experience the fourth dimension because we are "trapped" in three-dimensional space. Although we can't experience it, we can "deduce" it. To show that deducing a higher dimension from a lower dimension is possible, I will use an example of two-dimensional space. Assume that there is a two-dimensional creature standing on a sphere, how can that creature know that it is standing on a sphere when everything it experiences is two dimensional. That's easy. It can mark the place where it is now standing and start to walk straight forward. After walking for a while, this creature will find out that it returns to the spot where it started walking. Through this observation, that creature can deduce that the space it lives in is curved and have an extra dimension that he can't physically "see". Applying the same logic, we three-dimensional creatures can also deduce the existence of higher dimension by observing the phenomena that can only be explained when we add an extra dimension.

The recent discovery of scientists about the fourth dimension is exciting because it suggests that there may be a higher dimension out there. Although we can not "see" it, the theory suggests that we may be able to "observe" it. If the existence of the fourth dimension is confirmed, I can't wait to see how we relate it to the three dimensions that we have already known.