In Quest of Higher Dimensions – Superstring Theory and the Calabi

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In Quest of Higher Dimensions – Superstring Theory and the Calabi REVIEW ARTICLE 16 th August 2021 In quest of higher dimensions – S uperstring T heory and the Calabi – Yau manifolds Deep Bhattacharjee * , Sanjeevan Singh a Roy + * AATWRI – R&D Directorate Higher dimensions are impossible to visualize as the size of dimension varies inversely pr o- of Electro - Gravitation Simul a- portional to its level. The more the dimension ranges, the least its size. We are a set of points tion & Propulsion Laboratory, living in a particular point of space and a particular frame of time. i.e, we live in space - time. Bhubeneshwar, Odisha, India The space has more dimensions that meets the human eye. We are living in a world of hype r- space. Our world being a smaller dimension is flo ating in higher dimensions. The quest for the + Department of Physics, Birla visually of higher dimensions has been a fantasy to mankind but this aspect of nature is co m- Institute of Technology, Mesra, pletely locked. We can transform dimensions i.e., from higher to lower dimensions, or from Jharkhand, India lower to higher dimensions, but only through mathematics. The relative notion of mathematics helps us to do the thing, which is perhaps impossible in the experimental part of physical real i- * [email protected] ty. Humans being an element of 3 Dimensions – length, breath, height can only perceive one + [email protected] hi gher dimensions, that is space - time. but beyond that the notion of dimension itself changes. The dimensions got curled up in every intersection of the coordinates of space in such a way that the higher dimensions remain stable to us. But in reality it is h ighly unstable. In the higher dimensions, above 4, the space is tearing apart and joining again spontaneously, but the tearing portion i tself covered by 2 dimensional B ranes which acts as a stabilizer for the unstable d i- mensions. Dimensions will get smalle r and smaller with the space - time interwoven in it. But at Planks length that is 10 - 33 meter, the notion of space - time itself breaks down thereby making impossible for the higher dimensions to coexist along with space. Without space, there will be no ident ity of any dimension. The space itself is the fabric for the milestone of residing higher dimensions. Imagine our room, which is 3 dimensional. But what is there inside the room. The space and of course the time. Space - time being a totally separate entity is not quite separate when compared with other dimensions because it makes the residing place for the higher d i- mensions or the hyperspace itself. We all are confined within a lower dimensional world wit h- in a randomness of higher dimensions. Time being alik e like space is an arrow which has the capability of slicing space into different forms. Thereby taking a snapshot of our every nano - second we vibrate within space - time. As each slice of time represents each slice of space, s i- m i larly each slice of space re presents each slice of time. The nature of space - time is beyond human consciousness. It is the identity by which we breathe, we play, we survive. It is the whole localization of species that encompasses itself with space thereby making space - time a relativ e quantity depending upon the reference frame. The only thing that can encompass space - time or even change the relative definition of space - time is the speed, the speed far beyond the speed of light. The more the speed, the less the array of time flows. Sp ace - time being an invisible entity makes the other dimensions visible residing in it only into the level of 3, that is l, b, h. After that there is a infamous structure formed by the curling of higher dime n- sions called CALABI - YAU manifold. This manifold de picts the usual nature of the dime n- sional quadrants of the higher order by containing a number of small spherical spheres inside it. The mathematics of string theory is still unable to solve the genus and the containing KEYWORDS – Hypersurface – spheres of the manifold which can be the ultimate quest for the hidden dimensions. Hidden, as, Conifold Singularity – Higher the higher dimensions are hidden from human perspective of macro level but if we probe de e- th Dimensions – Glome – Torus – per into the fabric of the space - time of General Relativity then we will find the 5 dimension Calabi - Yau Manifolds – M - according t o the Kaluza - Klein theory. And if we probe even deeper into it at the perspective of Theory – Duality – Symmetry – string theory we will be amazed to see the real nature of quantum world. They are so marv e- Particles – Resonance - Mult i- lously beautiful, they contain so many forms of higher dimensions ranging from 6 to 10. And verse – Coordinates – No Ghost even many more of that, but we are still not sure about it where they may exist in a ghost state. After all, the quantum nature is far more beautiful that one can even imagine with a full faze of Theorem – Mobius Strip – Klein Bottle – Topology – D(p) - Branes weirdness. What is a dimension? – A dimension is an attribute by which dimension is measured by a single coordinate, whereas many the property of an object can be defined. Co - Dimension is an dimensions are measured by many coordinate. In normal we advanced concept which takes into account the observable use 'x', 'y', 'z', 'ct' – To measure the length, breadth, height and dimensions minus the unobservable one. In mathematics d i- space - time respectively. Sometimes for the sake of simplicity mensio ns are established by means of coo rdinates, A single 'x', 'y', 'z' are compacti fied within a single s patial dimensions 'x' and the 'ct' is denoted as the temporal dimensions Space - There are many and some are we can pass through a barrier Time. easily, we don't have to face difficulty is untying knots an d we can mage surgery without any penetration. What Physics say about dimensions? What is Hyperspace? Before 1 billionth billionth of a second of the Big Bang that is 1/1000000000000000000000000 our nature has 10 dime n- According to Str ing Theory our Space has upto 10 - sions but through quantum tunneling and tension force the Dimensions. Although sounds weird but still its a mathemat i- SYMMETRY got broken and our nature splits into a 4D and cal fantasy. Our Space can be imagined as a grid of numerous another 6D universe. 4D universe has a positive acceleratio n lines and within the intersection two lines there exists nume r- and it expands and 6D universe has a negative acceleration ous higher dimensions compactified in a K - Manifold or Cal a- and contracts. Laws of physics are simple in higher dime n- bi - Yau manifold. Our space has more dimensions that can sions but are stringent in lower dimensions. Transformation meet our eye. We are still unaware of many of the hidden from one dimension to other is impossible and a higher dime n- my s teries of di mensions of s pace and the se dimensions are sional object can visualize a lower dimensions but a lower called as h yperspace. Every known element of this nature like dime nsional object can not visualize higher dimensions. We Na, Ca, K, Mg, etc has a link to these higher dimensions. They will see why?? are made of quarks which are again made up of strings which vibrates at Planks Length that is 1.6*10 - 36 meter and they are Flatland vs. Higher Dimensions! linked with the higher dimensional universe. The strings v i- brate and each mode of vibration corresponds to a specific The minimum dimensions possible theoretically for an object element of this known universe. Our observable universe has to exist is 2 D. So, a piece of paper if be a uni verse of Flatland more than 4Dimensions but in essence only 3 - Dimensions are then all the square, circles, triangles are existent in this dime n- tangible. And our duplicate universe in a multiverse model has sions. They c an move freely sideways but can not move u p- 6 - Dimensions but in e ssence there can be more than 10 - wards and downwards because in doing so the Flatlander's will Dimensions but “NO GHOST THEOREM” forbids them to require to jump from 2 Dimensions to 3 Dimensions world and enter into physics because of their negative norms. A nd there that is not possible in viewpoint of Physics. Similarly we live exists any universe of a much more d imensions but they can in a 4Dimensional world but in actual our co - dimension is 4 - be beyond our known intuition & a variety of complicated 1=3. Why? Bec ause the temporal dimension of S pace - Time is creatures might live inside it. To us the higher dimensions are beyond our reach. It exists as if a continuous flow encompas s- complicated just like the 2D FLATLANDER's with the 3 D i- ing the lower dimensions. mensions. Why do we exist in a 3 - Dimensional world? Investigating the possible shapes of the unive rse – Our u n- iverse is definitely not a square or a triangle. The circle being Actually we being an object of 3 Dimensions are capable of a universal shape dominates our universe in the form of mu l- moving up, down, top, bottom, sideways – But we can not b e- tiple coordinates or higher dimensions. Nobody knows for hold the higher dimensions.
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