Mass as Gravitational Mass

Recent posts discuss the concept of mass concluding that gravitational mass appears to be primordial from which inertial mass is derived. The idea is to start with a Universe defined in terms of a gravitational potential $\phi (x,t)$ depending on a Euclidean space coordinate $x$ and a time coordinate $t$ as created in 3 steps:

1. The gravitational potential creates a mass density $\rho (x,t)=\Delta\phi (x,t)$, where $\Delta$ is the Laplacian differential operator acting instantly as a local operation in space. 

2. Mass is subject to free fall according to Newton's equations of motion subject to gravitational force $\nabla\phi (x,t)$. 

3. Redistribution of mass under free fall gives feed-back to gravitational potential.

We thus find a Newtonian Universe determined by gravitational free fall connecting motion of mass in space to gravitational force and so equating inertial mass to gravitational mass. This is a large scale in a sense complete Universe with a precise simple mathematical description, which can be complemented by electromagnetics without interference with gravitation on both macro-scale and atomic micro-scale into the Universe we can see and experience.  

Modern text-books tell another story with mass appearing as (i) gravitational mass, (ii) inertial mass, (iii) rest mass and (iv) Higg's mass, all of different nature, which is is very confusing and lacks reason.  

It seems to be more reasonable to define mass as gravitational mass, which is the operational definition according to SI 2019 standard of units, and then connect other expressions of mass to this standard. 

On the other hand, the formal presence of mass $m$ in the coefficient $\frac{h^2}{2m}$ of the Laplacian in Schrödinger's Equation SE , with the mass of a proton 1836 times that of an electron, is not connected to gravitation and free fall motion.  Instead $m$ here serves as a parameter to determine spatial size, with thus a proton having smaller size than an electron in an atom.  

Different concepts of mass in modern physics.

 

Mass of Many Different Forms and Origins

I have been led to the idea that there is in Newtonian mechanics only one form of mass, gravitational mass, which is derived from a gravitational potential as primordial, wit inertial mass = gravitational mass as a consequence of universality of free fall and conservation of energy. This is a clear picture, which can be understood by everybody, and which has shown to work excellent in practice. 

This is not the idea of modern physics, which plays with several different forms of mass:  

• gravitational mass
• inertial mass
• rest mass (relativistic)
• Higgs mass. 

with different origins:

• gravitation
• Higgs mechanism and strong force
• relativity theory
• Higgs mechanism.

No doubt this shows a very complex picture and the questions pile up: Why so many different forms with different origins and why then is an Equivalence Principle adopted stating that inertial mass = gravitational? 

• Warum es einfach machen, wenn mann es so schön kompliziert machen kann?

  

Inertial Mass = Gravitational Mass?

This is a continuation of previous posts on operational definition in SI 2019 of mass as gravitational mass. 

In Newton's mechanics inertial mass is exactly equal to gravitational mass as an expression of both (i) universality of free fall and (ii) conservation of energy.  A Universe without (i) and (ii) cannot exist.

In Einstein's mechanics this truly fundamental equality is no longer guaranteed by (i) and (ii), but has to be added as an independent Equivalence Principle EP, which has to be supported by experimental evidence. Accordingly major efforts have been made to find ever more precise experimental confirmation, where the current precision is $10^{-15}$, while new experiments are receiving funding to reach even better precision: 

✅ Best Precision to Date:

• Experiment: MICROSCOPE (CNES, ESA)

• Method: Differential accelerometry in space (free-falling test masses of different materials)

• Result: Difference in acceleration between test masses of different compositions was less than 2 parts in $10^{15}$.

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🚀 Future Target Precisions:

1. Galileo Galilei (GG) satellite – proposed

   • Target: $10^{-17}$

2. STE-QUEST (atom interferometry in space) – proposed

   • Target: $10^{-17}$ (depending on mission configuration)

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To a classical physicist these experiments are similar to precise testing of the validity of the equality 1+1 = 2. 

Einstein presented his Special Theory of Relativity SR in 1905 in a desperate effort to get a university position, and followed up in 1915 with his General Theory of Relativity GR in a desperate attempt to keep the position he managed to get in 1909 under severe criticism of SR. 

Einstein thus took on the role of challenging Newton's mechanics by connecting it to propagation of light which was not mechanics, and by assuming EP as a fundamental postulate of GR as a step away from Newton's mechanics.

Despite severe criticism of both SR and little acceptance of GR before his death in 1955, today Einstein is the undisputed hero of modern physics as the man who showed that Newton was wrong and so opened the door to all sorts of new physics desperately needed after the success of the atom bomb in 1945 had faded.   

How to Measure/Define Mass

This is a clarification of the previous post showing gravitational force without need of force carrier.

An instrumentalist definition of a certain quantity like mass depends on how the quantity is measured by a certain specified instrument. 

According to the SI 2019 system of units, mass $m$ is determined by a Kibble balance from gravitational force $mg$ measured as electromagnetic force, where $g$ is the local gravitational constant. 

We conclude that according to SI 2019 mass is gravitational mass as reaction to gravitational force. In other words, gravitational force as gradient of a gravitational potential is primary from which mass is derived as secondary as measured by a Kibble balance. 

This suggests that the relation between mass density $\rho (x)$ and gravitational potential $\phi (x)$ should be viewed to have the form, with $x$ a Euclidean 3d space coordinate and $t$ a time coordinate: 

• $\rho (x,t) = \Delta\phi (x,t)$           (1)

with $\phi (x)$ given and $\rho (x)$ derived by application of the differential operator $\Delta$ acting locally, rather than the standard form: 

• $\Delta\phi (x,t)=\rho (x,t)$,             (2)

with $\rho (x)$ given and $\phi (x)$ derived as solution to Poisson's equation as a differential equation.

We can view (1) as local instant action by differentiation, while (2) requires instant action at distance as integration/summation. 

By adopting (1) as the true connection between gravitational mass and gravitational potential, which fits with SI 2019 and is explored in many posts, we can thus circumvent to need of instant action at distance, which has been viewed as a stumbling stone for Newtonian mechanics, motivating Einstein's relativistic mechanics coming with many new difficulties.

Adopting (1) we thus (i) adhere to SI 2019, (ii) circumvent instant action at distance and (iii) do not need Einstein,  as a hat trick. 

In Newtonian mechanics inertial mass is defined as gravitational mass and their equivalence is not an assumption or Principle as in Einstein's mechanics. 

In the Standard Model, mass is not defined as gravitational mass as in SI 2019, but as an intrinsic quality/property carried by matter, which is formed in a very strange way by the Higg's mechanism. 

Altogether, mass as gravitational mass, appears as a very useful concept. It makes sense to define mass as gravitational mass, because gravitation is present virtually everywhere. A special feature is that free fall as motion under gravitational force, without presence of forces of other nature, is independent of the size of the mass, which defines mass as a form of sensitivity to gravitation which is additive: The mass of two particles of the same kind is twice that of one particle. 

But this is not how a modern physicist approaches the problem of defining what mass is and how to measure it. A modern physicist is trained to believe that mass according to the Standard Model is defined by QFT through the Higg's mechanism, and then connected to gravitation by General Relativity GR. The trouble is the QFT and GR are incompatible and so the mass problem is a mess problem. 

Force Carriers of Modern Physics without Meaning

 The Standard Model SM as the crown jewel of modern physics divides the World into:

• matter particles (fermions)
• force carriers (bosons) of different forms:
• photons for electromagnetic force
• W and Z bosons for weak nuclear force
• gluons for strong nuclear force 
• (gravitons for gravitational force, hypothetical not detected)  

A major short-coming is that SM does not describe gravitation, because the graviton as force carrier has not been identified/detected, while the other force carriers are claimed to have been detected in particle accelerators. 

ChatGPT admits that the whole idea of force carrier or mediator of force by exchange of bosons, may be wrong in the sense that this is not how physics really works. The fact that the idea does not work for gravitation, may indicate that it is an illusion that it works for the electromagnetic and weak/strong forces. Another troubling aspect is that mediation by force carriers come with questions about finite speed of delivery, since infinite speed is hard to imagine. 

Classical physics does not include any concept of force carrier, because it has no role to play. Forces in classical physics can be viewed to come in two forms:

• Potential forces as spatial gradients of potentials instantly delivered locally. Gravitational and electro-magnetic forces are derived this way from electro-magnetic and gravitational potentials. 
• Contact forces also instantly delivered locally in space. Elastic forces in an elastic solid have this form. 

These forces need no force carriers since forces act locally in space without time delay, and so there is no issue with action at distance asking for some form of force carrier. It is thus possible to view the apparent instant action at distance of gravitational force as a misconception since the force is in fact delivered locally by a potential with instant delivery. This is the theme of many posts.

It is thus possible to describe electro-magnetic and gravitational forces without force carriers and then circumvent the apparently unsolvable problem of instant action at distance deeply troubling SM. 

RealNucleus presents a model of an atomic nucleus in terms of only electro-magnetic force. 

Summary:

The fundamental component of SM of force carrier raises several questions:

• How is the force carried and by what?
• How quick is the delivery of force over distance?
• Why is there no force carrier for gravitation?
• How is electro-magnetic force carried by photons? 

Coupled with the fact that there may be no need of force carrier at all, since force is always delivered locally instantly, like no need of surface mail when there is instant email, it may seem better to eliminate it from the discussion altogether as only a novelty without lasting value invented by a modern physics in desperate need to deliver new physics. 

18th century Stangenkunst (system of linked rods) as carrier of mechanical force over long distance.

PS ChatGPT informs us: 

• The concept of force carriers was introduced out of necessity when physicists tried to extend classical ideas to the quantum world. It arose to explain how particles interact in a way consistent with both quantum mechanics and special relativity.
• The carriers of the electromagnetic force are virtual photons which are internal lines in Feynman diagrams. The were introduced to get around the contradiction between instant-action-at-distance and special relativity, which however does not arise since instant-action-at-distance has no role to play as we saw above.

There is thus no need of any virtual photons and so we do not have to worry about the physical meaning of lines in a Feynman diagram. The basic idea of RealQM is that there is no conceptual difference between macroscopic and microscopic physics, that is that the quantum world is not fundamentally different from the world we live in. If this is indeed the way things are, it will make the atomic world easier to understand and then to manipulate.   

Modern Physics as Extreme Physics in Simple Geometry

Modern physics can be described as the physics of the extreme, while classical physics concerns the normal non-extreme. The atomic bomb is an ultimate expression the extreme. Powerful particle accelerators force subatomic particles such as protons, electrons and heavy nuclei to smash into each other at extremely high speeds creating a spray of other particles collected in detectors, with the objective of discovering the inner structure of the particles which are smashing. It is similar to seeking to discover the inner structure of a Swiss clock or human cell by smashing it with a powerful hammer.

Einstein's Equations EE are presented as a more accurate/fundamental model of gravitation than Newton's Equations NE, and the evidence is picked from cases of very strong gravitation such as mergers of black holes, which can be described as extreme cases with simple geometry allowing solutions to EE equations to be determined, more or less. 

However, evidence that EE is a more accurate model of gravitation than NE for normal cases of classical physics such as planetary systems, which can be described as normal cases with complex geometry for which NE works fine, is missing because in such cases EE are uncomputable and thus cannot be inspected and compared with NE/observation. 

The argument appears to be that if a model works in an extreme case, it should work also in a non-extreme case, but it is not really valid here because the extreme case has simple geometry allowing solutions of EE to be constructed, more or less, while the normal case has complex geometry, which can be handled by NE. 

EE is presented as one of the two major achievements of modern physics as a more accurate/fundamental model of gravitation than NE, but this cannot be demonstrated in the vast majority of normal cases, because EE is uncomputable in complex geometry. 

The other major achievement of modern physics is quantum mechanics based on Schrödinger's equation SE with extensions as QED and QCD underlying the Standard Model of fundamental particles of spatial scale down to $10^{-18}$ m. But SE is uncomputable for normal systems with complex geometry just as EE, which has led physicists to shift focus to string theory of scale $10^{-32}$ m as an expression of ultimate extreme physics in simple geometry. 

Modern physics thus has come to concentrate on extreme physics in simple geometry, in an attempt to distance itself from classical physics of the normal in complex geometry, which covers the majority of cases. No wonder that modern physics is in a state of crisis.  

Extreme physics in simple geometry

  

Human Protein Atlas: Normal physics in complex geometry

Einstein's Equations vs Precession of Mercury

When Einstein in 1916 presented a new model of gravitation in the form of  Einstein's equations, he desperately needed evidence that his model was better than Newton's. He found this in a back-of-the-envelope computation adding precisely the missing 43 arcseconds in the extra precession of the perihelion of Mercury (slight perturbation of the rotation of the elliptical orbit of Mercury of 5600 arcseconds per century from other planets), to make the prediction by Newton's model of 531 arcseconds/century made by Le Verrier in 1859 to fit exactly with the observed 574 arcseconds/century. 

Einstein thus started from the known results of 531 by Newton and observed 574 and miraculously obtained exactly the missing 43 by a very simple computation which he claimed captured the difference between his and Newton's model.  

If we ask chatGPT about this apparent miracle we get the following information:

1. Le Verrier's 531 has been confirmed to within 1 arcsecond by modern high tech computation and precise data. This is in itself a miracle. No improvement since 1859!
2. It is impossible to directly compute the observed 574 by solving Einstein's equations including in particular the other planets, because the equations are impossible to solve both analytically and computationally. 
3. Computation always start from 531 with Newton's equations and 571 is obtained as a correction of 43 claimed to be based on Einstein's equations, even if they are impossible to solve. This is also a miracle.

To get perspective on these miracles as prime evidence that Einstein's equations are more precise than Newton's, let us note 

• 1 arcsecond/century corresponds to a relative accuracy of about $2\times 10^{-9}$ per revolution of Mercury (415 revolutions/century) if errors add up linearly. 
• Data errors cannot be expected to cancel and so may well add up linearly. 
• A precision of $2\times 10^{-9}$ is thus needed in data such as planet masses, gravitational constant G, initial data, composition of the Sun, tidal motions, other celestial objects than planets, to get the precession right to say 1 arcsecond over 100 year. 
• The gravitational constant is known to at best 6 decimal places, other data with less. 

The conclusion that the desired precision cannot be reached, cannot be avoided. There is factor of 1000 between required and available precision. Yet, the computation of the precession of the perihelion of Mercury by Einstein is still presented as prime evidence that Einstein's equations describe gravitation better than Newton and thus as an undeniable major victory of modern physics over classical physics. 

Check if this is confirmed by chatGPT after careful reading of the literature!

But at his deathbed Einstein begged: "Newton, forgive me!"

Politics vs Modern Physics

A common tactic in politics practiced by parties and governments is to construct or frame a problem and then position themselves as the best (or only) solution to the problem as agenda-setting, problem-framing and solution-ownership. The problem typically a fictitious invented problem that does not need to be resolved as a no-problem. 

The problem could be imminent invasion of a NATO country by Russia, like Sweden, which can be prevented/solved by boosting Swedish defense industry with tax payer money. 

The same tactic has been used to gain tax payer support to modern Big Physics in the form of particle accelerators and massive support to departments of theoretical/fundamental physics. 

It was Boltzmann who took the first step along this profitable road at the end of the 19th century by inventing statistical mechanics as a new form different from classical mechanics, to solve the constructed problem of explaining why time is moving only forward, which is a no-problem in physics following its own dynamics.  

Planck took the next step in 1900 coming up with a concept of quanta as small chunks of energy to solve the problem of ultra-violet catastrophe of black-body radiation giving all bodies the capacity of radiating an infinity of energy, as a no-problem in real physics.  

In 1905 Einstein followed by inventing the Special Theory of Relativity SR starting from a proclaimed difficulty for two (human) observers separated in space to decide if two events are simultaneous in time. This is a constructed purely observer dependent problem, which does not come up in real physics without observers. Physics happens here and now and simultaneity of events (widely) separated in space is a no-problem. 

In the 1920s modern physics took a big leap inventing quantum mechanics with inspiration from Planck to solve the problem of the Bohr model of the Hydrogen atom. The solution introduced a whole catalog of new problems asking for resolution including wave-particle duality, collapse of the wave function, Heisenberg Uncertainty, Pauli Exclusion, anti-symmetry, interpretation of the wave function...The next big leap took place in the 1960s inventing the Standard Model to solve the problem of stability of atomic nuclei and then coming with another catalog new problems including strong force and weak force as different from familiar Coulomb force, and nuclear force as residual of strong force.  

In the 1970s String Theory was invented to solve perceived problems of the Standard Model. Today it is clear it did not work.

We see a consistent development of modern physics since 1900 as ad hoc inventions to solve perceived problems of classical physics by going outside classical physics, which were either no-problems or problems which could have been solved within classical physics (see books listed on this blog),  but then produced a host of new problems asking for more tax money. 

This machine has served very well for 100 years, boosted by the triumph of nuclear bombs, but it seems that public support is now failing as an expression of a crisis of modern physics. 

What Is an Electron? RealQM vs StdQM.

Electrons are described by wave functions as solutions to Schrödinger's Equation SE as the basic mathematical model of the quantum mechanics of atoms and molecules which comes in two forms: Standard Quantum Mechanics StdQM and Real Quantum Mechanics RealQM:

• Wave functions of StdQM for a system with $N$ electrons have global supports and depend on $N$ 3d spatial coordinates, altogether $3N$ spatial coordinates. Wave functions are computable only for very small $N$ since computational complexity grows exponentially with $N$.
• Wave functions of RealQM are sums of one-electron wave functions with non-overlapping supports depending on the same 3d spatial coordinate, and meet with continuity at a free boundary between supports. Wave functions are computable for all $N$, since computational complexity grows linearly with $N$. 

We now consider in more detail electrons according to RealQM. Each electron is described as a charge density $\psi (x)^2$ of a real-valued wave function $\psi (x)$ with support (non-zero value) in a certain region $\Omega$ in space with boundary $\Gamma$. The electron charge density does not have to vanish on $\Gamma$. Electrons sharing a common boundary piece meet with continuity as a free boundary condition. This allows the kinetic energy of an electron measured by $\vert\nabla\psi (x)\vert^2$ to be small even if the size of $\Omega$ is very small, which is not possible if $\psi (x)$ is forced to vanish on $\Gamma$. In other words, in the presence of other electrons, an electron can have small support and small kinetic energy, which means that it can circumvent the dictate of Heisenberg's Uncertainty Principle.

RealQM describes protons in the same way as electrons, with only a shift of sign of the charge.  

RealQM allows electrons to appear in two different forms in atoms and atomic nuclei as: 

• Charge densities with large support in atoms around a nucleus of vanishing size, meeting the nucleus freely (RealAtom). 
• Charge densities with very small support in kernels of nuclei surrounded by protons meeting proton charge densities with continuity, making sense since the size of the kernel is not small compared to the nucleus (RealNucleus). 

RealQM thus offers a complete model of an atom + nucleus in terms of: 

• A Schrödinger equation for a collection of positive and negative charge densities with non-overlapping supports interacting by Coulomb potentials, 
• The large difference in mass between proton and electrons allows the electron to serve a double role with presence both outside and inside the nucleus.  

RealQM is non-relativistic with motivation from the fact that there is no charge density motion in neither atom nor nucleus at all, and then certainly not at any relativistic speed. This is fundamentally different in StdQM where inner core electrons of heavy elements like Gold are claimed to move at half the speed of light by a purely formal argument connecting kinetic energy to velocity. Electrons can in giant particle accelerators be accelerated to relativistic speeds with massive input of energy, but its is difficult to fathom that the same thing happens in an atom of Gold...

Summary:

• RealQM describes a collection of $N$ electrons as a charge densities with non-overlapping local supports in 3 space dimensions meeting with continuity and interacting by Coulomb potentials. RealQM is computable for all $N$.
• StdQM the collection as overlapping charge densities with global support in $3N$ space dimensions. StdQM is computable only for very small $N$. 
• RealNucleus describes a nucleus as a collection of non-overlapping electron and proton charge densities meeting with continuity and interacting by Coulomb potentials.
• The Standard Model of StdQM describes a nucleus as a collection of protons and neutrons interacting by a residual of a strong force.   

 

   

Modern Physics as Poker Game

Modern physics based on relativity theory and quantum mechanics has followed the pattern set by Einstein to continue to raise the bet without showing the cards, as in a no-limit-poker game with lousy cards, eventually forcing the other players to fold: 

1. When Einstein's Special Theory of Relativity SR (1905) was questioned, Einstein raised the bet to the General Theory of Relativity GR (1916).
2. When GR was questioned, Einstein raised the bet from scales of classical physics, to scales of the Universe including black holes which nobody dared to call. 

This showed to work fine and so the same strategy was adopted by leading physicists as concerns quantum mechanics:

1. When the physical meaning of Schrödinger's Equation SE (1926) for atoms of size $10^{-10}$ m as the first version of quantum mechanics without relativity theory, was questioned and no answers could  be given, it was replaced by Dirac's Equation DE (1930) including SR describing an electron.
2. When DE for the electron was questioned, the Standard Model SM (1960s) was developed as a theory of atomic nuclei of size $10^{-15}$ m built from the fundamental particles of protons and neutrons made up of quarks interacting by force carriers named gluons. 
3. When SM was questioned as an ad hoc model of a nucleus, String Theory ST (1980s...) was developed as an ultimate fundamental theory on a scale ($10^{-32}$ m ) which could not be called.   

ST/GR ars now being questioned, but the bet cannot be raised another time since the ultimate large and small scales have been reached. It is now time for physicists to call and to help there is a new card to play in the form of RealQM. Anyone with this card can make a call on ST/GR.

First Principle Model of a Nucleus

After a long discussion chatGPT arrives at the following conclusion about the present status of theoretical nuclear physics as concerns lack of mathematical model describing an atomic nucleus from first principles (check yourself): 

• We should admit that we still do not truly understand nuclear binding from first principles.
• Our models are ad hoc by necessity, if not by intention.
• This is not the end of physics, but a clear sign of its current limits.

The Schrödinger Equation SE of Standard Quantum Mechanics StdQM describes the ground state of an atom from first principles as minimisation of Coulomb potential energy + kinetic energy over electronic wave functions in a central Coulomb potential of a point-like nucleus of protons.    

There is no corresponding equation describing the nucleus of an atom, more precisely what keeps the nucleus together under proton-proton repulsion. There is a model assuming a central potential formed in the 1930s to do this job, but it is an ad hoc model, which is not based on first principles. There is a model of a single proton as the Standard Model SM, which however does not extend to a nucleus with many protons. 

This is very remarkable. SM is presented as the greatest achievements of all of physics, but is still after 60 years evidently severely limited. Something is apparently missing here. 

RealNucleus is a model of a nucleus based on the same first principles as SE for atoms, as an extension of RealQM for atoms offering a readily computable version of SE. RealNucleus models a nucleus as a collection of electron charge densities surrounded by a shell system of proton charge densities. RealNucleus is readily computable and delivers binding energies in fair agreement with observations. 

 

Computing Spectra of Nuclei

Quantum Electro Dynamics QED forms a low-energy version of the Standard Model SM within quantum electro-magnetics. QED theory agrees to high precision with  precise measurements of the (anomalous) magnetic moment of the electron using a Penning trap including a single electron. This device measures resonances of the electron in a way similar to measuring the spectrum of an atom, or resonance frequencies of a mechanical system, by subjecting the system to input of varying frequency and recording peaks in system output for certain frequencies showing resonance between input to and output from the system. 

The common understanding is that QED describes electrons of atoms and molecules, but not atomic nuclei composed of protons and neutrons asking for an extension of SM to Quantum Chromo Dynamics QCD including the strong force and the weak force of different nature than the Coulomb force of QED. 

The following question was asked 100 years ago during rapid development of quantum mechanics in 1920s with prospects to be all-encompassing: 

• Is it possible that QED can describe not only the electrons of atoms around nuclei with protons, but also also nuclei of atoms as systems of protons and electrons? 

The answer was negative: It is impossible for a nucleus to include an electron, because the nucleus is so small and squeezing an electron into that size would require energies of 100s of MeV, while the total energy of a nucleus per nucleon is around 8 MeV. 

RealNucleus takes up that old idea again from the new perspective of RealQM where charge densities of electrons and protons can meet with continuity, which allows electrons to be localised to the same extent as protons, thus allows electrons to hide inside a nucleus. RealNucleus thus offers a model of a nucleus as a system of non-overlapping charge densities of positive and negative sign interacting by Coulomb potentials. The model shows stability/existence of nuclei with in basic case $Z$ electrons forming a kernel surrounded by a shell system pf $2Z$ protons, with full quantum resolution of both electrons and protons, signifies by negative ground state energies in fair agreement with observation. 

The computational complexity of RealNucleus scales linearly with $Z$ which allows computation of full spectrum even for large $Z$, which is unthinkable with QCD. Results for RealNucleus under way...

Deterministic Measurement of a Quantum Systems

This a preparation of the next post on RealNucleus vs Standard Model/QCD.

Standard Quantum Mechanics StdQM says that measurement of the state of a quantum mechanical system like an atom/molecule or nucleus necessarily interferes with the outcome of the measurement. This is called "collapse of the wave function into a definite eigenstate" which happens with a certain probability during the measurement process, from an indefinite state in superposition of eigenstates described by the wave function prior to measurement. This is viewed as maybe the deepest mystery of StdQM still today 100 years after its formation. It is contrasted with measurement of a system of classical mechanics which can be done with insignificant interference with the measuring device. 

Yet measuring the spectrum, as the set of eigenfrequencies of an atom, always gives the same result with precision set only by the measuring device. No probability, no collapse of the wave function, no indeterminism, essentially no quantum. The same as recording the set of frequencies generated by plucking a guitar string using an app on your mobile. Same string, same frequencies. 

How is this possible? It is made possible by a phenomenon of resonance which is analysed in a context of blackbody radiation as Computational BlackBody Radiation. The measurement of the spectrum of a system like an atom or guitar string, is made by subjecting the system to periodic forcing of varying frequency as input and observing a peak in the response of the system to signal that an eigenfrequency of the system is close to the forcing frequency. In this procedure there is massive interference with the system through the forcing, while the reaction of the system revealing its eigenfrequencies can be viewed to be independent of the procedure and so expected to always give the same result. We thus find no principal difference as concerns spectrum of an atom and a classical system like a guitar string.  

But there is a difference between a classical mechanics guitar string and an an atom in the sense that the tone generated by a guitar string as a superposition of eigenfunctions as the wave form (which depends not only on the string but also on the plucking technique) can be listened to/measured, while the wave function/form of the atom as superposition of eigenfunctions cannot be observed, only the spectrum of the atom as the set of eigenfrequencies.  

How important is then interaction by resonance as determinism also in a quantum system? There are good reasons made as Computational BlackBody Radiation to view all interaction as somehow monitored by resonance. Listening to the tone/wave form generated by a plucked guitar string thus involves recording individual resonances (and amplitudes) by the ear which are then synthesized in the brain back to a wave form. It seems reasonable to expect that interaction between quantum system also primarily is monitored by resonances and then in a deterministic way and then not directly by wave form interaction.

Reducing measurement of a quantum system like an atom to resonance, makes it deterministic and circumvents the roulette game of "collapse of the wave function". Moreover, if interaction between quantum systems relies on resonance, then it can also be deterministic.

 

Limitation of the Standard Model

ChatGPT can tell you things about theoretical physics from reading what theoretical physicist have been writing, which a living theoretical physicist will not tell you unless you press hard. 

For example, chatGPT will tell you that the Standard Model SM of particle physics describing the ingredients of atomic nuclei (protons and neutrons), does not directly describe the structure, dynamics or properties of nuclei, not even the simplest nucleus of 2H (deuterium) formed by one proton interacting with one neutron. 

In particular, SM does not directly describe the (nuclear) force keeping 2H together, except as some form of residual force as a leftover of the strong force of SM supposed to hold the quarks forming a proton together, with the residual force given the role to overpower the Coulomb force of classical electro-magnetics (even if zero between proton and neutron).  

So SM can describe a single proton and a single neutron, but not really their interaction forming 2H. Yet SM is by physicists presented as "immensely successful" as the greatest achievement of science all categories. The success is demonstrated in a prediction of the "anomalous magnetic moment of the electron" agreeing with measurement to 13 decimal places. The measurement comes from using a Penning trap to confine a single electron into observation over long timescales. The proclaimed very high precision in this experiment is used as heavy evidence that SM is correct. Physicists agree that SM has many shortcomings, which cannot be compensated by increasing the precision from 13 to 15 decimal places.

RealNucleus offers an alternative to SM showing stability/existence of nuclei under Coulomb forces, thus without any leftover of some strong force. You can test yourself what chatGPT has to say about such a possibility. 

 

The Nucleus Enigma: Proton-Electron Symbiosis

The Standard Model SM offers an explanation of stability/existence of an atomic nucleus of charge $+Z$ consisting of in a basic case $Z$ protons and $Z$ neutrons in terms of new force beyond the Coulomb force of the Schrödinger equation named strong force meditated by force-carrying gluons. SM is an ad hoc model with many parameters invented in the 1960s serving as the main model of nuclear physics still today, as the greatest triumph of theoretical physics of all times.      

RealNucleus as an extension of RealQM for atoms to nuclei offers an explanation of stability/existence of a nucleus consisting of $Z$ electrons and $2Z$ protons (corresponding to $Z$ protons and $Z$ neutrons with formally a neutron = proton + electron), as an extension of the Schrödinger equation to a nucleus including only Coulomb force without the strong force. RealQM thus offers a model of an atom with full quantum mechanical resolution of both atomic electrons and nucleus based on Coulomb potentials/forces. If this model indeed holds up to such a proposition under closer evaluation, it could be viewed as as sensational. 

Let us here do a simple check in a toy model to understand why it is possible for RealNucleus to show stability of a nucleus as a system of protons and electrons interacting by Coulomb potentials. For the real model go to RealNucleus.

We start with the nucleus of 2H consisting of 2 protons surrounding a nucleus kernel of 1 electron. Suppose a linear particle configuration with the protons at coordinates -1 and +1 and the electron at 0. We have the following Coulomb potential energies: 

• proton-electron attraction = -1-1 = -2
• proton-proton repulsion = +0.5 
• total energy as (total potential energy)/2 = -0.75.       

We understand that this is a special case without electron-electron repulsion since self-repulsion is excluded.  

We next consider 4He consisting of 4 protons surrounding a nucleus kernel of 2 electrons, thus a case with non-zero electron-electron repulsion. Suppose a planar quadratic configuration with the electrons at (-0.5, 0) and (0.5, 0) and the protons at (-1.5,0), (1.5,0), (0,1.5) and (0.-1.5) in a 2d coordinate system, which gives the following Coulomb potential energies (with different spatial scale as compared to 2H)   

• proton-electron attraction $ < - 1-1-\frac{1}{2}-\frac{1}{2}-\frac{4}{1.5\sqrt{2}}$
• proton-proton repulsion $  = \frac{1}{3}+\frac{1}{3}+ \frac{4}{1.5\sqrt{2}}$
• electron-electron repulsion $= 1$ 
• total energy as (total potential energy)/2 $< -\frac{2}{3}$.       

We find a total energy which is clearly negative even in the presence of electron-electron repulsion from the kernel. This is made possible by assuming a distance between the electrons in the kernel (=1) to be comparable with the distance to the protons, thus with a nucleus kernel of size comparable to that of the nucleus. This is made possible by the presence in the Schrödinger equation of mass $m$ in the coefficient $\frac{1}{2m}$ of the Laplacian, which sets a spatial scale by the factor $\frac{1}{\sqrt{m}}$. Recalling that the $m$ for the proton Laplacian is much bigger than that of the electron Laplacian (factor 1836) we find a rationale for assuming that kernel is not small compared to the nucleus, thus allowing electron-proton attraction to dominate electron-electron repulsion. 

We thus find that system of $Z$ electrons forming a nucleus kernel surrounded by $2Z$ protons is stable under Coulomb attraction-repulsion, where the small electron mass vs proton mass plays a crucial role to allow domination of electron-electron repulsion by proton-electron attraction. 

We thus find the enigma of the stability of a nucleus can be resolved as marriage between the two components of the system: 

• control of electron-electron kernel repulsion by surrounding protons
• control of proton-proton repulsion by electron kernel
• a kernel of $Z$ electrons binding $2Z$ protons
• $2Z$ protons confining a kernel of $Z$ electrons,  

as an expression a fundamental principle of symbiosis. 

New Look at Nucleosynthesis: RealNucleus vs Standard Model

The Standard Model SM of particle physics, the most successful physical theory all times, says that the electron as a fundamental particle was created in the Big Bang slightly before protons and neutrons as composite particles built from a quark-gluon plasma. According to SM the electron with charge -1 and the proton with charge +1 were not created together in some form of split of zero charge into -1 and +1.  Why then there are as many electrons as protons remains as a main open question. 

SM says that an atomic nucleus consists of the protons and neutrons formed from quarks held together by a strong force carried by gluons, both from the early quark-gluon soup. SM appears as a very complex ad hoc model of a nucleus with more than 20 parameters. There is no room for electrons in this model.

RealNucleus offers a different model of a nucleus as a system of electrons and protons interacting by Coulomb potentials/forces without need of any strong force. RealNucleus thus connects to the above split of zero into -1 and +1 thus creating exactly the same number of electrons and protons leaving the SM open question with a clear simple answer. 

RealNucleus suggest the following initial formation sequence of nuclei:

1. Formation by an endothermic process of neutron as 1 proton surrounding 1 electron as an H atom with shifted roles of proton and electron. 
2. Formation of a 2H nucleus by exothermic fusion of 1 neutron with 1 proton into 2 protons surrounding a 1 electron kernel. 
3. Formation of 3H by fusion of 2H and 1 neutron into 3 protons surrounding a 2 electron kernel.
4. Formation of 4He by fusion of 2H and 2H or of 3H and proton into 4 protons surrounding a 2 electron kernel.   
5. Formation of heavier nuclei by successive fusion followed by fission.  

RealNucleus gives a  model of a nucleus as a system of non-overlapping charge densities with full quantum mechanical resolution of both electron charge densities in the kernel and surrounding proton charge densities. RealNucleus computes a total energy of -1 MeV for 2H and about -6 MeV for 4He in fair accordance with observation, with negative total energy the sign of stability/existence. RealNucleus thus shows stability/existence of 2H and 4He in a full quantum model of a nucleus as a system of proton and electrons charge densities interacting på Coulomb potentials/forces. RealNucleus offers an explanation of the observation that stable nuclei have about the same number of protons and neutrons,  in the form of (i) confinement of protons by Coulomb potential from electron kernel, and (ii) confinement of electrons by Coulomb potential of surrounding protons overpowering electron-electron and proton-proton repulsion and kinetic energies.   

It is natural to ask what RealNucleus would say about a hypothetical "double-neutron" consisting of 2 protons surrounding a kernel of 2 electrons as an analog to the Helium atom with the roles of protons and electrons shifted. RealNucleus shows positive total energy from kernel electron-electron repulsion and kinetic energy and thus non-existence of "double neutron" in the same sense a free neutron is not stable.

  

RealNucleus: First Full Quantum Model of a Nucleus with only Coulomb Forces

The article introducing RealNucleus, as an extension of RealQM for atoms as RealAtom, has now been updated. It appears to be the first full quantum mechanical model of an atomic nucleus showing that stability/existence as negative total energy is realised with only Coulomb forces in tests of basic cases, thus without need of the ad hoc strong force of the Standard Model. 

With this extension RealQM appears to offer a computable full quantum mechanical model of an atom-nucleus in a classical setting of Coulomb potentials, thus without need of uncomputable QED/QCD.   

Why No Unified Atom-Nucleus Model?

The previous post presented RealQM = RealAtom + RealNucleus appearing to be the first computable unified model of an atom including nucleus with full quantum mechanical representation in the form of non-overlapping charge densities of both electrons and protons interacting by Coulomb potentials. 

Is this really the first full quantum mechanical model of an atom + nucleus? What have theoretical physicists been doing during the 100 years since the advent of quantum mechanics in 1925? 

Yes, at least according to chatGPT, telling that there is QED for atoms = electrons+point-wise nuclei and QCD for nuclei = quarks and gluons, but QED and QCD represent different "sectors" and cannot be unified:

• There is currently no fully computable, unified quantum mechanical model of an , "atom that includes both the electrons and the atomic nucleus in full quantum detail and that is tractable for general-purpose computation.

How can this be? Is this the concrete meaning of the "crisis of modern physics" proclaimed by leading theoretical physicists? Is it a consequence of all the unresolved contradictions present in the mathematical foundations of quantum mechanics including "wave-particle duality", "complementary principle", "collapse of the wave function", "measurement problem", "statistical interpretation", "uncertainty principle", "exclusion principle", "anti-symmetry", "Born rule", "exchange energy", "indistinguishability of identical particles", "electron orbitals", "superposition", "entanglement", "decoherence", "spin-orbit coupling" + all the wonders of QCD…? 

When I ask if the lack of a unified atom-nucleus model is a sign of failure/crisis of modern physics, chatGPT explains:

• The lack of a unified, computable atomic-nuclear theory is not a failure — it's a reflection of the extraordinary success and specialization of the theories we already have (QED and QCD).  

This is the tragedy of modern physics: Too successful to fail. Like a Big Bank or Great Empire. If you find chatGPT's argument convincing, you have a position at a department of fundamental physics (about to collapse from missing unified theory).

RealQM as RealAtom + RealNucleus

RealQM has now been extended to a full Schrödinger Equation SE for an atom as an electron density of total charge $-Z$ surrounding a nucleus as a proton density of total charge $+2Z$ surrounding a nucleus kernel as an electron density of total charge $-Z$, as RealAtom + RealNucleus. The total energy includes the kinetic energies of both electrons and protons as well as all Coulomb potential energies including both electron-electron repulsion and proton-proton repulsion. The nucleus here appears as in inverted form of the atom with switched roles of electrons and protons, like a Russian doll system with an electron-proton-electron pattern from nucleus kernel -Z to nucleus +2Z to atom -Z (in basic form).

RealAtom computes binding energies of atoms in eV and RealNucleus binding energies of nuclei in MeV with a change of scale of about $5\times 10^5$ reflecting a change of spatial scale from nucleus to atom, while the change of scale from nucleus kernel to nucleus is much smaller around $10$. 

RealQM thus offers a full SE for an atom with nucleus based on a Hamiltonian including all kinetic and Coulomb potential energies. The model is parameter-free modulo the change of scale from nucleus to atom, assuming a mass ratio of 1836 between proton and electron. The computational complexity scales with $Z$.

Note that textbook Standard Quantum Mechanics StdQM including the Standard Model SM does not offer any such complete Schrödinger which is computable. What is offered is (i) SE for an atom with nucleus modeled as a point-wise charge density with zero kinetic and potential energies, and (ii) a shell model of a nucleus consisting of protons and neutrons swimming in a negative potential from a charge density without kinetic and potential energy. StdQM thus does not include the full SE of RealQM. 

In short, RealQM offers the first full SE of an atom including nucleus as a unified model in terms of non-overlapping electron and proton charge densities interacting by Coulomb potentials while adding kinetic energies to potential energies to total energy with computations geared to find minima corresponding to ground states.

Preliminary computations show that RealQM can match observations. RealQM may show a way out of the dead-end of uncomputable StdQM of atom including nucleus. 

Test case 1: 2H

The basic test for RealNucleus is the 2H nucleus in StdQM viewed to consist of 1 proton and 1 neutron, and in RealNucleus viewed to consist of 2 proton charge densities surrounding a nucleus kernel of 1 electron. This a the nucleus analog of an atom consisting of 2 electrons surrounding a nucleus of 1 proton, that is the $H^-$ ion of the H atom with one extra electron, which is known to be stable. If we then assume that the only electron of the nucleus kernel of 2H has zero kinetic energy and no self repulsion, we get the message that 2H should be stable. RealNucleus confirms by giving a binding $E\approx 1$ MeV including the kinetic energy and zero potential energy from no self repulsion of of the nucleus kernel.  

Test case 2: 4He

A more serious test case is the 4He nucleus in StdQM viewed to consist of 2 protons and 2 neutrons, and in RealNucleus viewed to consist of 4 protons surrounding a nucleus kernel of 2 electrons. In this case both kinetic and potential energy of the kernel add to the total energy, and the question is if then the total energy will be negative indicating stability, or not? We use this code realising RealNucleus in a simple implementation with spherical symmetry starting from this input screen with 2 electrons as red spherical nucleus kernel surrounded by 4 protons in a green-blue nucleus: 

Pressing start we get the following output showing electron/proton densities in red and total potential in blue as functions of radius in spherical symmetry:
    

We see that the electron and proton charge densities meet with continuity at the boundary of the nucleus kernel (crest of red curve) with the electron/proton charge density being attracted by the proton/electron charge density into a negative contribution to total energy dominating over kinetic energies, resulting in a total negative binding energy of $E\approx 7$ MeV with a spatial scaling of $4\times 10^5$ between between nucleus kernel and nucleus. We see that the radius of the kernel of the nucleus is about the half of the nucleus. 

Notice that a physicist properly trained by StdQM would say that a nucleus kernel of electrons is impossible because electrons are too big to fit and if fitted the kinetic energy would be in the 100s of MeV. But this is not what RealNucleus tells us as displayed in the output figure above: The radius of the kernel is not so small and the electron kinetic energy can remain small because the electron charge density does not have to vanish on the boundary, only meet the proton charge density with continuity.   

We understand that the balance of $Z$ electrons vs $2Z$ protons is instrumental to overcome the potential energy from electron-electron repulsion in the kernel of the nucleus. A configuration of $2Z$ electrons combined with $2Z$ protons as a form of neutral kernel as an analog to an atom with $2Z$ electrons surrounding a proton nucleus with the same number of charges, is unstable. 

We thus see that RealNucleus explains in particular why a nucleus with an approximately equal number of protons and electrons, can be stable.  

PS1 Use this code to test other nuclei.

PS2 In RealAtom electron densities meet at a free boundary with continuity (and zero normal derivative), and in RealNucleus electron and proton densities meet likewise. This gives an explanation of the fact that electrons and protons do not instantly annihilate under Coulomb attracting, but can coexist by occupying different regions of space meeting a free boundary with continuity of charge density of same or different sign. In StdQM electrons have global overlaying supports which is not compatible with either repulsion or attraction. RealQM resolves this contradiction by assigning charges separate domains in space. 

New Model of Atomic Nucleus with only Coulomb Potentials

RealNucleus is model of a nucleus as a collection of $P$ non-overlapping +1 proton charge densities surrounding a kernel as a collection of $E$ non-overlapping -1 electron charge densities interacting by Coulomb potentials without presence of the strong and weak force of the Standard Model. 

We consider here a reduced model assuming spherical symmetry in the form of a central sphere of negative density of total charge $E$ surrounded by a shell system of positive density of total charge $P$. The model can be tested using this code with settings for the nucleus of 4He consisting of 2 electrons surrounded by 4 protons.  

The model corresponds to, in the setting of the Standard Model, of a nucleus with $E$ neutrons and $P-E$ protons with in the basic case $E=P-E$ with thus $P=2E$.  

The Standard Model was formed in the 1960s to explain the stability of a nucleus by introducing an attractive force overpowering the Coulomb repulsion named the strong force as a new fundamental force asking for very elaborate quark-gluon physics. The present crisis of physics is directly connected to deficiencies of the Standard Model without resolution in sight. The Standard Model is proclaimed to be the most successful theory of all of physics and as such cannot be abandoned, but then serves as a road block to progress. 

RealNucleus offers a different explanation of the stability of nuclei which does not involve any strong/weak force and so is based solely on Coulomb potentials coming with Coulomb forces. RealQM shows that the negative charges in the kernel are confined by the surrounding positive charges. More precisely RealNucleus computes a total energy of the nucleus to be negative with thus the negative potential energy from charges of different sign overpowering the positive repulsion energy from charges of the same sign, in particular from the kernel repulsion between electrons. 

RealNucleus thus shows stability of a nucleus consisting of a kernel of negative charge $E$ surrounded by a shell system of positive charge $2E$. In particular it is shown that the fact that the mass of a proton is bigger than that of an electron making an electron occupy more space than a proton, is instrumental for stability with the radius of the kernel being comparable to the radius of the nucleus. 

A nucleus thus appears as an analog of an atomic ion with electrons and protons switching roles, with the kernel of a nucleus comparably much bigger than the nucleus of an atom.  

A physicist trained with the Standard Model would say that it is impossible that a nucleus has a negative kernel consisting of electrons, because by Heisenberg's Uncertainty Principle compression of an electron to fit inside a nucleus would require 100s of MeV which are not available. RealNucleus shows that this argument may well lack real physics.  

RealNucleus is a model of a nucleus without the heavy burden of the Standard Model. Note that there is a shell model connected to the Standard Model with a nucleus as a collection of protons and neutrons swimming in a negative charge potential coming from the strong force. 

RealNucleus keeps a nucleus together as a negative kernel of electrons of charge $E$ surrounded by a shell system of positive protons of charge $2E$ interacting via Coulomb potentials only by a combination of the following circumstances: 

• The radius of the kernel is a substantial fraction of the radius of the whole nucleus,  because electron mass is much than proton assigning electrons comparatively large volume. 
• The double number of protons vs electrons allows the surrounding protons to confine the electrons in the kernel thus overcoming electron-electron repulsion. 
• The boundary/radius of the kernel is determined to make electron charge density meet proton charge density with continuity. 

If Coulomb and Newtonian gravitational potentials suffice to describe both the macroscopics of the world we can see and the microscopics of atoms and nuclei, then Einstein's dream of a unified field theory would seem to be in reach. Maybe such a theory can find an audience outside the physics community tied to the Standard Model of quarks interacting be weak and strong forces transmitted by gluons as force carriers.

Note that there are two different ways of using the concept of force:

1. Force on a particle comes from instant local in space gradient of a potential. No transmission of  force over space-time. Instant local action.
2. Force between particles transmitted over space-time by force carriers connecting particles. Action at distance. 

It is natural by Ockham's Razor to favour 1. using only the concept of potential, before 2. asking for force carriers of unknown physical nature. 

PS1 Note that the Standard Model does not describe a nucleus, only the protons and neutrons supposedly forming the nucleus, not even 2H consisting of 1 proton and 1 neutron. This is a strange short-coming.

PS2 The common understanding of well educated physicists is that a nucleus is a collection of protons and neutrons and in particular that there is not even room for a single electron.  This conviction can be challenged by the following observations: (i) a neutron outside a nucleus decays within 15 minutes into a proton and an electron and (ii) a neutron inside a nucleus can decay into a proton staying in the nucleus and an electron, which is kicked out of the nucleus ($\beta$-decay). 

Post-Modern Physics without Relativistic Mass

The change from classical physics to modern physics has long been viewed to be marked by Einstein's Theory of Special Relativity SR published in 1905 coming with a fundamental revision of Newtonian mechanics introducing the new concept of relativistic mass increasing with velocity, as opposed to Newtonian invariance of mass under motion, and the mass-energy equivalence of the most famous equation in physics $E=mc^2$. 

When I discuss these topics with chatGPT I am informed that the idea of relativistic mass has been put aside as no longer relevant, in a return to the idea of classical physics that mass is invariant and so does not change under motion. That is certainly as step forward to more clarity since the concept of relativistic mass under motion coming with a concept of rest mass of bodies at rest, was $a source of endless confusion. 

What then about mass-energy equivalence $E=mc^2$? Has it also been abandoned? Here chatGPT is ambiguous:

• All forms of energy $E$ as potential, kinetic, electric, chemical and nuclear energy in principle can be traded with $m=\frac{E}{c^2}$  for some mass $m$. 
• As concerns potential, kinetic, electrical and chemical energy $E$ the corresponding mass $m$ is so small because $c^2$ is so large, that the trading does not make sense because sufficiently small coins are not available. 
• But for nuclear energy the trading is viewed to make sense because $E$ is so large that $m=\frac{E}{c^2}$ is not zero. 
• Accordingly, the nuclear fusion reaction in the Sun is viewed to result in a loss of mass about 4 million tons per second. The loss is estimated to be less than 0.1 percent after 10 billion years of burning mass. 

It appears the chatGPT still clings to $E=mc^2$ although the conviction is shaking: Mass-energy trading does in particular not make sense for chemical reactions, only possibly for nuclear reaction where an idea of loss of mass or mass defect still hangs on. 

We then ask chatGPT if there is a fundamental difference between chemical reactions supported by spatial re-configuration of electrons, and nuclear reactions supported by spatial re-configuration of nucleons? 

The answer is that the only fundamental difference is the nature of the forces involved, Coulomb force or strong force, and not $E=mc^2$. 

Quantum models of chemical reactions do not involve $E=mc^2$, because it has no role to play. Likewise, quantum models of nuclear reactions do not involve $E=mc^2$, since it has no role to play. 

So what remains is to give $E=mc^2$ a role by insisting that any $E$ computed by a quantum model without $E=mc^2$, in principle can formally be traded with some mass $m=\frac{E}{c^2}$ of unspecified nature. But this trade has no physical meaning and so is only a formality which can be viewed as the only remaining homage to Einstein, when now his relativistic mass has been put into the dust bin of meaningless physical concepts including phlogistons. 

It may be time to now let it be joined by $E=mc^2$. This would open to a clarification of the concept of energy as basically connected to work as force times displacement, then appearing in the form of kinetic energy, mechanical energy, friction energy, potential energy, electrical energy and chemical/nuclear energy connecting to inertial force, friction force, elastic force, gravitational force and Coulomb force.

This would essentially mean to give up SR and returns to rational physics. If you still want to speculate about space ships traveling at half the speed of light, you could then instead turn to Many-Minds Relativity connecting the views of observers traveling at very high speeds with inspiration from Ebenezer Cunningham seeking to make sense of SR in the 1910s.

Phlogiston Theory of Nuclear Physics

The phlogiston theory was a scientific hypothesis developed in the late 17th century stating that a combustible body contains a substance in the form of phlogistons, which during combustion is released into the air under loss of mass of the body. The theory was debunked by noting instead a gain of mass (in the form of oxygen taken from the air). 

Modern physics describes combustion in terms of chemical reactions where energy is released by rearranging electrons in space into lower total energy, not substantially as loss of mass or mass defect. 

Modern physics explains energy release in nuclear reactions in terms of mass defect with the products having smaller mass than reactants, as if mass is turned into energy according to $E=mc^2$.  

According to the (debunked) phlogiston theory, energy released in chemical reactions comes from "burning of phlogistons".  

According to modern physics, energy released in nuclear reactions comes from "burning of mass" with mass defect according to $E=mc^2$. Is this also a form of phlogiston theory not yet debunked? 

To seek an answer, recall that nuclear reactions can be described in terms of spatial rearrangement of nucleons, in the same way that chemical reactions can be described in terms of rearrangement of electrons.

Does this description capture all the energy released or only some of it, the remaining then coming from "burning of mass"? But why only some of the energy, and not all? 

With these arguments we are led to question the idea of "energy from burning of mass" as the prevailing idea. We are led to suspect that the mass defects trivially computed from list values of masses of reactants and products have been assigned values so as to allow mass defects to account for observed energy release as a form of self full-filling prophecy to impress the average mind along the Einstein model of the previous post.  

More Orwellian 1984 Physics

This is a follow up of the previous post identifying a practice in both modern western society and modern western physics to erode language of meaning by equating things which are different as a form of equality politics, used to keep the ruling class on top. 

In modern physics this practice was introduced by Einstein in his famous $E=mc^2$ equating energy $E$ with mass $m$ through the speed of light $c$ squared, over the heads of the people: 

• It follows from the Special Theory of Relativity that mass and energy are both (but different)  manifestations of the same thing, a somewhat unfamiliar conception for the average mind.   

 

In the 2019 update of the SI Standard of units in physics, this is incorporated by simply defining the unit of mass in terms of energy according to $m=\frac{E}{c^2}$ by a specific procedure using a Kibble balance as the official picture. 

Inspecting a Kibble balance we discover that it measures mechanical energy $mgv$ by equating it to  electrical energy $VI$, which is measured in the balance and so gives a measure of mechanical mass $m$ with given values of gravitational constant $g$ and velocity $v$. We thus understand that a Kibble balance measures mechanical mass as the classical form of gravitational/inertial mass, and there is here no role for $m=\frac{E}{c^2}$ in contradiction to the official picture. 

Even an average mind can now understand that equating mechanical energy connected to mechanical mass $m$ to some other unspecified form of energy $E$ somehow connected to $m$ through $E=mc^2$, means eroding the concept of both energy and mass of meaning. 

The physics community were long skeptical to Einstein's unspecified form of energy according to $E=mc^2$, but the temptation to fool the average mind has now taken over in a desperate effort to secure funding to fundamental physics. 

In classical physics there are ultimately only two forms of energy: mechanical energy and electrical energy connected to gravitational force and Coulomb force. There is no need of inventing some new unspecified form of energy as $E=mc^2$.  

But what about photon energy $hf$? Well, light can transmit energy between oscillating charges carrying electrical energy, but light cannot store energy, because it has no mass. This is seen in electrical grids which need rotating mechanical masses like turbines to stabilise the grid over variations in input and output.  

Summary: The relation $E=mc^2$ appears as an add on which serves no purpose to define the unit of mass and how to measure mass. It remains to understand its role to compute energy release in nuclear reactions from measured mass defects, which will be the topic in a next post.     

Einstein's Orwellian World of Physics

Orwell's Animal Farm:

•  All animals are equal, but some animals are more equal than others.

The US Declaration of Independence:

• All men are (created) equal (but some men are more equal than others)   

Einstein's World of Physics:

• Mass $m$ and energy $E$ are different manifestations of the same thing: $m=\frac{E}{c^2}$
• Mass and Energy are equal.

In the first two cases it is easy to see how a Declaration by a State of equality of all men, is used by the State as a cover up of strong inequalities in both a socialistic and capitalistic State. The idea is to erode language of meaning by claiming as in 1984 that War = Peace, Freedom = Slavery, Ignorance = Strength, an so maintain the State. (this is what we see today in the Western World)

 

We now ask if Einstein's Mass = Energy can also seen as an erosion of language/meaning with objective to maintain a State (of Modern Physics)?

We then recall that mass is gravitational mass, which is the same as inertial mass, manifested by following the law of free fall in a gravitational potential, also manifested in Newtons 2nd Law connecting force $F$ to mass $m$ and acceleration $a=\frac{dv}{dt}$ by $F=ma$ with $v$ velocity.   

Energy is work $Fv$ performed over time $t$ from $t=0$ to $t=T$ assuming $v(0)=0$, given by  

• $\int_0^T Fvdt=\int_0^Tm\frac{dv}{dt}vdt=\frac{1}{2}mv(T)^2.$   

thus accumulated as kinetic energy. 

We see that there is a fundamental difference between mass and energy in physical meaning and physical unit. Energy $E$ per unit time is $Fv$, while mass $m=\frac{F}{a}$ and there is no clear connection between $E$ and mass $m$. 

Nevertheless modern physicists have decided to follow Einstein's Mass = Energy.  Since the physics is missing this is instead stipulated (since 2019) in the SI Standard as a definition of the unit of mass in terms of energy according to $m=\frac{E}{c^2}$. The SI unit of mass is thus stipulated so as to please Einstein by making $E=mc^2$ true.   

The lack of physics of $E=mc^2$ is thus compensated by an agreement that $E=mc^2$ is correct, even if the physics is different.  This is like a Declaration that "all men are equal", even if the reality is different. 

It is possible to see $E=mc^2$ as a Declaration to maintain a State of Modern Physics. 

The Standard Model follows up by zoo of particles described by the strange play of words borrowed from Finnegan’s Wake.

Why It Is so Difficult to Discuss with Physicists

My experience as a mathematician is that discussing some aspect of physics with a physicist many times leads into an abyss of confusion. A root cause is that the distinction between definition and physical fact can be unclear to a physicist with inspiration from Einstein who was a master of double-speak using this confusion to win any argument. 

For a both a mathematician and man in the street the nature of a definition is clear as a specification of how to use language. A definition has no truth value as concerns some factual circumstance. To define a meter to be equal to 100 centimeters is just a clarification of a short hand notation. To make an experiment to test the physical validity of this definition would not make any sense. 

But to a physicist there are two fundamental laws, which act as definitions but are viewed to be physical facts: (i) constancy of the speed of light and (ii) $E=mc^2$ , both directly connected to Einstein as master of double-speak. The units of length, time, energy and mass are today defined so that (i) and (ii) are upheld no matter what the Creator of World could have to say. To question (i) or (ii) would be met by a physicist only as a sign of ignorance about physical facts: The speed of light is constant, and energy is equal to mass.  

But does it matter if (i) and (ii) are definitions or physical facts or maybe both at the same time? Yes, such an ambiguity would not make a mathematician feel well at ease, and probably not a man in the street either. Only a physicist inspired by Einstein would welcome the confusion as a way to stay on top of the discussion.

What can then be the pitfall to confuse definition and physical fact? Well this would invite to view (i) and (ii) as physical fact which cannot be wrong. It gives the physicist rock solid knowledge about the physics of the world which cannot be contradicted by any observation of the physics of the world. It gives the physicist a very strong position when asking for more taxpayer funding of fundamental physics. In particular massive funding has gone into experimental investigation of (i) and (ii) always coming out as full confirmation and always asking for an even more precise confirmation. But it could also lead astray in navigation and misdirect research on energy production. 

In any case, the mathematician and man in the street would clearly understand that the meter is defined in terms of a preset value of the speed of light and of unit of time in terms of a certain atomic clock, and mass is defined as  $\frac{hf}{c^2}$ in terms of electromagnetic energy $hf$ with preset value of Planck's constant $h$ and frequency $f$ as periods per unit of time, that is would understand that (i) and (ii) are definitions only and not physical facts. A physicist inspired by Einstein would not agree, and so discussion is very difficult as an experimental fact. 

But what then about the mass defect in nuclear reactions claimed to be the difference in mass before and after nuclear reaction? Is it not real? Or is it just the result of attributing energy release in nuclear fusion to decrease of mass, then measured in terms of mass? Here a physicist would insist that the decrease in mass is real and not just a matter of book keeping performed by clerk physicists. If mass is measured in terms of energy then energy production requires loss of mass. But what is mass in fact? Isn't it rather connected to gravitation as gravitational mass = inertial mass as in classical physics?

This connects to the recents posts on RealNucleus as a model of an atomic nucleus with total energy carried as Coulomb potential energy in the same way as chemical energy, thus without connection to mass. If this model describes physics, then there is no need of a strong force and a window towards  a Grand Unified Theory including both Newtonian mechanics with gravitation and atomic physics, appears to be open.     

RealQM as RealAtom + RealNucleus

RealNucleus is a model of an atomic nucleus obtained by switching roles of electrons and protons in RealAtom as a model of an atom consisting of a nucleus of protons surrounded by a shell system of electrons. RealNucleus thus consists of a kernel of electrons surrounded by a shell system of protons.   

Together RealAtom and RealNucleus offers a complete model of an atom as a nucleus surrounded by electrons and a nucleus as a kernel of electrons surrounded by protons. 

The model is described in detail in this article. 

Resolution of Hilbert's 6th Problem

Sabine Hossenfelder in her last post tells about a possible breakthrough by mathematicians on a 125 year-old physics problem formulated as Hilbert's 6th Problem concerning the emergence of irreversibility in reversible laws of physics expressed in the 2nd law of thermodynamics or arrow of time.  

The proclaimed breakthrough appears to be another resort to statistics based on an idea that the evolution of a physical system forward in time is more probable than backward in time: Physical systems tend to evolve from less probable states to more probable states. This may seem convincing to some, but the physics of such a statement appears elusive. 

I have presented a resolution which is not based on statistics but on finite precision computation meeting instability as big effects from small causes appearing in backward time. This is the problem of unscrambling a scrambled egg, which requires precision overpowering instability. If physics is limited by finite precision, then the precise separation required for unscrambling cannot be performed and so the scrambling of an egg becomes irreversible. This has nothing to do with statistics, but is simply a lack of sufficient precision to overpower instability. This is all carefully explained in Computational Thermodynamics and blog posts on the 2nd law. 

Does Quantum Mechanics Explain Chemistry?

There is an extensive literature seeking to come to grips with the following Question: Is chemistry explained by the physics of the Schrödinger Equation SE as basis of Quantum Mechanics QM? Physicists in general claim that this is so, without supplying much detail of any QM explanation, while chemists wanting to see the details in general resort to their own explanations with only vague connection to QM. 

The basic trouble is that solutions to SE are uncomputable for multi-electron molecules and so cannot be inspected to reveal the physics of chemical bonding as the central aspect of the Question. What is available are other equations supposedly motivated by SE for which solutions can be omputed, but then with unclear status as approximate solutions to SE. In practice this works to accept approximate solutions which fit with observation and reject those who do not. This can result in ad hoc fitting of model to data missing the predictive first principle power of SE, then taken for granted. 

Here is an illuminating discussion with chatGPT showing how the scientific community grapples with the Question.

My own grapple has resulted in RealQM as Real Quantum Chemistry. 

    

Atomic Nucleus Secret Revealed?: Revision

We continue the exploration of RealNucleus as a RealQM model of an atomic nucleus consisting of 

• a kernel as an inner shell of non-overlapping $-1$ charge densities of total charge density $-Z$ 
• an outer shell of non-overlapping $+1$ charge densities of total charge $+2Z$
• interacting by Coulomb potentials.  

The key question is:

• Is such nucleus stable in the sense of having a negative total energy as the sum of kinetic and potential energy? 

Let us start with $Z=1$, thus with a -1 kernel surrounded by two +1 charges. The atom analog obtained by switching the sign of the charges is a proton surrounded by two electrons, which is an $H$ atom with an extra electrons.  This is the $H^-$ ion, which is known to be stable. RealNucleus confirms by computing the total energy 

Next, we consider $Z=2$, thus 4He with a kernel inner shell of a -2 charge density surrounded by an outer shell of four +1 charges. We use this code to find an energy from the outer shell of about -6 MeV per nucleon when the radius of the inner shell is small (less than 1 percent) compared to the radius of the outer shell. We thus get a clear signal of stability of the outer shell. 

 

The inner shell charge is subject to a constant potential from the outer shell, which is compatible with a constant charge density without kinetic energy.  What remains is the potential energy from overlap of two constant -1 charge densities. Can the inner shell be stable despite the repulsion present from charge density overlap and so the whole kernel be stable? We shall seek an answer using the spherical symmetry of the overlapping -1 charge densities hoping to find some form of cancellation compatible with stability. 

The bottom line is that the RealNucleus model shows existence of a +Z nucleus formed by 2Z protons surrounding a constant negative kernel charge density -Z, which is not subject to de-stabilising self-repulsion as key open problem. The constant inner charge density will act on the outer shell protons as a -Z central charge with the radius of the inner shell acting as model parameter. Charge densities from inner and outer shells can meet without continuity, in contrast to electron densities in RealQM meeting with continuity.  

 

RealNucleus

RealNucleus is a  model of an atomic nucleus which is an analog of RealQM for an atom, with shifted roles of electrons and protons. The RealNucleus model of a nucleus of charge $+Z$ thus consists of a shell system of $2Z$ non-overlapping charge densities of charge +1 held together by Coulomb attraction from a kernel of negative charge density $-Z$. RealNucleus is thus a model of  a nucleus which does not involve the ad hoc strong force of the Standard Model. 

RealNucleus has been added to the list of articles about RealQM. 

Update Fusion of 2H into 4He by RealQM

RealQM offers a new model of an atomic nucleus as a kernel of negative charge density surrounded by a shell structure positive charge density, as an analog of an atom with roles of protons (p) and electrons (e) switched. 

The model is parameter-free up to the change of scale from atoms to nuclei S and the radius of the kernel of the nucleus R, which can be used to fit the model to observations. Let us use this option to compute the binding energies E of the two basic nuclei of 2H (1e+2p) and 4He (2e+4p) by RealQM  using this code. We get the following results with a change of scale from atom to nucleus $S=2.5\times 10^{-6}$ with the size of an atom $10^{-10}$ m 

• 4He  E = 27 MeV,  R = 0 
• 2H    E = 2 MeV,  R = $2.5\times 10^{-17}$ m

We thus see that using the scale factor S we can fit E for 4He to observed 28.30 MeV and then using R to fit E with 2H. 

RealQM then offers a model of the fusion of two 2H into one 4He as the basic fusion process in the Sun with an energy release of 27-4 =23 MeV: 

Note that the atom analog of 2H nucleus is $H^-$ atomic ion, while the atom analog of 4He nucleus would be the ion $He^{-2}$, which is not stable. The 4He thus has 4 protons in a first shell, while the $He$ atom has no room for 4 electrons. 

The RealQM model for both atom and nucleus can be seen as the result of a shell packing problem, and thus comes with different shell structures. In an atom the first shell cannot contain more than two electrons, while in a nucleus the first shell appears to be able to hold up to 8 protons, thus with denser packing in a nucleus than in an atom. 

Modern Physics as Virtual Physics

Recents posts explore the possibility of extending the RealQM model of an atom, built by a positive nucleus attracting a negative electronic charge density around itself by the electromagnetic force, to a analogous model of a nucleus simply by switching the roles of proton and electron. 

In this model a nucleus is held together by the same electromagnetic force keeping an atom together, which is the electromagnetic force of classical physics as a force transmitted by an electric potential or field. This goes back to an idea naturally presenting itself as soon as an atom model was formed in the 1920s. But the idea was given up after the detection of the neutron by Chadwick in 1932 kicking out the electron from the nucleus preparing for the development of the Standard Model in the 1960s as the current model of a nucleus as part of StdQM. 

In the Standard Model a nucleus thus consists of protons and neutrons (not protons and electrons as in RealQM) each built as a triple of quarks held together by a strong force transmitted by force carrying particles named gluons (because they are supposed like a glue). From classical physics point of view this is a mind boggling model with both quarks and gluons beyond experimental detection thus as truly virtual and not real as detectable.

To make the Standard Model credible with its quarks and gluons, the ground-breaking idea of force carrying particles is extended to the old electromagnetic force, so well described as transmitted through electric potentials/fields, into a new explanation in terms of virtual photons as force carrier depicted by Feynman in this illuminating diagram explaining repulsion between two electrons through a $\gamma$-wiggle:

The argument is that if the well known electromagnetic force in fact is transmitted by photons (as depicted in Feynman diagrams), then it is not so strange to think of the strong force keeping a nucleus together by force carrying gluons. By expanding a fantasy story it can be made more credible, in the same way a big lie can be more credible than a small. 

A basic trouble with the Standard Model is that it contains more than 20 parameters, which have to be determined experimentally but that is impossible.

On the other hand, the only parameter in RealQM is change of scale between atom and atom nucleus (in the range $10^5$) which is possible to measure experimentally. 

We understand that modern physics with its virtual photons as force carriers of the electromagnetic force depicted in Feynman diagrams, can be be seen as a form of virtual physics fundamentally different from classical physics as real physics. 

Keep an eye on new post on RealQM as an alternative to the Standard Model for atomic nuclei.