Draft:Ghosal's Space-Time Hypotheses and laws of Space-Time

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Sounak Ghosal's spacetime hypotheses. states that spacetime can be represented as a two-dimensional fabric where hypothetical lines run parallel to the axis of space and through an object's center of mass, forming a cylinder-like structure. These lines bend due to light or the object's structure, causing tension and pulling objects inward. Curvature of these lines increases near the surface, is maximum at the surface, and decreases with distance, eventually becoming zero. The axis of reference is the central line through the object's center, intersecting with the x, y, and z axes to form a net-like structure in 3-D space. Axioms and laws of 2-D spacetime representation include: curvature dependency on the object's nature (ñ); maximum curvature at the object's surface; defining the central axis; decreasing curvature with distance; tension from congestion near the surface; repulsion between lines preventing intersection; dynamic interactions causing perpetual motion; and perspective variability showing concentrated gravity zones.

Overview

Ghosal's Space-Time Hypotheses is a theoretical framework proposed by Indian author and researcher Sounak Ghosal. These hypotheses present a conceptual representation of spacetime as a two-dimensional fabric, aiming to provide a clearer understanding of gravitational phenomena and general relativity. Ghosal's work contributes to the ongoing exploration of the nature of the universe, particularly in how massive objects influence spacetime.

Background

Sounak Ghosal has authored multiple works in both literature and theoretical physics. The book "The Space-Time: As I Know It..", which lays the foundation for Ghosal's Hypotheses

Main Concept

Ghosal’s Axioms and Laws of 2-D Spacetime Representation

When we consider the fabric of spacetime as a two-dimensional sheet, we establish certain axioms that are essential for the discussions that follow. These foundational principles help us visualize and understand the complex interactions within spacetime, particularly in the context of general relativity and the curvature caused by mass and energy.

By imagining spacetime as a two-dimensional sheet, we can more easily grasp how massive objects like stars and planets create indentations or curvatures in this fabric. These curvatures represent the gravitational effects that dictate the motion of objects within spacetime. This simplified model allows us to explore various phenomena, such as the bending of light, the formation of black holes, and the propagation of gravitational waves, in a more intuitive manner.

These axioms serve as the groundwork for deeper explorations into the nature of gravity, spacetime, and the universe, providing a clear framework for the complex discussions and analyses that will be presented later.

1. When considering spacetime as a fabric or cloth sheet beneath a celestial object, light will consistently travel parallel to that sheet. From a top-down perspective, its trajectory will be diagonal across the grid.

   

2. The nature of spacetime fabric is such that it does not adhere to any specific plane or axis of reference. As a result, it holds true for any plane and is entirely dependent on perspective, which is inherently variable

   

3. The trajectory of light remains constant, and may bend due to curvature in space-time. It continues in its original direction unless it changes material medium or undergoes physical change. Light travels parallel to the space-time fabric and space-time warps to allow the shortest path for light to move in situations of hindrance.

   

Ghosal’s 2-D Cartesian Representation of Space-Time and Equations

INTRODUCTION

Suppose a planet or any spatially oriented object of symmetry around the polar axis and a near-uniform surface. Now you can visualise it as a 2-D shape.

so, the effective gravity curve can be represented by a curve line, whose endpoints coincide with the equatorial axis of the main object.

Here,

Where l₂ is mathematically defined as:

here, G is the universal gravitational constant, M is the mass of the body and r_av is the average radius of that body. l₂ is the semi-minor axis of the feasible/effective gravity curve, and l₁ is the semi-major axis of the same, r₁ is the semi-minor axis of the celestial body and r₂ is the semi-major of the same, if the celestial body is assumed to be elliptical in shape.

Feasible Gravity:

The actual attractive effect that a celestial body has on another body, that pulls the body towards its centre of mass is called Feasible Gravity.

It is defined as a function of ñ, which is also known as SG’s “n” operator, which is the ratio of the minor and major radius of the elliptical curve defined as the "Feasible gravity curve".

The depression at a point on the effective gravity curve at any distance x (Taking the centre of mass of the object as the origin),

the equation of the y-coordinate at that point will be:

Here ñ is constant for the single celestial body throughout. And is also the ratio of l and r for that object.

Graphical Representation

The planet and the curve are represented by:

Planet:

Curve:

The Distance between two celestial bodies curvature points due to the effective gravity

This is given by R:

"The equation calculates the square root of the difference between the square of the average distance between the centers of mass of the two bodies and the sum of the ratios of the square of the semi-major axis to the semi-minor axis for each body. Specifically, it involves squaring the average distance d between the centers of mass of Body A and Body B, and then subtracting the sum of two terms: one for Body A, which is the ratio of the square of its semi-major axis a_A​ to its semi-minor axis b_A​, and one for Body B, which is the ratio of the square of its semi-major axis a_B​ to its semi-minor axis b_B​."

The Feasible Gravity Equation

The Feasible gravitational force of attraction between two celestial bodies is defined by using a modified version of newton’s gravity equation.

This equation represents the gravitational force between two bodies, A and B, based on Newton’s law of gravitation. It is the product of the universal gravitational constant G, and the masses of bodies A and B, divided by the square of R, which is a modified distance between the centers of mass of the two bodies.

The term R is defined as the square root of the difference between the square of the average distance between the centers of mass of the two bodies (d) and the sum of the ratios of the square of the semi-major axis to the semi-minor axis for each body. Specifically, this involves squaring the average distance d between the centers of mass of body A and body B, and then subtracting the sum of two terms: one for body A, which is the ratio of the square of its semi-major axis a_A​ to its semi-minor axis b_A​, and one for body B, which is the ratio of the square of its semi-major axis a_B​ to its semi-minor axis b_B​.

This holds account for minute calculations and decimals and is called Feasible Gravitational force of Attraction represented by ^EF_G

Ghosal’s Gravitation Hypothesis

There are hypothetical lines that run parallel to the axis of space and the line passing through the centre of mass of an object in space.

When bundled up, they form a cylinder-like structure. These lines bend around a body due to various reasons, such as the bending of light around the body or the body’s rigid and non-permeable structure.

The bending of these lines causes tension in them, which pulls any object approaching the centre.

Postulates

1. The curvature of these hypothetical lines depends on the ñ for that object and it increases as we approach the surface of that object.
2. At the surface, the curvature is maximum, and these lines do not run beyond the surface of that object.
3. The central line which passes through the centre of mass of that object, is called the axis of reference for that particular geometry. In the 3-D space, the x,y, and z axes lines intersect each other forming an interwoven net-like structure.
4. The curvature of these lines decreases as we move away from it, and at a particular distance away from that object, the curvature lines of these objects become zero.
5. As the lines near the surface become more congested due to the curvatures, it creates tension, which pulls objects toward the surface.
6. The lines seem to have some kind of repulsion between them, due to which two lines never intersect each other and run from infinity towards infinity in time. Due to this force, they tend to push the approaching object towards the more congested area.
7. However, as we now understand, these lines do not extend beyond the surface. When we dig a hole from one side of the object to the opposite side, through the center, and drop an object from the top, something strange happens. The axes of reference intersect at a point in the center, making it the most concentrated point below the surface. As a result, the object will move in an accelerated motion towards the center. Once it reaches the center, the repulsive forces between the axes will be so strong that they will push the object towards the downward surface, causing the object to repeat this motion indefinitely. This phenomenon may be due to the Earth’s magnetic field.
8. These axes of reference are not just the x, y, and z axes; they can be any axes of reference, depending on the perspective. If we take an infinite number of these axes and form an image by intersecting them, we can clearly observe concentrated zones where the “gravity” is strong

Implications

The hypotheses provide a foundational framework for further investigations into the relationships between mass, energy, and the structure of the universe. By representing spacetime in a simplified, two-dimensional model, Ghosal's work aims to make complex gravitational concepts more accessible and comprehensible.