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Let's begin with the derivation of the most famous equation, also across disciplines...

The purported derivation of E = mc² according to Special Relativity
A critical analysis with comparison to the Elementary Body Theory

Summary
The equation E = mc² is regarded as the most famous formula in physics. The standard answer to the question of its derivation is: From Albert Einstein's Special Theory of Relativity (SRT). This document presents the three common SRT‑derivations in detail: Einstein's original thought experiment of 1905, the modern derivation via four‑momentum, and the derivation via the energy‑momentum relationship. Each of these derivations is critically analyzed. It turns out that all SRT‑derivations are based on unproven postulates, contain arbitrary assumptions, or use approximations. In contrast, the derivation of the Elementary Body Theory (EBT) is presented, which derives E = m₀c² exactly, dynamically, geometrically vividly, and parameter‑free from the evolution equations r(t) = r₀ sin(ct/r₀) and m(t) = m₀ sin(ct/r₀). The appendix contains explanations on the history of thought models, the problems of quantum electrodynamics (QED), and some phenomenological foundations of the Elementary Body Theory.
[pdf-document E=mc² open in new browser window]

The alternative thought-model described below (Elementary Body Theory, EBT for short) is based »catchword‑psychologically« on the assumption that significantly simpler, consistent descriptions of matter and resulting simple formalizations exist than those announced in the standard models. The following remark by Karl Popper (1902 – 1994) addresses the psychological problem of the »modern scientist« in the context of highly complex, mathematical model concepts:

…" Our investigation shows that even obvious connections can be overlooked if we are repeatedly hammered that the search for such connections is ‘meaningless’."

Karl Popper, The Logic of Scientific Discovery. 9th ed. Mohr, Tübingen 1989, p. 196. Ed. E. Botcher: Die Einheit der Gesellschaftswiss. Vol. 4; The Logic of scientific discovery. (1935); 2nd Ed. London , New York : Basic Books 1959

The Elementary Body Theory (EBT) represents a radical break with established theoretical physics. Instead of secondary concepts such as mass, energy, or charge, the primary, sensually experienceable quantity of radial extension (r) takes center stage as the sole parameter. Based on a fundamental equation, the mass‑radius constant equation [F1], m₀ · r₀ = 2h/(π · c), both microscopic quantities (such as proton radius, electron radius, Rydberg energy, neutron mass, magnetic moments, fine‑structure constant) and macroscopic quantities (e.g., age, mass and radius of the universe, temperature of the background radiation, vacuum energy density) can be calculated analytically without free parameters. The Elementary Body Theory refutes the theory‑postulated existence of neutrinos, quarks, and dark entities of the standard models, identifies these as theory‑laden artifacts, and traces all phenomena back to mass‑radius coupling. The justification and the resulting formalism is, literally, remarkably simple. Standard model physics gives space no energetic meaning. However, as soon as »space as a form of energy«* is understood, an energy‑conserving, consistent, easily formalizable, phenomenologically representable thought model emerges in which mass and space are energy carriers. Whereby, unlike the (concept of) space, the secondary concept of mass (the mass) is derived in the phenomenological origin of the EBT from the primary concept of space (body radius) mass‑radius coupled. The epistemological foundations are examined in the field of tension between Euclidean intuition and Hilbertian axiomatics.

E = m · c² “everyone knows”. »Warm up«, as a concrete work performance of the EBT in the form of a pdf document (optionally in English or German), is therefore the first article published on dualismus.net in arXiv style, before the fundamentals and further thought‑model consequences of mass‑space coupling are presented online here. This will happen gradually.

*

Established physics postulates an incomplete energy conservation because it does not know the space energy contained in the phenomenologically founded mass‑radius coupling. It must therefore postulate new, not directly detectable entities such as neutrinos for every apparent violation of the balance – as in beta decay – instead of recognizing the phenomenological reason for the energy transformation: dynamic space.

The consistent formulation must therefore be: The sum of kinetic energy, mass energy, and space energy is constant. To speak of the law of energy conservation without understanding the phenomenological role of the coupled mass‑radius system is incomplete. Energy conservation holds strictly, but not in the incomplete balance of standard physics. Mass and space are mutually conditioning energy carriers whose common product – expressed by the mass‑radius constant equation: m₀ · r₀ = 2h / (πc) – is the actual invariant.

To speak of the law of energy conservation therefore requires awareness of the mass‑space coupling. The energy distribution can be described neither by mass nor by space alone, but only by their dynamic relationship.

In the Elementary Body Theory, the rest mass m₀ is a measure of the oscillation frequency of the elementary body. Elementary bodies with smaller radii have a larger mass because this is equivalent to the (possible) motion of the oscillating surface. In the picture of the elementary body, mass is therefore synonymous with internal motion and is traced back to the radius via reciprocal proportionality. Mass is thus not an isolated ‘partner’ in an energy redistribution, but a derived, secondary quantity. The energy conservation is a direct consequence of the synchronous transformation of this fundamentally coupled system.

** Fundamental Remark on QM

Interestingly, it was Albert Einstein (1879 – 1955) who identified quantum mechanics “early on” – with comprehensible argumentative reasoning – as unusable:

…"the ψ‑function is to be understood as a description not of a single system, but of a community of systems. Roughly put, this result states: In the framework of statistical interpretation, there is no complete description of the individual system. Cautiously stated: The attempt to conceive the quantum theoretical description of individual systems leads to unnatural theoretical interpretations, which become immediately unnecessary if one accepts the view that the description refers to the ensemble of systems and not to the single system. Then the whole rigmarole to avoid the ‘physically real’ becomes superfluous. There is, however, a simple physiological reason why this obvious interpretation is avoided. For if statistical quantum theory claims not to completely describe the single system (and its temporal course), then it appears unavoidable to search elsewhere for a complete description of the single system, whereby it would be clear from the outset that the elements of such a description would not be contained within the conceptual scheme of statistical quantum theory. One would thereby admit that this scheme cannot in principle serve as the basis of theoretical physics. The statistical theory would – in the event of the success of such efforts – assume a position within future physics somewhat analogous to that of statistical mechanics within the framework of classical mechanics."… A. Einstein, Out of my later years. Phil Lib. New York 1950  page 498

Einstein's argument can be broken down into the following logical structure:

Premise 1 (Observation):
Quantum mechanics in its orthodox (Copenhagen) interpretation describes physical systems by the wave function ψ. This provides exclusively statistical statements about measurement results on a large number of identically prepared systems (an ensemble).

Premise 2 (Definition):
A “complete description of an individual system” would have to capture its individual, temporal course completely and deterministically, without relying on statistical averages over hypothetical ensembles.

Conclusion 1 (logical deduction):
If QM only makes statistical statements about ensembles (Premise 1), then by definition it cannot provide a complete description of the individual system (Premise 2). This is a purely definitional logical conclusion: A statistical theory is not a theory of the individual object, but a theory of the totality.

Premise 3 (Philosophy of science norm):
A fundamental physical theory should claim to describe reality itself, i.e., to provide a complete description of the individual physical system.

Conclusion 2 (Consequence):
QM can therefore – if its own statistical nature is accepted – not serve as the fundamental basis of theoretical physics. It would then assume a position analogous to statistical mechanics, which is known not to be a fundamental theory, but an approximation method that builds on (the more fundamental) classical mechanics.

Einstein's unbeatable arguments were and are still “simply” ignored to this day. Einstein's critical remarks, especially on quantum mechanics, ultimately led to his isolation. Although he later became a “media star”, he was scientifically without further significance.

What is it about?

A sustainable paradigm shift.

What is meant by paradigm shift here?

The replacement of the standard thought models [SM ΛCDM] of theoretical physics.

[SM] Standard Model of Particle Physics (SM)
[ΛCDM] Cosmological Standard Model (ΛCDM model)

What takes its place?

A much more vivid, more effective, interdisciplinarily communicable, mathematically simpler thought model [EBT], which unifies and predicts the micro‑ and macro‑cosmos across scales.

[EBT] The Elementary Body Theory (EBT) deals in particular with answers to the question of how mass and space are fundamentally linked and, in “interplay”, lead to understandable formations of matter that can be calculated formally‑analytically – both microscopically and correspondingly macroscopically. For an illustrative understanding and for the phenomenologically based equations of the Elementary Body Theory, demonstrably neither a variable time, nor mathematical space‑time constructs, nor any form of substructuring are necessary.

What arguments speak for this paradigm shift?

The Principle of Parsimony

[: Occam's razor      lex parsimoniae     law of parsimony]

The strictly analytically motivated use
of the Principle of Parsimony
in the present explanations

Thought models can (only) be evaluated on consistency, internal axiomatic freedom from contradiction, with regard to the ability to make concrete predictions of actually measured quantities, and on minimalism.

In order to describe experimentally verifiable relationships formal‑analytically within the framework of thought models, the thought model that makes the most precise predictions with the fewest (physical) variables and mathematically simplest equations is to be preferred. Furthermore, the most suitable thought model is the one that, besides the mathematics used, is phenomenologically graspable and consistent, can describe both the micro‑ and the macro‑cosmos (cross‑scale), and captures a formal and phenomenologically justifiable connection between light (more precisely photons^Ph) and matter.

[^Ph] The term photons was first proposed in 1926 (21 years after Albert Einstein's work on the photoelectric effect) by the American physicochemist Gilbert Lewis in a paper titled “The Conservation of Photons”. He speculated whether light consisted of a new kind of atom, which he called photons, that could neither be created nor destroyed, thus obeying a conservation law [A. Pais  “’Subtle is the Lord’… Albert Einstein – A Scientific Biography”, Vieweg 1986, p. 413].

A Comparison

Thought Model Chemistry and Thought Model Physics

First of all, according to my own authentic experiences and observations, university practical courses in chemistry cannot be compared with on‑the‑job training or everyday work in a company. I am a trained chemical laboratory technician, and as such I briefly worked rotating shifts in the production control of dyes. During my physics studies, I worked as a student assistant in physics education and occasionally as a temporary chemical laboratory technician for various companies in heavy industry, and I chose organometallic chemistry as a minor subject in my main physics studies. For both the physics and the chemistry sectors, it holds true that most teachers and many academically trained people, as well as doctors, are not researchers in their everyday professional lives. Applied physics is similar to chemistry. Practice makes one wise. The difference between chemistry and physics is that in chemistry, even the success of theoretical chemistry is mostly practical‑constructive, as applications follow (process engineering, products). In fundamental theoretical physics (especially the Standard Model of Cosmology [ΛCDM model] and the Standard Model of Particle Physics [SM]), there are no applications. Theory creation and theory extension remain pure speculation.

I see chemistry didactics in upper secondary school or in basic studies as less problematic, because the “simple” models taught practically lead to good approximations. In physics, the situation is different. There, simplified concepts and theory elements are already “sold” to (upper) school students, which on closer inspection originate from philosophical and not physical thought models. Ultimately, theoretical physics defines itself through belief in a creative mathematics and postulated theory objects and interactions that cannot be directly detected, as well as a large number of free parameters. And as I said, this is only possible because no applications (have to) follow. For the transfer of knowledge, teachers and university lecturers are “forced” (to be) to convey the prevailing standard models, as it were. Personal views are, so to speak, “pedagogical‑administratively” not desired if they deviate significantly from the common method and/or from established thought models.

Although this is a scientific examination of the subject, there is also room for humor and interdisciplinary references. The mathematical and physical explanations are deliberately embellished with artistic visual elements, as it is fun to illustrate the vitality of the theory. The authenticity and egocentricity of the theory’s originator are not meant to remain a secret—and they will not.

Higgs Mechanism

There is a multitude of “treatises” on the Higgs mechanism. Everyone can pick their favourite description. Here, only the formal development and the arbitrariness of the “procedure” shall be outlined.

The following fact is hardly discussed or is “partially concealed”: The Higgs mechanism starts with a tachyon field and thus inherently with a negative mass squared (m² < 0). Note: The original Higgs field is a tachyon field – mathematically definable, physically unreal. In order to “bypass” the tachyon term, the field is re‑parameterised as a variation around a vacuum state. This changes the sign of the mass term.

The required properties of the Higgs field are:
“Higgs particles” are bosons, because only then is a coherent wave function possible. For the same reason, “Higgs particles” must interact with each other. The Higgs field is scalar in order to preserve the symmetry of the vacuum. In the present case of the U(1)_em gauge theory, the field must be charged in order to couple to the photon. The Higgs field satisfies the Klein–Gordon equation:

As a reminder: From the standpoint of relativity theory, the Klein–Gordon equation necessarily appears as the only possible form of the quantum‑mechanical equation of motion for a free particle of mass m. There is, however, a problem: the time evolution is not linear; that, however, is in contradiction with the group structure of time translations together with the probability interpretation of Hilbert‑space vectors. That was the reason for Schrödinger to eventually discard the – by himself proposed – Klein–Gordon equation and to limit himself resignedly to the non‑relativistic case of the Schrödinger equation. A solution of the formal problems “succeeds” within the framework of quantum field theory, in which the idea of individual particles existing in isolation from one another is abandoned…

The general solution of the free Klein–Gordon equation is a superposition of plane waves: for a given momentum, there exist (“on an equal footing”) solutions with positive and negative energy. This fact is ideologically blanked out methodically within mainstream physics and “relativised” by interpretations that are prone to arbitrariness.

The so‑called “Dirac sea” was followed by the Feynman–Stückelberg interpretation for “inexplicable” negative energy values of the Dirac equation. In the picture of quantum mechanics, one supposedly “solved” this problem with the help of the Heisenberg uncertainty principle by arbitrarily interpreting the corresponding solutions as entities with positive energy that move backwards in time. The negative sign of the energy is transferred to the time (Feynman–Stückelberg interpretation). Dirac understood the Dirac sea as the vacuum being an infinite “sea” of particles with negative energy, without any further free spaces for negative energies (?!?). One probably had to be called Dirac, Feynman or Stückelberg to be able to afford such naive “magic”. The will to replace the lack of intuition by formal auxiliary constructions or wild imagination is strikingly obvious. Mathematically that is not a problem; epistemologically it is.

It is postulated that the Higgs field in the ground state has a vacuum expectation value |Ψ₀|² = const ≠ 0. The demand for a non‑vanishing expectation value in the ground state is not trivial and can only be “fulfilled” with a self‑interaction of the field. In order to realise mass generation in the Standard Model through the Higgs mechanism, one can, as the minimal variant, set up the Higgs field as an isospin doublet. In the course of this mathematical procedure, it turns out that a further massless vector boson, the so‑called Goldstone boson, appears. However, since there is no experimental evidence for this boson, it is declared as “unphysical” and mathematically eliminated (“gauged away”).

However, it is important to note: the Higgs potential, and hence the spontaneous breaking of the electroweak symmetry, is added “by hand” to the SM. There is no dynamical explanation for this mechanism. The self‑perpetuation of mathematical SM‑abstractions demonstrably leads (also in the context of the Higgs mechanism) to arbitrary fantasy constructs. The formalism enables the supposed “convenience” of not having to engage in real‑object content with the phenomenology of what is happening in order to obtain “results”.

Let us spare ourselves further arbitrarily postulated SM‑theoretical elements at this point…

Given this “Higgs construction” – bursting with arbitrariness, capriciousness and inconsistencies – every language holds expletives at the ready that would be appropriate here. Readers may give free rein to their imagination in this regard. Is this Higgs confusion really meant seriously? That cannot be, can it? It received a Nobel Prize? Here we are talking only about the theory for the moment. The practice looks similarly bleak. At least ten billion collisions are needed to produce a single “Higgs particle”. This is, however, not even detected, since, like all other unstable (postulated) particles, it is only indirectly “detectable”. Let us conclude: phenomenologically completely unfounded mathematical procedures deliver “free‑parameter equations” that lead to no result. One measurement event occurs per 10 billion failed attempts. For more on this, see the pdf‑document↓ among other things regarding the comparison with the mass‑radius‑coupled Higgs‑mass calculation in the Elementary Body Theory…

Summary

This document compares the Standard Model of particle physics (SM) with the Elementary Body Theory (EBT), with particular focus on the Higgs boson. While the SM cannot derive the Higgs mass from first principles and relies on theory‑laden, indirect detection methods, the EBT offers a parameter‑free, epistemologically grounded alternative. The analysis shows that the alleged “discovery” of the Higgs boson at the LHC is strongly theory‑dependent – the raw detector resolution of about 5–6 % is “improved” to ±0.1–0.2 GeV by SM assumptions. The EBT, in contrast, calculates a Higgs‑like mass [↓Equation 2q0q0]  from the proton–proton interaction of roughly 128.6 GeV – without free parameters, without Monte‑Carlo simulations, without theory‑laden calibration:

In comparison with the EBT the SM is characterised as epistemologically naive, mathematically overloaded and barely falsifiable. The EBT appears as a primary‑quantity‑based, simple and precise new beginning.

The purported derivation of E = mc² according to Special Relativity

A critical analysis with comparison to the Elementary Body Theory

Summary

The equation E = mc² is regarded as the most famous formula in physics. The standard answer to the question of its derivation is: From Albert Einstein's Special Theory of Relativity (SRT). This document presents the three common SRT‑derivations in detail: Einstein's original thought experiment of 1905, the modern derivation via four‑momentum, and the derivation via the energy‑momentum relationship. Each of these derivations is critically analyzed. It turns out that all SRT‑derivations are based on unproven postulates, contain arbitrary assumptions, or use approximations. In contrast, the derivation of the Elementary Body Theory (EBT) is presented, which derives E = m₀c² exactly, dynamically, geometrically vividly, and parameter‑free from the evolution equations r(t) = r₀ sin(ct/r₀) and m(t) = m₀ sin(ct/r₀). The appendix contains explanations on the history of thought models, the problems of quantum electrodynamics (QED), and some phenomenological foundations of the Elementary Body Theory.

[BASIC SEARCH AlexDirkFreyling 59ndf Photo by T.B.]

Author

Dirk Freyling – independent researcher & artist

[Artist name AlexD, hence also adf as author abbreviation]

contact adf