About
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Introduction
Graduated with honors from high school at 13 years old. Three-year Honor Student at Pasadena City College (PCC). Awarded "Honors Extraordinary in Physics" for finishing all courses in Physics within two years. Earned equivalence to BS in Physics, with grade A, while at PCC, just in pre-COVID times. Physics graduate studies in private and safe setting. Learning Python and PHP, and applying to Quantum Computation and Physics.
Current institution
a startup
Current position
- Research Assistant
Additional affiliations
June 2018 - present
Planalto Research
Position
- Researcher
Description
- Planalto Research is a scientific cooperative, laboratory, work group, consultancy, legal expert witness provider, knowledge aggregator, and successor of Gerck Research.
September 2017 - present
Position
- Student
Description
- At 14 years old, finished courses at PCC, in Physics, Mathematics, Astronomy, and English, with a total GPA of 4.0. Awarded High School diploma and "Honors Extraordinary" in Physics at PCC, at 13 years old. Received SAT score of 1490/1600 at 12 years old.
January 2018 - present
Gerck Research
Position
- Associate
Description
- Research
Publications
Publications (16)
![FIG. 2. Example of integral transform. From [3], page 934.](profile/Edgardo-Gerck/publication/331025041/figure/fig2/AS:725244587278336@1549923192257/Example-of-integral-transform-From-3-page-934_Q320.jpg)
This work is an exploration of complex analysis as a tool for physics and engineering, offering new topics. Although nothing in reality is a “complex number,” it includes an overview of the topics in four investigations. Results begin and end in real number theory, but have a path through the complex plane, which influences the result, but remains...
Without using Maxwell's equations, this work introduces the Electron Magnetism Model (EMM) of electromagnetism. The EMM is an invariant, gauge model, overcoming special relativity limitations, without necessary collective effects (can be a single particle). The EMM generates a correct electromagnetic field, as well as experimentally-correct E and B...
This is the fourth of five installments on the exploration of complex analysis as a tool for physics and engineering. This includes results that begin and end in real number theory, but have a path through the complex plane, which remains hidden. This investigation includes real integrals, inverse Laplace transforms, quantum physics, electrical eng...
This is the third of five installments on the exploration of complex analysis as a tool for physics. This third work explores the residue theorem and applications in science, physics and mathematics. This includes results that begin and end in real number theory, but have a path through the complex plane, which remains hidden. We clarify concepts t...
This is the second of five explorations of complex analysis as a tool for physics and engineering. This second work explores the subject of analytic continuation in complex analysis. This investigation explores analytic continuation itself, in geometric and algebraic conditions, including singularities, the Wick rotation, the spacetime algebra (STA...
This is the first of five explorations of complex analysis as a tool for physics and engineering. This first work deals with the connection between geometric and analytic aspects of complex analysis. This includes results that begin and end in real number theory, but have a path through the complex plane, which remains hidden. We clarify concepts t...
We consider the Sturm-Liouville Eigenvalue (SLE) problem, and also the inverse SLE (iSLE) problem. This work presents a mathematical model for the Matrix-Variational Method (MVM), to solve both SLE problems, in physics, due to Gerck et. al., from 1979. We show an intuitive model, with fitting suggestions that can be used for teaching physics, inclu...
This work highlights the MVM, in terms of differences with conventional methods. In the MVM, a very sparse matrix is used to represent a complex problem. This is done through the expansion in a few, suitable base functions, depending on only one parameter. The matrix is of the order of 5x5, even 3x3, trivially diagonalized, and can be evaluated eve...
Here we answer practical questions when special relativity is applied to accelerated motion. Specifically , how it is possible to treat accelerated motion in an inertial frame. It seems not possible, but using an adequate unitary-speed parametrization, given by the inverse function of the arc-length of the curve representing the trajectory, we achi...
This finalizes the Mathematical Model using the matrix-variational solution (1979-82 method used by Gerck et. al. in physics), in support of the Intuitive Model, and with suggestions for teaching physics, including quantum mechanics, motivating that there must be a solution valid for the given null boundary condition at Infinity (common in physics)...
Part II of the tutorial, in four parts, on special relativity applied to accelerated motion.
This is part one of four, discussing the Matrix Variational Method (MVM), for solving the Sturm-Liouville differential equation. In this first part, we include a preamble, with the Introduction, Description, Intuitive Model, Mathematical Model, Alternatives for Solution, as well as References.
The general problem being addressed in this tutorial series is that of special relativity in varying, accelerated, arbitrary motion. Physically, we understand, a non-inertial frame of reference should change but not shut-off length contraction, or time dilation, compared to what is calculated solely for inertial frames. The laws of special relativi...
We set a stage of two limiting cases, called Blue for external appearance, and Red for underlying reality, critically studying a popular interpretation of thermodynamics. We use the lenses of classical thermodynamics, statistical thermodynamics, information theory, game theory, mathematical finance, biology, psychology, and literature, trying to ob...
The Gibbs vector calculus is still studied today, e.g., in Multivariable Calculus, even though it is an outdated model of vectors, with no path forward in scientific terms. For example, the cross-product of two vectors is not a vector, which is well-known. This paper adds a more general objection in the quotient space of two vectors, otherwise well...
This work reports an apparent innovative Conjecture, intersecting cybernetics and topology. This is akin to finding a "wormhole", connecting different realities, different mathematical structures. The Conjecture is, "Curves with higher homotopy equivalence (e.g., more 'loops') have higher-order derivatives in their Taylor representation." For examp...
Questions
Questions (7)
In the paper,
Deleted research item The research item mentioned here has been deleted
, we will test potentials in highly oscillatory modes. The question is, which potentials to use? They must be significant, and show some interesting behavior. We can take three cases, which we will explore. One of the cases should be the harmonic potential, the other case the Coulomb potential, and the third case to be chosen, here. What is your suggestion?The question is whether (A) an analog system, or (B) a digital system, reflects the reality we see.
The A solution can be represented by (1) derivatives, and (2) include the hypothesis of continuity. They both, (1) and (2), match each other; without continuity there is no derivative, and without derivative there is no continuity. They both were used by Isaac Newton in his theory of "fluxions" in calculus. A fluxion is "the term for derivative in Newton's calculus" [1].
The B solution cannot be represented by derivatives, nor include the hypothesis of continuity. Again, the absence of both conditions, (1) and (2), match each other. This fact (i.e., the absence of (1) and (2) is not important) remained hidden for centuries in the fake controversy of primacy of calculus that followed, and was flamed by Newton as president of the Royal Society, against Leibniz, in 1713.
But Galois, around 1830, rediscovered a problem standing for 350 years, determining a necessary and sufficient condition for a polynomial to be solved by radicals, allowing calculus to be done by finite integer fields or Galois fields, thus eliminating the need for continuity in calculus.
How? Usual calculus requires continuity for the existence of derivatives, based on the four operations of arithmetics. It does seem necessary to require continuity, as Cauchy did in analysis in the field of real numbers. However, in the field of finite integers, such as Galois fields, calculus can be defined exactly, not requiring continuity.
Continuity is therefore an artifact of the formulation, and should be avoided. This complies with quantum mechanics and the work of Leon Brillouin, in 1956. It is fictional to consider continuity in mathematics, physics, computer science, and code. We are led today to consider finite integer fields, such as Galois fields, in calculus. We eschew the considerations of so-called "real numbers," as they include irrationals, which cannot be counted. The sum of two numbers in a Galois field is always a number in a Galois field. The sum of two numbers in the real set is never an infinitesimal; they can never be created nor exist.
The conclusion is that digital signal processing is the reality, not analogue processing. There is no effective quantization in digital processing, the quantum nature simply asserts itself. And this changes how we should view calculus: continuity is not required if one uses Galois fields. What is your opinion?
