Dimensions to be simple are the number of independent coordinates that are required to specify a point’s position. Like in one dimension, you need only x-axes to tell the position. For two dimensions, you have a grid of x-axes and y-axis,and similarly for three dimensions you have x-,y- and, z- axes. Dimensions can also be the number of independent spatial directions a body can move in, like in 1-D it’s just left-and right or forward-backward or up-down, in 2-D any of the two, and in the 3-D space that we live in we have up-down, forward-backward and left-and right. But the question is are there any more dimensions? Perhaps hidden dimensions?
The concept of extra dimensions isn’t new. In 1919 Theodor Kaluza modified Einstein’s theory of relativity which include four dimensions (3-space and 1-time) into a new form to include five dimensions, which was later given a quantum interpretation by Oskar Klein and is now called Kaluza-Klein theory. Many other theories predict multiple dimensions and the most famous of them is the so dubbed ‘the possible unified theory’, the String Theory. Higher dimensions come naturally in the theory, and not just an add-on. A mathematical equation of the string theory involves a very troublesome part which is multiplied by (D-10), where D is the number of dimensions. Now the only way to get rid of this troublesome part is to make it zero, and this can be done if our universe actually has 10 dimensions(10-10 =0; Anything multiplied by 0 = 0). Thus, the theory it self predicts and requires the existence of ten dimensions including one for time. Now some can say that why not abandon this theory and find some other with 3 dimensions. Well, the theory makes very accurate predictions about particles, which match the current existing most accurate model called The Standard Model, and naturally combines Theory of Relativity and Quantum Mechanics in to one STABLE unit, which has NEVER been possible before.
So where are these extra dimensions you ask? Well, they are curled up to scales so small that right now, they cannot be detected directly even by the LHC, because it requires tremendous amounts of energy to ‘see’ at their scale which is of orders of Plank Length. A Plank length is the smallest distance at which the term length has a meaning (≈10¯³³ cm). Mathematics shows that these dimensions might be curled up in the shape of geometrical shapes called Calabi-Yau shapes, but their thousands of numbers makes it hard to tell which one exactly. Now you might say this is a wild claim, how can it be true. Well, let me help you with an example. Imagine a rope. As far as you are concerned, you can travel, in either forward or backward directions along the rope, so you will say its 1-D, but for a tiny ant, it can move forward-backward but also sideways, left or right, and so for it the rope is essentially 2-D. Similarly, a tall building if viewed from sufficiently far distance will appear as a simple line, a 1-D object, but it is actually a 3-D building. This is exactly what is happening here, in our universe. We experience only the expanded 3 dimensions and time, and miss out on the others because they are curled to astonishingly small sizes.
The interests in extra dimensions was sparked mostly by the sci-fi novel, Flatland, a place whose citizens were 2-D creatures, and identified themselves as the normal 2-D shapes, like a square, a circle, or any polygon. In such a place the common experience and life would be different. Ladies would say, ” a handsome square”, or you might call a lady ” a pretty triangle”. 3-D terms like height, “body” would be meaningless. A point is a zero dimensional body. When you put it in 1-D it can be stretched and called a line, in 2-D that line can be stretched in a newer direction and becomes a square, in 3-D this square becomes a cube. We cannot tell what it will look like in 4-D space, but when can tell what its shadow would look like, like your shadow in 2-D. This body has been named a ‘tesseract’, a 4 dimensional cube. We can show its image as a cube inside a cube with corners joined, but still it is hard to imagine what it actually looks like in 4-D.
A newer independent dimension means alternative ways to observe and interact with stuff in lower dimensions. You get newer perspectives, and directions to act in. In 4 dimensions you trouble of taking off your pants after a long day by pulling them down and all the hassle would disappear because you could just take them off through the fourth dimension(Like Sheldon tried to show in TBBT, but failed. Miserably). Let me put this in perspective. In flatland, all the creatures were ‘limited’ to two dimensions, they could not see “height”. For them, if they were to see a cube in front of them, they would see just a square, because they cannot view in the higher dimension of height. But when one of them became a 3-D being, he could explore the unexplored. He had access to this dimension of “height” , the new third dimension. He could see inside the 2-d creatures from above, inside the 2 -D buildings, all banks would be at risk because he could just “lift up” the gold in the third dimension, and all the beings of flatland would think that all of it just vanished magically. They cannot see him. Similarly, a 4-D being can steal money from our ‘closed’ 3-D banks through the fourth dimension. Still think your investment is safe?Higher dimensions answer many other questions, other than easing robberies and helping you taking off your pants, like why is gravity so weak? Basically, it gets ‘diluted’ in all the multiple dimensions, whereas the other forces don’t interact with them. ( you can read more about it online, but otherwise I am going to write a post on it shortly).
Higher dimensions have a lot of mathematical reasoning behind them. Experimentally, though they cannot be detected directly, yet, there are some other indirect ways of detecting them. If LHC in the near future detects a graviton, the particle associated with gravity, ,measuring its properties can help as evidence for higher dimensions. Another way is that if String theory is proved experimentally, one of its most important feature, the higher dimensions is also proven. This can be done by studying gravitational waves among other things. Higher dimensions are truly a treat for the mind. After all this you must be asking why are we living in a space that expanded in only three dimensions. Hold on, I will be posting about that and more in my next post to avoid making this one too long. Once I do, I will provide a link below. So stay close, enjoy science, and Happy Reading!
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-The Cosmogasmic Person
PS: If you wan’t to know more about these topics here are some suggestions:
1. Parallel Worlds by Michio Kaku
2. The Hidden Reality by Brian Greene
3. Flatland by Edwin Abbott Abbott