Split Second Intersection Deep Bhattacharjee

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 = 2휋𝑖 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 = −2휋𝑖 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+ = 2휋𝑖 ∗ −2휋𝑖 = 4휋2 … 퐸푞푢푎푡𝑖표푛(∗) 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’. It is said that ‘a picture speaks a thousand words’, therefore, I felt the necessity to introduce a picture here…

Which clearly looks like a ‘HORN-TORUS’. Here the middle blue spot is the time machine and the even R2 circles it shrunken from the boundary of R3 spheres appears to be that of a ‘HORN-TORUS’ such that the particles trajectory along the R2 circles will yield a ‘stress-energy-momentum tensor’ in the form of the matrix having signature of (+,-,-,-) with all the positive energy values while travelling through time (Provided we have 2 Dimensions of time instead of 1) as….

3 2 The ‘universe boundary’ is a giant R sphere with many R circles sharing the X0 X1 X2 X3 universe center labeled in the picture as ‘hidden circle 1 and 2’ as only 2 circles are shown here. Now, if we introduce a time machine and as its seen E T00 T01 T02 T03 from the picture that ‘the time machine is at the centre of the universe’ 1 mv T10 T11 T12 T13 obviously stating that ‘every point on the universe is at its centre’, the ‘time 2 machine has the capacity, or rather the arbitrary advanced civilizations that mv T20 T21 T22 T23 2 created the time machines has the technology to grab the R circles and 3 mv T30 T31 T32 T33 shrink them to a much smaller circle such that, the ‘time machine’ will capture the R2 circles in always an ‘even number’ as because each R2 circles are of opposite orientations meaning one is going from ‘past to future’ while The interesting fact is that, when the 2D circles of time are spread across the other is going from ‘future to past’ meeting at the common epicenter in the boundary of the universe, they are embedded in R3 Spheres behaving like 1D time machine where the ‘temporal agent’ has shrunken the even R2 circles in Time with 4 Space-Time dimensions but when they shrink and got close, they such a way that they gets joined inside the time machines and thereby behave as 5D Space-time (3 Spatial dimensions + 2 Time dimensions) as allowing the time machine to send a ‘particle’ or ‘a human’ across the loops because this shrinking makes the other hidden dimensions of time ‘either in past or in future’ to accomplish the travelling in both directions of embedding in the universe boundaries clearly visible in close proximity of the time. The circles if we assume are always of ‘unit radius’ and as usual as they ‘time machine’ and as the circle is unitary as assumed before, we will take are shrunken from the large sized circles, the 2 shrunken circles are always the (Major Radius ‘R’ and Minor Radius ‘r’ both as 1) getting the surface area be in the same shape then, this curve shortening [4] can be best expressed same as Equation (*) thereby paving the way of 2 Time Dimensions making a via this equation such that… Horn Torus of Surface area calculated as…..

3 March 15, 2020 Split Second Intersection Deep Bhattacharjee

퐴푟푒푎 표푓 퐻표푟푛 푇표푟푢푠 = (2휋푅) ∗ (2휋푟) = 4휋2 ‘past’ of ‘t=2’, that is he can reach to the past of his commencement of journey through the wormhole having keeping his energy conditions as The Particle will act as a time-traveler moving back and forth in time along ‘positive’ definite. the formed CTC’s with the central spot acting as a time Machine. Here Sᵀ be a curved manifold with the chronology horizons 퓗 [5] generated To analyze further let’s consider infinitesimal distance dxu and dxv such that by ‘time-machine T’ with generators 퓖 [5] such that... the ‘stress-energy-momentum tensor’ satisfy the relations…

T --> 퓖 (퓗 )⁺

. T --> 퓖 (퓗 )⁻ 푢 푣 ∮ 푇푢푣 푑푥 푑푥 > 0 퐶푙표푠푒푑 푇푖푚푒푙푖푘푒 퐶푢푟푣푒푠 Where 퓖 (퓗 )⁺ be the future chronology horizon and 퓖 (퓗 )⁻ be the past 푂푟, chronology horizon. . 푢 푣 ∮ 푇푢푣 푑푥 푑푥 ≤ 0 퐶푙표푠푒푑 푇푖푚푒푙푖푘푒 퐶푢푟푣푒푠 Let P be a set of points along O⁺ and Q be a set of points along O⁻ then...

O⁺ ⋂ O⁻ = Time Machine T with P ⋂ Q points. There can be either of the 2, which we will decide by the ‘eigenvalues’ of the 퐝훙 energy as according to Schrodinger Equation, 𝑖ℏ = ℏ훚훙 Where, ℏ훚 is 퐝퐭 Let M be a particle travelling from 퓖 (퓗 )⁺ to 퓖 (퓗 )⁻ then the Particle will 퐝 the Eigen value of the energy operator of < 훙 |𝑖ℏ | 훙 > with 훙 as the 퐝퐭 satisfy a mapping U such that... Eigen function. U₁ : 퓖 (퓗 )⁺ --> 퓖 (퓗 )⁻ 푇 is the stress-Energy-Momentum Tensor having a (+,-,-,-) Signature which 푢푣 suits with our universe having positive energy and negative pressure. If we a ‘T’ or ‘Present Time’ or ‘Time Machine’ or "t=2" is the union of O⁺ ⋂ O⁻ or the take 푇푢푣 as the Unitary Matrix then we can form V as the timelike vector along the curve with Va being an Eigen vector having its components vector directions 2πi ⋂ - 2πi. calculated as… U₁ be the compact region 퓢 such that... 1 0 0 0 1 1 0 −1 0 0 * 0 = 1 * 0 퓢 = Sᵀ(ᶜ). 0 0 −1 0 0 0 0 0 0 −1 0 0 X * 2πi(P) ⋂ X * -2πi(Q) satisfies at location 퓢 . 푎 푎 Which satisfies the Eigen equation 푇푢푣 푉 = λ푉 with λ = +1 and Eigen Provided "X" has the same value in both cases thereby making the Horn 1 Torus of Unit Radius 4π². vector 푉푎 = 0 . 0 0 There can be more than 2 curves, so, let’s consider 4*2 even curves such that if the picture can be seen from upwards leading to an image where colors are . 푢 푣 So, we can conclude ∮퐶푙표푠푒푑 푇푖푚푒푙푖푘푒 퐶푢푟푣푒푠 푇푢푣 푑푥 푑푥 > 0 푡ℎ푎푡 𝑖푠 = +1 as used to denote the even curves and the ‘T’ point is denoted as the ‘Plain of

λ of 푇푢푣 = +1 . Singularity’ as shown below…

Therefore, we can conclude that the energy will remain positive throughout the curve or CTC’s. Now, from the 2 R2 circles, we can deduce a wormhole having its one mouth at future point while other at a past point with another additional mouth having more ‘past’ relative to the ‘past’ mouth as it will enable a traveler to reach the point in time which is before than that he had travelled his journey as ‘one past mouth of the wormhole will move relative to the other mouths in hyperspace. The below picture clearly illustrates this point having times labeled as ‘different values of ‘t’’…

Diverse Mapping like....

2πi(P₋₁) ⋂ -2πi(P₋₂) 2πi(P₋₂) ⋂ -2πi(P₋₃) Here a person starts his journey from ‘t=2’ at present reaching ‘t=3’ in the 2πi(P₋₃) ⋂ -2πi(P₋₄) future while if he goes back he can be there at the mouth ‘t=-1’ which is 2πi(P₋₄) ⋂ -2πi(P₋₁) 4 March 15, 2020 Split Second Intersection Deep Bhattacharjee

‘temporal agent’ can accommodate for’ time travel’. Now, the time machine Considering P having a Maximum limit of 4. can be ‘active or passive’ temporal agent. In case of an active agent, the time machine will always be with the time traveller or temporal sub agent or (Here 1 is A, 2 is B, 3 is C, 4 is D) agents in course of time travel which means the time machine will also travel in time with the time traveller to past or future and helps the sub agent to 퓖 (퓗 )⁺ is always at the Cauchy Horizon having a single future identity with 1 return back in time after completing the time travel. But, if the temporal Past identities 퓖 (퓗 )⁻. agent is possible, then the consequences will be much more dangerous as ‘it can only be used to send a person back and forth in time’ but as the time Time is dilated in both mouths.... machine or temporal agent itself is absent from time travelling, therefore after the person gets into its destination time, there will be no time machine As T'(퓖 (퓗 )⁺) ≠ T"(퓖 (퓗 )⁻) to return him back from that point in time to the point from where he begins his journey. This notion is dangerous and can be used to send criminals to a Where all T' T" are different given by the time dilation formulae 혵ˣ = 혵 √(1- further past or future or if some time traveller having a passive temporal V²/C²) agent comes to us, then we may use our passive technology to send him back in his destination. The final mapping is done as, There are 6 parameters that needs to be programmed in the time machine ᴄʟᴏsᴇᴅ ᴛɪᴍᴇʟɪᴋᴇ ᴄᴜʀᴠᴇs: { 2πi(P₋₁) ⋃ 퓖 (퓗 )⁺ } ⋂ { -2πi(P₋₂) ⋃ 퓖 (퓗 )⁻}... EQ(†) for proper function and we can’t just programmed the parameters as per our free will, rather we have to know what parameters the nature allows the (where a Particles goes from Present to Past taking the CTC (O⁺ ⋂ O⁻) as (P₋₁ - time machines to follow in space and time and we should program them -> P₋₂). accordingly. They are as follows...

This is enough mathematics, now its time to appreciate both the beauty and  What will be the place of arrival? As in all cases a ‘temporal disaster of time travel and finding out the relation between spatial and relocation’ occurred but its not necessary that ‘spatial relocation’ temporal relocation as travelling through time. So, the philosophy is rather has to be occurred as because you can go to the same place in complicated and we would be seeing it below. different time or different place in different time. But if its in ‘same time’ then its meaningless to use a time machine as Section II because ‘temporal relocation’ has to be occurred even if a ‘spatial relocation’ occurs or not. One of the most prominent consequences of the time machine is anti-gravity,  How many seconds will the time traveller or the ‘temporal sub not normal gravity. Its the negative pressure zone which is created by virtue agent (or agents) will last in this ‘temporal relocation’ provided of the wormhole, which would such you inside the wormhole. This anti- there is any ‘spatial relocation’ or not. This can be expressed as gravity zone which when created at the close vicinity of the wormhole will make every such object to lift up in space due to mass-reduction and loosing how long will a person becomes there in his new destination will of apparent weight principle. The wormhole which acts as the time machine depend entirely on how long the time machine or temporal agent is actually a point of the unification of gravity and electromagnetism. As can accommodate him to stay there by keeping the wormhole because the boundary of the wormhole is made of photons and inside it mouth open. there is gravity although at the mouth there is anti-gravity. This shows us the  How many days forward or backward can a person travels in phenomena of the famous Kaluza-Klein [6][7][8][9] hypothesis where the time? It can be 1000 years past or future or just some 2 or 3 hours unification of gravity with electromagnetism takes place. Notionally, there in the back or future. This solely depends on the magnitude and are 5 dimensions in space-time after the wormhole is getting created like the ‘3 space dimensions’ and ‘2 time dimensions’ provided the 2nd dimensions of power of the temporal agent that it can behold while sending the time is prominent now due to capturing of the ‘2 time dimensions’ by the temporal sub-agent back and forth in time. micro black holes which as a result is a ‘noncompact’ [5] regions as because  How many ‘sub agents’ can the ‘temporal agent’ allows to travel the ‘time loops’ passes through singularity and this leads to the destruction in time. Is each sub-agent be accompanied with a separate agents of time loops via any outside information, but we will consider t he or a single agent can accommodate a number of sub agents to ‘singularity’ to be enclosed properly, or the ‘micro black hole containing the travel back and forth in time. singularity’ to be enclosed properly by the time machines thereby making it a compact region of space-time containing the CTC’s. The unification of  If a causal loop is created then ‘is it possible a sub agent can meet ‘gravity with electromagnetism’ will make another small spatial dimension his own self forward or backward in time?’ but this needs to be visible making the wormhole of 6 dimensions with ‘4 space dimensions’ and prevented and we will come back to the logic shortly. ‘2 time dimensions’. Assuming ‘temporarily we are neglecting the 2nd  The more the person travels backward or forward in time, the dimensions of time’, the mathematics of gravity with electromagnetism is more the spatial [10] and temporal divergence occurred and all given by ddecomposing the metric, the 5D metric potential is… these will occur from the present point in ‘Minkowski lightcone’,

that means the more you are travelling, the more the boundary of 𝑔̃ = 𝑔̃ + ∅2 퐴 퐴 푢푣 푢푣 푢 푣 the cone diverges and how much divergence can be accomplished or hold by the temporal agent regarding the temporal sub agent Where 퐴푢 is the 4-Vector current potential which will couple with gravity. as because ‘randomness’ or ‘entropy’ will increase which may But the Anti-Gravity is also existent there, moreover its very much needed to collapse the time travel, hence, ‘What will be the maximum keep the mouth of the wormhole from collapsing. number of days or months the time machine can afford?’ before getting collapsed in temporal and spatial relocations. The below Now, the time machine is the ‘temporal agent’ while the time traveller is the diagram will give a clear insight about this... ‘temporal sub agent’ provided that in each time machine or ‘temporal agent’, there can be more than one ‘temporal sub agent’ and proper mathematics is required to limit the maximum number of ‘temporal sub agent’ that a 5 March 15, 2020 Split Second Intersection Deep Bhattacharjee

is better to travel only in future. Here, one thing needs to be noticed that the theory of ‘Split Second intersection’ will intersect between two splitting reality of the same temporal sub agent or the time traveller in a form that ‘no time traveller can encounter its past self or future self if he travels through time’. But is the reality indeed so paradoxical? What if we can see the time travellers from future or the future time travellers can see us if and only if they travels in time to past up to the maximum of ‘his birth time’ or to future up to the maximum of ‘his death time’, now, there rises one question that... can any future civilisations prepare any time machines so strong and advanced that they will violate the ‘Split Second intersection’ and can travel in past to a distance of thousands or millions of years back. Is this possible? [10] of course if this has been possible then there will be no more paradoxes as their own self won’t exist in such far times but their ancestors will exist and Now, comes the main theory of ‘Split Second intersection’ that... killing the ‘grandfather of the grandfather of the grandfather...... ’ of him will lead to paradoxes, but we have to question that, in case of chronology to the ‘We can only travel in future up to the point when we die as past is it plausible for anyone to remember the ‘grandfather of the because if we go further than that then we are not existent in grandfather of the grandfather...... ’ and get him killed. No, he couldn’t do it reality for that future time frame beyond our death and hence no because again ‘Split Second intersection’ will come in the way. spatial or temporal relocation could be occurred’ From the ancient historic times to the modern days, UFO’s have been Suppose a person wants to travel in time in 2030, 10 years ahead encountered in thousands in sight and in pictures and we believe that those of his time but he forgot to take his recourses like money or other UFO’s are actually the ‘Extraterrestrial Biological Entities’ or Aliens from a important things with him in the course of travel, so, in that case different planets who are so advanced that they can travel to thousands of the person as a time traveller is an accelerated observer while his light years without the need of any propulsions through wormholes to see own self existing in 2030 as an inertial observer. Its just like a ‘twin the humans of earths. But, all these can have some different meanings like paradox’ of both twins. It will simply be a disaster if the person ‘What if? They are not coming from any far away planets?’ but are actually goes to his own house to ask his own self that ‘give me some coming from Earth by means of ‘back in time’ to see how their past selves money’, this is a total disaster and so we are not allowed to do would look like? This can be a reason to believe that our future ancestors this. Hence in the same reason if our future self in 2030 will invent who have discovered a time machine actually comes in past in the form of a a time machine and travels back in 2020, we can’t see them as its UFO through the wormholes to see the past of the Earth. We can’t blame this prohibited from happening by the ‘Split Second intersection’ . idea for no apparent reason as this can be viable both in terms of advanced future technologies and advanced civilisations.

Now, there are ‘2’ open questions which I need to ask about this... So, if this is the case, then we can argue that ‘time machine’ would be

created in far future. And in future if there is no bar in technological 1. How many attempts could a time machine makes advancements then these UFO’s are the actual time machines or temporal before getting collapsed or for each travel a time agents with the EBE or Aliens being our future ancestors. And we can’t rule machine needs to be newly created, if not then, what out this fact either! is the number of attempts that the time machine could make before getting collapsed? Many sightings of UFO’s are seen that they appears out of nowhere and they

vanishes in thin air which opens up a possibility that ‘there can be portals in 2. If a person travels from 2020 to 2030 but his death time and the advanced beings from future earth knows how to harness occurred at 2025 (which he of course doesn’t know in them”. 2020), so, in that case can he travel beyond 2025 to 2030? Because ‘Split Second intersection’ will not hold Section IV true as ‘he can only travel into the future up to the time he lived or else, there will be no dummy copy of Now, it has been customary to show a working model of the Time-Machine. him from which he needs to hide himself in the future’. But, there seems to have a compactified dimension and to compactify dimensions or to take into account the compacted dimensions we have to So, the important question is ‘does time travel induces immortality?’ As the consider again the Kaluza-Klein metric such that the metric has the form… person dies in 2025 but the temporal agent takes him in 2026, he will simply vanish at the point he landed from the temporal agent to the future as 𝑔̃푢푣 𝑔̃푢5 𝑔̃ = ( ) [11] because he is simply non-existent in that time fame or he in his own timeline 푢푣 𝑔̃5푣 𝑔̃55 gets died in 2025. This also proved the point that ‘past, present and future exists simultaneously’... So ‘Split Second intersection’ works afterall. Here Klein provided a topology of the fifth dimension to have a circular topology having ‘y’ as the periodic coordinate as 0 ≤ y ≤ L where L = 2πR Section III where R is the topology of the circle R2.

This point is quite credible that we haven’t found any time traveller from Now, as gravity and electromagnetism has been magnified in this 5th future. Well, if time machines can me made some hundreds not less than dimensions, we have to consider the generic case of the unification while thousands of years into the far future, then why not the time travellers come considering the wormhole. Therefore, the internal circuitry of the time to the present to see their own self or to see the past world. There is a fact machine can be given as the picture… that time travelling in past leads to different sorts of paradoxes, therefore it 6 March 15, 2020 Split Second Intersection Deep Bhattacharjee

compactified dimensions would act like a bridge through which a particle of mass ‘m’ can pass in one direction from past to future and in other direction from future to past provided that the 2 2D timeline has an opposite orientations. The BH will be covered by a metal conductive oblate sphere which will be connected to a high voltage circuit that will provide 2 electrodes with the positive electrode bounded inside the oblate sphere giving positively charged ions and the negative electrode at the outer surface area providing negatively charged electrodes. There will be small pores in this oblate sphere by which the positive charges from the front will create a push by moving towards the negative charges outwards and attracting with them and by this an artificial anti-gravity field will be generated outside the oblate sphere whereas a high potential gravity field will be generated to the centre of the sphere will help to preserve the micro BH from getting washed away completely. I have conjectured that through this mechanism we can preserve the BH and help in creating a time machine capable of transferring a particle back and forth in time. In this picture, we should consider the presence of the extra dimensions that is required to bring the Black Hole formation from 1019 GeV to 1 TeV. This can Here one thing needs to be mentioned that when the particle comes closer only be achieved by the increment of dimensions provided we have a mass 2 to the BH, its lightcones will be tilted along the plane making a transition ‘M’ concentrated on a very small radius of SR = GM/c , with the reduced from timelike to spacelike in the following equations as… Compton wavelength is λ = ℏ/Mc, this summarizes the equation as…

2 2 푑푆 →푇푟푎푛푠푖푡푖표푛 푓푟표푚 푡푖푚푒푙푖푘푒 푑푆 푡표 푠푝푎푐푒푙푖푘푒 푑퐿 푑퐿 GM ℏ ℏ푐 ℏ퐺 푆 ≈ λ = ≈ ≡ 푀 = √ 푎푛푑 퐿 = √ 푟 c2 푀푐 푃퐿 퐺 푃퐿 푐3 And the change in the area of the particle will decrease logarithmically as due to Fitz-Gerald Lorentz Contraction as To probe into the Plank Length and Plank mass, we need such a high energy 퐴 that modern technology is not sufficient to do this; therefore by imposing the ∆퐴푟푒푎= 퐿표𝑔̃푒 extra dimensions ‘k’ as (4 + k) we can reduce the energy scale from 1019 GeV 퐴 − 1 to 1 TeV or 1000 GeV.

However, the condition for imposing extra dimensions is very rigorous and this has to be implemented by taking the Gauss Law. Moreover, Gravity as a force provides a hierarchy problem where it is about 1024 times weaker than Electro-weak scale. The weakness of gravity can be thought of ‘k’ extra spatial dimensions large than the weak scale and this large extra dimensions can have the size of 10-13 cm if ‘k = 1’. [12]

The new dimensions can be compactified with the periodic identification as 푦 ~ 푦 + 퐿 [12] 푘=1 푘=1

퐺푚 푚 Now Newtonian gravity states that 퐹(푟) = 1 2 which can be generalised 푟2 Clearly we can see the lightcones getting stretched as they arrive in close in any number of arbitrary dimensions such that if a mass ‘m’ is there at the vicinity of the BH. origin, then, the distance 푟 ≫ 퐿, they will look like an infinite ‘k’ dimensional line where ‘k=1’ as either 2πi or -2πi which when merges forming the Now, there is a formulation that we need to make. The necessity of the equation O⁺ ⋂ O⁻ ≡ 2πi ∗ −2πi = 4π2. formulation arises from the fact that, nothing can cross the singularity. However, as we can see that singularity is the notion of ‘infinite time’ hence Considering this above picture if we consider a cylinder C around the ‘k=1’ if the 2D timelines passes through the singularity then the very notion of Dimensional line then this cylinder with length ’l’ will act as a wormhole singularity will forbid this. Hence, we need to make a minute change in time collapsing into the 3 dimensional Black Hole forming the relation… as we have already mentioned O⁺ ⋂ O⁻ ≡ 2πi ∗ −2πi = 4π2 where the ‘Plane of Time’ is imaginary. Hence, it is presumed that the time would also . ∫퐶푙표푠푒푑 푆푢푟푓푎푐푒 퐶 퐹푑푆 = 푆3+푘(퐾=1)퐺4+푘(푘=1) ∗ 푀푎푠푠 푒푛푐푙표푠푒푑 𝑖푛 퐶 [12] be imaginary. The benefit of this imaginary time is that ‘the singularity can be totally removed and the singularity is non-existent which makes the journey 푙푘 through the ‘Plain of Time’ without any hindrance’.... In other words, The 푀푎푠푠 푒푛푐푙표푠푒푑 𝑖푛 퐶 = 푚 ∗ where Lk is the compactified dimensions 퐿푘 singularity is smoothed out by imaginary time. having the particle transported through wormhole has mass m. The formulation can be made by... Now, to clarify this picture, we have used Electrohydrodynamics or Semi- Quantum Kinetics and its actually a conjecture about the internal circuitry of ∆2= 푥2 + 푦2 + 푧2 − 푡2 the time machine. At 1 TeV a micro BH would be formed with a singularity at π the centre. The BH being rotating rapidly will end up as the victim of Hawking Performing a ‘wick rotation’ by and taking time ′푡 = 𝑖푡′ the equivalent Radiation which will radiate the BH away. We can consider the singularity as 2 relation to the above equation is... the Kerr singularity, a noncompact region which is subject to 2 2D time Dimensions that actually makes the BH a time machine where a Cylinder C of 7 March 15, 2020 Split Second Intersection Deep Bhattacharjee

∆2= 푥2 + 푦2 + 푧2 + (𝑖푡)2 2. The person is not above the ground, he is stick to the ground which means the Gravitational constant holds not only true for men but for the trees, Or, buildings and everything’s around it even lights but it's too small to gets observed. 2 2 2 2 2 ∆ = 푥 + 푦 + 푧 − 푡 3. The sun is setting and hence it's in horizon not zenith. As, the Black hole will be faded away by Hawking Radiation and it will ultimately lead to the Schwarzschild metric with a Signature (+, −, −, −) as 4. Ponzo illusion holds true as the sun irrespective of large distances appears larger than smaller. 2푀 푑푟2 푑푠2 = (1 − ) 푑푡2 − − 푟2(푑휃2 + 푆𝑖푛(휃)2푑∅2) 푟 2푀 1 − 5. Sunlight turns into reddish hue. 푟

Assuming (G = c = 1)... 6. The street where the leaves are not protecting it from the Sun has more light than the other parts. If we take 푑푡2 ≡ (𝑖푑푡)2... the metric signature will be (−, +, +, +) 7. Glasses of buildings reflect the sunlight. And the corresponding metric will be... 8. The shadow changes with every small perturbation the person made. 2푀 푑푟2 푑푠2 = − (1 − ) 푑푡2 + + 푟2(푑휃2 + 푆𝑖푛(휃)2푑∅2) 2푀 9. Although the road is parallel, but the projective geometry shows that the 푟 1 − 푟 footpaths are appearing closer to each other in the far distance guarded by the men. Now, to consider the particles own frame while travelling through time, we would consider the Lemaitre coordinates of the time component as.... 10. If any extra person comes into the picture then, the other variables with respond to the new simulations of the added person and the whole scenario 2푀 2푀 푑τ = 푑푡 + √ (1 − )−1 푑푟 [14] [15] changes thereafter. 푟 푟

12. At the left footpath, there is a road marker and that road marker in red is Where the coordinates ‘dt’ of Schwarzschild coordinate is changed to ‘푑휏’ visible than other colors as red light scatters the least and hence visible the most. 1 2푚 From this the time frame X0 will be ( 휕 − √ 휕 ) where this X0 1− 2푚/푟 푡 푟 푡 THE MOST IMPORTANT PART will become spacelike as the worldline of the infalling observers will tilt.

Therefore, introducing the 2nd Time dimension with 3 Space Dimensions, that These observations exist as because there is an observer. If there is no one to [4] got increased by another 1 Space dimensions due to Kaluza-Klein effect and observe then the observations cease to exist. there lives the normal time dimensions total about 6 all being perpendicular to one another is really a diverse concept in the theoretical physics provided Each single variable has several variables attached to them to make its the time is ‘imaginary’ paving the way for time travel. position in this earth perfect and each variable when respond to other variables, the previous simulations gets multiplied. Section V Now, we took into consideration the variables attached mostly to the Consider an image on your mind..... A person is walking in a streets alone shadow & light. If there are other variables like the buildings and cars and during a setting sun whose hue is coming across the branches of the tree, and trees then each will have several other variables attached to it. This there are buildings in both sides of the footpath, it appears as if the parallel simulation represents itself to another simulation which again responds to footpath is getting merged in the distance due to projective geometry and the another simulation which again responds to another simulations which to streets are half lighten and there is only one person walking on the road. another depending upon the previous one and its observations. So, simulations are increasing exponentially by responding to other simulations The interpretation of the image is that every possible variables associated and this exponential increase in simulations is a fact that the "Nature tries to with this picture needs to be perfect. adjust itself constantly from creating any errors that might light an alarm to the observer that, this is a simulation, not a reality" [13] Nature behaves as a huge supercomputer and it gives the simulations which are too perfect to get distorted. So, reality is a simulation of exponential wavefunctions and we live in a programmed world where the nature as a supercomputer programs our What are the conditions that need to be fulfilled to prove that this is a identity into precise detailing so that our mind doesn’t arouse any suspicion. perfect simulation? We live in an augmented reality of simulation. And this simulation can only Condition.... be observed when there is an observer. Else it doesn’t make any sense. That's the Anthropic Principle. Universe tends to exist as humans are there to 1. The person has a shadow which is inclined as per the position of the sun observe every details of it. (that is Sun is in front and the shadow is in back) and cut off in certain regions because of the tree above him. [13] 8 March 15, 2020 Split Second Intersection Deep Bhattacharjee

"Combining the timelike timelines with the exponential term, we get the can’t realize the mistake as if we observe multiple times then at one point of exponential wavefunctions of 4-Dimensions".... time we will eventually correct our mistakes.

Now, coming to the point… If nature really is a giant supercomputer and To support the above bold statements, we will make an analysis based on the everything we see are just the simulations then the small margin of errors most famous unsolved millennium prize problems “P vs. NP” Conjecture. As that we noticed are the Glitches in the Natures Supercomputers. And these we are a simulation, so we have no problem in considering “nature’ a vast glitches tend to show us that we are living in a simulated structure. super-powerful computer with a high processing power beyond the limit of the human imagination and present super computers that we have now. If Nature really builds a simulation then, surrounding that simulation there needs to be evidence that the object has been correctly simulated like the We will consider “Why time is exponential rather than polynomial?” shadow of the object, the reflection of the object, the things related to this object. And so to make the related things, Nature produces another Let’s consider a single person ‘A’ and 5 variables of nature related with him, Simulation. And then to reproduce the further related things, nature  Light, Shadow, Gravity, Trees, Projective Plane. Lets denote the inputs as produces another simulation [13]. These simulations will eventually increase “S”, such that S = 5. To select the best simulations among the 5 variables, exponentially and merged with our own wavefunction of the Time Stream nature will make a loop around the 5 variables first and then it will make 5 that is TIMELIKE. individual loops surrounding the parent loops. Such that 5 Parent loops with 5 individual separated loops. (If considered then around each of the Considering our wavefunction as the “Timelike Interval” with an added individual loops, another 5 loops can be made, but we won’t go into such exponential ‘e’ term, we can conclude the following mathematics. complexity here). As a result, we have “S” loops (Parent) times “S” loops (individual)… To make S*S or S2, we will denote 2 as “K” such that it becomes K S where “S” is the number of input variables while “K” is the number of Here for general convention, we will use time as 1-Dimension. lopping occurred. (K can be greater than 2 depending on complexity). This is the example of a Polynomial Growth. Consider the value of "e" ~ 2.718…….. (We will use this along with the Timelike Interval) Now, let’s consider 5 persons, A, B, C, D, E instead of only A. Therefore each person has 5 Variables of simulation that we need to consider as before. Consider our timelike curve as our Wavefunction Ξ(σ) where σ = 3 Space + 1 However, in the previous case, (where 5 parent loops has 5 individual loops Time Dimensions. and if each individual loops has 5 more loops related to that, then the 3 K looping would increase polynomialy as S*S*S or S or S ), this time the input This implies..... variable is 5 as before but, the input remaining the same, with each increase in persons like adding more persons F,G and so on…… the looping will Ξ(σ) = |ds² - e| = |- c²dt² + dx² + dy² + dz² - e| … Equation (*) increase exponentially and it will be the number of persons raised to the number of inputs, such that, for 7 persons (A,B,C,D,E,F,G)… the growth Taking all the dimensions & speed of light as unitary we find the difference as occurs PersonsInput or 75 or KS . Here the increase is much more sharp and 2.718..... - (-1+1+1+1) = .718..... exponential and this is the nondeterministic exponential growth that we need to consider in real life simulations when related with nature to give us This is the small glitch that builds up when exponentially repetition occurs Exponential Growth, paving the way for exponential wavefunctions while and when it approaches e∞ then the Wavefunction Ξ(σ) blows upto infinity deducting from the timelike Minkowski line element. and collapse. That is why small perturbations works as false memories and confabulation of Physical world but infinite exponential collapses them.

WHAT IF OUR WORLD IS A SIMULATION? If we take e⁻∞ then the Wavefunction Ξ(σ) is same as 2 like before when there is no "e" in Equation (*) We can say that what we observed becomes the part of our physical reality.

And our observations when cease to exist, our brain turns on an AUTOPILOT Reality merges in unitary perturbations. MODE which is to save the memory power. What if? Nature also tries to save Reality collapses in infinity. its data or processing power by observing certain things once in a wrong way Reality is same thing if it happened at a very long ago beyond ones & then continuously reflecting on that image without considering the need creation. for further observation. What if? Nature is a giant supercomputer with a processing power far beyond the reach of individuals. Enormous power that As Reality collapses in infinity, We can’t observe or penetrate the depicts the observable physical reality. simulated Collections of the creator. It becomes difficult to reach to the creator as time goes by. First let me give you an example of AUTOPILOT MODE of Brain. Suppose, you are going on a car in an infinitely long straight road where there are no EQUATION :: ∞ twists, turns & not even other vehicles. Your brain will notice this for Ξ(σ) = |ds2 − ∏ em | sometime & then makes an image in front of our eye as if the same thing m=1 repeats forever. So, we are lost in a false vision that has been depicted initially but if later on any vehicles suddenly come in front of your car, you Where || Symbol denotes the absolute. will eventually fail to notice that and an accident occurs.

Nature also did the same thing to us. It recognizes the initial pattern & embedded this in reality without the need of any further observation and we 9 March 15, 2020 Split Second Intersection Deep Bhattacharjee

Consider a Past wavefunction Ξ(σ) = |e1 − ds2|, here the margin of error is small as Exponential has a power of only 1. However if Exponential has a Power of 2 or 3 or 4…… like Ξ(σ) = |e1 − ds2| or e2 or e3 …… Then its obvious that the Past timeline with the wavefunction containing e1 will choose the future timeline with wavefunction e1…. But if it deviates from this then time will form a Closed loop (that is, the timeline bifurcates) and will unite to one soon after.

Consider the below image….

Now, from this picture, it is seen that for a few past timelines, there are many future timelines. This means that our past is a nondeterministic algorithm which predicts the future. As world is a simulation, and nondeterministic means, for every input, there are several outputs, and this exactly happens with our future. For “N” past timelines, there are “N+1+1+1+1+1…….” Future timelines. But, for each past timelines, there should be only 1 future timelines and how will the past timelines consider which future timeline to predict and join. This is shown by the exponential wavefunctions and in general, the wavefunctions with the lowest margin of error of future timelines will get selected and attached to, with the past timelines. However, this is not the case as it seems everytime, the nondeterministic timelines will tend to make the past timelines to get split into more than one future timelines which ultimately leads to paradoxes and Here we can see that there are loops in the timelines. This bifurcation and looping of time (we will consider this concept soon after this). looping occurs when the wavefunction Ξ(σ) deviates to two more

wavefunctions δ1 Ξ(σ) & δ2 Ξ(σ). Here one thing needs to be specially noted that for a single past timeline, there will be different future timelines, but if this process repeats then there The complete function will be like this… will be infinite timelines for an event. So, to prevent this, let’s consider this ∞ picture… δΞ(σ) = |δds2 − ∏ δem| m=1

Here, a Single timeline bifurcates into two timelines which intersects the present and then again divides into two timelines, which ultimately joins into as single timeline in future. This looping of timelines can be best visualized in the below diagram…

There is one past timelines in CONE 1, which produces, 3 future timelines, however, in CONE 1, only 1 future timelines passes through CONE 2, where it has 4 future timelines, only one of them goes to CONE 3 which again produces 4 future timelines in CONE 3. So, there can be multiple timelines related to a single timeline, but only one of them gets through the other cone, while rest timelines simply vanished. 10 March 15, 2020 Split Second Intersection Deep Bhattacharjee

This situation can be best described as “Imagine you wake up in the morning and went to the roof to feed the pigeons but suddenly being slightly Consider the below image… unconscious you fell down from the roof of the house. But before you fell, you watched that there are 3 pigeons chattering on the top of water tank. Now, as soon as you fell from the roof and hit the ground, you suddenly woke up as if it’s a dream. You then went to the roof to feed the pigeons but mistakenly fell down from the roof. Again, you realize that it’s a dream and you woke up. As per your regular duty, you went to the roof and feed the pigeons and fell down, and again woke up realizing it’s a dream….. This continues. Ultimately you realize that, you will wait and watch yourself doing the same things over and over again, so, you wake up and instead of going to feed the pigeons you start hiding behind the water tank…. You will see that your same copy is feeding the pigeons and feel down from the roof. Then another copy of you will watch you standing behind the water tank watching you feeding the pigeons. Then another copy of you will watch you, watching you watching yourself feeding the pigeons….. You have entered in the loop of time which constantly bifurcates in the future and past with the common centre at the origin or present…..” We will try to interpret the grandfather paradox using this “exponential

wavefunction”. This can be expressed as breaking a single wavefunctions Ξ(σ) into multiple smaller wavefunctions like δ1 Ξ(σ) , δ2 Ξ(σ) and so on………. Suppose, the person (or the child of the daughter of grandfather) present in

2020. He goes back to 1940, to kill his grandfather before the grandfather This is a Sci-Fi Concept which has been described by different movies over gave birth to the mother of the child as seen in Scenario (a). different situations as examples. What I have tried is to give a more logical & mathematical concept to the examples. Now is it at all possible for the child to go back in 2020? , as his timelines

then becomes nonexistent. It simply ceases to exist as he is not born. Then Self Inflicting timelines and death loops… how should he returns to 2020 from 1940…. He can’t as because as soon as

he killed his grandfather, the specific wavefunctions of “e” to the power 1 As nature uses nondeterministic algorithm to transfer from one phase to term blows up along with the least degree of errors and all the other another that is from present to future the input timelines in the present has wavefinctions with “e” term 2,3,4,5,6,7,8,9…… will accumulate to an infinite one wavefunctions Ξ(σ) = |ds2 − e1|, that is, “e” to the power 1 which has possibilities but here nature ceases to find the least possibilities among them the least degrees of errors and when proceeded to the future, it has as “e” to the power 1 is already destroyed and the wavefunction gets numerous wavefunctions to choose from, like Ξ(σ) = |ds2 − e1| or Ξ(σ) = collapsed. Let’s see how? |ds2 − e2|or Ξ(σ) = |ds2 − e3| and so on…. with the increasing power of the “e”. But in most general cases, nature would chose the function identical Here the wavefunction stands out to be Ξ(σ) = |ds2 − e∞| which results in to the present or so called past when compared with the future, that is Ξ(σ) = ∞ and if we examine further then it is also not possible for him to go Ξ(σ) = |ds2 − e1| as in general case the wavefunctions with “e” to the to the past to kill his grandfather. Why? Because if he goes to past then, power 1 has least degree of errors when concluded among the various Nature has to face an infinite amount of wavefunctions as nature has to powers of “e” to the wavefunctions mentioned before. choose among a variety of timelines or wavefunctions which will take him to the desired event in 1940, when he would kill his grandfather, therefore, the Now, in this section, we will see a very different thing such like splitting of wavefunction will also accumulate exponentially but in this time there should wavefunctions into loops, like a single wavefunction Ξ(σ) can split into 2 be a “-∞” term raised to the power of “e” like be Ξ(σ) = |ds2 − e−∞| which 1 2 1 2 smaller wavefunctions like δ Ξ(σ) , δ Ξ(σ) such that δ Ξ(σ) + δ Ξ(σ) = shows that the wavefunction is just simply a line element of timelike Ξ(σ)…. Which tells us that, after the splitting, the loops which are crated are coordinates as "e−∞" is 0, so that, Ξ(σ) = ds2. He is at the 2020 and always the smaller parts of the parent wavefunctions and the loops when joined be at 2020. together again in some future time becomes the parent wavefunction same as before, that is Ξ(σ). Now, we will jump into a more rigorous explanation of the wavefunctions where “DEATH LOOPS” can be created. However, in case of self inflicting timelines (or wavefunctions) which creates the death loops, a single wavefunction Ξ(σ) can split into various loops like [ 1 2 11 22 111 222 δ Ξ(σ) , δ Ξ(σ) ] or [ δ Ξ(σ) , δ Ξ(σ) ] or [ δ Ξ(σ) , δ Ξ(σ) ]……. Note: 1 ( ) 2 ( ) ( ) 11 ( ) 22 ( ) ( ) 111 ( ) such that δ Ξ σ + δ Ξ σ = Ξ σ , δ Ξ σ + δ Ξ σ = Ξ σ , δ Ξ σ + 1. DEATH LOOP is a hypothetical concept which I have introduced 222 ( ) ( ) δ Ξ σ = Ξ σ . here. 2. The value of ‘e’ is taken upto 3 decimal places that is 2.718….. and Here Ξ(σ) is the parent wavefunction and the constants δ1 , δ2 or δ11 , δ22 or all calculations are done step by step in CASIO fx-82ES PLUS δ111 , δ222 represent different loops of the same wavefunction Ξ(σ). Calculator.

Here we will make one important assumptions, the wavefunctions contains the exponential term “e∞” when one proceeds forward in time and the exponential term “e-∞” when we proceed backwards in time. Why this ambiguity, we will discuss below. 11 March 15, 2020 Split Second Intersection Deep Bhattacharjee

Consider the image below… Ξ(σ) 푑푠2 − 푒1 푑푠2 푒1 2 = | | = | − | = | − 1| e1 e1 푒1 푒1 2.718 … … = 0.2641648271 … … 퐸푄(4)

Ξ(σ) This implies = 0.2641648271 in EQ(4). e1

Next Step is we will take the exponential term e1 and perform a division like 푒1 = 10.28903064……EQ(5) 0.2641648271

So, 0.2641648271 has to repeat 10 times to reach e1 as per EQ(4)….Therefore minimal 10 loops are required if “e” has the power 1 to escape from the (PLANE OF EXPONENTIAL (see the above diagram)) to reach time “t=4”. Now, we will see the gap which is very important here…. The gap must be on the order of equal to or greater than e1or (10.28903064 - 2.718) that is 7.57103064 EQ(**) in order to get through the portal or time tunnel to start looping. And maximum 10 loops can be done approx as seen from EQ(5)

Now we will perform the operation with the exponential wavefunction e2 such A Person say “Bob’ goes to sleep at point “Y” at “t=1”. He wake up from the that…. sleep at Point “Z’, “t=2” which is the Present. He has a perfect wavefunction at Point ‘t’ and ‘z’, such that, Ξ(σ) = |ds2 − e1|. Now From point ‘z’, the Ξ(σ) 푑푠2 − 푒2 푑푠2 푒2 2 = | | = | − | = | − 1| wavefunction bifurcates into 2 loops δ1 Ξ(σ) = |δ1 ds2 – δ1 e1| and δ2 Ξ(σ) = 푒2 e2 푒2 푒2 7.387524 |δ2 ds2 – δ2 e1|and created the loop “a” such that δ1 Ξ(σ) + δ2 Ξ(σ) = Ξ(σ). = 0.7292732991 … … 퐸푄(6) The loop would be created as the wavefunction Ξ(σ) got divided by the exponential term “e−∞”…. The equation becomes, Next Step is we will take the exponential term e2 and perform a division like 푒2 = 10.12998009……EQ(7) 0.7292732991 ( ) 2 1 Ξ σ 푑푠 − 푒 2 − 2.718 −∞ = | −∞ | = | | = ∞ … … 퐸푄(2) e e 0 So,0.7292732991 has to repeat 10 times to reach e2 as per EQ(6) and

EQ(7)….Therefore minimal 10 loops are required if “e” has the power 2 to Then Bob arrives at the vertex “t=3” and Nature will try to nullify the EQ(1), escape from the (PLANE OF EXPONENTIAL) to reach time “t=4”. Now, we will by multiplying the term “e−∞" on both the sides which has been divided by see the gap which is very important here…. The gap must be on the order of “e−∞" on both sides previously…. The Equation becomes, equal to or greater than e2 or (10.12998009 - 2.718) that is 7.41198009

EQ(**) in order to get through the portal or time tunnel to start looping. And Ξ(σ) e−∞ ∗ = ∞ ∗ e−∞ = 0 … … 퐸푄(3) maximum 10 loops can be done approx as seen from EQ(5) and EQ(7). e−∞

Now, from “t=3”, the timeline loops back to the present Point “z” and again A coincidence is that Approx EQ(5) = Approx EQ(7). followed by EQ(2) makes a loop “b” and reaches at the vertex “t=3”, then 3 followed by EQ(3) loops back to the present point “z”. Now what will happen if we take e as the exponential term…

Ξ(σ) 푑푠2 − 푒3 푑푠2 푒3 2 “This situation can be best described by the previously encountered example, 2 = | 3 | = | 3 − 3 | = | − 1| Bob goes back to sleep at “t=1” , wakes up “t=2” which is his present and 푒 e 푒 푒 20.07929023 = 0.9003948856 … … 퐸푄(8) Death Loop started following the EQ(2) , timeline reaches “t=3’ where he feed the pigeons at the front of the water tank and EQ(3) takes place, he unconsciously fell down from the roof and again wakes up at Point “z” 푒3 Now, here from e3 onwards we will see that = 22.30053788. The Present, enters into another Death Loop “b”, EQ(2) & EQ(3) takes place like 0.9003948856 before and he returns to present point “z”. Again he wakes up and death gap is less than e1(2.718…) that is 22.30053788 - 20.07929023 = loop “c” started, now, Bob wants to see what he is doing previously, in that 2.221247651 … … 퐸푄(5) 푎푛푑 퐸푄(7). Here the “Exponential Gap” is not case he will see himself feeding the pigeons which is loop “b’ “ at “t=3’ “… sufficient to pass through the portal and hence no looping occurs. Here “b’ “ is a Past Loop that he already encounters and he then goes on to feed the pigeons but fell from the roof and get awake at point “z” which is If we take e4 then the answer comes to 2.076081049 which is also less than Present and enters loop “d”. He will watch himself watching himself watching 2.781…… behind the tank that he is feeding the pigeons in the Past loop “c’ “…. (He is obviously watching his Past)…. And the situation repeats itself until and ……. unless a certain condition is met, now, we will see the conditions… …….

Here a list of conditions needs to be fulfilled to escape from the Death Loop, If we take e10 the answer comes to 2.000181805 which is also less than here, if nature selects his wavefunctions with the exponential term “e1 “… 2.781…… Then, both sides of the equation Ξ(σ) = |ds2 − e1| needs to be divided by “e1 “… Such that, ……. ……. 12 March 15, 2020 Split Second Intersection Deep Bhattacharjee

If we take e20 the answer comes to 1.999999 which is also less than 2.781……. Now, we want to make 3 Parameters and identify them as...

If we take the value as e24, then the solution is 푃− 푓표푟 푃푎푠푡, 푃 푓표푟 푃푟푒푠푒푛푡, 푃+ 푓표푟 퐹푢푡푢푟푒

Ξ(σ) 푑푠2 − 푒24 푑푠2 푒24 2 Then we can decide two consequences upon the mapping of U00 as, = | | = | − | = | − 1| 푒24 e24 푒24 푒24 2.642328795 ∗ 1010 = 0.9999999999 … … 퐸푄(9)  What will happen if a person goes time travel to Past or Future and died there? 푒24 Now, = 2.642328795 ∗ 1010 …. Here the “Gap’ is 2.718 (e1) -  What will happen if a person goes time travel in past and future 0.9999999999 2.642328795 ∗ 1010 = 2.642328795 ∗ 1010 … … 퐸푄(10) which is less than and unfortunately, his time machine failed to function? e1, hence no looping occurs. 00 This gives rises to 4 Functionality like with the map of U as, From e25 onwards, the function returns the value itself when divided by e25 as 00 Ξ(σ) → + 푈 → … 퐸푞(푎) we can see below that, = 1 푃 퐷푖푒푑 푒25 00 → − 푈 → … 퐸푞(푏) Ξ(σ) 푑푠2 − 푒25 푑푠2 푒25 2 푃 퐷푖푒푑 = | | = | − |=| − 1| 푒25 e25 푒25 푒25 7.181849664 ∗ 1010 00 = 1 … … 퐸푄(11) →푃+ 푈 →퐷표푢푏푙푒 … 퐸푞(푐)

푒25 00 Now, = 푒25…. Here the “Gap’ is (e25) which returns the value of the → − 푈 → … 퐸푞(푑) 1 푃 퐷표푢푏푙푒 function itself. Hence from e25 and onwards, it is not accountable to take into the equation of looping. 퐸푞(푎) shows that if a person goes to the future and get died then, the Ξ(σ) solution is that, as soon as he dies his original (inertial wordline) cease to From these calculations, we can conclude that the function if and only if y 푒푦 exist and he will be completely out of this world. = 1,2…. The function has a time loop of 10 times and its also greater than the minimal exponential gap e1 as seen from EQ(**)(in page 20 and 21)…. After 퐸푞(푏) shows that if a person goes to the past and get died then, this will lead that upto y=24, the result is less than the minimal exponential gap. And from to paradoxes as he is not existent in future. However, this is not the case if y=25 onwards, the equation repeats the value of the function itself. we look closely into the matter. As soon as he died, what actually died is his

future self but not his past self and to compensate the situation, the (inertial So, e1 & e2 has the minimal exponential gap and close to the line element ds2 worldline or the non-time travelling observers) will die in the same time from (-1+1+1+1 = 2). These are the two loops through which time travel can be which his future self started his journey to the past. done with repetition of events like 10 as per EQ(5) and EQ(7). After that from e3 to e24…. Time travel can be done with no repetition of events as its close to 퐸푞(푐) shows that if a person goes to the future and his time machine is ds2 but less than the exponential gap e1 which provides looping. And from e25 broken, then there seems to be a double entity. The inertial him along with onwards, no time travel is possible as the function repeats the exponential the time traveller him. In that case, as he cannot return to the present, his itself. identity will remain in future as long as the wormhole remains open. When

the wormhole gets closed, he has lost his affine connection with the past PLANE OF EXPONENTIAL lies as a Superposition of all “t=3” which provides world from which he started his journey, this affine connection once gets the way to “t=4”. (see the previous diagram) destroyed, he not only disappears from the future but also, gets displaced to

a random time from which he will again gets disappeared due to his double The loops bb’, cc’, dd’ are depicted as δ1 , δ2 or δ11 , δ22 or δ111 , δ222 , a has identity and this process will continue upto the limit when he will be there at no a’ factor as it’s the first and foremost loops. the time of his death. Then, after that he will lost his existence.

Result: 퐸푞(푑) shows that if a person goes to the past and his time machine lost its 2 wavefunctions for repetition of events and time travel, e1 and e2. functionality then, again in the past he will have a double entity and as this 22 wavefunctions for time travel with no repetition of events, from e3 to e24. cannot happen for long (as he will be existent as long as the wormhole 25th wavefunctions and onways, the door for time travelling is closed that remains open), he however will again gets disappeared like 퐸푞(푐) and he will is from e25… end up in some random timeline and this process will continue upto the

point when he approaches his death time before getting finally disappeared. “The Philosophical implications has been decided very beautifully here with the detailed examples of ‘Under what conditions the time travel is possible “Therefore, the most important thing that we deduced in this section is that and under what conditions it won’t?” as a person travels to Past or Future, there will always be a certain time limit

upto which he can stay and after that the wormhole will get closed and as he Section VI is nonexistent therein this timeline (provided he is not in the moment of his

death), showing us that there must be some affine connection between the From EQ(†) on Page 4, Section I, we get a final mapping of time travel time traveller and the wormhole like the time traveller will be existent in the through the closed timelike curves, that is... newtimeline only upto the time, the wormhole or time machine remains open

and as soon as the time machine gets closed he will simply vanish to some { 2πi(P₋₁) ⋃ 퓖 (퓗 )⁺ } ⋂ { -2πi(P₋₂) ⋃ 퓖 (퓗 )⁻} : U00 random timelines (either in future or in past) upto the timeline of his death 13 March 15, 2020 Split Second Intersection Deep Bhattacharjee

time. And this affine connection between the person and the wormhole is ‘spooky’ like the ‘quantum entanglement’ and this ‘spookiness’ has to be {퐴, 퐵, 퐶 … … ) 휖 푆퐸푇 푋 푎푛푑 {1,2,3 … … } 휖 푆퐸푇 푌 there and implided by the nature to remove every possibilities of paradoxes.” Or,

Section VII 퐹(퐴) = 1, 퐹(퐵) = 2, 퐹(퐶) = 3 푤ℎ푒푟푒 퐹 = 푋 → 푌

If we predict the time as numbers and if we plot the numbers then there is a In each of these functions (F) there exists an additive property of total randomness in them. Like, the velocity of different objects in this ‘Superposition’ such that there exists a SET Z which has the following universe, the number of computations that gets evolved with time, the property… absolute uncertainty in weather prediction, the waves of oceans, the symphony of primes, the collision of two binary stars associated with the 푆퐸푇 푍 = { 퐹(퐴, 퐵, 퐶 … ) = (1,2,3 … ) | {퐴, 퐵, 퐶 … … ) 표푓 푋 travelling of gravitational waves in different directions of varying magnitude → {1,2,3 … … ) 표푓 푌 } over time, the numbers in the day to day events like the lottery tickets, share markets, the number of persons born and died in a single day, the amount of This SET Z is the Present or the notion of ‘PRESENT TIME’… accidents occurs, the numbers of galaxies evolving thereby generating new stars and abolish old ones…. Each and everything is a number and if we Here, as a person moves from A to 1, there exists a mutual string attached to studied theses numbers carefully, then we will find a specific pattern the ‘element A’ which preserves the notion of space from ’A to 1’ or “B to 2’ or associated with these numbers. This specific patterns although appears “C to 3’… This ‘strings has 3 parameters for preserving the ‘Spatial Uniformity’ ‘randomness’ at first is usually a byproduct of ‘determinism’ which means in as a Set P = {(Right Accession, Declination), Local Coordinates, Gravitational every numbers associated in the past there exists a relation to every Acceleration}. numbers associated in the future with present being their superposition. This means what we are experiencing now are just the ‘superposition of the Past Here, we will now discuss why Set P is important. Suppose a person moves and Future in a specific order or patterns’ but sadly to say we as a human from ‘Event A’ in past to ‘Event 1’ in future then that means ‘A ‘ is correctly being are unaware of this patterns. If there are patterns and orders in the being mapped to ‘1’ in time and space such that, ‘A’ is correctly being moved randomness as associated with time, then there must be some form of from Set X to Set Y in point ‘1’ without any mistake, which means there is a commons between these numbers, there must be something very similar to ‘Celestial Coordinate system, Local coordinate System and Gravitational all the patterns and we humans are too fooled to find the commons between Acceleration’ attached to ‘A’ that transfers it to ‘B’ so that ‘A’ from Set X goes them. If the commons can be found, then there will be nothing as a surprise, correctly in Set B without ending in Mars as we have a ‘Set P’ as a condition we can predict each and every events in time with respect to certain events attached to them which correctly determines the position of ‘1’ with respect that we are concerned of. This indicates that every graphing pattern of to ‘A’ in terms of Right Accession, Declination, Local Coordinates and numbers shows us a sense of ‘causality’ between them. This causality is the Gravitational Acceleration. Of course a person can end up in Mars but that present which is the connecting link between the events which are causes in means he needs to alter the ‘Strings’ of the Program within SET P such that the past to the events which are effects in the future. This causal relationship event ‘1’ ends up in Mars related to event A in Earth but there must be a lot is everywhere, at every point in the world and with this concept we can enter of intermediate events in between them, but for the ease of calculation, we into the world of ‘determinism’…. According to quantum theory ‘information will consider only the ‘Initial and final events’. We can tell ‘Set P’ as the is conserved’ that means ‘information’ can’t be created or destroyed but ‘identifier’ Set related to ‘Set X’ in Past and ‘Set Y’ in future. what I mean by this is that information unfolds or evolves with time. The more the time passes, the more the past information unfolds and this paved 푆퐸푇 푃 ∶ 푋 → 푌 ∃ 푃 𝑖푠 퐶표푛푡. 표푟 푙푒푠푠 푉푎푟𝑖푎푏푙푒 푤ℎ푒푛 푐표푚푝푎푟푒푑 푡표 푠푚푎푙푙 푑𝑖푠푡푎푛푐푒푠 the way for the deterministic universe. Everything has been there in past and 푎푛푑 푚표푟푒 푤ℎ푒푛 푐표푚푝푎푟푒푑 푡표 푙푎푟𝑔̃푒 푑𝑖푠푡푎푛푐푒푠. everything will be there in future, all happening at the same places but in different times. Nothing new is created in course of time and nothing old is What do we actually mean by the above statement of logic? When ‘Alice’ destroyed. What happens is that information unfolds at the very onset of the moves from ‘A’ to ‘1’ and if both are in Earth then Set P is Constant in terms arrival of the current time. By means of determination, we can pave that of ‘Celestial Coordinates’ but not ‘Gravitational Acceleration’ as ‘Gravitational every mapping from past to future happens for a reason and that mapping is Acceleration’ changes with elevation in space and in this case ”Set P is Less of two types as classified by ‘topology’… the ‘bijective’ mapping for day to Variable” but if ‘Alice’ moves from ‘A’ to ‘1’ where ‘A’ is in Earth and ‘1” is in day events and the ‘surjective’ mapping for the travelers in time. These two Mars, “Set P is More Variable” when compared to ‘large distances’ as ‘Both mappings preserve the information’s which arises as a subset of time. Now Celestial Coordinates and Gravitational acceleration’ of Earth and Mars are the main ingredient of time is that it has been programmed, ever timeline or hugely different. worldline at the onset of journey is being programmed till the end in a ‘deterministic’ way that that program is done by an agent of nature which we Now, we will see the mapping of events in Time for a ‘Time traveler’ which is will introduce in this paper. ‘surjective’ and will discuss why?

An agent is an inert agent of pre-deterministic nature that allows the time to program against itself by means of a mapping from Past to Future. This mapping is done in the form of ‘bijection’ which we will see below.

Here, everything is same as before except for the fact that, ‘event 3’ in Set Y has a different mapping from ‘event C and D’ in Set X. Here lies the fact, that a ‘Time Traveler’ can choose the right Possible ‘Paths’ to travel from Past to Future or there are 2 Time Travelers each at ‘event C’ and ‘event D’ but they wanted to go to the same event in Future as ‘event 3’. That is why the Here, these exists two sets…. SET X and SET Y which denotes ‘past’ and mapping of a ‘Time traveler’ is different than a mapping of a normal person ‘future’ respectively. Event ‘A’ in past is mapped against event ‘1’ in future. where the ‘Agent’ Programs his transformation from one event in past to a Similarly event ‘B’ to ‘2’ and event ‘C’ to ‘3’ is being mapped according to this specified event in future via Set P, which shows that there is only 1 image. This mapping is in respect to the worldline of a normal person (not a designated directions in between 2 events in case of a normal traveler rather time traveler) in the spatial coordinates. Speaking mathematically… than many possible paths of a time traveler. A time traveler is free to choose 14 March 15, 2020 Split Second Intersection Deep Bhattacharjee

any possible paths whereas a normal person has only 1 degree of freedom or [4] Chou, Kai-Seng; Zhu, Xi-Ping (2001), The Curve Shortening Problem, Boca 1 paths that is destined to take him from past to future where future Raton, FL: Chapman & Hall/CRC, doi:10.1201/9781420035704, ISBN 1-58488- becomes present. 213-1, MR 1888641. [5] Thorne, K.S. "Closed Timelike Curves," in General Relativity and 퐶 → 3 𝑖푛 푐푎푠푒 표푓 푁표푟푚푎푙 푃푒푟푠표푛 푎푛푑 퐶 표푟 퐷 Gravitation, 1992, Proceedings of the 13th International Conference on → 3 𝑖푛 푐푎푠푒 표푓 푎 푇𝑖푚푒 푇푟푎푣푒푙푙푒푟 General Relativity and Gravitation, edited by R.J. Gleiser, C.N. Kozameh, and O.M. Moreschi, (Institute of Physics Publishing, Bristol, England, 1993), pp. Now, we will delve into a more advanced concept by considering the below 295-315. image. [6] Th. Kaluza, “Zum unitätsproblem der physik,” Sitzungsberichte der Preussischen Akademie der Wissenschaften Physikalischmathematischer Klasse, pp. 966–972, 1921. [7] O. Klein, “Quantum theory and five-dimensional theory of relativity,” Zeitschrift fur Physik, vol. 37, no. 12, pp. 895–906, 1926. [8] O. Klein, “The atomicity of electricity as a quantum theory law,” Nature, vol. 118, no. 2971, pp. 516–517, 1926. [9] G.Nordström,“Überdiemöglichkeit,daselektromagnetische feld und das gravitationsfeld zu vereinigen,” Physikalische Zeitschrift, vol. 15, pp. 504–506, 1914. [10] Schwarz, Rob “John Titor: The man with the machine”, February 4, 2013 https://www.strangerdimensions.com/2013/02/04/john-titor-the- man-with-the-machine/ [11] Satheeshkumar, V. H., & Suresh, P. K. (2011). Understanding Gravity: Some Extra-Dimensional Perspectives. ISRN Astronomy and Astrophysics, [10] 2011, 3. doi: 10.5402/2011/131473 [12] N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, Phys. Rev. D59 (1999) RANDOMNESS increases the ENTROPY. When we are moving from future F-1 086004. to a further future F-2, there is an increase in randomness and when in future [13] “The Mandela Effect”, Dir. David Guy Levy, Perfs. Charlie Hofheimer, F-3, the randomness increases. This denotes an increasing of the angle θ. The Aleksa Palladino, Robin Lord Taylor, Clarke Peters, Madeleine McGraw, Tim more the angle θ, the more the randomness which can be expressed in the Ransom, Ptolemy Slocum, Vernee Watson, Elena Campbell-Martinez, Steven following relationship… Daniel Brun, Salme Geransar. Periscope Entertainment 2019. [14] G. Lemaitre (1933). "L'Univers en expansion". Annales de la Société 휽 ∝ 푹푨푵푫푶푴푵푬푺푺 Scientifique de Bruxelles. A53: 51–85. Bibcode:1933ASSB...53...51L. English translation: Lemaître, Abbe Georges (1997). "The Expanding Universe". And this increases the DETERMINISM or the CAUSAL CONNECTION between General Relativity and Gravitation. Kluwer Academic Publishers-Plenum CAUSE and EFFECT within a string of Randomness. This Programming which Publishers. 29 (5): 641–680. Bibcode:1997GReGr..29..641L. has been done by the Agent of Nature specifies the Deterministic logic where doi:10.1023/A:1018855621348. every event of Past are connected with every event of Future through a Pre- [15] L. D. Landau and E. M. Lifshitz. The Classical Theory of Fields. Course of Destined Logic into the chaos of Randomness. Therefore, the relation is…. All Theoretical Physics. Vol. 2. … Andre Gsponer (2004). "More on the early the events are causally connected in this chaotic and random future. There is interpretation of the Schwarzschild solution". arXiv:physics/0408100. a specified pattern in the randomness, a synchronicity, a pattern connecting two distinct events in space-time.

CONCLUSION

Although the idea of a portable small time machine sounds promising that, it can be taken with the time traveller to move back and forth in his timelines, however, to build this time machine, there are still many technological challenges that recent technologies has to face. In theoretical physics, with the help of philosophy combined with mathematics, we can prove anything in pen and paper but to make this in reality, it needs a lot of work as because without the advanced technology of the arbitrary advanced civilisation, its quite impossible to build a time machine. In this theory a 6 Dimensional BH with 2D Timelike Timelines has been presented with noncompact singularity (when surrounded by a conductive sphere becomes compact)will only can be achieved some far days in the future. Moreover, the ‘causal loops’ have been concerned in details and we can have a fair idea about the physics and philosophy of time travel.

REFERENCE

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