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.