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.  

  

RealQM vs StdQM: Binding Energy of 4He

This is a clarification of recent posts on RealQM vs StdQM for small nuclei.

To determine the binding energy of the 4He nucleus built from 2 protons and 2 neutrons is an elementary exercise in high school physics: Compute the mass defect as the difference in mass of 2 free protons 2 + 2 free neutrons and the mass of 4He determined experimentally to be with c2 the speed of light squared:

• mass of a free proton $m_p= 938.272$ MeV/c2
• mass of a free neutron $m_n= 938.565 MeV/c2
• mass of nucleus 4He  $m_{4He}= 3727.38$ MeV/c2

and compute using Einstein's E=mc2 to find the binding energy BE as

• BE = $2m_p+2m_n-m_{4He} = 26.289$ MeV or 7.1 MeV per nucleon.

This value stands out as very large compared to 2.2 for 2H (Deuteron), 2.8 for 3H (Tritium) and 2.6 for  3He MeV per nucleon. It is explained as an expression of a doubly magic number present in the 2 protons and 2 neutrons of 4He. 

Is it possible that the BE for 4He determined from mass defect using E=mc2 as above, does not represent true physics? Is it possible that the rationalisation with reference to magic numbers is not real physics? 

Note that there is a gap in the above mass defect computation in the sense that the mass of the protons and neutrons inside the nucleus is not available to measurement and they enter into an energy budget required to break the nucleus apart. If the protons and neutrons in fact take on bigger mass inside the nucleus than outside then the binding energy will shrink maybe towards normality. The above high-school energy computation may reflect rather a convention than reality.

We compare with the BE about 1.7 MeV/nucleon for 4He computed by RealQM as a parameter free mathematical model without experimental input assuming a change of scale of $10^5$ between atom and atomic nucleus. Changing the scale a little then gives BE of about the same size as those above for 2H, 3H and 3He. 

Let us see what StdQM has to offer. We thus ask chatGPT if it is possible to determine BE without experimental input from the Standard Model (QCD) as the present mathematical model of atomic nuclei within StdQM.  Here is what chatGPT delivers as a conclusion of a lengthy report:

• A fully QCD-derived prediction of ⁴He’s binding energy without any experimental input is not yet realized, but current methods are closing in, and future simulations at physical quark masses are expected to reach this goal.

Summary: RealQM delivers BE for 4He in the range 2-3 MeV/nucleon with only experimental input the change of scale between nucleus and atom. StdQM struggles to deliver a result. The list value of 7.1 MeV/nucleon stands out as 2-3 times too large. 

What is Wrong with Newton's Law of Gravitation?

The corner stone of classical mechanics/physics is Newton's Law of Gravitation taking the form of the Newton/Poisson Equation NPE

• $\rho =\Delta\phi$         (*)

connecting mass density $\rho (x)$ to gravitational potential $\phi (x)$, where $x$ is the space coordinate of 3d Euclidean space. 

In modern physics this mathematical model is replaced by Einstein's Equation EE in "curved space-time" of his General Theory of Relativity GR preceded by the Special Theory of Relativity SR. EE reduces to PE in flat Euclidean space without time and so EE is viewed to be a generalisation of PE into curved space-time.   

To mark a shift between classical (obsolete) physics and modern physics a lot of effort has gone into showing that NPE contradicts observations and so must be replaced by EE. In particular NPE is viewed to contradict the following consequences of SR/GR:  

1. Finite speed of light.
2. Gravitational lensing. Bending of light 
3. Time dilation. Clock rates affected by motion and gravitation.
4. LIGO detection of gravitational waves with finite speed of propagation.
5. Precession of Mercury Perihelion.  

But NPE says nothing about propagation of light or the rates of clocks and so 1-3 cannot be viewed to contradict NPE. 

As concerns 4, it is well known that a delay in the action of the gravitational pull on Earth from the Sun will make the Earth orbit away from the Sun. Finite speed of propagation of gravitational force thus appears to contradict the stable orbit of the Earth. In EE this is explained as a form of compensation of the delay in some form of prediction effectively cancelling the delay to no delay. Strange.

So the evidence against NLG shrinks down to 5 with the claim that NPE gives an incorrect prediction of the observed orbit of Mercury, while that of SR/GR is correct. But making a prediction requires input of positions and velocities of all celestial objects in the Solar system at some specific time and in addition their masses and G. To claim that NPE gives the wrong prediction in the form of a very small deviation from observation requires a very accurate NPE computation taking all celestial objects including their internal motion correctly into account. Such a computation has not been made. 

Another argument against NPE is that it requires a notion of absolute time, something which is supposed to contradicts the relative time of SR. Is this a valid argument? 

In the sequence of posts on Neo-Newtonian Gravitation I have tested the idea that the gravitational potential $\phi (x)$ is primordial from which mass density is $\rho (x)$ is delivered by the local action of the Laplacian according to (*) as if time does not enter. 

Combining NPE with Newton's 2nd Law $F=am$ law brings in a notion of time since acceleration as change of velocity per unit of time refers to time, as well as velocity as change of position per unit of time. This gives a notion of local time for each body interacting with all other bodies through the time-less gravitational potential, which does not ask for coordination of local times into a global time. Maybe Newtonian mechanics in fact does not require a notion of global time? Only a notion of a global time-less gravitational potential. 

Binding Energy of a Nucleus from Mass Defect?

In the previous post when comparing binding energies by RealQM and StdQM for small nuclei, we were led to question the binding energies in StdQM computed from estimated mass defects with the masses of protons and neutrons as input. 

We find that the binding energy of nucleus according to StdQM is mainly potential energy created by the strong force, which does not depend on the mass of neutrons and protons. We thus learn that the binding energy of a nucleus does not depend on the mass of neutrons and protons. These masses only enters in a supplementary computation connecting energy to mass defect including $E=mc^2$. 

We can thus speak about two versions of binding energy:

1. Physical Binding Energy PBE determined by the strong force without input of the mass of neutron/proton.
2. Computed Binding Energy CBE from mass defect determined using $E=mc^2$ to make CBE=PBE.

It may then be tempting in a situation when PBE is impossible to assess either theoretically or experimentally, which is usually the case, to simply replace PBE by CBE and declare that CBE is physical binding energy and not just computed. 

Doing so StdQM delivers a very small drop of binding energy when changing one of the two neutrons of 3H into a proton thus forming 3He, which can be seen as a major change. RealQM gives here a large drop which maybe is more line with physics. 

Mystery of Nuclear Physics: StdQM vs RealQM

The Standard Model as part of Standard Quantum Mechanics StdQM delivers the following total binding energie E in MeV with p proton and n neutron 

• 2H     1p+1n   E = -1.71
• 3H     1p+2n   E = -7.97 
• 3He    2p+1n   E = -6.70
• 4He    2p+2n   E = -28.30

The large jump of more than 20 MeV by adding 1 neutron to 3He into 4He is viewed as very remarkable asking for an elaborate explanation in terms of the strong force within StdQM boiling down to 4He having a "doubly magic" number of protons and neutrons. 

RealQM delivers the following energies (with atom to nucleus size scaling set to $10^6$) and shell configuration indicated:  

• 2H      1p+1n  E= -0.5         1st shell: 2
• 3H      1p+2n   E = -2.7       1st shell: 1  2nd shell: 2 
• 3He    2p+1n   E = -0.5       1st shell: 2  2nd shell: 1
• 4He    2p+2n   E = -2.5       1st shell: 2  2nd shell: 2

We see in RealQM  the same large jumps from 2H to 3H and from 3He to 4He with roughly a factor 5 as in StdQM. This can in RealQM be understood from the fact that adding 1 neutron doubles the central negative charge density and so doubles the negative potential. 

RealQM thus captures a basic feature of StdQM in particular the "magic number" of 4He, which thus after all may not be so magic. 

But there is a notable difference in the change from 3H to 3He by replacing a neutron by a proton. StdQM gives a small decrease of energy, while RealQM gives a much bigger decrease. 

In RealQM this comes again from a decrease of central negative density. 

In StdQM the strong force is the same and the only difference is the proton-proton repulsion in 3He claimed to be small compared to the strong force. Recall that energy is not directly measured but is computed from mass defect using $E=mc^2$, where mass defect is not directly measure but computed  from measurements of proton and neutron mass. There is thus a lot computation involved which may not capture true physics. In any case it is strange that replacing a neutron by a proton has only marginal effect on energy.   

Summary:

• RealQM offers a model of a nucleus with only Coulomb forces.
• StdQM offers a model of a nucleus with an additional new strong force.
• Ockham's Razor would select RealQM, 

  

 

Binding Energy of 4He by Mass Defect?

RealQM gives using this code the following binding energy E per nucleon (in MeV) of atomic nuclei with charge Z=1,2,...,8, assuming a change of spatial scale from atom to nucleus with a factor $10^6$:

• Z=1  E = -0.5   2H
• Z=2  E =  -1.0  4He
• Z=3  E = -2.2   6Li
• Z=4  E = -3.2   8Be
• Z=5  E =  -5.0  10B
• Z=6  E = -5.5   12C
• Z=7  E = -6.5    14N
• Z=8  E = -6.6    16O

We see a nearly linear increase from Z=1 to Z=5 followed by much slower increase into constant value. 

We compare with the following list values (in MeV):

• Z=1  E = -0.86   2H
• Z=2  E =  -6.82  4He
• Z=3  E = -5.08
• Z=4  E = -6.81
• Z=5  E =  -6.22
• Z=6  E = -7.42
• Z=7  E = -7.22
• Z=8  E = -7.72

We see a very quick jump from 2H with Z=1 to 4He into nearly constant value, thus without the gradual increase suggested by RealQM. The explanation by StdQM for the surprisingly large jump is very complicated. A fusion process with two 2H being combined into one 4He would thus deliver about 25 MeV, to be compared with 2 MeV for RealQM. 

In this situation, it is natural to ask how the large binding energy for 4He is determined in StdQM. We recall that the fusion of two 2H into one 4He is the fusion process fueling the Sun. It is impossible to directly measure the energy release in a fusion process and so it is instead determined according to a certain standard, where mass is traded for energy according to Einstein's $E=mc^2$. But because of the factor $c^2$ is very large, the mass lost or mass defect in a fusion process is too small to be directly measured. The mass defect is instead computed according to a certain standard, from which the binding energy is computed using $E=mc^2$. 

We are thus led to ask if the large computed large binding energy of 4He is the real one? Is it possible that the smaller jump by RealQM is closer to reality? Which value is relevant for the Sun: 25 or 2? How can this question be answered?

 

We meet here a a situation where a certain standard procedure replaces direct measurement and the question is if the procedure captures reality. 

The Kinetic Energy of StdQM and RealQM

The Schrödinger Equation SE as the basic mathematical model of Standard Quantum Mechanics StdQM in terms of (here for simplicity) a one-electronic wave function $\Psi (x)$ depending on a 3d spatial coordinate $x$, gives rise to a contribution to total energy named kinetic energy of the form 

• $E_{kin}(\Psi )=\frac{h^2}{2m}\int\vert\nabla\Psi (x)\vert^2 dx$ with $\int\Psi^2(x)dx=1$, 

where $h$ is Planck's constant and $m$ the mass of the electron. If $\Psi (x)$ is globally defined with $\Psi (x)$ tending to zero for $\vert x\vert$ tending to infinity, the coefficient $\frac{h^2}{m}$ determines  the size of the electron to scale with the $\frac{h}{\sqrt{m}}$ with thus a larger size for smaller $m$. 

Viewed the other way around, $E_{kin}(\Psi )$ scales with the factor $D^{-2}$ with the size $D$ of the electron, which means that electron concentration comes with large kinetic energy. 

In RealQM as an alternative to StdQM an electronic wave function has local support over a domain in space and is not restricted to vanish on the boundary of the domain. This allows the kinetic energy to stay bounded with decreasing size of the electron. This is the secret of covalent bonding as shown here and allows RealQM to extend to a model of an atomic nucleus as shown here. 

The salient feature of RealQM is that electrons have wave functions with non-overlapping support representing non-overlapping unit charge densities which meet a free boundary with continuity. 

Covalent bonding is thus realised in RealQM by allowing electrons to meet between kernels without increase of kinetic energy. 

A RealQM model without need of a strong force of a nucleus can thus be built as an electron density of very small size surrounded by protons of larger size. Electrons thus appear in two sizes, large for an atom and small for a nucleus. 

Covalent bonding is not well explained within StdQM, and is still after 100 years subject to debate without conclusion. The Standard Model of a nucleus built by quarks and gluons/strong force is very complicated.  

RealQM Goes Nuclear

RealQM offers a model of an atomic nucleus as being composed of protons and electrons just like an atom but with shifted roles. An atom consists of a collection of electrons with negative charge surrounding an atomic nucleus including protons with positive charge. Similarly RealQM suggests to view an atomic nucleus to consist of a collection of protons surrounding a kernel including electrons compressed into a negative charge density. See this article.

In the atom model of RealQM electrons appear as negative non-overlapping charge densities with a spatial  extension measured as kinetic energy. Likewise, in the nucleus model of RealQM protons appear as positive non-overlapping charge densities with spatial extension measured by kinetically energy. An atom has a size of about $10^{-10}$ m, while the size of a nucleus may be about $10^{-16}$ m. The change of scale of about $10^6$  translates to a change of scale of total energy with the same factor, thus roughly from eV for atoms to MeV for nuclei. 

RealQM thus offers a unified model of an atom including its nucleus, where electrons appear with vastly different spatial extension of size $10^{-10}$ outside a nucleus for an atom, and of size smaller than $10^{-16}$ inside a nucleus. 

The basic RealQM model of a nucleus of positive charge $+Z$ consists of $2Z$ protons surrounding a kernel of negative density of total charge $-Z$. A neutral atom can then be built around such a nucleus by adding Z electrons. This atom model thus consists of altogether $2Z$ protons and $2Z$ electrons and there is no need for neutrons.  

We then have to ask from where neutrons can come, if they are not hiding inside atomic nuclei. Well, neutrons were experimentally detected by Chadwick in 1932 when bombarding beryllium with 4He (alpha-particle) as a neutral penetrating radiation able to knock out protons, which could not be explained as gamma-rays (electrons). Chadwick declared that he had detected a particle of no charge with a mass about that of a proton, a neutron which gave him the Nobel Prize in Physics in 1935. 

Once the neutron was detected it was shown that it could decay into a proton + electron (+neutrino) with release of energy of about $0.78$ MeV which opened to a possible reverse process of forming a neutron from a proton + electron under input of energy. This showed to appear in the chain reaction of nuclear fission where a nucleus is divided into pieces under ejection of neutrons sustaining the reaction. 

RealQM computes the total energy of a nucleus and shows that for $Z<26$ fusion of two nuclei into one nucleus is energetically favourable. This is in particular the fusion process in the Sun with two $Z=1$ nuclei combing into one $Z=2$ nucleus, thus with two 2p+e transforming into one 4p+2e or two 2H as deuterium transforming into one 4He, thus without invoking any neutron. The process may take several intermediate steps as displayed in this picture, showing in particular that neutrons (if present at all) have no role to sustain the fusion process:

All this is wildly speculative, but there is a bit of logic which may open to physical realisation. 

If RealQM can model not only atoms and molecules but also atomic nuclei,  a unified field theory may be possible. 

Recall that the Standard Model is very complex and in particular involves force carrying particles so called leptons, which have no role to play in RealQM

RealQM: Unified Field Theory/Model

If you (like Einstein) have been looking for a unified field theory including both quantum mechanics and gravitation in a single mathematical framework, here is something to inspect to see if it meets your criteria of a unified theory in its form of RealQM.

RealQM offers a mathematical model of atoms and atomic nuclei in a form of classical continuum mechanics as systems of non-overlapping charge densities interacting by Coulomb potentials/forces. RealQM directly extends to Newtonian gravitation in its form of classical continuum mechanics. 

The previous post gave the last piece to this puzzle in the form of a model of atomic nuclei as composed of protons and electrons interacting by Coulomb potentials without need of the strong/weak force of the Standard Model. 

Recall that the search for a unified model has been going on for a long time and physicists of today still repeat a 100 year old mantra that quantum mechanics and Einstein's general theory of relativity/gravitation as the pillars of the immense success of modern physics, are incompatible and so pulls the carpet under the success. So physicists have desperately been searching to squeeze one theory into the other as quantum gravity or quantum relativity, but without notable success. 

It is agreed that Newtonian gravitation covers all situations but some very extreme cases. RealQM with Newtonian gravitation thus offers a unified model covering all scales from atomic to cosmic scales. I am searching for at least one physicist open to discussion of such a possibility. Maybe this is all fiction, but maybe it has a connection to reality...maybe fundamental physics is not infinitely complex...

RealQM is presented in series of short easy to digest articles here.

RealQM: Nucleus without Strong Force

Update:

Here is new RealQM article in this list of articles: 

• RealQM for Nucleus 

where an atomic nucleus is viewed as a small scale analog of an atom with positive and negative charge shifted. In this model a nucleus consisting of Z electrons and 2Z protons is held together by Coulomb forces without need of the strong force. This is made possible by a denser packing in a nucleus than in atom made possible by absence of Pauli Exclusion in RealQM.

RealQM thus offers a model of both an atom and a nucleus both consisting of protons and electrons held together by Coulomb forces with a shift of roles. The nucleus model thus does not require ad hoc invention of strong force overcoming proton-proton repulsion as in the Standard Model. This is so remarkable that it is hard to believe. But the math shows that Coulomb attraction is enough if dense packing can be realised...

RealQM shows that 4He as a 2-electron kernel surrounded by a 4-proton shell is stable. But a configuration into a 2-shell system with 2 protons in each is unstable, as an analog of an unstable He2- ion with two extra electrons. 

  

RealQM vs EPR Paradox and Bell's Inequality

The Einstein-Podolsky-Rosen EPR paradox was constructed in 1935 to show that Standard Quantum Mechanics StdQM in its statistical Copenhagen Interpretation CI of Bohr-Born-Heisenberg, cannot give a complete description of reality and so that there must be a deeper deterministic theory with variables hidden to CI describing the reality of the microscopics of atoms and molecules. In short that StdQM/CI is incomplete. 

This was meant to be death blow to CI rooted in Einstein's deep conviction that God does not play dice. But Bohr was not impressed and Einstein was finally eliminated from QM as an old fool and EPR felt into oblivion. 

In 1964 EPR was brought back to the discussion about the foundations of CI by John Bell proving a mathematical result named Bell's Theorem stating that the physics of any theory built on a certain set of physical assumptions 1-3, must satisfy Bell's Inequality, which in principle can be tested experimentally. The assumptions are: 

1. Realism: The theory describes a unique existing reality independent of observation by any observer.
2. Locality: Effects are not propagated infinitely fast.
3. Free Observer: Settings of measurement apparatus not pre-determined.     

Here 1 includes the same form of determinism (and observer independence) as in classical physics and 2 also has a classical meaning. Only 3 brings in a non-classical concept by referring to measurement by some form of observer. Bell's results were by physicists first viewed as pure philosophy, but were quicklyly given a form of concrete meaning, when John Clauser as observer in 1964 made a measurement showing violation of Bell's Inequality, which was welcomed as evidence that 

• There is no theory describing reality which satisfies all of 1-3.   

This served as a final blow to EPR asking for a theory satisfying 1 and 2 thus gave renewed support to the canon of StdQM/CI with thanks to Clauser given as a Nobel Prize in Physics in 2022 (why did it take so long?). But the conclusion to dismiss Einstein now as a dead fool was maybe too quick, since EPR did not really ask for 3. 

Recall that Bohmian mechanics can be viewed to satisfy 1 and 3 but not 2, and that the Many-Worlds Theory of Everett like CI can be viewed to satisfy 2 and 3 but not 1. 

It is natural to ask if there is any theory in the spirit of Einstein-Podolsky-Rosen, which satisfies 1 and 2 without involving 3 and so cannot be dismissed by Clauser's experiment. A quantum theory different form StdQM (which Einstein probably like Schrödinger would have welcomed, if available). 

Yes, you are right: RealQM is a theory which satisfies 1 and 2 and does not require 3, where the variable hidden to CI is the free boundary of RealQM as a new element to the picture. 

Concerning 3, note that it is not necessary to make a distinction between an experiment and any other physical process, and so include the experimental apparatus in a RealQM simulation while keeping out the observer.   

RealQM for Nucleus

Here is a new article in the series on RealQM: 

• RealQM: Nucleus

The idea is to view an atomic nucleus to be composed in the same way as an atom with a switch of roles between electron and proton, thus with a collection of protons as charge densities around a pointlike negative charge. Such a nucleus is held together by Coulomb attraction from the negative charge overcoming Coulomb repulsion between protons. 

What Does the Schrödinger's Equation Say?

Nobel Laureate in Physics Gerhard t' Hooft is not happy with the prime jewel of modern physics in the form of Schrödinger's Equation SE as expressed in Un Unorthodox View on Quantum Mechanics:

• We know very well how to use the equation. The properties of atoms, molecules, elementary particles and the forces between all of these can be derived with perplexing accuracy using it. The way the equation is used is nothing to complain about, but what exactly does it say?
• What do these wave functions represent? In particular the ones that are not asso- ciated to photons (the energy packets of the electromagnetic field, which we think we understand very well). 
• What do those waves stand for that are associated to electrons, or other elementary particles, or even molecules and larger things, including cats, and eventually, physicists? What happens to its wave function when you actually observe a particle?
• Almost a full century has passed since the equation was written down, and fierce discussions have been held, quite a few standpoints were vigorously defended and equally vigorously attacked. We still do not know what or whom to believe, but it still goes on, while others get irritated by all this display of impotence. 
• Why is it that we still do not agree? I think I know the answers, but almost everyone disagrees with me.
• Not only may quantum mechanics be a description of the sub-microscopic world that is profoundly different from what is often asserted, particularly concerning 'what is really going on', but questions such as these may well be essential for finding new ways of constructing models beyond what is now called the Standard Model of the sub-atomic particles.

t' Hooft describes modern physics in a state of stalemate, impotence and irritation and asks for new ways of constructing models. 

I will send RealQM t' Hooft RealQM and will report his reaction. 

Note that t' Hooft repeats the mantra the physicists know very well how to use SE to derive properties of atoms and molecules with perplexing accuracy... there is nothing to complain about. Yet t' Hooft does complain because he does not understand what all this highly accurate information in fact does say? 

RealQM: Helium and Orthohelium

Here is a new article about RealQM:

• Helium and Orthohelium

added to a list of articles.

RealQM: Towards Big Molecules

Here is a new article in the series on RealQM:

• RealQM: Towards Big Molecules

Philosophy of Classical Physics vs Modern Physics

Here is a new article in the series about RealQM:

• RealQM vs StdQM: Philosophy

The idea is that philosophy enters into physics when there is a need to clarify the meaning of concepts of physics. The Philosophy of Quantum Mechanics is an academic discipline itself, typically part of a department of philosophy rather than a department of physics, powered by the fact that the Quantum Mechanics is filled with contradictions and mysteries which are not part of classical physics.

 

Germany/France/Sweden: War with Russia

Sweden, France and Germany all waged wars against Russia (1700-21, June-Dec 1812, 1941-45) and lost.

It seems that this has not been forgotten by the leaderships of these countries and that time has now come to seek revanche by escalating the US proxy war in Ukraine into a full war with Russia with victory guaranteed, even if the people has not been asked if they want to send their sons to the trenches.  

To guarantee victory military budgets are quickly tripled, conscription is planned and the delivery of weapons to Ukraine will get a new boost by eliminating any range restrictions to hit Russia. Effectively, a declaration of war has been made only awaiting formal confirmation.  

Are the chances for Sweden, France and Germany really better this time? Sweden has 10.000 soldiers, France 270.000 and Germany 180.000, none with any combat experience. Russia has about 1.3 million active with combat experience and 2 million in reserve, nuclear arms more powerful than the US, and hypersonic missiles which have no defense. Russia can take out the capitals of Sweden, France and Germany in one first strike without nuclear warheads. The nuclear umbrella of France is rusty.  

These facts are hidden to the people by big media directed to send the message that like in 1914 war (now with Russia) is necessary and a victory will be quick. The defeats have not been forgotten. Karl XII, Napoleon and H are waiting to come back..it is up to the people to stop this madness…

  

RealQM: Shell Structure and Periodic Table

Here is a next article in the series on RealQM posted in recent posts:

• RealQM: Shell Structure and Periodic Table

World expert on the Periodic Table Eric Scerri has investigated to what extent the Periodic Table can be explained by StdQM and seems to say that there are pieces missing in this puzzle. The article gives a first hint into explanations based on RealQM to be complemented with more details.

 

RealQM: First Molecule

 Here is a new article in a series about RealQM

• RealQM: First Molecule He+H

The article presents a RealQM simulation of the formation from a Helium atom He and a proton H+ the molecule He+H  from a transfer of one electron from He to H+ thus combing He+ and H into the first molecule formed after Big Bang, from which H could form from dissociation of He+H. Altogether a process to form H from He with He by its stronger kernel attraction forming before H in a sea of electrons.  

RealQM models this process as endothermic requiring input of energy (from Big Bang) to position H+ close to He with the distance determined so as to arrive at a ground state energy of He+H lower than -2.500 Hartree allowing He+H to dissociate into He+ of energy -2.000 and H of -0.5. 

StdQM gives a different perspective with instead a molecule HeH+ formed in a weakly exothermic reaction with a He atom incorporating a H+ proton. 

He+H can thus serve as a test of validity of StdQM vs RealQM since they give radically different messages.

Download article and open in Acrobat to get active hyperlinks.

See also earlier post1 and post2.

Quantum Mechanics All Wrong

In the above interview of Tim Maudlin by Brian Green we hear a message that Quantum Mechanics QM  is filled with mysteries and paradoxes. That QM does not make sense. We also hear that despite this undeniable fact, QM is a theory about atomic physics with a wave function describing in principle everything that can be known about a world built from atoms although the connection between the wave function and the real world is hidden to inspection by humans. So we've gotten a lot wrong a lot about QM but Maudlin gives no hint to a more correct theory. This is a report about a theory in stagnation since 100 years. As a possible way out of stagnation take a look at RealQM.

Weak Reactivity of Gold by RealQM

 Here is a new article to the series about RealQM as an alternative to StdQM:

• Real Quantum Mechanics: Weak Reactivity of Gold

RealQM explains why Au with electron shell configuration 2+8+18+32+18+1 with 1 valence electron in a last shell outside a sphere of radius R containing all other shells, does not form a molecule Au2 by covalent bonding as a geometric effect of large R preventing electron accumulation between kernels.

RealQM explains covalent bonding of H into H2 and non-bonding of He2 in this earlier article in the series:

• Real Quantum Mechanics: Covalent Bonding. 

Download files and open in Acrobat to get active hyperlinks.

Origin of CMBR?

Here is an interesting video about the possible origin of the Cosmic Microwave Background Radiation CMBR other than an "afterglow" of a Big Bang proving the Big Bang hypothesis to be correct, as the currently most popular cosmological theory:  

The video recalls early theories about a static Universe filled with some form of interstellar dust radiating a Planck spectrum of around 2-5 Kelvin. Such a thing was detected in 1967 at 2.7 K and was then  connected to Big Bang deleting the old theories from the map. In particular the Big Bang theory claimed to resolve the mystery of the observed red-shift of galaxies increasing with distance suggesting an accelerated expansion of the Universe. 

One of the old theories was the "tired light" hypothesis presented by Zwicki in 1929 suggesting that the red-shift could be the result of a loss of energy of light passing through interstellar dust over long distance with energy scaling with frequency.  

The idea of an active interstellar dust actively radiating at 2.7 K seems more natural than that of a Big Bang "afterglow" still hanging on after 13.8 billion years. 

Zwicki's "tired light" hypothesis can be connected to some form of dark matter as source of gravitation which shows up as CMBR resulting from sucking up energy from passing light.  I have discussed dark matter in posts on Neo-Newtonian Gravitation.   

Computational vs Theoretical Mathematics in Physics

The mathematical models of physics take the form of partial differential equations like Euler's Equations for incompressible inviscid fluid flow EE, corresponding Navier-Stokes equation for viscous flow NSE and Schrödinger's equations for atoms and molecules SE. 

The task of a theoretical mathematician has been to prove by symbolic analytical techniques (i) existence, (ii) uniqueness and (ii) regularity of solutions to a given equation with data given in some large class of possible data with data including initial data, forcing and parameters like viscosity in NSE. 

The task of a computational mathematician has been to compute solutions for specific choices of data which in each specific case can answer (i)-(iii) by inspection of the computed solution. 

It has been argued that computation is not enough, even if for each specific choice of data (i)-(iii) can be answered, because only a limited number of specific choices can be inspected. The possibly very large class of data can thus never be exhausted by computation, which gives analytical symbolic mathematics a role to play by covering a large class of data.

It is natural to ask if there are examples of equations for which the class of relevant data is so small that it can be exhausted by computation. This means first that the equation cannot contain any parameter like viscosity. Are there any models of interest which are parameter free? Inspection of EE and SE shows that they are both parameter free, and so meet the requirement of Einstein of an ideal mathematical model opening to say something about the world without measuring anything. This is like learning the area of a circular disc by computation with unit radius as only input.

Solving EE computationally thus delivers the drag of a body moving through a slightly viscous fluid such as air and water at a subsonic speed with the only data being the shape of the body and not any viscosity as parameter. This limits the class of data to shapes of bodies with a limited range of shapes of interest to be covered by computation. This is all described here.

The case of SE is in its traditional form of Standard Quantum Mechanics StdQM troubled by the fact SE by its multi-dimension nature is uncomputable and so needs dimensional compression which introduces parameters. 

RealQM is different realisation of the same parameter-free Hamiltonian as StdQM into computable form without introduction of any parameter. RealQM thus expresses SE in parameter-free computable form and so opens the possibility of saying something about the atomic world without experimental input. RealQM thus computes the ground state of an atom with the only input being the number of electrons and so can exhaust the Periodic Table.      

An analytical estimate of ground state energy as the result of a longer or shorter sequence of successive bounds, can be seen as a form of symbolic computation, while a numerical computation can be seen as very long arithmetic proof.

Computation with a parameter-free mathematical model can produce a rich set of outputs from very limited structural input, which can serve as data for AI in need of rich data. Computation is then used both to produce data and to learn from data. Symbolic mathematics has an important role to set up computation.

The Clay Institute Millennium Problem on (i)-(iii) for NSE is still open in the form of symbolic mathematics with no progress reported over 25 years. Can computation get the million dollar Prize?

Covalent Bonding by RealQM

Here is the next article in a sequence of articles exhibiting the capabilities of RealQM as an alternative to StdQM as the canon of modern physics: 

• RealQM: Covalent Bonding

with earlier articles in recent posts. Download article and open in Acrobat to get hyperlinks to essential codes to run, inspect and modify.

Shut up and Calculate vs Compute, Learn and Speak

Here is a reflection connecting to the previous post on RealQM as a computable model of atoms and molecules and Mearmin's Shut up and Calculate desperate reaction to the difficulty of making sense of the theory of Standard Quantum Mechanics StdQM. 

Let us recall the following views on the divide between StdQM as the theoretical foundation of chemistry according to physicists and the theoretical chemistry actually used by chemists. 

Eberhardt 2012:

• Chemistry is a discipline of two faces, one applied and the other theoretical. The applied face focuses on the design and synthesis of molecules and solids, while the theoretical face looks for explanations of a molecule or solid’s properties.

Bader 2011:

• ....the divide that exists in chemistry between those who seek their understanding within a universe wherein the laws of physics apply and those who prefer alternative universes wherein the laws are suspended or bent to suit preconceived ideas.

Dirac 1929:

• The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.

Dirac identifies the root cause of the divide as the impossibility of solving Schrödinger's equation of StdQM for the complex atomic systems of chemistry. If computational solution was possible there would be no divide and the whole of chemistry would be like an open book to read by computation. 

RealQM is an alternative to StdQM which is ab initio computable for the complex atomic systems of chemistry and is also understandable in the same sense as classical continuum mechanics. If RealQM indeed shows to models physics, then there is no longer any reason for a divide between theory and practice. The Shut up and Calculate can then be replaced by Compute, Learn and Speak. 

 

RealQM Article: Stability of Atoms

Here is another article in a series of articles about RealQM to be submitted:

• Real Quantum Mechanics: Stability of Atoms 

Recall the first article in the series:

• Real Quantum Mechanics: Introduction

Download file and open in Acrobat to get active hyperlinks.

RealQM Article to Submit

I am now now preparing to submit a sequence of articles about Real Quantum Mechanics to relevant journals and here is a first test to check out reaction:

• Real Quantum Mechanics

Take a look and give a comment. 

Political Role of Quantum Mechanics

The shift from the old quantum mechanics of Niels Bohr happened with Werner Heisenberg's July 1925  "Reinterpretation" article introducing a new form of matrix mechanics without Bohr's electron trajectories to form the new quantum mechanics.  

Heisenberg was a student of Max Born at the University of Göttingen with the mathematician Hilbert as world authority of mathematical physic acting as Born's mentor. Göttingen mathematical physics was an important part of the "Weimar Renaissance" during the recovery of Germany after the defeat in WWI getting momentum in 1925. 

It is thus possible to give Heisenberg's new quantum mechanics political dimensions stretching into WWII with Heisenberg as leading scientist in Germany's quest for an atomic bomb in the "Uranium Club".  

Planck had a similar role at the height of the German Empire when he in 1900 took on the responsibility to resolve the outstanding open physics problem of black-body radiation, when to avoid failing he resorted to statistics of quanta which resurfaced in Born's interpretation of Heisenbergs new quantum mechanics.

Heisenberg worked as Bohr's assistant in 1925 and Bohr invited Born to Copenhagen in 1926, and so they came to form the Bohr-Born-Heisenberg Copenhagen school setting the agenda for quantum mechanics from its beginning into our time. 

Schrödinger entered in 1926 with his equation showing to be equivalent to matrix-mechanics, but Schrödinger did not accept the Copenhagen Interpretation and so left the field to come back only in 1954 to discover that BBH still controlled the scene. 

After WWII the US took over quantum mechanics still in the spirit of BBH.

All physicists of today say that following the idea of the mathematician von Neumann that the wave function of quantum mechanics lives in a Hilbert space of infinite dimension and most physicists will confess to the Copenhagen Interpretation even if its meaning is unclear. Schrödinger's request of physicality is met with "shut up and calculate". 

What do the Chinese say? Is it time for Schrödinger to come back in the form of RealQM in the "China Renaissance" that is now reshaping the world? It is not impossible since the Chinese are very clever, very organised and result oriented towards a clear plan.

ChatGPT: After completing his doctoral work in Budapest and Zurich, von Neumann spent the academic year 1926–27 at Göttingen. There he

• Studied under David Hilbert, attending Hilbert’s lectures on the mathematical foundations of quantum mechanics,

• Sat in on Max Born’s seminar on the new quantum theory, and

• Published his first quantum‐mechanical notes out of Göttingen later that year.

Issues with Standard Quantum Mechanics 1926-2026

There are basic unresolved foundational "issues" with Standard Quantum Mechanics StdQM based on Schrödinger's Equation SE, basically issues with SE: 

1. Unitary deterministic evolution of the wave function.
2. Collapse of the wave function upon observation.
3. Statistics of collapsed wave function by Born's Rule. 

There are many more issues (ontology, correlation, non-locality...) but the all connect to 1-3 in one way or the other. 

Major efforts have been made since the 1926 when Schrödinger formulated SE, to resolve the issues but there is still no resolution in sight accepted by most physicists. There are several very different proposals (Copenhagen, Many-Worlds, Bohmian Pilot Wave...) with the great variety suggesting that they are all wrong. 

The previous post exhibited the "weirdness" of SE in the sense of electrons having both separated existence in different worlds and existence in a common shared world. This is expressed in the multi-dimensional nature of the Hamiltonian $H_{weird}$ underlying SE. 

But there is a different interpretation of $H_{weird}$ named RealQM, which is not weird because the electrons in RealQM have only shared existence with the corresponding Schrödinger equation taking the form of classical continuum mechanics.  

By restricting electrons to share the same 3d world/coordinate system, all the issues troubling StdQM evaporate. RealQM comes out as a form of classical continuum mechanics without issues beyond those of classical physics. RealQM thus offers a unified continuum model including both micro and macro-scopic physics. 

It is a mystery why RealQM was not tried in 1926, since it is the most natural way of generalising Schrödinger's equation from one electron to many electrons, staying within classical continuum mechanics without all the issues of StdQM, which was Schrödinger's approach.

It seems that it was Heisenberg and Born who made history turn in the direction of StdQM and not RealQM. 

The following quotes of Heisenberg shows his ideas rooted in his matrix-mechanics as a new form of physics, which express essence of StdQM:

• What we observe is not nature itself, but nature exposed to our method of questioning.
• Not only is the Universe stranger than we think, it is stranger than we can think.
• The reality we can put into words is never reality itself.
• The atoms or elementary particles themselves are not real; they form a world of potentialities or possibilities rather than one of things or facts.
• The existing scientific concepts cover always only a very limited part of reality, and the other part that has not yet been understood is infinite.
• The ontology of materialism rested upon the illusion that the kind of existence, the direct "actuality" of the world around us, can be extrapolated into the atomic range. This extrapolation is impossible, however. 
• The conception of objective reality ... has thus evaporated ... into the transparent clarity of mathematics that represents no longer the behavior of particles but rather our knowledge of this behavior.

Born came to the help of Heisenberg with the statistical interpretation of the wave function of StdQM:

• If God has made the world a perfect mechanism, He has at least conceded so much to our imperfect intellect that in order to predict little parts of it, we need not solve innumerable differential equations, but can use dice with fair success.
• I am now convinced that theoretical physics is actually philosophy.
• The universe is not a puzzle to be solved, but a mystery to be embraced.

Bohr from his failed attempt to give physics to an atom, also jumped in to help Heisenberg in support of StdQM:

• It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we say about Nature. 
• Nothing exists until it is measured.
• Opposites are not contradictory but complementary.
• When we measure something we are forcing an undetermined, undefined world to assume an experimental value. We are not measuring the world, we are creating it.
• When it comes to atoms, language can be used only as in poetry.
• There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about Nature.

Together Bohr-Born-Heisenberg formed a very strong team setting the agenda of modern physics to be  StdQM against the will of Schrödinger who wanted something like RealQM. 

It may be that all the unresolved issues with StdQM having taken toll for 100 years finally will open for a come back of Schrödinger and RealQM.

Why Quantum Mechanics is "Weird"

All leading modern physicists agree that quantum mechanics is so "weird" or "absurd" that it cannot be understood: 

• Quantum mechanics describes nature as absurd from the point of view of common sense. And yet it fully agrees with experiment. So I hope you can accept nature as She is - absurd. (Feynman)
• I think I can safely say that nobody understands Quantum Mechanics. (Feynman)
• If quantum mechanics has not profoundly shocked you, you have not understood it yet. (Bohr)

The "weirdness" of quantum mechanics comes from its foundational principle in the form of Schrödinger's equation based on a Hamiltonian $H_{weird}$ of the following form for an atom with kernel of positive charge $Z$ at the origin of a 3d Euclidean coordinate system $R^3$ surrounded by $N=Z$ electrons labeled $i=1,2,...,N$:

• $H_{weird}= \sum_{i}(-\frac{1}{2}\Delta_i -\frac{Z}{\vert x_i\vert}) +\sum_{j<i}\frac{1}{\vert x_i-x_j\vert}$                                        

where each $x_i$ is a 3d coordinate for a separate copy of $R^3$ and $\Delta_i$ the Laplacian differential operator with respect to $x_i$. The Hamiltonian $H_{weird}$ acts on wave functions $\psi (x_1,x_2,...x_N)$ depending on $N$ 3d spatial variables $x_i$, each $x_i$ serving to represent an electron with presence over the whole of its own copy of $R^3$, thus based on electronic wave functions having global supports.

The weirdness comes from the many dimensions where each electron $i=1,...,N$ is equipped with a separate copy of $R^3$, where it is acted upon by a Laplacian differential operator $\Delta_i$ giving it kinetic energy, yet the electrons interact in a common $R^3$ by the presence of $\vert x_i-x_j\vert$ in the term representing Coulomb electronic repulsion. The electrons thus have both separated individual existence and shared existence. That is weird from classical continuum mechanics point of where a shared single physical 3d space is the only one available. With a travesty of Bohr, one could maybe say

• If from a  knowledge of classical continuum mechanics, you are not shocked by $H_{weird}$, then you have not understood classical continuum mechanics.

Quantum mechanics is thus weird unphysical because it is based on a Hamiltonian $H_{weird}$, which is weird unphysical. Of course, if you are dealing with something which is partly weird, then you have to get rid of the weirdness and keep whatever is not weird and maybe useful.  Efforts to this end e g in the form of Density Functional Theory have been made without however completely getting rid on the weirdness. RealQM is a based on $H_{weird}$ but with a new meaning which is physical and not at all weird, see this post for an intro. 

 

Physics and Mathematics of Schrödinger's Equation

The Schrödinger equation describes the ground state of the Hydrogen atom by the wave function $\Psi (x)$ with $x$ a 3d spatial variable, which minimises the total energy

• $E =E_{kin} + E_{pot}$

as the sum of 

• $E_{kin} =\frac{1}{2}\int\vert\nabla\Psi (x)\vert^2dx$     (electronic kinetic energy)
• $E_{pot} =  -\int\frac{\Psi^2(x)}{\vert x\vert}dx$              (electronic Coulomb potential energy)

under the side condition

•  $\int\Psi^2(x)dx =1.$

The model contains the following three components as functions of $x$: 

1. Distributed charge density: $\Psi^2(x)$ with unit total charge.
2. Distributed kinetic energy: $\vert\nabla\Psi (x)\vert^2$.
3. Distributed potential energy: $-\frac{\Psi^2(x)}{\vert x\vert}$.  

The solution can be computed analytically to be $\Psi (x)=\frac{1}{\sqrt{\pi}}\exp(-\vert x\vert )$. The total energy represents the ground state energy of a Hydrogen atom with kernel at $x=0$. The Coulomb potential is classical physics, while the kinetic energy is a new form of energy measured by the gradient $\nabla\Psi (x)$ as an analog to classical elastic energy. The model has a clear physical meaning and the ground state is characterised by a charge density which concentrates around the kernel paying a kinetic energy cost. 

The Schrödinger equation for the Hydrogen atom in charge density is an example of an Eulerian continuum model of the same form as the Navier-Stokes equations for fluid flow in terms of velocity and pressure as distributed functions of a 3d space coordinate, where individual particle trajectories are not followed. A major advantage of a continuum model is that it allows very efficient computation under discretisation of different spatial resolution.

Schrödinger's equation does not involve point positions of electrons, just distributed charge density, and thus has nothing to say about point positions of electron. At least this is what a mathematician would say understanding that a mathematical model does not contain more than what is put in. Even an emergent phenomenon is a consequence of input. It is not meaningful to ask about point positions of the planets in the Solar system at some given time from a model that only contains time-less orbits of the planets. 

A mathematician would add that neither can exact point position of the electron of a Hydrogen atom be determined experimentally. Wittgenstein would agree that asking about electron position does not make sense in the Schrödinger charge density model and so should not no be spoken of.  

But physicists would not hesitate to say that it is meaningful to ask about the position of the Hydrogen electron, even if it is not contained in the model and cannot be experimentally determined. A physicist would insists that Schrödinger's equation is to be viewed to be formulated in terms of a probability density of electron point position, and not charge density. 

But a probability density is not by itself any physical quantity, and is instead by physicists described as a catalog of possible electron point positions. But physics does not keep such a catalog. Changing from charge density to probability density thus turns Schrödinger's equation from being a model of physics into a model of non-physics. 

So why did physicists take this step in 1926 when seeking to give a meaning to Schrödinger's equation for the Hydrogen atom, which had shown to accurately capture the spectrum of the Hydrogen atom from electronic energies of excited states of the ground state. Schrödinger certainly viewed his equation for Hydrogen in terms of charge density and not probability density.

The switch to probability density came with an ad hoc generalisation of Schrödinger's equation for atoms with more than one electron in terms of a multi-dimensional wave function depending on $3N$ spatial variables for an atom with $N>1$ electrons. With the help of Max Born this model was given an interpretation in terms of probability density to form Standard Quantum Mechanics StdQM as the foundation of modern physics. Here Born's rule states that experimental observation of a prepared quantum state as a given linear combination of eigen-states, choses one of the eigen-states with probability measured by its coefficient in the linear combination. 

This is called collapse of the wave function and has remained a true mystery from physical point of view. The eigen-states are deterministically determined by Schrödinger's equation and so the spectrum. Statistics thus enters only in experimental observation of prepared states while the spectrum is always the same. 

This connects to the view of Bohr that the objective of StdQM is to predict outcomes of prepared experiments, not to model reality. This is mind-boggling and does not seem to make any sense. 

 

Main efforts have been made over the 100 years since 1926 to give StdQM back some physical meaning but no consensus about interpretation in terms of charge density has been reached. 

RealQM presents a new different generalisation to $N>1$ of the Schrödinger equation for $N=1$ in terms of a system of electronic non-overlapping charge densities, which keeps the physicality of the Hydrogen atom. RealQM is a continuum model in 3d with computational cost scaling linearly with $N$, compared to StdQM with exponential scaling. 

The linearity of the Schrödinger equation of StdQM invited to a mathematical analysis using the machinery of the new field of functional analysis developed by Hilbert in terms of Hilbert spaces, which von Neumann exploited in a form of axiomatic formal mathematics (in uncomputable form) with axioms without clear physical meaning.   

Mathematics can thus serve to keep physicality of quantum mechanics as in RealQM, but also by von Neumann abstraction leave physicality as in StdQM. Physics education has been locked on StdQM with all its complications from non-physicality as expressed by Nobel Laureate Murray Gell-Mann 50 years ago:

• Niels Bohr brainwashed a whole generation of theorists into thinking that the job of interpreting quantum theory was done 50 years ago.

The brainwash has continued since text-book physics still today is StdQM. Attempts have been made to give StdQM physical meaning like Many-Worlds and Bohmian Pilot Wave but are not viewed to be successful. RealQM opens a new way of thinking, which apparently has been brainwashed away for 100 years... 

Bohr quotes:

• Physics is not about how the world is, it is about what we can say about the world.
• Those who are not shocked when they first come across quantum theory cannot possibly have understood it.

Yes, it is shocking to learn that StdQM it is not about how the world is, that StdQM is non-physical. Schrödinger would have welcomed RealQM as a theory about physics, while such a thing would have shocked Bohr again...

RealQM is based on the same physics as the Hydrogen atom: Coulomb potential energy and kinetic energy. RealQM appears to be about how the microscopic world is...just like Newton's mechanics based on Newton's laws of motion appears to describe how the macroscopic world is...and RealQM connects seamlessly to Newton's mechanics in a unified continuum model.  

Why Was RealQM Not Found in 1926?

Schrödinger's equation SE in its linear multi-dimensional form with wave function solution $\Psi (x)$  depending on a $3N$-dimensional spatial variable $x$ for a system with $N$ electrons is viewed to be the foundation of quantum mechanics of atoms and molecules as Standard Quantum Mechanics StdQM. 

Without SE physics would be thrown back to 1924 with only Bohr's model of the atom in a form of classical physics. There are no physicists of today that advocate that this makes any sense. 

But SE has been subject to deep dispute since its formulation by Schrödinger in 1926 followed by Born's suggestion of giving the wave function $\Psi (x)$  a meaning by saying that $\vert\Psi (x)\vert^2$ represents the probability of an electron configuration described by $x$. This means that $\Psi (x)$ is given an epistemic meaning as what "a physicist can say", and not an ontic meaning as physics independent of what a physicist may have to say, as expressed by Bohr. 

But Bohr's view was not satisfactory to many physicists who wanted to find an ontic meaning of $\Psi$ independent of what people may have to say, but nothing really convincing was ever found. The $3N$-dimensionality of $\Psi (x)$ defied real physical meaning and then the only option was an epistemic statistical meaning. 

This means that the basic foundational problem of SE has never been resolved despite intense debate over 100 years with no consensus in reach, except an agreement that after all the physical meaning of $\Psi (x)$ does not matter much, since it has shown to always deliver predictions in full agreement with observations, but then predictions with unclear physical meaning of course. 

But there is an alternative to StdQM which could have been formulated in 1926, but for some reason was missed, see this post. This is RealQM as a different form of Schrödinger's equation as a non-linear system of one-electron wave functions $\psi_i(x)$ for $i=1,...N,$ with non-overlapping supports depending on a common 3d space variable $x$ with $\vert\psi_i(x)\vert^2$ as physical charge density with direct ontic meaning. 

Connecting to the previous post, RealQM can be seen as a Platonic/mathematical generalisation from $N=1$ to $N>1$ where the physicality for the Hydrogen atom with $N=1$ is kept. On the other hand, StdQM can be seen as an Aristotelian/pseudo-mathematical generalisation where physicality is lost. 

When I present RealQM as an alternative to StdQM to quantum physicists and chemists I meet little understanding indicating that the pseudo-mathematization of StdQM has a very strong grip of minds. Nor do mathematicians show interest because StdQM already in 1933 by the mathematician von Neumann was translated into an impressive abstract world of Hilbert spaces occupied by multi-dimensional wave functions subject to Hermitian operators satisfying axioms without physics.  

But there is a good chance the situation can change in 2026 since RealQM is continuing to deliver new results in accordance with observations. 

PS Bohr claimed that the purpose of quantum mechanics is to make predictions of experiments as testable events, not to compute e g the energies of ground state or excited state of an atom regardless of actual experiment being made. This opened to a confusion between deterministic computation of ground/excited state and probabilistic outcome of an experiment suggesting that the model behind the computation itself is of probabilistic nature although in fact fully deterministic. There is nothing probabilistic with the spectrum of an atom as difference between energies of ground/excited states, nor in computation nor in experiment except those from external inputs.

Quantum Mechanics: Aristotle or Platon?

This is inspired by a very informative article by Matthew Ehret: Unravelling The Jesuit Enigma.

The Scientific Revolution is viewed as a triumph of Platonic mathematization over Aristotelian natural philosophy expressed in classical Newtonian mechanics based on the Calculus of Leibniz and Newton. 

But in modern physics based on Quantum Mechanics QM, the roles appear to have shifted. 

Classical mechanics as macroscopic physics with causality is based on clear physical principles and logical argumentation, and is understandable in theory and very useful in practice. Together with the computer, classical mechanics is a formidable tool and machine.

QM as microscopic physics without causality is based on evasive principles, lacks logic and is understood only by its high priests of Nobel Laureates in Physics, to be used by all others under the command "Shut up and calculate" as the foundation of modern information society for all to accept. In this respect it connects to the Jesuit Priest Ignatius Loyola's view on education as expressed by Bertrand Russell: 

• Education in a scientific society may, I think, be best conceived after the analogy of the education provided by the Jesuits. The Jesuits provided one sort of education for the boys who were to become ordinary men of the world and another for those who were to become members of the Society of Jesus. In like manner, the scientific rulers will provide one kind of education for ordinary men and women and another for those who are to become holders of scientific power.

But why is macroscopic physics Platonic rational, while microscopic physics is Aristotelian irrational? 

The irrationality of QM is expressed by its statistical interpretation without causality, which neither Einstein nor Schrödinger ever accepted: "God does not play dice". It is unthinkable that the Hydrogen atom as most common stable element in the Universe is the result of a roulette game inside the atom. Yet this is what we are ordered to believe by QM. It is like having to accept the dogma that "snow is black" connecting again to Russell in Science and Society (1955):

• First, that the influence of home is obstructive. Second, that not much can be done unless indoctrination begins before the age of ten. Third, that verses set to music and repeatedly intoned are very effective. Fourth, that the opinion that snow is white must be held to show a morbid taste for eccentricity. It is for future scientists to make these maxims precise and discover exactly how much it costs per head to make children believe that snow is black, and how much less it would cost to make them believe it is dark gray.

recalling Ignatius Loyola’s 13th Rule of his Spiritual Meditations: 

• To be right in everything, we ought always to hold that the white which I see, is black, if the Hierarchical Church so decides it, believing that between Christ our Lord, the Bridegroom, and the Church, His Bride, there is the same Spirit which governs and directs us for the salvation of our souls.

But there cannot be a dichotomy between macro and micro, it must all be Platonic. That is the idea of RealQM.

Computational vs Analytical Proof vs AI

An important part 20th century mathematics has been devoted to analysis of partial differential equations PDEs as concerns (i) existence and (ii) regularity of solutions. A PDE is a continuum model with infinitely many degrees of freedom. 

Proofs of existence typically start from some a priori bounds on solutions to regularised equations with existence of solutions settled and then obtain solutions of the original equation through a limit process. 

The main components of an existence proof are the a priori bounds, which can require complicated and lengthy mathematical analysis. 

Once existence of solutions is proved, further mathematical analysis can prove properties of solutions typically as bounds on derivates showing regularity. Again the analysis can be complicated and lengthy.

A famous challenge in the form of a Clay Millennium Prize Problem is to give an analytical proof of existence and regularity of solutions to the Navier-Stokes equations for incompressible fluid flow. No progress on this open problem has been reported since 2000. 

But there is a different approach to (i) and (ii) in terms of computation where in each given case a an approximate solution to the equations is computed in a step by step manner after discretisation of the PDE into a finite number of degrees of freedom which can be processed by numerical linear algebra. The computational process either halts or delivers after a finite number of steps of choice an approximate solution, which can thus be inspected a posteriori as to qualities.  It is thus possible to evaluate in what sense the approximate solution satisfies the PDE and accept or recompute with better discretisation. 

We can thus meet a fundamental difference:

• (A) Analytical mathematics proving properties of solutions of a PDE for many possible data a priori before/without computation.  
• (C) Computational mathematics producing for given data an approximate solution for inspection.  

With suitable regularisation/discretisation (C) always will deliver, while (A) can only in simple cases. In the case of the Navier-Stokes (A) has not delivered anything, while (C) has delivered turbulent solutions for inspection. 

The fundamental equation of Standard Quantum Mechanics StdQM is Schrödinger's Equation SE as a linear partial differential equation in $3N$ spatial dimensions for an atomic system with $N$ electrons. Because of the linearity existence of a solution can be proved as (A), but the high dimensionality defies closer analysis of solutions. Neither can (C) deliver because computational cost is exponential in $N$. The result is that both (A) and (C) meet serious difficulties in StdQM.

In RealQM the situation is different as concerns (C) because computational complexity is linear or quadratic in $N$, and the computation does not break down because  of the presence of the Laplacian in SE acting as regularisation. (C) thus can reveal everything in RealQM in principle.  For (A) the task is more challenging since RealQM is a non-linear model and only an a priori bound on total energy is directly available. 

Sum up: (C) delivers for Navier-Stokes and RealQM, while (A) meets very big difficulties.  

Successful computation of an approximate solution can be seen as a mathematical proof of existence of that particular approximate solution, a computational proof. A priori analysis can be important to design the computational process, but is not needed for existence or a posteriori evaluation. 

With increasing computer power (C) gains more momentum and combines with AI.  (A) has to struggle with limited human brain power, which does not really grow, and it is not clear what help AI can give. 

In particular, (C) can deliver massive training data for AI in a case by case manner to learn about the world including turbulent flow and molecules. (A) offers training in analytical proofs but less about the world. What can AI learn from the 100-page proof of Stability of Matter by Dyson-Lenard discussed in recent posts?

 

  

Stability of Matter: Basic Math vs Miracle

1. Recent posts have discussed the fundamental problem of Stability of Matter SM, including stability of single atoms and collections of atoms as bulk matter, maybe the most fundamental problem of all of physics. 

With the help of chatGPT I have learned about the heroic work by Dyson-Lenard and Lieb-Thirring to mathematically prove SM within Standard Quantum Mechanics StdQM and Density Functional Theory DFT, which boils down to very intricate book-keeping to prevent collapse of potential energy to minus infinity by local accumulation of electron charge densities. The main difficulty to handle is the overlap in StdQM/DFT of electron wave functions with global support. The proof is lengthy and complicated and not easy to follow. It is not part of text books/courses in QM, even if completely fundamental. 

It is natural to ask how it can be so difficult to prove SM within StdQM/DFT, when SM is such a basic property of the physics modled by StdQM? Does real physics also have to handle intricate bookkeeping to avoid collapse?

Or is the proof difficulty of SM within StdQM/DFT yet another indication that there is something seriously unphysical with StdQM connecting to the difficulty of giving StdQM a physical meaning? Seems so.

On the other hand SM within RealQM directly follows from the stability of the Hydrogen atom with potential energy dominated by kinetic energy using the additive form of RealQM with a global wave function as a sum over one-electron wave functions with local non-overlapping supports. 

RealQM is a physical model with SM safely mathematically built in. StdQM is an unphysical model with SM basically a mathematical miracle. SM with RealQM could be essential part of even introductory texts/courses in QM.

According the chatGPT, SM is by physicists viewed as "settled" once and for all by Dyson et al, and it is not meaningful to teach the proof since it is so difficult and and non-illuminating. The advice to students appears to be to just accept SM and not ask about any justification. Seems a bit strange...

Summary:

1. StdQM in 1926 faces a fundamental problem: Prove Stability of Matter.
2. No progress towards solution until 1966 when Dyson-Lenard gives a dense 26-article page proof in the form of "awful mathematics" according to Dyson. 
3. Lieb-Thirring compresses the proof into a 3-page article 1975, which is then expanded into the 300 page book Stability of Matter in 2005.
4. The problem is viewed to be "settled" and there is nothing more to say according to chatGPT in 2025. The proof is not part of text-books on QM.   

This is a typical progression as concerns fundamental problems in StdQM: 1. State problem as fundamental (interpretation, measurement, complementarity...). 2 Realise that the problem cannot resolved. 3. Claim that there are solutions, but very difficult to understand. 4 Decide that the fundamental problem as been "settled" and that there is noting more to say. 5. Declare that it is sufficient to know that the problem has been solved and that asking for why is not part of physics education. 

Shell Structure: StdQM vs RealQM

A fundamental conception of atom physics is that the electrons surrounding an atomic kernel are arranged in a sequence of shells $S_n$ for $n=1,2,3,...$ with $S_n$ containing $2n^2$ electrons when filled, which gives the Periodic Table with periods 2, 8, 8, 18, 18, 32,,,  including repetitions.

A fundamental question in Standard Quantum Mechanics StdQM is if the shell structure of the Periodic Table is carried by solutions of the Schrödinger equation for the atom? Can an answer be given when such solutions are uncomputable because they involve $3N$ spatial dimensions for an atom with $N$ electrons? 

• Does the shell structure of an atom come out from StdQM? 
• Is the Periodic Table well explained by StdQM? 

The view of Eric Scerri as world leading expert on the subject is summarised as follows by chatGPT:

• In short, Scerri agrees that quantum mechanics supplies the essential skeleton of the periodic system, but he rejects the stronger claim that Schrödinger’s equation alone “explains” the periodic table in a purely deductive sense. The full story, in his view, requires a blend of quantum theory, empirical ordering principles, and chemical reasoning.

OK, so the answer is No rather then Yes. 

On the other hand, in RealQM as an alternative to StdQM, the shell structure comes out in a deductive sense as solution to a non-overlapping electron packing problem resulting in the shell structure of the Periodic Table. Details are given in the RealQM book. 

Comparison RealQM vs StdQM and DFT

Standard Quantum Mechanics StdQM based on Schrödinger's equation SE with standard interpretation of a Hamiltonian acting on wave functions with $3N$ spatial dimensions for a system with $N$ electrons, has only statistical meaning and is computable only for very small $N$, thus can be said to be non-physical and uncomputable.  

Density Functional Theory DFT seeks to reduce StdQM by averaging 3N-dimensional wave functions  into a single electron charge density $\rho (x)$ depending on a 3-dimensional coordinate $x$, and identifying ground states of StdQM with DFT densities satisfying a reduced SE with Hamiltonian only implicitly determined and so has to be approximated. DFT is the main computational method for $N>100$ currently available.

RealQM is based on a different interpretation of the Hamiltonian of SE acting on a wave function $\Psi (x)$ as a sum 

• $\Psi (x) = \sum_{n=1}^N\psi_n(x)$ 

of one-electron wave functions $\psi_n(x)$ with non-overlapping supports depending on a common 3d spatial variable, which meet at a Bernoulli free boundary with continuity and zero normal derivative. The corresponding electron charge density $\rho (x)$ is a sum

• $\rho (x)=\sum_{n=1}^N\psi_n^2(x)$     

of non-overlapping charge densities $\psi_n^2(x)$. 

A fundamental difference between RealQM and DFT is that electron densities in RealQM carry identity by occupying distinct regions in space and so can be numbered, just like pool balls on a pool table, while identity is lost in the common density of DFT (which creates a lot difficulties when having to recreate lost identity to keep physicality).

The zero normal derivative free boundary condition satisfied by meeting wave functions keeps electron identity which is not expressed by continuity alone. 

Recall that wave functions of StdQM have overlapping global supports, which makes identification difficult/impossible, while wave functions in RealQM have non-overlapping local supports, which makes identification direct.

We further recall from recent posts that stability of matter is a direct consequence of the structure of RealQM, but is less obvious in StdQM and DFT.

A basic postulate of StdQM is that electrons carry no identity, that they are indistinguishable, and that is the basic difference with classical physics, which can be viewed to carry identity. So identity vs no-identity can be viewed to be the dividing line between classical mechanics (not including statistical mechanics) and quantum mechanics. 

The dividing line shows that modern physics as microscopic quantum mechanics is different from macroscopic classical mechanics, more precisely so fundamentally different that quantum mechanics is said to be "weird" by the most knowledgable physicists, while saying the same about classical mechanics would simply express ignorance.  

To speak about electrons without any from of identity is according to Leibniz really "weird" since it contradicts his Principle of Identity of Indiscernibles PII.

The fact that RealQM respects PII, while StdQM does not, eliminates the dividing line between microscopic and macroscopic physics and so opens to a unified mechanics on all scales. 

To allow microscopic objects to carry identity allows perception of the microscopic world to be similar to that of the macroscopic world, thus understandable and not only "weird".  

Here is a comparison in condensed form:

• StdQM: explicit Hamiltonian, no electron identity, non-physical, uncomputable, stability non-obvious, "weird".
• DFT: implicit Hamiltonian, no electron identity, physicality?, computable, stability non-obvious, "weird"? 
• RealQM; explicit Hamiltonian, electron identity, physical, computable, stability obvious, understandable not "weird". 

chatGPT says that stdQM violates Leibniz PII and that efforts to change StdQM to "save" identity, like Bohmian mechanics with its "pilot wave", have all failed. Here RealQM comes in...