Theory of Everything "Prime Mechanics"

[Baron d'Holbach]

I placed this here right away as speculation on others but this is my theory and my belief. Please disprove it and debunk it. I am serious because I need to know. The debunk is not this amateur post but my book as a whole. Not telling to buy the book but click on "see book" on amazon and debunk the first 8 pages or substack stuff but it should be the book. 

If not, I will place myself;

 

Newton = Gravity (Principia)

Einstein = Gravity (General Relativity)

Delamotte = Gravity (Prime Mechanics)

 

Only three people got it right. 

 

March 14, 2023 I published Prime Mechanics. 

 

"Prime Mechanics is based on a science that follows the laws of Prime Physics. The main subject is based on The Origin of Gravity and provides a complete singular framework for the Theory of Everything."  

I already started here: https://primemechanics.substack.com/archive

Abstract — Elemental Gravity is a cosmological model proposed by the book called Prime 
Mechanics that posits Gravity as the Steady State and the creator of the universe. According to this 
model, spacetime fabric is Gravity, and it represents the Steady State, which unifies Dark Energy, 
Dark Matter, and the fundamental forces as one entity. Dark Matter and Dark Energy are not 
separate substances but properties of the universe itself. Its dimensional topological spacetime 
field consists of multi-layered homogeneous curvature planes known as Prime Fields. These fields 
are determined mathematically using fundamental and dimensional constants that converge 
towards an equilibrium point of ½ between 0 and 1 based on Prime Numbers. This convergence 
leads to a rarefaction, which marks the beginning of creation.

Elemental Gravity 
Gravity is the beginning of the beginning, the emergent out of itself. It is a fundamental force that 
plays a crucial role in shaping the universe as we know it. Gravity is mathematically determined 
by a combination of dimensional and fundamental constants, which enable us to understand its 
behavior on different scales, from the microscopic to the cosmological. At its core, Gravity is a 
smooth, deterministic function that is both transformationally invariant and follows the principles 
of general covariance and the equivalence principle. These principles state that the laws of physics 
remain unchanged regardless of the coordinate system used to describe them and that Gravity is 
indistinguishable from any form of acceleration, respectively.
The principle of general covariance states that the laws of physics look the same in all coordinate 
systems and is invariant under coordinate transformations.
The equivalence principle states that Gravity is locally indistinguishable from any form of
acceleration and constants and looks the same in all coordinate systems. 

In General Relativity, Gravity is not a force between two objects as in classical mechanics. Instead, 
Gravity arises from the curvature of spacetime caused by the presence of massive objects. The 
curvature of spacetime determines the motion of objects, which follow the shortest path, called 
geodesic. Massive objects such as planets and stars curve the fabric of spacetime, causing smaller 
objects to move along curved paths. It has four dimensions because it involves three dimensions 
of space (length, width, and height) and one-time dimensions. Space and time are combined into 
a single four-dimensional entity called spacetime.

In Prime Mechanics, Gravity is the Steady State, the emergent force, the attraction of self-positive 
attraction within time. It is the force that unites all entities in the finite State of spacetime, with 
each entity having discrete infinity limits known as manifolds. These manifolds are represented by 
points, dimensions, coordinates, and degree of freedom points, and they determine the impact of 
Matter creation on the curved spacetime, resulting in acceleration along curved paths. Similar to 
General Relativity, Prime Mechanics also has four dimensions, but it incorporates additional 
dimensions to describe Gravity’s internal acceleration and orientation. This includes Dark Matter
and Dark Energy. These dimensions provide a comprehensive understanding of the mechanics of 
Gravity, including its internal and external structure and the forces that govern it.
Gravity is a dimensional topological curvature of a spacetime manifold. Its curvature and
substance are Dark Matter, a transparent geometric structure within the confinement of the 11-
dimension. On the surface, it is a flat homogeneous elemental fabric structure with stages in which 
objects can move, and universally it can be stretched, bent, curved, and punctured by the presence 
of mass and energy. Spacetime is not limited to four dimensions. In Prime Mechanics, it can be 
described as an 11-dimensional manifold. This manifold can be discrete and continuous, meaning 
it can have both discrete and continuous points and be connected to other manifolds. This allows 
for the inheritance of properties from one manifold to another and the addition of new features to 
a given manifold.

This means that Gravity is an elemental materialized dimensional steady-state force. This 
elemental dimensional force is a transformational orientation of an 11-dimensional manifold with 
a determined path of external influences from mass and energy in the universe. The effects of 
Gravity can be seen on all scales, from the motion of planets and stars to the bending of light by 
massive objects like galaxies.

Gravity arises from the collective behavior of many individual particles or entities, like Dark
Matter. It can exchange energy and momentum with other physical systems and Matter, exchange 
gravitational energy and momentum, and remain conserved. The system, the mass density that 
Dark Matter centers and overlaps and creates manifolds, is the fundamental building block of Dark
Matter, generating proto-mass/electric charge, serving as the origin of time and energy. This makes 
Gravity a two-system, open and closed elemental system. 

 

 

 

S_phi = ∫ d^11x √|g| [(1/2) g^{ij} ∂_i phi ∂_j phi - V(phi)]
where:

S_phi is the action for the scalar field phi in 11-dimensional spacetime
∫ d^11x denotes the 11-dimensional integral over all spacetime coordinates
√|g| is the square root of the determinant of the 11-dimensional metric tensor g_{ij}, which 
describes the geometry of spacetime

g^{ij} is the inverse of the 11-dimensional metric tensor g_{ij}
∂_i phi is the partial derivative of the scalar field phi with respect to the i-th coordinate
V(phi) is the potential energy function of the scalar field phi
This action describes the dynamics of a scalar field in 11-dimensional spacetime, including its 
kinetic energy and potential energy. The equations of motion for the scalar field can be derived by 
varying this action with respect to the scalar field phi.

The action is a scalar quantity that describes the dynamics of the scalar field phi in 11-dimensional 
spacetime, taking into account the effects of Gravity, Dark Matter, and Dark Energy through the 
11-dimensional metric tensor g^{ij}. The action is used to derive the equations of motion for the 
scalar field phi, which describes how the field evolves in time and space.

The action in this equation is a proposed theory of everything that attempts to unify all fundamental 
forces and particles in physics. The first term describes the kinetic energy of the field, while the 
second term describes its potential energy. The equation is integrated over all 11 dimensions of 
spacetime, and the resulting value gives information about the overall behavior of the field. The 
equations of motion for the field are derived by varying the action with respect to the field, which 
yields the equations that describe how the field evolves over time and space.

 

 

 

 

[Baron d'Holbach]

The picture above is the main diagram of Prime Mechanics. It explains in the most simplistic way possible the creation story. 
Gravity as zeros based on Prime Numbers gravitates towards Prime ½, a place between 0 and 1. This region is a confinement area, a placeholder that densifies and creates Prime Matter, a vessel, and a place to build a rarefication called Aether, Prime Energy. 

Every word has been reformatted, changed, and embellished. 

"Aether, Steady State, and Dark Matter and Dark Energy has been fully explained and expanded upon in Prime Mechanics. 

Steady State is Gravity.

Aether is the equilibrium point, "the center" and much more.

Dark Matter and Dark Energy is Gravity itself. 

Gravity created everything. Every single force, Fundamental Dimensional constants. Everything. 

We live in a Steady State system, with a physical creation at the equilibrium point. 

 

 

[Mordred]

No I will not download your book nor join the site it is on. However from what I have thus far your theory smacks of numerology.

 I do not see any importance or practicality in designating any significance on prime numbers with regards to spacetime. Nor do I see any practicality behind needing 11 dimensions or effective degrees of freedom in describing spacetime.

 Unfortunately none of the math you have posted answers the latter part. 

 \[g_{ij}\] at best describes a geometry with a Kronecker delta function that one would find in a Euclidean geometry. You do not so any Levi-Cevita connection that would find relevant for curved spacetime. So obviously you are not using any standard forms.

 By the way welcome to the forum just a forwarning the first day of new membership you will be limited to 5 posts the first day. After that it's unlimited.

How does prime numbers handle the vectors of spacetime. You might want to start there

 

 

Edited May 12, 2023 by Mordred

[Baron d'Holbach]

14 minutes ago, Mordred said:

theory smacks of numerology.

Yeah, it was great. Prime Numbers is the key. 

14 minutes ago, Mordred said:

11 dimensions or effective degrees of freedom in describing spacetime.

This is not a conventional dimensions, but a field. A geometric field of manifolds that build upon itself. This is Gravity as a self building block (Prime Matter aka Dark Matter). The degree of freedom and everything is involved. I follow General relativity 100%. Prime Mechanic is beyond it, as a expansion. Gravity is a closed and open system. The 11 dimensions are within it. Within Gravity as a orientation. 

19 minutes ago, Mordred said:

Unfortunately none of the math you have posted answers the latter part.

It was never the point but a single out the post and book as see the first errors. 

20 minutes ago, Mordred said:

geometry

Prime Mechanics as stated above has one and much more detailed and complete. The prime Field is a 11 manifold. A building block of matter. A layering effect that generates and cause Gravity to become Elemental. 

 

Hence, Elemental gravity = GEM = Gravitational Elemental Matter = Gravity, Energy and Matter. 

22 minutes ago, Mordred said:

curved spacetime

Gravity is not only Curved. It is a element, a transformational manifold that is open and closed. it can be harvested and extracted of its potential energy. 

24 minutes ago, Mordred said:

new membership

Im from 2017, yeah maybe I am still new. Maybe one more post today  

[Mordred]

If it's not the physics application of dimensions then how can I trust it to define define a manifold ? Keep in mind verbal descriptive are never sufficient for me. This includes professional peer reviewed literature. I never accept claims that cannot be shown mathematically.

 Mathematically one rarely ever needs more than 4 dimensions to describe spacetime paths that result from spacetime curvature. So why do you require 11 ?

 You claim to be 100 percent compatible with GR then you should have no problem addressing the fundamental aspects I have mentioned involving GR and geometry in the above questions.

Edited May 12, 2023 by Mordred

[Baron d'Holbach]

Because I am a new member it seems. I will post the scope of the great work called Prime Mechanics. 

Only on high demand of the specific topic requested down below will be post maybe 100% from the book. Only could be demanded on 1 of course. Any one, ask.

 

Prime Mechanics 

Intro: Explains the book is about the origin of gravity and the creator of everything. 

Part 1:

Chapter 1 Explains the basic of Prime Mechanics, Prime numbers involved, Zeta function and all the connections. it explains it will build a filed. A prime Field. A Field of geometric scale that can excite potential energy. 

Chapter 2: Explains the Prime Field in 11 Dimensions. 

11 Dimension : Prime Field Grid , Riemann zeta function (Prime Mechanics states as true and shows proofs) 

10 Dimension : Yang Mill’s ideas, Mass Gap and proves alot. 

09 Dimension : here I declare "The Unification of General Relativity and Quantum Mechanics" = Prime Mechanics, and I explain gauge transformation.

08 Dimension : 

The main ideas will be;
Birch and Swinnerton-Dyer Conjecture 
The L-function
Re(ζ) ½
 

07 Dimension : More Prime Field, as it is the Geometry of the system. Chains of zeros of Prime Constants, a laminar flow of a diagram 

06 Dimension : distribution of Prime Numbers (Proving Prime Numbers as true). Proving a Finite system. Proving the universe is not infinity and no such thing. 

05 Dimension : The construction of the Field (More Prime Field) 

04 Dimension : 

Let us continue with the Twin Prime ideas and add other concepts to understand this;
Twin Prime
Riemann zeta function
Elliptic curves
 

03 Dimension : 

The introduction of PRIME0, PBIT and Prime Computing
P=0

Prime Mechanics is Yes to P=NP 

 

02 Dimension :UNIFICATION 

I posted this on Substack, the layers of gravity 

01 Dimension : I state,  "We finally made it to Dimension 1, let us talk about Singularities and Infinities.

 

Chapter 3: I explain Newton and other Aether ideas  and finalize the proper Aether of Prime Mechanics. incorporating Navier Stoke into it. 

Part 2: Prime Selection.

Chapter 1 : Prove Darwin is correct and the Alien Specie

Chapter 2 : Prove Religion is Earth-based

Chapter 3 Prove Religion is Human made

Part 3: Prime Principle

Explain all the tools, and applications and explain how to create the ultimate A.I Robot. 

Conclusion; end the book from 2007 notes. 

 

Prime Mechanics March 14, 2023 by Ronald Delamotte 

15 minutes ago, Mordred said:

GR then you should have no problem addressing the fundamental aspects

Sure what is the full question. If this is what you want to know. Prime mechanic is 100% GR, so.... Ask again please. 

Also, substack don't need to subscribe. just click continue reading and scroll to the bottom of March 30 and read upwards. Its all free. The first 7+ post. 

 

[swansont]

7 minutes ago, Baron d'Holbach said:

Because I am a new member it seems. I will post the scope of the great work called Prime Mechanics.

!

Moderator Note

You’ve been a member for almost six years. You’re not considered a new member, and expected to follow the rules. Advertising is not permitted.

What is required is the (alleged) science, not an outline of the book. 

 

[Baron d'Holbach]

Alleged science, 

Prime Mechanics provides ideas, solutions, and answers to many unresolved scientific problems, including Gravity, Locality, Excitation, Dark Matter, Dark Energy, EPR Paradox, Universal Gravitation Laws, General Relativity, Quantum Mechanics, Unification, Prime Numbers, the Creation of Energy, Poincaré, Riemann, Hodge, Navier–Stokes, Yang-Mills, Birch, and Swinnerton-Dyer, and P versus NP conjectures, among others.

I needed to solve these ideas to solve the theory of everything. I combined them all plus more, many more to publish my works. With proofs, maths and ideas. 

I declare that Gravity is Elemental. It is a Elemental Matter. it is open and a closed system that can be harvested and extract of energy. it is the host of the universe. it is as 1, a finite, infinity limit system. 

 

[Mordred]

Ok the very statement open and closed system alone tells me you are not using correct mathematical terminology but are throwing buzzwords without understanding the mathematical implications of those terms.

All systems or states in any and every physics theory is mathematically defined. 

 Yet you still have avoided the essential question.

How does one employ prime numbers to define a geometric object ?

Every theory you mentioned above applies geometry so this is of essential importance 

Edited May 12, 2023 by Mordred

[Baron d'Holbach]

Just now, Mordred said:

open and closed system

Prime mechanic pg. 4-5. Please read carefully. 

 

Gravity is the beginning of the beginning, the emergent out of itself. It is a fundamental force that plays the main role in shaping the Universe as we know it. Gravity is mathematically determined by a combination of dimensional and fundamental constants, which enable us to understand its behavior on different scales, from the microscopic to the cosmological. At its core, Gravity is a smooth, deterministic function that is both transformationally invariant and follows the principles of general covariance and the equivalence principle. These principles state that the laws of physics remain unchanged regardless of the coordinate system used to describe them and that Gravity is indistinguishable from any form of acceleration, respectively.
Gravity at the macro level uses the principle of general covariance, which states that the laws of physics look the same in all coordinate systems and is invariant under coordinate transformations.

Gravity at the based level “stage” uses the equivalence principle, which states that Gravity is locally indistinguishable from any form of acceleration and constants and looks the same in all coordinate systems.  

Gravity external and internal use dimensional constants (acceleration) and fundamental constants (orientation) to explain the behavior of Gravity on different scales, from the microscopic scale of atoms to the cosmological scale of the entire Universe.

In General Relativity, Gravity is not a force between two objects as in classical mechanics. Instead, Gravity arises from the curvature of spacetime caused by the presence of massive objects. The curvature of spacetime determines the motion of objects, which follow the shortest path, called a geodesic, in the curved spacetime. Massive objects such as planets and stars curve the fabric of spacetime, causing smaller objects to move along curved paths. It has four dimensions because it involves three dimensions of space (length, width, and height) and one-time dimensions. Space and time are combined into a single four-dimensional entity called spacetime.

In Prime Mechanics, Gravity is the Steady State, the emergent force, the attraction of self-positive attraction within time. It is the force that unites all entities in the finite state of spacetime, with each entity having discrete infinity limits known as manifolds. These manifolds are represented by points, dimensions, coordinates, and degree of freedom points, and they determine the impact of matter creation on the curved spacetime, resulting in acceleration along curved paths. Similar to General Relativity, Prime Mechanics also has four dimensions, but it incorporates additional dimensions to describe Gravity’s internal acceleration and orientation. This includes Prime Matter and Prime Energy. These dimensions provide a comprehensive understanding of the mechanics of Gravity, including its internal and external structure and the forces that govern it.
 

2 minutes ago, Mordred said:

mathematically defined. 

Yes, Prime Mechanic declares, All values, constants deterministically define from the start. Right. Because of the Fundamental Constant. 

We know this as correct. From the Start the constants are the same, never evolved. 

4 minutes ago, Mordred said:

How does one employ prime numbers to define a geometric object ?

Wow, the best question. This is it. 

This is the outline post above: 11 Dimension : Prime Field Grid , Riemann zeta function (Prime Mechanics states as true and shows proofs) 

So yeah... I have to prove the Riemann zeta function. Listen to debunk Prime Mechanic is to disprove zeta... 

Okay so, the Prime Field is based on 0 and 1, everything is station at 1/2. 

Here is a picture of a bump function. 

Prime Mechanics pg, 51

"We will treat the Riemann zeta function as not a purely mathematical object but as a physical system that will be mapped onto the Prime Field as a guide. We will use the critical line section as a one-dimensional ground state for potential energy and excitation with the distribution of Prime Numbers."

The Prime Field is a place for excitation. I am declaring and stating that using Prime Numbers, its distribution we can locate and predicte and plan and determine all locations. Proving determinism, and disproving infinities, uncertainties and chaos. 

So, essentially explaining, Dark Matter as a manifold. We are explaining it as a geometric field. A locality. A place of time and start. we are doing is creating a section and pin-pointing exact location with Zeta 1/2, right the proper distribution of Prime Numbers. 

 

Causing a chain reaction, a Connection, a Twin Prime Connection. 

What I am proving in the last section is the spooky at a distance also. No such thing as it is like Prime Numbers, especially Twin Prime connection.

Prime Field is a geometric island of stability. A section, a locality, a object, a place for potential energy and extraction and harvestation. 

Prime Mechanic pg, 47 (This might be too advance for non-prime mechanic users) 

 

 .. . .   . .   . .   .     . .     .   . .   .     .     . .     .   . .     .   .     .       . 

. .   . .   .             .   .     . .         . .     .     .   .     .     . .         . .   . .

          .           .   . .   .     . .         .     .     .     . .     .   . .         .    

      .   . .   .             .     .         . .   .     .       .     .     .   .     .         .

.       .         . .         . .     .   .     .       .   . .   .           .       .   .       .

 

                                                                                                              (Each dot is a representation of Prime Numbers)

The picture above shows 1 to 500 Prime Numbers positioned across the Prime Field with a positional mapped-out locality. It is where Gravity creates Prime Matter, a discrete unit of blocks—a repeated sequence of orderly functions.
Numbers 7 and 3 and a duality of 73 are spots of containment. This field is an island of stability with calculated measurements on Prime Numbers based on a symmetrical, orderly sequence. A place of curve fitting leads to smoothing and a data point to extract energy. The 73 is an image of a bump function representing a potential energy and starting point of an isolated spot of building blocks. 
 

and continues onwards  

[Mordred]

Sigh I don't need to know what GR  states. I'm very well versed in GR, nor do I need prime numbers to describe that bump. I can describe it using differential calculus. Hence my comment above on Kronecker delta and Levi- Cevita connections.

I can further describe every single particle interaction utilizing the same geometry. The very purpose of mathematics in physics is to describe physical objects and physical processes .

Hence the very name of the science. (Physics).

Do you honestly expect me to interpret images and words ?

Where is the mathematical proofs behind your statements?

 

 

 

 

Edited May 12, 2023 by Mordred

[Baron d'Holbach]

4 minutes ago, Mordred said:

describe physical objects

Oh, I am beyond that. I am explaining before the big bang, Prime Mechanics is explaining how the physical universe was created. 

 

So, you want to know basic stuff? Sure I guess. 

Prime Mechanics pg, 302

Ground State, 1 Dimension, zero spins, confine between [0,1] 

Part 1

The ground state refers to the lowest energy state of a system and can be described by a wave function Ψ(x), which is a mathematical representation of the probability density of finding the system in a particular state. The wave function of the ground state is a stationary wave meaning that it does not change with time. This is because the ground state has the lowest possible energy, and therefore there is no energy available to cause the system to change or evolve over time. It is a fixed, stable wave that represents the lowest energy state of the system.
Let us create a one-dimensional ground state stationary wave function with zero spins that are stationary between 0 and 1. 
Ψ(x) = √(2/L) * sin(πx/L)
This wave function describes a particle that is confined to the region between x=0 and x=L, and has zero spins. The probability density |Ψ(x)|^2 is uniform over the entire length of the box, and the energy of the ground state is given by:
E = (π^2 * h^2) / (2mL^2)
where h is Planck’s constant and m is the mass of the particle.
To apply the wave function Ψ(x) = √(2/L) * sin(πx/L) between 0 and 1, we need to normalize the wave function such that the integral of the probability density over all space is equal to 1. We can do this by using the following normalization condition:
∫0^1 |Ψ(x)|^2 dx = 1
Plugging in the expression for Ψ(x), we get:
∫0^1 |Ψ(x)|^2 dx = ∫0^1 [√(2/L) * sin(πx/L)]^2 dx
Simplifying this expression, we get:
∫0^1 |Ψ(x)|^2 dx = 2/L * ∫0^1 sin^2(πx/L) dx
Using the identity sin^2(θ) = (1/2) - (1/2)cos(2θ), we can rewrite this integral as:
∫0^1 |Ψ(x)|^2 dx = 2/L * [x/2 - (L/2π)sin(2πx/L)] evaluated from x=0 to x=1
Evaluating this expression, we get:
∫0^1 |Ψ(x)|^2 dx = 2/L * [1/2 - (L/2π)sin(2π/L)]
Now, to find the wave function between 0 and 1, we need to normalize Ψ(x) by dividing it by the square root of the integral we just calculated. That is,
Ψ_norm(x) = Ψ(x) / √[2/L * (1/2 - (L/2π)sin(2π/L))]
Substituting in the expression for Ψ(x), we get:
Ψ_norm(x) = [√(2/L) * sin(πx/L)] / √[2/L * (1/2 - (L/2π)sin(2π/L))]
Simplifying this expression, we get:
Ψ_norm(x) = √(2/L) * sin(πx/L) / √(1 - (L/π)sin(2π/L))
This is the normalized wave function for a particle in a one-dimensional box of length L, with the ground state described by Ψ(x) = √(2/L) * sin(πx/L), restricted to the interval from 0 to 1.

Part 2

To apply a node at x = 0.5 to the wave function Ψ(x) = √(2/L) * sin(πx/L), we need to introduce a phase shift of π/2 into the sine function. This is because a node is a point where the wave function goes to zero, and this can be achieved by introducing a phase shift of π/2 into the sine function, which changes its sign at the node.
The modified wave function with a node at x = 0.5 is given by:
Ψ(x) = √(2/L) * cos(π(x - 0.5)/L)
To normalize this wave function, we need to use the same normalization condition as before:
∫0^L |Ψ(x)|^2 dx = 1
Plugging in the expression for Ψ(x), we get:
∫0^L |Ψ(x)|^2 dx = ∫0^L [√(2/L) * cos(π(x - 0.5)/L)]^2 dx
Simplifying this expression, we get:
∫0^L |Ψ(x)|^2 dx = 2/L * ∫0^L cos^2(π(x - 0.5)/L) dx
Using the identity cos^2(θ) = (1/2) + (1/2)cos(2θ), we can rewrite this integral as:
∫0^L |Ψ(x)|^2 dx = 2/L * [x/2 + (L/4π)sin(2π(x - 0.5)/L)] evaluated from x=0 to x=L
Evaluating this expression, we get:
∫0^L |Ψ(x)|^2 dx = 2/L * [L/2 + (L/4π)sin(π)] = 1
Now, to find the normalized wave function with a node at x = 0.5, we need to divide the wave function by the square root of the integral we just calculated. That is,
Ψ_norm(x) = Ψ(x) / √[2/L * (L/2 + (L/4π)sin(π))]
Substituting in the expression for Ψ(x), we get:
Ψ_norm(x) = [√(2/L) * cos(π(x - 0.5)/L)] / √[1 + (1/2π)sin(2π(x - 0.5)/L)]
This is the normalized wave function for a particle in a one-dimensional box of length L, with the ground state described by Ψ(x) = √(2/L) * cos(π(x - 0.5)/L), with a node at x = 0.5.
The wave function describes a particle that is most likely to be found in the region around x = 0.5L, and is less likely to be found as you move away from this point.

Part 3

To apply the standing wave and confine it between 0 and 1, we need to modify the wave function by rescaling it and shifting it along the x-axis.
First, we will scale the wave function by a factor of 1/L, so that it is confined to the interval [0,1]:
Ψ_scaled(x) = √(2/L) * cos(π(x - 0.5)/L) / L
Next, we will shift the wave function by adding 0.5 to x, so that it is centered at x = 0.5 and confined to the interval [0,1]:
Ψ_shifted(x) = √(2/L) * cos(π(x - 0.5)/L) / L, where 0 ≤ x ≤ 1
This is now a one-dimensional stationary wave function that is confined to the interval [0,1] and has zero spin. The amplitude of the wave function is greatest at x = 0.5 and decreases as x moves away from this point, with nodes at x = 0 and x = 1. The wave function is also properly normalized over the interval [0,1] by the normalization factor in the denominator.
The function has been slowly transformed and have shifted into a standing wave, and the node is not strictly at .5 anymore.
The wave function Ψ_shifted(x) is a standing wave, which means it has multiple nodes and antinodes. 

Part 4

Ground State, 2 Dimension, 1/2 spin, confine between [0,1] 

To extend the given equation to two dimensions, we can simply add another dimension, let’s say “y,” to the equation. We can write the two-dimensional equation as:
Ψ_shifted(x, y) = (√(2/L) * cos(π(x - 0.5)/L) * cos(π(y - 0.5)/L)) / L^2
Here, we have multiplied the equation with the cosine of “y” in addition to the cosine of “x”. The equation still satisfies the condition of 0 ≤ x, y ≤ 1.
To describe a spin-½ particle, we can use the concept of spinors. A spinor is a mathematical object that describes the state of a particle’s spin. For a spin-½ particle, the spinor can be written as a two-component column vector. Let’s call the spinor for our particle “ψ.”
ψ = [a, b]^T
Here, “a” and “b” are complex numbers that satisfy the normalization condition |a|^2 + |b|^2 = 1, which ensures that the probability of finding the particle in any state is 1.
To make the particle spin at ½, we can choose “a” and “b” such that the particle is in a superposition of the spin-up and spin-down states. Let’s choose:
a = 1/√2
b = 1/√2
This spinor represents a particle that is equally likely to be found in the spin-up state and the spin-down state.
We can combine this spinor with the position wave function we derived earlier to get the full wave function of the particle:
Ψ(x, y) = (√(2/L) * cos(π(x - 0.5)/L) * cos(π(y - 0.5)/L)) / L^2 * [a, b]^T
Here, “^T” denotes the transpose of the matrix.
The probability of finding the particle at any position can be calculated by taking the absolute value of the wave function and squaring it:
|Ψ(x, y)|^2 = |√(2/L) * cos(π(x - 0.5)/L) * cos(π(y - 0.5)/L) * a|^2 + |√(2/L) * cos(π(x - 0.5)/L) * cos(π(y - 0.5)/L) * b|^2 + 2Re(√(2/L) * cos(π(x - 0.5)/L) * cos(π(y - 0.5)/L) * a * b^*)
Here, “*” denotes the complex conjugate of the spinor, and “Re” denotes the real part of the complex number. The third term represents the interference between the two spin states, and it arises because the two spin states are not orthogonal.
The probability of finding the particle in a particular region can be calculated by integrating this probability density over that region.
Ground State, 3 Dimension, 1 spin, confine between [0,1] and applying a 1% heat bath to showcase a thermal fluctuation. 

Part 5

To extend the given equation to three dimensions, we can simply add another dimension, let’s say “z,” to the equation. We can write the three-dimensional equation as:
Ψ_shifted(x, y, z) = (√(2/L) * cos(π(x - 0.5)/L) * cos(π(y - 0.5)/L) * cos(π(z - 0.5)/L)) / L^3
Here, we have multiplied the equation with the cosine of “z” in addition to the cosines of “x” and “y.” The equation still satisfies the condition of 0 ≤ x, y, z ≤ 1.
To make the particle spin at 1, we can choose the spinor “ψ” as:
ψ = [1, 0]^T
This spinor represents a particle that is always in the spin-up state.
To describe the time evolution of the particle, we can use the master equation, which describes the time evolution of the density matrix “ρ” of a quantum system. The master equation has the form:
dρ/dt = -i[H, ρ] + ∑j (L_j ρ L_j^† - 1/2 {L_j^† L_j, ρ}) + δ(ρ_eq - ρ)/τ
Here, “H” is the Hamiltonian of the system, “L_j” are the Lindblad operators that describe the effects of the environment on the system, “{ , }” denotes an anticommutator, “ρ_eq” is the equilibrium density matrix, and “τ” is the relaxation time.
In our case, since we have only one particle, the Hamiltonian is simply the kinetic energy operator:
H = -ħ^2/2m (∂^2/∂x^2 + ∂^2/∂y^2 + ∂^2/∂z^2)
The Lindblad operators describe the effects of the heat bath on the particle. We can choose the Lindblad operators as:
L_x = √γ σ_x L_y = √γ σ_y L_z = √γ σ_z
Here, “γ” is the rate of decoherence, “σ_x” “σ_y” and “σ_z” are the Pauli matrices, which describe the effects of the environment on the particle’s spin. The Lindblad operators represent the effects of the heat bath on the particle’s position and spin.
The equilibrium density matrix is given by:
ρ_eq = |ψ><ψ|
Here, “><“ denotes the outer product. The equilibrium density matrix represents the particle in its steady state, where it has reached thermal equilibrium with the environment.
Finally, we can add the effect of the heat bath to the master equation by adding the term δ(ρ_eq - ρ)/τ, which represents the relaxation of the particle toward its equilibrium state. We can choose the relaxation time as τ = 100/γ.
Putting everything together, the master equation for our system becomes:
dρ/dt = -i[-ħ^2/2m (∂^2/∂x^2 + ∂^2/∂y^2 + ∂^2/∂z^2), ρ] + ∑j (L_j ρ L_j^† - 1/2 {L_j^† L_j, ρ}) + δ(|ψ><ψ| - ρ)/(100/γ)
This equation describes the time evolution of the density matrix of the particle in the presence of a heat bath.

Part 6

Master Equation 

dρ/dt = -i[-ħ^2/2m (∂^2/∂x^2 + ∂^2/∂y^2 + ∂^2/∂z^2), ρ] + ∑j (L_j ρ L_j^† - 1/2 {L_j^† L_j, ρ}) + δ(|ψ><ψ| - ρ)/(100/γ)

The equation is a master equation that describes the time evolution of the density matrix of a system with three spatial dimensions, one spin degree of freedom, and subject to a thermal bath at 1% temperature.
The first term on the right-hand side of the equation corresponds to the Hamiltonian evolution of the system, which involves the Laplacian operator acting on the spatial part of the wave function. The second term describes the effect of the Lindblad operators, which represent the coupling of the system to its environment. The third term models the effect of the thermal bath on the system by imposing a relaxation time scale on the system’s approach to its equilibrium density matrix. The initial state of the system is given by the density matrix |ψ><ψ|.
 

Here is pg, 301, i call Prime gravity with scalar field 

 

S_phi = ∫ d^11x √|g| [(1/2) g^{ij} ∂_i phi ∂_j phi - V(phi)]

This equation is an action in an 11-dimensional system that describes the dynamics of a scalar field phi. The action consists of two terms:
1. The first term is the kinetic energy term, which describes the energy associated with the motion of the scalar field phi. It is given by (1/2) g^{ij} ∂_i phi ∂_j phi, where g^{ij} is the inverse of the 11-dimensional metric tensor and ∂_i phi is the partial derivative of phi with respect to the i-th coordinate. This term is the same as the one in the Klein-Gordon equation, which is a relativistic wave equation that describes the motion of a spin-0 particle.
2. The second term is the potential energy term, which describes the energy associated with the interactions of the scalar field phi with itself and with other fields in the universe. It is given by V(phi), where V is the potential energy function of phi. This term is similar to the potential energy term in classical mechanics.
The action is a scalar quantity that describes the dynamics of the scalar field phi in 11-dimensional spacetime, taking into account the effects of Gravity, Dark Matter, and Dark Energy through the 11-dimensional metric tensor g^{ij}. The action is used to derive the equations of motion for the scalar field phi, which describes how the field evolves in time and space.
 

On substack, (its free to look) I wrote the mass gap and how Strong force creates particles from the vacuum. Boring. 

https://primemechanics.substack.com/p/final-relativity

I call this final Relativity. 

prime Mechanics pg, 76 explains Mass gap and how particles are made. I give you the ultimate answer. Not the boring one. 

 

Gravity is a elemental Matter. This means Gravity is leading itself, building upon itself (force, acceleration, curvature) toward the physical creation of the universe.

Gravity created everything! 

 

 

 

[Mordred]

Finally some of the related mathematics. Now just to get it into a more readable form hallelujah.

 At least it's a start....

Overall you have standardized common knowledge stuff until you deviate to your own model.

Since when is a 2 dimensional tensor the inverse from an 11 dimensional tensor yes I'm back at 

\[g^{ij}\]

How did you arrive at a 2 dimensional tensor by inverting an 11 dimensional tensor ?

Edited May 12, 2023 by Mordred

[Mordred]

I went through what you had on that website. I sincerely hope you have better detail beyond a bunch of claims that you haven't included the mathematical proofs behind them.

 By mathematical proofs I am not talking formulas one can readily find from other authors or textbooks. 

 I am specifically talking about mathematical proofs that you can truly account for observational evidence for claims in regards to dark matter, dark energy etc. Not flim flam verbal claims that A results in B but your specifically derived mathematical derivatives.

 For example inverting an 11 dimensional tensor is not a straightforward procedure it is a very process. How you arrived at 

 \[g^{ij}\] by doing so is something your going to have to demonstrate. I can't even imagine what steps you missed.....

 You mentioned above the Rheimann zeta function but I have yet to see any mathematical detail directly related to it. Yes it is oft used in numerous physics applications. That doesn't tell me how you applied it specifically. Once again not the verbal description or a bunch of pictures but how you specifically mathematically apply it to your theory. 

A little golden rule a true physics theorist does everything in his ability to prove his own theories wrong. It is one of the best ways to develop a robust theory. All physics theories must make testable predictions. That inherently requires the relevant mathematics. Without that it is nothing more than personal belief.

If you are willing to honestly develop a proper working theory then the direction I would recommend is to apply the Lanqrangians via the covariant derivatives of each field in the standard model including the minimally coupled Langrangian to spacetime. Include any relevant manifold connections to preserve invariant between transformations.

Needless to say your claim of dark matter and dark energy in regards to gravity is extremely outlandish and I have yet to see anything from what you posted here on that site to convince me otherwise 

Edited May 12, 2023 by Mordred

[Baron d'Holbach]

13 hours ago, Mordred said:

2 dimensional tensor by inverting an 11 dimensional tensor

I am assuming this? 

S_phi = ∫ d^11x √|g| [(1/2) g^{ij} ∂_i phi ∂_j phi - V(phi)]

11-dimensional tensor is a 11-dimensional tensor. 

The metric tensor is a rank-2 tensor that relates the distances between nearby points in spacetime.

Its inverse g^{ij} is also a rank-2 tensor, but with the indices raised and lowered using the metric tensor, such that g^{ij} g_{jk} = δ^i_k, where δ^i_k is the Kronecker delta symbol.

The inverse metric tensor can be used to raise and lower indices of other tensors, and other parts.

This is where Prime Mechanics goes beyond anything. 

I am trying to explain, in which I had done, (Prime Mechanics) that gravity has internals. It is a open and closed system that can be open and harvested and extracted of its energy potential. Using tensors and other methods on gravity itself and explaining dark matter as a building block that we can use 'action' upon it. 

These are the proofs and claims prime mechanics are making. 

Now let me state this. It's not the traditional string theory 11 dimensions that people need to worry about. 

It's about gravity and it's internals and externals. I am stating that gravity created from itself energy and matter that led the way to the physical creation aka big bang. So, explaining that gravity itself can be build. 

                                                                           GEM 

11 Dimensions are my tools and connections to prime numbers as I stated as a guide, as a proof mechanism to lead me towards this. 

Anyway, it is another unification equation to combine all fields as 1 and describe it as full unification. 

Your next post I will answer once I get home. Its the most crucial post you ask of.  😀 it's actually the heart of my work, so it will be answered 😀

[Mordred]

No problem with what you have specifically on the Kronecker delta with the notations involving the raising and lowering the indices. That part is correct. Do you also have the Rheimann permutation tensor (Levi-Cevita) psuodo tensor in your derivatives ?

 Yes further detail as to how you went from the formula you posted as well as the elements in your GEM 11 dimensions would be helpful. 

 I look forward to the further details you mentioned. It's hard to examine a theory with essential details missing lol. I assume your applying the Kronecker delta in coordinate basis ?

Edited May 12, 2023 by Mordred

[Baron d'Holbach]

18 hours ago, Mordred said:

claims

You are right. I philosophize the theory. 
GEM = Gravitational Elemental Matter, It’s about Gravity as the steady state, a force that interacts with itself (internals) that leads it to build upon itself (externals) that generates electromagnetism and strong and weak force. I am stating that Gravity created energy and matter (GEM) from itself that led the way to the physical creation, aka the big bang.
Yeah, do not worry, I know… This is an impossible task, and no one said and done it and explained it like how I am saying it. So what do I do? Furthermore, how to even do this? 

18 hours ago, Mordred said:

I can't even imagine what steps you missed.....

I am serious, already stated this:

Let it be known that Prime Mechanic was published on March 14, 2023. Conceptualized in 2007, drafted in 2012, reworked in 2016, and finished in March 2023 at the age of 36.

Let it be known:
Only 3 people have gotten it right
Newton = Gravity (Principia)
Einstein = Gravity (General Relativity)
Delamotte = Gravity (Prime Mechanics)

 

18 hours ago, Mordred said:

By mathematical proofs I am not talking formulas one can readily find from other authors or textbooks. 

So what’s the math I am using? (Note to reader, I am doing the impossible) 

Riemann zeta function
Birch and Swinnerton-Dyer conjecture
Hodge conjecture
Yang-Mills existence and mass gap problem
Navier–Stokes existence and smoothness
P versus NP problem
Poincaré conjecture
All Clay Mathematics Institute questions and all the unsolved math, physics, and science-related questions combine as 1 to solve this. 
Prime mechanic is Yes, and states them all as all True. Prime Mechanic is the true Langlands program. It should be called Prime Land! 

Where to start the impossible? 

Let us build a Field. A Prime Field. Sure, with what? Showcase Riemann zeta function as correct, Introduce Prime Numbers, Prove Prime numbers and its conjectures, and, place them in the Field. Solve Zeta and use that as a guide foundation. 

PM pg, 10 

“Throughout the chapter, you will see Prime Numbers as a representation of Nature, Forces, and Constants;”

“Prime Mechanics, two philosophies are called the Repetitious Function and the Loop System. The Repetitious Function is a systematic iteration, a continuous, repeated, deterministic polynomial-time towards the equilibrium point called Aether. The Loop System is a periodic operation of two. The first is a systematic operation of repeating two arithmetic operations that decrease/collapse into a positive integer of 1. The second systematic operation is a reversible loop that switches number positions, moves upwards, switches again to follow operation one, and begins a loop operation downwards.”

Prove Prime numbers, Twin primes, Prove Collatz conjecture, okay, sure. 

Apply this to Prime Field with Zeta as the primary guide. 

PM pg, 11

“The Prime Mechanic system employs a geometric space with manifold dimensions and curvature to explain a dimensionless field based on natural mathematical numbers.”
Sure, but how? 

PM pg, 11

“The Prime Field is governed by a fundamental dimensional constant of 1/137, which sets the order for the numerical values of the key components: One Gravity, One Aether, Three Strong Forces, and Seven Weak Forces. The foundation of the Prime Field is represented by the number 1 (11), which corresponds to the 11 dimensions comprising the gravitational constant Field within the system.”

This is philosophy, Thanks Poincare for this   it means nothing to you but everything to me to work with.   The first 10 pages is Prime mechanic philosophy. 

PM pg, 12

S = ∫d^4x√g [Λ(g) - 1/2κ^2(R + m^2(z)h) + L_m]

where Λ(g) is a scalar function of the metric g that determines the cosmological constant, κ^2 = 8πG_N is the gravitational constant, R is the Ricci scalar, h is a transverse traceless tensor field that describes gravitational fluctuations, and L_m is the Lagrangian for matter fields. The function m(z) is a running mass parameter that depends on the energy scale z, and is chosen such that all energies are bounded between 0 and 1. The equation is well-behaved and does not have blow-ups or singularities due to the property of asymptotic safety, which ensures that the action remains finite at all energy scales. 

This property also resolves the hierarchy problem and the problem of ultraviolet (UV) divergences. The inclusion of a running mass parameter is a common feature and is included. However, the specific form of the function and its implications for the behavior of Gravity at high energies may depend on the particular approach taken. The use of regularization techniques such as zeta regularization to renormalize the equation is also included in this framework.
Overall, the equation is designed to be finite at all energy scales, and prevents blow-ups, singularities, and infinities. The equation provided is a form of the gravitational action that unifies Gravity with matter and could potentially describe physics at energies up to or beyond 10^16 GeV, making it an example of a UV-complete of Gravity.

I want to know only Gravity, GEM! 

Where do we go here? Back to the Prime Field. 

Gμν = 8πTμν + Λgμν = 2π(α^2 + θ_W^2) ħ^3 c^5 / [(4πα_s G)^2 m_p^2] * (ζ_R(1/2) / ζ_R(1))^2 + (Q - W)

 
The equation is Einstein’s field equation, which describes the relationship between the curvature of spacetime and the distribution of matter and energy. The left-hand side of the equation represents the curvature of spacetime, which is determined by the distribution of matter and energy represented by Tμν, and the cosmological constant Λ. The right-hand side of the equation represents the thermodynamic effects of the fundamental forces (electromagnetic, weak, and strong) on the system, as well as the thermodynamic processes occurring within the system, such as heat exchange (Q) and work done (W), which affect its energy (ΔE).
The right-hand side of the equation are the sources of the gravitational Field. The first term on the right-hand side represents the energy-momentum tensor of matter and radiation, while the second term represents the cosmological constant, which is a constant energy density that drives the expansion of the universe.
Prime Mechanic states that the creation of particles from the vacuum state occurs at a specific energy scale, which is related to the Riemann zeta function evaluated at 1/2. This energy scale is often referred to as the “vacuum energy” or “zero-point energy.”

PM pg, 19 

“Before we dive deeper into building the Prime Field in Chapter 2, a place with a grid, a place of position that we know excitation can exist. We must discuss the incremental steps of the system cores—the system’s functions, actions, and motions.”

So you are still introducing Prime Mechanics and only on page 19 out of 340? And from 29 to 40 you explain what the heck is these buzzwords open and closed Gravity? It is not a buzzword. 

It is Gravity. Gravity can be opened, closed, extracted, and harvested for potential energy. 

Finally, I made it to the ground state. And the construction of the Prime Field.  

PM pg, 45

Must show proof of Zeta to be true and apply it the Field. Use the prime number as a distribution center and determine the exact location of potential energy.
I stated this above what I am using, Math? 

Prime Field is based on this:

s = 1, which means that the function goes to infinity at that point. 
Re(ζ) = ½, which means all real numbers are place here. 
s = 0, which means the singularity, is undefine and removable.

Once figured out and showcased, lets move on. 

Prove it:
ζ(1/2) = 2(2π)-1/2 Γ(1/4) ∑n=1^∞ σ0(n) n-1/4

We are on page 60-340

We will apply Yang Mill’s equations and math to solve mass gap, symmetry breaking, and particle creation. And so much more.
Remember, we will apply all to the Prime Field. 

F^μν = ∂^μA^ν - ∂^νA^μ - i[A^μ,A^ν]

Remember, we are building a Field, a Prime Field, A geometric structure—Gravity itself. 

PM pg, 70 

We apply Hamiltonian, Lagrangian, Hilbert space , Yang-Mills, Noether’s theorem, Gauge Fields, QCD
Simple math:

    S = ∫ d^4x [L(Q) + JQ - mΦ(Q)]

So far, Prime Mechanics must have over 100 concepts, conjectures, and ideas, and it's only page 70. 

Prime Mechanics continues, explaining Mass gap, symmetry breaking, Chiral symmetry, prove the steady state and explains Deformation.

Later we continue and explain Gravity force with:

G_{\mu\nu} = 8\pi T_{\mu\nu} + \frac{\omega}{\phi^2} \left( \nabla_\mu \phi \nabla_\nu \phi - \frac{1}{2}g_{\mu\nu} \nabla^2 \phi \right)

This leads us to:

E = G/EM11 * P0^2 * Prime(1/2)

Where:
E represents the energy generated by the gravitational interaction between matter (M) and the gravitational field (G).
EM11 is the constant related to the gravitational energy matter.
P0 is the rapidly approaching function, which approaches 0 near 0.
Prime(1/2) is the well-behaved function that does not blow up or become infinite as s approaches 1/2.
This equation suggests that the energy generated by the gravitational interaction is proportional to the product of the gravitational energy matter constant, the square of the rapidly approaching function, and the well-behaved function evaluated at the central point s = 1/2. It also implies that the gravitational interaction between matter and the gravitational field is seamless, smooth, and behaves well, without any infinities or singularities.
This will lead us to create a smooth curve to map a smooth function onto a physical system. This creation process is the building block of creating a smooth curve at 100% mapping points. The creation of Matter. 
The achievement of a geometric curve, a smooth, flat curvature motion. It is based on P=0 and P ½. The fastest 1,2 step process at the gravitation spot of the massless location to form a unit number 1. Here we will combine the major players to the Prime Field.

We will add Birch–Swinnerton-Dyer idea and the elliptic curve to understand The Field and position better.

From Page 100 to 200

We prove Prime Numbers, Prove Finite, Prove Infinity Limits, prove Birch and Swinnerton-Dyer Conjecture, P=NP, Prove smoothness, Prove transformations and so much more. 

My favorite was transformations, an invariant transformation from one to another. 

And around this point:

Δ = g^(-1)(∂^2/∂z_i ∂z^i)

where g is the Kähler metric on the manifold, z_i are complex coordinates, and z^i are the complex conjugates of the coordinates.
We can conclude that parallel lines in a plane intersect at a point at infinity and are the origin spot ½. A positional spot that densifies and transforms, and extends into another with an invariant property. This, in return, generates a temperature distribution throughout and becomes, over time, radioactive; hence Gravity becomes Elemental.

I am establishing my main theory that Gravity is ELEMENTAL. 

I will not add any more; I will speak only on the above as this is enough.  You must understand that I am building up the Prime Field System, a step by step approach and coming to a conclusion. From discrete units to a continuous smooth system. Everything  I missed? I actually have it, but not posted here. I have all unsolved questions sprinkled in the book. Answered or not but is inside as a connection of 1. 

 

5 hours ago, Mordred said:

Kronecker delta

I use Riemann zeta function as my primary tool. They are not the same but very similar, but Zeta is more complex and more intuitive. 

s=1

And the coordination are used with Prime distribution, Zeta and Symmetries.... eg, reflection symmetry. 

And what I found interesting is any missing concept or theory or idea and later apply to GEM makes GEM even more correct? If you haven't notice name is Baron d'Holbach, this should mean to others is that, yes I tried my best to debunk my own theory but couldn't. 
 

                                                                                                                GEM = Gravitational Elemental Matter 

[Mordred]

Ok this is getting to be a waste of time. Its obvious you have far more claims than the mathematical proof to substantiate your claims.  So lets start with something simple.

gravity itself forget everything else. Lets toy model a system where you have a stress energy momentum tensor where \[T^{\mu\nu}=0\] you have  zero spacetime curvature setting k=0. Whatever mass/energy value you like doesn't matter as this defines the T_^00 component. In essence you have a uniform mass/energy distribution.

 Now apply Newtons shell theorem which shows in this case g=0. aka no gravity. Why would this situation cause the creation of our universe as you claim when you have in essence a condition of zero gravity ? Mathematically prove this is possible and arrive at the covariant derivative for the standard model

\[\mathcal{L}=\underbrace{\mathbb{R}}_{GR}-\overbrace{\underbrace{\frac{1}{4}F_{\mu\nu}F^{\mu\nu}}_{Yang-Mills}}^{Maxwell}+\underbrace{i\overline{\psi}\gamma^\mu D_\mu \psi}_{Dirac}+\underbrace{|D_\mu h|^2-V(|h|)}_{Higgs}+\underbrace{h\overline{\psi}\psi}_{Yukawa}\].

Don't worry I honestly don't expect you to be able to do so but lets see if you can which amounts to what your claims and boasts have been gearing towards in regards to a GUT theory.

lets examine a professional example done properly to simply examine the possibility of the cosmological constant (dark energy as the result of the Higgs field and subsequently connecting it to inflation.. (not my work credit will be included.)

Higgs Inflation Single scalar field Modelling.

\[S=\int d^4x\sqrt{-g}\mathcal{L}(\Phi^i\nabla_\mu \Phi^i)\]

g is determinant

Einstein Hilbert action in the absence of matter.

\[S_H=\frac{M_{pl}^2}{2}\int d^4 x\sqrt{-g\mathbb{R}}\]

set spin zero inflaton as

\[\varphi\]

minimally coupled Langrangian as per General Covariance in canonical form. (kinetic term)

\[\mathcal{L_\varphi}=-\frac{1}{2}g^{\mu\nu}\nabla_\mu \varphi \nabla_\nu \varphi-V(\varphi)\]

where \[V(\varphi)\] is the potential term

integrate the two actions of the previous two equations for minimal scalar field gravitational couplings

\[S=\int d^4 x\sqrt{-g}[\frac{M_{pl}^2}{2}\mathbb{R}-\frac{1}{2}g^{\mu\nu}\nabla_\mu\varphi \nabla_\nu \varphi-V(\varphi)]\]

variations yield the Euler_Langrene

\[\frac{\partial \mathcal{L}}{\partial \Phi^i}-\nabla_\mu(\frac{\partial \mathcal{L}}{\partial[\nabla_\mu \Phi^i]})=0\]

using Euclidean commoving metric

\[ds^2-dt^2+a^2(t)(dx^2+dy^2=dz^2)\]

this becomes

\[\ddot{\varphi}+3\dot{\varphi}+V_\varphi=0\]

\[S=\int d^4 x\sqrt{-g}[\frac{M_{pl}^2}{2}\mathbb{R}-\frac{1}{2}g^{\mu\nu}\nabla_\mu\varphi \nabla_\nu \varphi-V(\varphi)]\]

and 

\[G_{\mu\nu}-\frac{1}{M_{pl}}T_{\mu\nu}\]

with flat commoving geometry of a perfect fluid gives the energy momentum for inflation as 

\[T^\mu_\nu=g^{\mu\lambda}\varphi_\lambda \varphi_\nu -\delta^\mu_\nu \frac{1}{2}g^{\rho \sigma} \varphi_\rho \varphi_\sigma V(\varphi)]\]

 

\[\rho=T^0_0=\frac{1}{2}\dot{\varphi}^2+V\]

\[p=T^i_i (diag)=\frac{1}{2}\dot{\varphi}^2-V\]

\[w=\frac{p}{\rho}\]

\[w=\frac{1-2 V/\dot{\varphi^2}}{1+2V/\dot{\varphi^2}}\]

***method by Fernando A. Bracho Blok Thesis paper.***

https://helda.helsinki.fi/bitstream/handle/10138/322422/Brachoblok_fernando_thesis_2020.pdf?sequence=2&isAllowed=y

that is what I am looking for. This example tells me how the author arrived at the equation of state where w=-1  using the Higgs field. This is what is meant by a mathematical Proof...

The author provides all the pertinant mathematical detail required for a thesis paper.

 

Edited May 13, 2023 by Mordred

[Baron d'Holbach]

48 minutes ago, Mordred said:

Its obvious you have far more claims than the mathematical proof to substantiate your claims

Yes, I do. It is overwhelming. Thats why I simplified all my equations and ultimately ended with GEM. 

I will work on your equation and apply it to GEM and see what happens. Not sure when ill post back but will with hopeful results.

Cheers 

 

Edit* its funny that when I over look the above equation, my simplified equations are better, but owell...

Challenge accepted anyway, just a added equation for GEM.

Edited May 13, 2023 by Baron d'Holbach

[Mordred]

Well technically every equation I just posted is the simplified form. With the exception of the SM Langrangian the remaining equations are in the Newtonian limit.

The first equation would take roughly 30 pages of partial derivatives.

Lol yet the highest dimension involved is 4. So I wouldn't hate to see the chain rules applied to 11 dimensions.

By the way +1 on your last post. It is a daunting task but an essential step to validate any formula or model. There is mathematical proof behind every equation even simple ones like f=ma.

Edit I should also point out having a large number of dimensions isn't desirable. You always want to reduce any formula to the lowest number of dimensions possible to describe a system or state. The fewer dimensions the better.

Edited May 13, 2023 by Mordred

[Baron d'Holbach]

@Mordred

 

How nice of the 1 votes  , the others red are Fernando's  Prime Mechanic is one of greatest scientific masterpiece of the 21 century. I would of loved for a book like this 10 years ago. 

Alright let’s get started 
So there’s a lot of problems with what you are asking. Not your fault. As I stated many times, we are stuck in the 1960s. Almost everyone can not understand Gravity, so they will rely on Quantum Gravity, String theory ideas, and old habits. 
Also, correct on the last post, Gravity and the universe itself is 4D. All this 11D is not necessary and wrong and must always drop back down. The extra ‘D’ is within Gravity itself. 

Prime Mechanic states: Gravity is an elemental matter. 

1.    Newtons shell theorem which shows in this case g=0. aka no gravity.
Gravity is technically never zero, even at the furthest distance from an object, it will appear zero but will always have a motion within it. This is the heart of Prime Mechanic, as stated as the core tenets. 
Gravity is a fundamental force of 1 that is itself the emergent—the Steady State. Gravity is always in constant motion within itself that generates and layers upon itself to form energy and matter. GEM. Prime Mechanic is 100% general relativity with expansion to it. This is why I call it Final Relativity. 
Even in regions of space (Gravity) that appear to be empty, virtual particles are popping in and out of existence, and these particles (Gravity pockets) can have mass and energy (its Gravity itself, Dark Matter) that contribute to the overall gravitational field. 
This part might be too much lol, “Gravity is a self-creating particle machine. The density generates and pops virtual particles into and out of themselves (Gravity existence).  
Therefore, as long as mass or energy is present in the universe, there will be Gravity and vice-versa. 

2.    The by Fernando A. Bracho Blok Thesis paper equation.
I like it. It explains that matter and energy produce Gravity. Paper is boring like all science papers lol, one of the reasons we are stuck in the 1960s, but great basic stuff overall. 
I think he got his equation wrong. The one you posted? 

(φ˙^2 + V(φ)) instead of φ2˙. The correct expression for w is:
w = 1 - 2V(φ)/(φ˙^2 + V(φ))

If that is an error, the thesis might be full of e…..? No offense, Fernando. Prime mechanic has been published 😊 
So, Prime Mechnaic is proving the opposite of Fernando A. Bracho Blok Thesis paper while agreeing too. He and all are always 50% right. The other 50% is that Gravity within itself created energy and matter. GEM 

No offense Fernando, but papers like yours will always keep people stuck in the 1960s. Sorry.
PM is GR 100%, with this understanding, there are dozens of ways to explain this. As stated in point 1, we can start building a system automatically. 
So, with that mention, I will explain it like this.

3.    GEM created the physical universe, aka the big bang. 
Gravity self-attracted itself, causing energy into matter to become more and more concentrated in certain areas, eventually forming a massive, dense object. This geometric object is concentrated enough that it reaches a point of infinite density and temperature. This would result in the formation of a singularity.
Once the singularity is formed, it becomes unstable and rapidly expands, creating a massive release of energy and matter that we know as the Big Bang. As the universe expands and cools, the energy and matter from the singularity will eventually form stars, galaxies, and planets.
(This is written here like this, the book is well written of this story) 

Now show the math of this impossibility, right?

Let’s call this Prime Field 0.4 equation.

Here I will explain a 4 Dimensional system. Starting off as an open system, it can exchange energy, matter, or information with its environment. I am basically saying that Gravity is self-interacting with itself. 
After, I will explain a transition to the singularity (I won’t explain it here, its in the book with Ricci ideas)
After I will resolve the singularity into the big bang
After the system becomes a closed system

So yes, Gravity plays a significant by affecting the Hamiltonian term, which describes the system’s energy. It includes a gravitational potential term, it has a dynamic im-pack on the system and the transformation of the system and the distribution of matter in the system.
I also sneaked in my Riemann zeta function into this 😊 

Math:

dρ/dt = -i[H_grav+H_matter, ρ] + ∑j (L_j ρ L_j† - 1/2{L_j† L_j, ρ}) + δ(|ψ><ψ| - ρ)/(100/γ)

This equation is known as the Lindblad master equation and describes the time evolution of the density matrix ρ of a quantum system in the presence of both a Hamiltonian and interaction with the environment. Here are the individual terms:
•    dρ/dt: This is the time derivative of the density matrix, which describes how the system’s state changes with time.
•    -i[H_grav+H_matter, ρ]: This term describes the effect of the Hamiltonian terms H_grav and H_matter on the density matrix. H_grav is the Hamiltonian that describes the gravitational potential of the system, while H_matter is the Hamiltonian that describes the matter distribution in the system based on prime number sequences and their relationship to the Riemann zeta function at the point 1/2. The commutator [H_grav+H_matter, ρ] is used to describe the time evolution of the density matrix due to the Hamiltonian terms.
•    ∑j (L_j ρ L_j† - 1/2{L_j† L_j, ρ}): This term describes the effect of the interaction with the environment, modeled by jump operators L_j. The first term in this expression describes how the density matrix evolves due to the system-environment interactions, while the second term describes the effect of the environment on the system by “collapsing” the density matrix. The sum over j accounts for all possible interactions with the environment.
•    δ(|ψ><ψ| - ρ)/(100/γ): This term describes a hypothetical mechanism for preventing the system from diverging or collapsing completely. It adds a small amount of noise to the density matrix in the form of a delta function, which keeps the system in a stable state.
dρ/dt = -i[H_grav+H_matter+H_singularity, ρ] + ∑j (L_j ρ L_j† - 1/2{L_j† L_j, ρ}) + δ(|ψ><ψ| - ρ)/(100/γ)
This equation is similar to the previous one, but includes an additional Hamiltonian term, H_singularity, which accounts for the gravitational potential of a singularity at the center of the system. 

dρ/dt = -i[H_grav+H_matter+H_cosmological, ρ] + ∑j (L_j ρ L_j† - 1/2{L_j† L_j, ρ}) + δ(|ψ><ψ| - ρ)/(100/γ)

This equation includes an additional Hamiltonian term, H_cosmological, which accounts for the cosmological constant and the Big Bang event. The cosmological constant is a term in Einstein’s field equations that describes a repulsive force that counteracts Gravity and causes the universe to accelerate in its expansion. The Big Bang event refers to the moment of the universe’s origin, when it began expanding from a single point in space and time. The delta function in this equation describes the transition from an open system to a closed system.

If the system undergoes a Big Bang event with a cosmological constant and subsequently turns into a closed system:

dρ/dt = -i[H_grav+H_matter+H_cosmological, ρ] + δ(|ψ><ψ| - ρ)/(100/γ)

where H_grav is the Hamiltonian term due to Gravity for a 4-dimensional system, H_matter is the Hamiltonian term due to the matter distribution according to prime number sequences and their relationship to the Riemann zeta function at the point 1/2, H_cosmological is the Hamiltonian term due to the cosmological constant and the Big Bang event, and the delta function describes the transition from an open system to a closed system.
Overall, this a Lindblad master equation with an additional Hamiltonian term due to the cosmological constant and the Big Bang event. The system undergo a Big Bang event and becomes a closed system, and the delta function in the equation represents the transition from an open to a closed system. The Hamiltonian terms H_grav and H_matter represent the gravitational potential and matter distribution of the system, respectively. The equation also includes the Lindblad terms, which account for the interaction with the environment modeled by jump operators L_j. Finally, the last term in the equation adds a small amount of noise to the density matrix to prevent the system from diverging or collapsing altogether.

The end  

This system explained a transition from an open to a closed system. Here on the closed system, we are a flat surface that stays the same forever. An unalterable flat field that will continue to expand forever.

…. Seriously, that’s it…., I wrote and published this in prime mechanic in a book format. My book should technically be the standard for Gravity and the theory of everything. I also use PM applications as a tool to create a Terminator robot, lol. Proving how to create a sentient machine. I know my book is claiming the theory of everything, ironically,…
 

[swansont]

2 hours ago, Baron d&#x27;Holbach said:

Seriously, that’s it…., I wrote and published this in prime mechanic in a book format

!

Moderator Note

Seriously - we don’t allow advertising or promotion. If you keep bringing this up the topic will be closed. 

 

[Mordred]

3 hours ago, Baron d'Holbach said:

@Mordred

H

2.    The by Fernando A. Bracho Blok Thesis paper equation.
I like it. It explains that matter and energy produce Gravity. Paper is boring like all science papers lol, one of the reasons we are stuck in the 1960s, but great basic stuff overall. 
I think he got his equation wrong. The one you posted? 

(φ˙^2 + V(φ)) instead of φ2˙. The correct expression for w is:
w = 1 - 2V(φ)/(φ˙^2 + V(φ))

If that is an error, the thesis might be full of e…..? No offense, Fernando. Prime mechanic has been published 😊 
So, Prime Mechnaic is proving the opposite of Fernando A. Bracho Blok Thesis paper while agreeing too. He and all are always 50% right. The other 50% is that Gravity within itself created energy and matter. GEM 

No offense Fernando, but papers like yours will always keep people stuck in the 1960s. Sorry.
 

 

Every single inflationary related theory will have its own variations on the equations of state. The w=-1 is an approximation that essentially states its constant. However it also doesn't require to start out prior to electroweak symmetry breaking as precisely w=-1. The primary goal however is to include the Mexican hat potential of the metastability conditions. Predict the correct number of e=folds and have the correct slow roll to match observational data. The minimum required e-folds needed is 55 anything lower will not match however higher values still have the potential to match depending on slow roll rates.

 Anyways the real reason I posted those equations was to give an example of what steps are required to develop a proper theory. Yet they never ever take the time to provide the details on how they precisely derived their equations. EVER>

 If you cannot provide the mathematical steps to derive a given formula then the formula is absolutely useless to anyone else.

 Every formula has a mathematical Proof, that mathematical proof gives all the required steps on how that formula was mathematically derived. No formula is ever randomly created by intuitive imagination....It simply doesn't work that way.

 

 

3 hours ago, Baron d'Holbach said:

@Mordred

1.    Newtons shell theorem which shows in this case g=0. aka no gravity.
Gravity is technically never zero, even at the furthest distance from an object, it will appear zero but will always have a motion within it. This is the heart of Prime Mechanic, as stated as the core tenets. 
Gravity is a fundamental force of 1 that is itself the emergent—the Steady State. Gravity is always in constant motion within itself that generates and layers upon itself to form energy and matter. GEM. Prime Mechanic is 100% general relativity with expansion to it. This is why I call it Final Relativity. 
Even in regions of space (Gravity) that appear to be empty, virtual particles are popping in and out of existence, and these particles (Gravity pockets) can have mass and energy (its Gravity itself, Dark Matter) that contribute to the overall gravitational field. 
This part might be too much lol, “Gravity is a self-creating particle machine. The density generates and pops virtual particles into and out of themselves (Gravity existence).  
Therefore, as long as mass or energy is present in the universe, there will be Gravity and vice-versa. 

 

spacetime itself is not gravity. Spacetime is the geometric field, You can have spacetime without gravity. That is the point I was making. Gravity results form spacetime curvature itself not from a uniform distribution. Or more accurately spacetime curvature aka what we consider gravity is a result of a non zero stress energy momentum tensor. If every particle is non accelerating ie in the freefall equivalent state you can motion without gravity. Google Einstein's equivalence principle for further details on that

 

3 hours ago, Baron d'Holbach said:

 

dρ/dt = -i[H_grav+H_matter, ρ] + ∑j (L_j ρ L_j† - 1/2{L_j† L_j, ρ}) + δ(|ψ><ψ| - ρ)/(100/γ)

This equation is known as the Lindblad master equation and describes the time evolution of the density matrix ρ of a quantum system in the presence of both a Hamiltonian and interaction with the environment. Here are the individual terms:
•    dρ/dt: This is the time derivative of the density matrix, which describes how the system’s state changes with time.
•    -i[H_grav+H_matter, ρ]: This term describes the effect of the Hamiltonian terms H_grav and H_matter on the density matrix. H_grav is the Hamiltonian that describes the gravitational potential of the system, while H_matter is the Hamiltonian that describes the matter distribution in the system based on prime number sequences and their relationship to the Riemann zeta function at the point 1/2. The commutator [H_grav+H_matter, ρ] is used to describe the time evolution of the density matrix due to the Hamiltonian terms.
•    ∑j (L_j ρ L_j† - 1/2{L_j† L_j, ρ}): This term describes the effect of the interaction with the environment, modeled by jump operators L_j. The first term in this expression describes how the density matrix evolves due to the system-environment interactions, while the second term describes the effect of the environment on the system by “collapsing” the density matrix. The sum over j accounts for all possible interactions with the environment.
•    δ(|ψ><ψ| - ρ)/(100/γ): This term describes a hypothetical mechanism for preventing the system from diverging or collapsing completely. It adds a small amount of noise to the density matrix in the form of a delta function, which keeps the system in a stable state.
dρ/dt = -i[H_grav+H_matter+H_singularity, ρ] + ∑j (L_j ρ L_j† - 1/2{L_j† L_j, ρ}) + δ(|ψ><ψ| - ρ)/(100/γ)
This equation is similar to the previous one, but includes an additional Hamiltonian term, H_singularity, which accounts for the gravitational potential of a singularity at the center of the system. 

 

That is not the Limblad master equation.

here is the mathematical proofs related to the Limblad master equation.

https://arxiv.org/pdf/1906.04478.pdf

see the required steps to arrive at equation 92 of said article. If you wish to counter me on that last statment feel free to provide a peer reviewed article showing the equation you provided as the Limblad master equation.

Edited May 13, 2023 by Mordred

[Baron d'Holbach]

20 minutes ago, Mordred said:

spacetime itself is not gravity. Spacetime is the geometric field, You can have spacetime without gravity.

That's old school way of thinking. Gravity is Spacetime. Space is gravity. 

My mathematical proofs are all the equations and even new discovery that will all be popping up soon. Example, gravity created light. That was stated in my work and its been discover by physicist now. And this will only be the beginning. it took 4 years until General Relativity to be proven right. 

So, technically all my proofs are my equations, models and countless predictions. I rather see a disprove of my equations, models and notations. 

Unless Prime mechanics gets billions of funding to properly study and build a gravity machine. The proof will be in the simple simplified equations, notations and soon to be discoveries. 

[Mordred]

so you claim but have not supplied the required details. I have a bridge to sell you in Brooklynn enough said

39 minutes ago, Baron d'Holbach said:

That's old school way of thinking. Gravity is Spacetime. Space is gravity. 

My mathematical proofs are all the equations and even new discovery that will all be popping up soon. Example, gravity created light. That was stated in my work and its been discover by physicist now. And this will only be the beginning. it took 4 years until General Relativity to be proven right. 

So, technically all my proofs are my equations, models and countless predictions. I rather see a disprove of my equations, models and notations. 

Unless Prime mechanics gets billions of funding to properly study and build a gravity machine. The proof will be in the simple simplified equations, notations and soon to be discoveries. 

this statement alone counters any claims that you model is compatible with GR it also counters your claim of General Covariance. Einstein also provided a mathematical proof of every one of his theories no one took his word of honor that his mathematics works. He had to mathematically prove they would work with known physics at the time. 

Edited May 13, 2023 by Mordred