1 March 15, 2020 Split Second Intersection Deep Bhattacharjee Split Second Intersection Deep Bhattacharjee (Hobbyist Theoretical Physicist), Independent Researcher, KOLKATA, WEST BENGAL, INDIA Correspondence should be made at [email protected] Phone: +91-8282923025 ABSTRACT An arbitrary advanced civilization might have the technology to travel back and forth in time and that too within a large timescale like say ‘a thousand years’ into the past or future. But to us, in present day scenario, this ‘time travel’ seems impossible. Although many mathematical thesis have been published with sound theories about the structure and definitions’ of ‘time travels’ but still from an engineering feet, it’s practically impossible. Therefore, the time travel is a far more mathematical abstract concept and a source of science fiction for today’s physicists. However, theorists are not restrained by any limits or bounds and they likes to explore the plausibility of travelling through times and its fundamental overlying principles. Firstly, its necessary to develop a theory that is suitable for humans to travel in time like ‘without falling inside a black hole’ or ‘without any need of exotic matter’ or ‘without creating any paradoxes’ but we will consider ‘micro black hole and high gravity potentials’. So, to develop a more practical theory, its necessary that one needs to consider the factors which is not too hypothetical to be achieved by human beings at the present notion of technologies available to us. So, if such a theory can be achieved with a high degree of accuracy then the travelling through time will be possible by manipulating the circuits and machinery and creating a time machine after all at the end. However, travelling to future, although is theoretically plausible, travelling to past is always restricted due to the nature of ‘the birth of various paradoxes’ that may happen in due times. So, to extent the notion of casual loops without getting too far away with the absurdity of the physics, this paper will view the time from a new perspective and then it will aim to develop a theory so that its best fit within the current feats of technological challenges that we are facing today. Starting from the ‘relativity’ which first gives the scientific definition of ‘time travel’, ‘time’ as a whole has always been considered as 4th dimensions along with space and the other 3 spatial dimensions being orthogonal to them. But, what if there already exists an embedded 2-time dimension [1][2] in our space-time and there is already existent ‘causal loops’ in our universe but what needs to be done is the action of a ‘temporal agent’ who can make the hidden 2nd dimensions of time prominent ‘from hiding’ and we are free to explore the ‘temporal loops’ in our space-time. This temporal agent can be any human beings with a high source of available technology or can be in any form of machinery like the ‘time machines’ which will allow the ‘embedded 2 nd dimensions’ prominent from the hiding so that humans could explore the feats of ‘time travelling’. This paper is typically presented to deal with these ideas of 2nd time dimensions and causal loops in space-times where any object (or rather humans) can travel back and forth in time riding on these 2-time dimensions. My objective will always remain to focus ‘time’ from the perspectives of ‘2 dimensions’ in the form of a ‘circle’ rather than a linear straight line of 1 dimension and thereby manipulating the idea of this extra dimensions in such a way that, travelling through time can be achieved in practicality without getting washed away by too much abstract mathematics as theoretical physicists often likes to do. Its not quite easy to present time in such a form but I will try my best to do so and also keeping in mind that my theory is consistent with the current available technological challenges faced by experimental physicists and engineers in designing a time machine. I will also deal extensively with ‘imaginary time’ [3] and its consequences. A consistent theory is always necessary for practical implementation and that’s what I always intend to do and this paper is just the reflections of my ideas to provide an easy through to ‘time travel’ by focusing the extra hidden dimensions of time in nature. The possible outcome of these phenomena has been discussed thoroughly using logics & mathematics which will insight into a far more in- depth concept by taking us in exploring the 2-Time Dimensions (Instead of 1) [1][2] in this universe and the related outcome or consequences of this more than 1 Time Dimensions. Moreover, this paper aims to provide the repetition or Looping of Timelines in a 2D Minkowski lightcone with the help of induced mathematics (exponential wavefunctions) which results in the occurring of same event in a synchronic pattern as predicted by different fiction stories along with a desired property which will pave the way to prove that, ‘N” past timelines are connected with “N+1+1……” future timelines and it is the law of nature to select the appropriate future timelines related to the past timelines in which the past timelines will be attached to those future ones which have the least degrees of errors in the “exponential wavefunctions” introduced in this paper. After completing this, we will go to a further analysis of the ‘self inflicting timelines and the death loops, which has been a source of major Sci-Fi motion pictures and we will mathematically prove the minimal and the maximal amount of “time loops’ in our 4-Dimensional world. We will give an insight about the metric by taking time as ‘imaginary’ and how it solves the ‘singularity problem’ from Schwarzschild and Lemaitre metrics respectively. Then we will proceed to see the deterministic nature of time and the ‘topological mapping’ of time with a predefined coordinates (as specified by the nature) for a normal person as well as time traveler with application to ‘spatial divergence’ which will ultimately lead to the fact that, the more you travel in time, the more its harder for the time machine due to the increase of chaos and randomness. 2 March 15, 2020 Split Second Intersection Deep Bhattacharjee 푑퐿 INTERPRETATION = − ∫ 푘2 푑푠 푑푡 Section I Where L is the decreasing length, as per the interval taken over the curve as 2π, k is the curvature and ds is the change of arc length over the curve where Time has always been in a straight line with one way orientation that is in each shrunken circle will preserve its symmetry in space-time manifold or future and also at a specific pace such that ‘one cannot move too fast in ‘universe’ by the killing equation… future neither can move back to the past’, but irrespective of this, Einstein’s theory of relativity teaches us to dream about travelling in time unless and ξ푎,푏 − ξ푏,푎 = 0 until some special conditions are imposed. Time has always been a singular dimensions unlike space which has many dimensions with varying degrees of where , is the covariant derivative between them. To objectify the idea freedom, all orthogonal to each other. Time, as we know, has no such further, let’s develop a complex integral of ‘unit circles’ in both ‘clockwise’ degrees of freedom, that is, in a way it is ‘stringent’. But although Einstein’s and ‘anticlockwise’ directions as per the equations… theory teaches us to dream about time travel, its only possible if one can create a ‘CTC or closed timelike curves’ in space-time which is quite . 1 2휋 1 − impossible to make from the present technologies. However, if one tries to 푂 = ∮ 푑푧 = ∫ 푑푧 = 2휋 푐 푧 0 푧 explore the CTC’s of nature, then he has to enter inside a ‘wormhole or Einstein-Rosen bridge’ which is near to impossible in aspects of present day . 1 −2휋 1 technologies. But, time can have ‘an additional degrees of freedom’ if we 푂+ = ∮ 푑푧 = ∫ 푑푧 = −2휋 푧 푧 think time as a closed loop, or if we extend the 1-dimensional line to a 2- 푐 0 dimensional circle. Then time can loop back to itself and that’s what my main They merge yielding the positive results assuming Radius always 1…. aim is, if time can be a closed loop, then we don’t have to create the CTC’s rather, CTC’s are already there and we just need to grab them and focus 푂− ∗ 푂+ = 2휋 ∗ −2휋 = 4휋2 … 퐸푞푢푎푡표푛(∗) them to make us travel in time. If we consider our universe as a R3 manifold or a sphere, then, there are numerous R2 circles embedded in the surface Where 푂− and 푂+ are the opposite orientations which when merge in the area of the universe. This R2 circles are the hidden second order dimensions time machine ‘assuming its always at the centre’ yielding a surface area of of time and by considering this embedded dimensions, one thing I would like 4휋2 which is that of a ‘HORN-TORUS’ such that there are not 2 R2 circles but to point out is that, ‘time doesn’t actually increases the dimensions of space- numerous circles of same length and are always countable to even such that time’ rather its hidden, embedded inside the R3 sphere as a R2 circle with the every clockwise oriented R2 circles have an anticlockwise orientated R2 pair dimensions of R2 circles hidden on the surface area of the R3 sphere with the giving us the below diagram… centre of the R3 sphere being the same as that of a R2 circle, ‘that is they are sharing a common center’.