Russian Doll Fractal Atomic Physics

Big Doll = Atom with Nucleus = Small Doll .

RealQM presents a new Schrödinger equation for atomic physics as a positive nucleus of size $10^{-15}$ m surrounded by a collection of non-overlapping electrons densities without self-repulsion of size $10^{-10}$ m, which in ground/excited states organise into shells as solution to an energy minimisation packing problem under Coulomb attraction/repulsion.

RealQM is a classical continuum model in 3 spatial dimensions describing deterministic physics, fundamentally different from standardQM in multidimensional configuration space with unclear physics as statistics.  

Similarly RealQM presents a Schrödinger equation for an atomic nucleus of size $10^{-15}$ m as a negative kernel of size $10^{-20}$ m surrounded by a collection of non-overlapping proton densities without self-repulsion of size $10^{-15}$ m organizing into shells under Coulomb attraction/repulsion.

The change of spatial scale between atom and atomic nucleus of $10^5$ is translated to binding energies with the same factor.

The basic case is represented by two possible configurations of 1 proton and 1 electron: As a H atom with proton kernel surrounded by an electron density with binding energy 13.6. eV, and as a neutron N as an electron kernel surrounded by a proton density with binding energy 0.78 MeV with a factor of about $10^5$. 

What emerges is a form of Russian Doll with an H atom as a Big Doll with nucleus as a Small Doll composed in the same way with just a switch of sign of charge. It is possible to think of even bigger dolls built in a similar way such as planet systems around a star. 

In RealQM an atomic nucleus is held together by Coulomb attraction between electron kernel and surrounding proton density thus overpowering proton repulsion, in the same way an atomic ion is held together by Coulomb attraction between proton nucleus and surrounding electron density overpowering electron repulsion. There is here no need to ad hoc introduce a strong force as in the Standard Model. 

The configuration can in principle be repeated with an even smaller doll with positive kernel of even smaller size of $10^{-25}$ m. But that is beyond observation and so it seems reasonable to search for an explanation why there are so to speak only two atomic dolls: Atom = Big Doll and atomic  nucleus = Small Doll. 

That requires that the kernel of an atomic nucleus as a negative charge of strength more than 1 is free of self-repulsion, since it has no positive kernel overpowering repulsion as in Big and Small Doll. This remains to be understood. Can two electrons be compressed to a negative charge density -2 without self-repulsion? Is this possible by some form of quantum gravity? In any case this makes two electrons fundamentally different from two protons for which there is no need of compression to +2 without self-repulsion.

A Russian Doll system as a form of fractal system describing the Universe as a repeating pattern, would thus end with a Small Doll in the form of a nucleus as a negative charge density of size $10^{-20}$ m without self-repulsion surrounded by a collection of non-overlapping proton densities organised into shells as solution to an energy minimisation packing problem. Such a nucleus would be held together by Coulomb attraction overpowering repulsion without need of the strong force of the Standard Model.  

Recall that the early Bohr model of an atom was a planetary system of electrons/planets orbiting a nucleus/Sun. In RealQM this is replaced by a stationary system of non-overlapping electron densities surrounding a nucleus as solution to an energy minimisation packing problem. Compare with Fractal Cosmology. It seems that we can find fractals on largest scales governed by gravitational attraction and smallest scales governed by Coulomb electric attraction, but not on human scales showing more complexity.  

Note that it would be sensational if nuclei show to be held together by Coulomb attraction as classic physics, rather than by a residual of a strong force between quarks as postulated in the Standard Model. 

PS1 When I ask professional physicists if in the existing literature there is something like RealQM, they do not give any answer, but tell me that standard Quantum Mechanics, whatever that is, and the Standard Model are by far the best theories about physics ever created and that they agree with all experiments to an incredible precision and so there is no reason to look at anything else, in particular nothing from a mathematician. In the next moment they tell that in fact both models have severe shortcomings, which motivate more tax payer money to new fundamental theoretical physics to be discovered by a new much bigger Large Hadron Collider.

PS2 From A Search for Exotic Higgs Decays by Burzynski: In spite of the overwhelming successes of the SM, there are several glaring issues with the SM which remain unresolved. First and foremost, there are many fundamental phenomena observed in nature that are not predicted or explained by the SM. These include gravity, the nature of dark matter, neutrino masses, and the matter-antimatter asymmetry observed in the universe, among others. Second, there are theoretical problems with the SM which imply a lack of complete understanding of underlying phenomena. Examples include the hierarchy problem and the strong CP problem.

RealQM for Atom and Nucleus

Real Quantum Mechanics RealQM offers a new model of atoms and atomic nuclei in the form of a classical 3d continuum system of partial differential equations describing a set of non-overlapping charge densities interacting through Coulomb potentials. This is a generalisation of Schrödinger's equation for the Hydrogen atom consisting of one proton and one electron, to configurations with many protons and electrons, which is different from the multi-dimensional Schrödinger equation in configuration space as the basic model of standard Quantum Mechanics stdQM. 

RealQM models an atom as a point-like nucleus/kernel of positive charge $+Z$ surrounded by $Z$ electron densities of charge -1 organised in shells with the innermost shell containing 2 electrons, the next shell a maximum of 8 electrons, the next 18 according to the pattern $2*n^2$ for $n=1,2,...$. The shell system is formed as resolution of an energy minimisation packing problem of non-overlapping electron densities of width scaling with (inverse of) the effective kernel potential reduced by shielding from electrons in inner shells, thus with increasing width for outer shells. 

RealQM models an atomic nucleus as a point-like kernel of negative charge $-Z$ surrounded in the basic case by $2*Z$ proton densities of charge +1. Only Coulomb potentials are involved. No need of strong/weak nuclear force as in the Standard Model of stdQM.

The basic difference between an atom and a nucleus both consisting of a system of protons and electrons, is then the geometric size of the system, with $10^{-10}$ m typical of an atom, and $10^{-15}$ m that of a nucleus, thus with a factor about $10^5$.

The binding energy of RealQM system scales with the geometric size of the system, and so we expect to pass from eV to MeV from atom to nucleus, which is what is observed and also computed by RealQM Nuclear Simulator. The basic reason is that a Coulomb potential scales with 1/distance.

RealQM thus offers an explanation of the $10^5$ factor between atomic and nuclear energies as a geometric scale effect. The basic element is here the concept of non-overlapping charge densities of different widths, which is not an element of stdQM. 

As an example consider the formation of the nucleus of Deuterium from 1 electron kernel surrounded by 2 proton densities (under high pressure and temperature) as a nucleus analog of a $H^-$ ion with 1 proton kernel surrounded by 2 electron densities, under the release of 1 MeV as an analog to the formation energy of about 10 eV of $H^-$. 

To form a $^4 He$ nucleus from 2 electrons surrounded by 4 proton densities, as an analog to $He^{2-}$, the two electrons have to be compressed (under high pressure and temperature) into a -2 kernel under additional release of energy to give the observed binding energy of about 7 MeV. This process remains to be explained.    

The binding energy in RealQM scales with $Z^3$ with only one shell, and with $Z^2$ with a typical sequence of shells as observed, and so with $Z$ per nucleon as roughly observed for $2\le Z\le 30$, which shows release of energy under fusion (up to $^{56}Fe$):

Recall that a nucleus in the Standard Model is viewed as an aggregate of protons and neutrons held together by a strong nuclear force as new physics, while in RealQM a nucleus is considered to be an aggregate of protons and electrons held together by classical Coulomb physics. Ockham would probably choose RealQM before the Standard Model. 

Modern vs Newtonian Physics

The concept of force carrier is central to modern physics crowned by the Standard Model of atomic/nuclear physics, with the force between two particles established by a carrier particle bouncing back and forth. The photon is identified as the carrier of the electromagnetic force and gluons as carriers of the strong nuclear force between protons and neutrons, while the graviton as carrier of the gravitational force has not been identified despite major efforts. 

In contrast, the concept of force carrier has no role to serve in Newtonian physics since forces are either transmitted by instant action by contact or by instant action at distance as gradients of electric or gravitational potentials connected to distributed charges and masses, as discussed in more detail in blog posts under tag New View on Newtonian Gravitation.

It is natural to ask if the concept of force carrier is useful, if carriers of gravitational force are missing and if electromagnetic forces more naturally arise from electric potentials rather than from photons bouncing back and forth as unnatural physics? 

But what about gluons as carriers of the strong nuclear force needed to keep protons and neutrons together in a nucleus?

In recent posts, I have tested the idea that a nucleus can be held together by electromagnetic forces, thus without need of any strong force, in basically the same way an atom is held together by Coulombic interaction between charges of different sign. Computations with RealQM suggest that this may be possible. A nucleus here consists of a central point-like negative charge density (electrons without internal repulsion) surrounded by non-overlapping positive charge densities (protons), with the "compression" of the electrons in fusion releasing massive energy.

In any case, the idea of force carrier presents severe difficulties to modern physics and one way to handle this situation is to give up the idea in a return to Newtonian physics.   

 

Chadwick: Neutron = Proton + Electron

Let me backtrack the idea explored in recent posts of neutron = proton + electron, with the electron as a negative point kernel surrounded by cloud of positive charge as a proton, as a small scale analog of a  Hydrogen atom as a proton as positive point charge surrounded by a a cloud of negative charge as electron with observed change of spatial scale of about $10^5$. 

The 1935 Nobel Prize in Physics was awarded to English physicist James Chadwick for the discovery in 1932 of the neutron, described by Chadwick in his Nobel Lecture as follows:

• The idea that there might exist small particles with no electrical charge has been put forward several times. 
• Nernst, for example, suggested that a neutral particle might be formed by a negative electron and an equal positive charge.
• The first suggestion of a neutral particle with the properties of the neutron we now know, was made by Rutherford in 1920. He thought that a proton and an electron might unite in a much more intimate way than they do in the hydrogen atom, and so form a particle of no net charge and with a mass nearly the same as that of the hydrogen atom. 
• On the other hand, a structure of this kind cannot be fitted into the scheme of the quantum mechanics, in which the hydrogen atom represents the only possible combination of a proton and an electron. 
• The first real step towards the discovery of the neutron was given by a very beautiful experiment of Mme. and M. Joliot-Curie.

We here find the idea of a neutron = proton + electron, however with the caveat that such a thing does not fit with quantum mechanics. Chadwick (1891-1974) thus had to wait to the emergence of the Standard Model in the 1960s with neutron = two down quarks + one top quark, glued together by gluons.  

But maybe the idea of neutron = proton + electron was dismissed too quickly. In any case, the binding energy of an electron kernel + surrounding proton cloud is about 0.8 MeV, to be compared with the binding energy of a Hydrogen atom as a proton kernel surrounded by an electron cloud of 13.6 eV, with a change of scale of about $0.5\times 10^5$ matching the change of spatial scale between proton and electron.  

It is possible that Chadwick would have been happy to see something like this, rather than the quark mystification of the Standard Model. What about you? 

Newtonian Gravitation Compatible with Real Quantum Mechanics

Real Quantum Mechanics + Newtonian Gravitation covers all scales. 

The two main theories of modern physics, standard Quantum Mechanics stdQM for small scale physics (less than $10^{-10}$ m) without gravitation, and the General Theory of Relativity GR for large scale gravitation (bigger than $10^{10}$ m), have been understood to be incompatible since their advent 100 years ago without any progress to compatibility into our days as expressed in particular in endless expert panel discussions. 

This means that there is no unified theory of physics for the wide range of scales from $10^{-10}$ to $10^{10}$ m containing most of the World of importance to humanity.  

Why are then stdQM and GR incompatible? How can two theories about a common reality be incompatible? Reality cannot be incompatible with itself.

GR is a deterministic continuum theory in 3d space plus time (even if combined into 4d space-time), while stdQM is a statistical theory in multi-d configuration space.  Unsuccessful attempts to create a unified theory have been made to change GR into a form of stdQM as quantum gravity, while no attempt to change stdQM into a deterministic continuum 3d model has been made. Modern physicists are stuck with two incompatible theories without any way to go forward to compatibility. No wonder that modern physics is in a state of crisis (witnessed by all leading expert panels). 

Real Quantum Mechanics RealQM offers an alternative to stdQM in the form of a deterministic continuum model in 3d space, which is perfectly compatible with Newton's Theory of Gravitation NR. 

Recent posts open RealQM to scales of atomic nuclei, and so Real QM + NR opens a possibility to cover all scales in a unified compatible model and so a possible way out of the crisis of modern physics.      

New Model of Atomic Nucleus

Modern physics involves four fundamental forces: 

1. Electromagnetic force described by Coulomb Law.
2. Weak nuclear force involved in radioactive decay. 
3. Strong nuclear force describing the force keeping an atomic nucleus together.
4. Gravitational force described by Newton's Law of Gravitation (or Einstein's general relativity).   

The Standard Model of atomic physics formed in the 1960s includes 1-3 but leaves out 4. The dream of a modern physicist is to unite at least 1-3 into one unified electromagnetic-nuclear force with the ultimate goal of including also 4. Little progress towards this goal has been made. 

In recent posts I have tested an idea to unify 1-3 into a single electromagnetic force captured by Coulombs Law. In this model we start with a Universe of high temperature consisting of free protons of charge +1 and equally many free electrons of charge -1. We assume that about half of the protons and electrons fuse to form neutrons and that as temperature drops the rest combine to Hydrogen atoms. Both neutron and H-atom then consists of a proton-electron pair, but the physics is vastly different. A seemingly natural way to understand the difference is to switch roles: 

• H-atom = proton kernel surrounded by electron cloud.
• Neutron = electron kernel surrounded by proton cloud.    

In both cases we have a particle-like kernel surrounded by a cloud of opposite charge, which can be described by the same Schrödinger's equation with only a change of scale, showing to be about $10^5$ according to observation: The size of a Hydrogen atom is a about $10^5$ times that of a neutron, with a corresponding scaling of binding energy: The observed binding energy of a neutron is a bout 1 MeV and that of an H-atom about 10 eV with again a factor of roughly $10^5$.  

The non-standard element here is that a neutron consists of a kernel as a very compressed electron surrounded by a proton cloud. In the Standard model a neutron is composed of three quarks as a more complicated model. 

We now have a Universe consisting of an equal number of neutrons and H-atoms and it is possible to envision a next step where an H-atom combines with a neutron to form a deuterium atom with a nucleus composed of a proton and a neutron, and in a next step we could expect two deuterium nuclei to fuse into a 4Helium nucleus consisting of 2 protons and 2 neutrons. The binding energy per nucleon is 1.1 MeV for deuterium and 7 MeV for 4Helium and so the fusion delivers massive energy. 

Inspired by the idea of a neutron as an electron kernel surrounded by a proton cloud, we can think of the 4Helium nucleus to consist of 4 protons altogether of charge +4 surrounding an electron kernel of charge -2, with a net charge of +2. 

Switching roles we then compare with an atom with a +2 proton nucleus surrounded by 4 electrons thus a Helium atom with 2 extra electrons forming He2-. This is a stable atom with an observed binding energy of about 80 eV, which with a change of scale/role forms a 4Helium nucleus with binding energy in the range of 27 MeV with here a factor of about $3\times 10^5$. 

To obtain a large binding energy of a 4Helium nucleus as 2 compressed electrons surrounded by a 4-proton cloud, it is necessary to discard the repulsion energy between the electrons, which would appear as the energy released in the fusion of deuterium. We then have the same situation for a nucleus as for an atom with in both cases no repulsion between same charges in the kernel.

It is thus possible to explain how that not only an atom is held together by attractive Coulomb forces between charges of different sign, but in an analogous way also an atomic nucleus by switching the roles of proton and electron. 

What remains to explain is how electron-electron repulsion can be cancelled in a nucleus with electron kernel. If that can be achieved we would have a unified model built on electromagnetic Coulomb forces without need of inventing weak and strong nuclear forces as in the Standard Model asking for quarks.

Further fusion into nuclei with the same number of protons and neutrons can be similarly envisioned in agreement with observations.

The key role of the strong force is to overcome the repulsion between protons in a nucleus. In the above model this is achieved by Coulomb force through the presence of neutrons and electron kernels.  

It is possible to envision a model based on protons and electrons interacting by electromagnetic Coulomb forces which describes both atoms and atomic nuclei. A key element is a kernel of a nucleus consisting of compressed electrons without repulsion, like a negative point charge bigger than one. 

You are now invited to choose one of the following models of a neutron:

• A proton cloud surrounding an electron kernel.
• Two down quarks of charge -1/3 combined with an up quark of charge +2/3, all of different colors.  

In any case, the formation of neutrons is essential, assuming we start from protons and electrons. 

Recall that electric charge density $\rho$ is connected to electric field $E$ by Poisson's equation $\Delta E=\rho$ opening the possibility of creation of equal amount of positive (protons) and negative charge density (electrons) from a fluctuation around zero of $E$, as out of nothing.  

If nuclear physics can be understood as geared by Coulomb force, then a unification with gravitational physics geared by Newton's Law is natural.  

The binding energy of a nucleus with $Z$ protons and $Z$ neutrons scales with $Z^2$ and so with $Z$ per nucleon, which is roughly what is observed for $2\le Z\le 56$.