Excerpt from journal, needs math symbols generated for this webpage

Model Einstein’s Mass Energy balance equation such that pc in that equation can be modulated in relation to a Sum of diverse vectors of p (momentum). The purpose is to identify pc in both the mass and the minor term pc. Convert scalars of momentum (p) into vectors. And identify and test for “types” of energy different than scalar energy. Energy that acts differently than observable in common experiments.

https://sl.bing.net/fWOYxSB1h0e

First, let’s recall Einstein’s mass-energy equation, which states that the energy (E) of a body is equal to its mass (m) times the square of the speed of light (c): ²

E = mc^2 + pc

This equation implies that mass and energy are equivalent and can be converted into each other. For example, in nuclear reactions, some of the mass of the atoms is converted into energy.

Now, let’s look at the term pc in this equation, where p is the momentum of the body. Momentum is defined as the product of mass and velocity: ⁷

$$p=mv$$

Using this definition, we can rewrite the mass-energy equation as follows:

$$E=\frac{pc}{v}$$

This equation shows that the energy of a body depends on its momentum and its velocity. If we want to model this equation using a mathematical series, we need to find a way to express pc as a sum of terms involving p.

One possible approach is to use a power series expansion, which is a way of approximating a function using an infinite sum of powers of a variable. For example, the exponential function can be written as a power series as follows: ⁶

$$e^x=\sum_{k=0}^\infty \frac{x^k}{k!}=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\cdots$$

Using this idea, we could try to write pc as a power series in terms of p, such as:

$$pc=a_0+a_1p+a_2p^2+a_3p^3+\cdots$$

where $a_k$ are some coefficients that we need to determine. To do this, we would need to find a function that has pc as its value when evaluated at p, and then use its power series expansion. For example, if we had a function f such that f(p)=pc, then we could write:

$$pc=f(p)=\sum_{k=0}^\infty \frac{f^{(k)}(0)}{k!}p^k$$

where $f^{(k)}(0)$ is the kth derivative of f at zero. However, finding such a function f may not be easy or possible.

Another possible approach is to use a Fourier series expansion, which is a way of approximating a periodic function using an infinite sum of sines and cosines. For example, a square wave function can be written as a Fourier series as follows: ⁸

$$f(x)=\frac{4}{\pi}\sum_{n=1}^\infty \frac{\sin((2n-1)x)}{2n-1}$$

Using this idea, we could try to write pc as a Fourier series in terms of p, such as:

$$pc=b_0+\sum_{n=1}^\infty (b_n\cos(np)+c_n\sin(np))$$

where $b_n$ and $c_n$ are some coefficients that we need to determine. To do this, we would need to find a periodic function that has pc as its value when evaluated at p, and then use its Fourier series expansion. For example, if we had a function g such that g(p)=pc and g(p+2\pi)=g(p), then we could write:

$$pc=g(p)=\frac{a_0}{2}+\sum_{n=1}^\infty (a_n\cos(np)+b_n\sin(np))$$

where $a_n$ and $b_n$ are given by:

$$a_n=\frac{1}{\pi}\int_{-\pi}^\pi g(x)\cos(nx)dx$$

$$b_n=\frac{1}{\pi}\int_{-\pi}^\pi g(x)\sin(nx)dx$$

However, finding such a function g may not be easy or possible either.

Modeling Einstein’s mass-energy equation using a mathematical series is not a straightforward task. It may require some creativity and ingenuity to find suitable functions and series expansions.

¹ https://www.britannica.com/science/E-mc2-equation

² https://www.nrc.gov/reading-rm/basic-ref/glossary/mass-energy-equation.html

³ https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_A_Molecular_Approach_%28Tro%29/20%3A_Radioactivity_and_Nuclear_Chemistry/20.08%3A_Converting_Mass_to_Energy-_Mass_Defect_and_Nuclear_Binding_Energy

⁴ https://www.vedantu.com/physics/mass-energy-equivalence

⁵ https://www.discovermagazine.com/the-sciences/e-mc2-what-does-einsteins-most-famous-equation-mean

⁶ https://en.wikipedia.org/wiki/List_of_mathematical_series#Power_series

⁷ https://www.math.net/series

⁸ https://en.wikipedia.org/wiki/Fourier_series

Source: Conversation with Bing, 7/14/2023

(1) E = mc² | Equation, Explanation, & Proof | Britannica. https://www.britannica.com/science/E-mc2-equation.

(2) Series (mathematics) – Wikipedia. https://en.wikipedia.org/wiki/Series_%28mathematics%29.

(3) List of mathematical series – Wikipedia. https://en.wikipedia.org/wiki/List_of_mathematical_series.

(4) Series – Math.net. https://www.math.net/series.

(5) Mass-energy equation | NRC.gov. https://www.nrc.gov/reading-rm/basic-ref/glossary/mass-energy-equation.html.

(6) 20.8: Converting Mass to Energy- Mass Defect and Nuclear Binding Energy. https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_A_Molecular_Approach_%28Tro%29/20%3A_Radioactivity_and_Nuclear_Chemistry/20.08%3A_Converting_Mass_to_Energy-_Mass_Defect_and_Nuclear_Binding_Energy.

(7) Mass – Energy Equivalence – Derivation and Applications – Vedantu. https://www.vedantu.com/physics/mass-energy-equivalence.

(8) E=mc2: What Does Einstein’s Most Famous Equation Mean?. https://www.discovermagazine.com/the-sciences/e-mc2-what-does-einsteins-most-famous-equation-mean.

(9) Series (Mathematics) – Definition of Series, Finite and Infinite Series. https://byjus.com/maths/series/.

_________ temporary thought capture

The following is meant to explain the basis of my question, since space in the question is limited.

Can Einstein’s mass energy equivalence equation be vectorized, and made part of a series, such that mass becomes insignificant based on sympathetic recursion. New references for speed of light and momentum relative to a different dimension of consideration.

Simething like Tensors, but actively correlating equations with actual physics. Having other dimensions of actual physics shape equations through sympathetic recursion.

Quantum Physics variation profiles stimulating recursive formations; adjusting the modals of weighted variables in the equivalence equation. Breaking up variables into more descriptive variables where modals tend to diverge.

Mathematical operators seem to represent types of entanglements. Associating influence from a distance.

To detect and manipulate other dimensions (part of actual physics) requires manipulating/violating every law of physics we consider, or it would not be another dimension.

Or the model might have vector notation and weightings to represent dimensional influence in the mutually consistent dimensional perspective desired.

How would laws of physics exist, and yet be part of other dimensions. Like Dark Matter and Dark Energy?

Manipulating aspects of laws of physics together and/or in sequence; to cause changes differently than naturally observable; space/time manipulation. Everything mutually influences everything else in “actual” physics.

Mathematical models do NOT accurately represent actual physics; partial perspectives. As an example. Mathematical models do not at all represent the complex “evolution” of states from every perspective. Modern physics is a mathematical snapshot of “a” condition.

Quantum Mechanics is stateless.

How do other dimensions become represented in laws of physics?

What variables and/or symbols can be broken down into more descriptive variables,that include other dimensions?

For example matter and antimatter:

E^2 = +/- (mc^2)^2 +/- (pc)^2

Perhaps converting the right side into a series that modulates pc, sympathetic recursion results and pc becomes a significant factor in the energy equation.

Mass becoming an insignificant factor.

Momentum representing something else than a scalar of mass times velocity; vectors.

Sympathetic recursion (sequencing of a series) produces a type of energy that has a profile.

In quantum mechanics, the distribution of variation develops a profile. A recognizable dimension.

Potentially being able to manipulate mass; to manipulate gravity. To manipulate vectors of gravity.

To be able to design detectors to see Dark Matter, and potentially detect structures within the Thermally Flat Universe before the first galaxies were observed to be formed.

The complex formed galaxies first detected seem to suggest the presence of physics not yet observable. So a new type of detector is needed.

Can the significance of pc dominate Mass through some form of sympathetic recursion?

______ continued

My thought is that mass is bound physically with gravity. Manipulation of mass also manipulates gravity.

p as momentum different than m mass related momentum.

In mass, there are manipulated equations that isolate momentum. Though it is a complex undertaking.

But because the momentum factor I separate in mass is different from PC, the concept is that there are two types of momentum may be modulated in regards to each other. Two or more different vectors may cause this mass to act differently in regards to a different mass modulating differently. Different systems of mass where momentum in each modulates differently.

Common Scalar bodies of masses of differently modulating masses, acting as a tractor to move interstellar hydrogen ; to move intergalactic hydrogen. Long range particle accelerators.

Sympathetic recursions along a path of travel; a projected tractor that extends far out in front of a craft.

A craft falling into a lower pressure vacuum. With less vacuum, conceptually higher potential speeds. Acceleration different than ion acceleration; charge-less.

My thoughts are not well developed. Conceptual.

_________ revisiting

The following is meant to explain the basis of my question, since space in the question is limited.

Can Einstein’s mass energy equivalence equation be vectorized, and made part of a series, such that mass becomes insignificant based on sympathetic recursion. New references for speed of light and momentum relative to a different dimension of consideration.

Simething like Tensors, but actively correlating equations with actual physics. Having other dimensions of actual physics shape equations through sympathetic recursion.

Quantum Physics variation profiles stimulating recursive formations; adjusting the modals of weighted variables in the equivalence equation. Breaking up variables into more descriptive variables where modals tend to diverge.

Mathematical operators seem to represent types of entanglements. Associating influence from a distance.

To detect and manipulate other dimensions (part of actual physics) requires manipulating/violating every law of physics we consider, or it would not be another dimension.

Or the model might have vector notation and weightings to represent dimensional influence in the mutually consistent dimensional perspective desired.

How would laws of physics exist, and yet be part of other dimensions. Like Dark Matter and Dark Energy?

Manipulating aspects of laws of physics together and/or in sequence; to cause changes differently than naturally observable; space/time manipulation. Everything mutually influences everything else in “actual” physics.

Mathematical models do NOT accurately represent actual physics; partial perspectives. As an example. Mathematical models do not at all represent the complex “evolution” of states from every perspective. Modern physics is a mathematical snapshot of “a” condition.

Quantum Mechanics is stateless.

How do other dimensions become represented in laws of physics?

What variables and/or symbols can be broken down into more descriptive variables,that include other dimensions?

For example matter and antimatter:

E^2 = +/- (mc^2)^2 +/- (pc)^2

Perhaps converting the right side into a series that modulates pc, sympathetic recursion results and pc becomes a significant factor in the energy equation.

Mass becoming an insignificant factor.

Momentum representing something else than a scalar of mass times velocity; vectors.

Sympathetic recursion (sequencing of a series) produces a type of energy that has a profile.

In quantum mechanics, the distribution of variation develops a profile. A recognizable dimension.

Potentially being able to manipulate mass; to manipulate gravity. To manipulate vectors of gravity.

To be able to design detectors to see Dark Matter, and potentially detect structures within the Thermally Flat Universe before the first galaxies were observed to be formed.

The complex formed galaxies first detected seem to suggest the presence of physics not yet observable. So a new type of detector is needed.

Can the significance of pc dominate Mass through some form of sympathetic recursion?