Relativity and Cosmology

   

Time as an Imaginary Space: A New Framework for a Predetermined Universe

Authors: Sardar Dilbag Singh Khalsa

Interpreting spacetime as a 4-dimensional manifold, an entity that locally resembles $mathbb{R}^4$ but may possess global geometric or topological characteristics, leads to asymmetry when time is treated differently from space. We propose a manifold having three spatial dimensions $mathbb{R}^3$ and time as three spacelike imaginary construct where every spatial dimension associated as $t = itau quad text{with} quad tau in mathbb{R}$ treated as an imaginary space $iotamathbb{R}$. It preserves the Minkowski interval $Delta s^2$ without explicit time requirement for lorentz boost along (x). Conventionally, time is treated as an entity passing from one time $t_1 text{ to } t_2$, and all the objects observed at a single instance are called $t_{now}$. Contrary to this, objects that are in two distinct times called $t_{now}^{1}$ and $t_{now}^{2}$ can exist simultaneously! We can explain this perspective of reality by viewing time as an imaginary space within the 6-dimensional Space-Imaginary Space manifold. We will raise the conjecture that the 6-dimensional volume ( for simplicity, we take it for the cubic object) $V =[ (text{length}),(text{breadth}),(text{height}),bigl(i,c_xbigr)Delta T_x bigl(i,c_ybigr) Delta T_y bigl(i,c_zbigr) Delta T_z$] of the object is independent of the observer in a frame. Where $Delta T_x$, $Delta T_y$ and $Delta T_z$ are the time intervals along the length, breadth and height, respectively. We also postulate that the now-frame of time isn't a single specific time but an interval $iotadelta$.

Comments: 28 Pages.

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Submission history

[v1] 2025-02-06 21:33:52

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