Sabine Hossenfelder has taken up the mission to expose the so called crisis in physics, or rather in her words the stagnation of fundamental physics presented in this long interview starting out
We haven't really made any progress on the big open questions since they occurred a century ago.
We still do not understand how Quantum Mechanics QM works.
QM has a problem of inconsistency.
Here Sabine gives reason for the stagnation of fundamental physics ultimately based on QM as atom physics:
If we do not understand QM, how can we understand anything based on QM?
QM is not understandable, because it does not make sense as a theory of physics.
A physical theory which does not make sense as real physics cannot be understood in a real sense.
In this situation, there are two possibilities:
QM is anyway accepted even if does not make sense. This is the current agreement by the physics community.
QM is discarded (since it does not make sense).
I have followed 2 by developing a different form of atom physics named Real Quantum Mechanics RealQM, which is fundamentally different from the accepted QM which I refer to as Standard QM or StdQM initiated by Schrödinger in 1924.
RealQM is understandable as a physical deterministic continuum mechanics model in 3 space dimensions. The reason StdQM is not understandable, is that it is a statistical model in many-dimensional configurations space without physical meaning. Compare with John Clauser.
Sabine has emerged as a very successful presenter of science, after giving up a career as fundamental physicist, since quantum gravity did not make sense, with particular mission to expose the stagnation in fundamental physics. This is admirable. What is less admirable (from my point of view) is that Sabine does not show any interest in finding some path to progress away from stagnation, such as RealQM.
There is a Grand Unified Theory of physics GUT (or Theory of Everything TOE) in the form of Newton's Mechanics + Maxwell's Electromagnetics + Quantum Mechanics expressed as partial differential equations over continua of 3d Euclidean space coordinate systems and time:
Newton's equations of macroscopic motion of matter/mass subject to gravitation.
Maxwell's equations for light without mass/charge and matter with charge.
Schrödinger's equations for microscopics of electromagnetics.
But this form of GUT is rejected by modern physicists following Einstein in his pursuit of replacing Newton's Mechanics by his General Theory of Relativity GR from 1915 initiated by his Special Theory of Relativity SR from 1905.
Einstein was driven by a fixed idea (strike of genius?) that physical laws must take the same form independent of the choice of coordinate system, named covariance. He found this to be the case for Maxwell's equations taking the same mathematical form under Lorentz transformations, but not Galilean transformations. Einstein observed the opposite to be true for Newton's equations and so, seemingly out of the blue, he decided that Newton's Mechanics had to be replaced by his new theory of relativistic mechanics in the form of SR/GR. This was a monumental proclamation which was for a long time met with much skepticism, but gradually through clever marketing has come to represent the major advancement offered by modern physics as opposed to classical Newtonian physics.
Einstein’s leading idea that mathematical expressions (formulas, equations) of physical laws must literally letter by letter look the same in different coordinate systems, is absurd. It is the same as saying that there can be only one language word by word letter by letter, describing a common physical world. Of course the choice of coordinate system in general will affect the letters of the mathematical expression of a physical law. Nevertheless Einstein used his fixed idea to discriminate Newton’s equations because they changed form under Lorentz transformations. And after 50 years of brooding modern physicists jumped the band wagon against Newton.
Critics point to the following consequences replacing Newton by Einstein/SR/GR:
SR/GR is claimed to differ from Newton's Mechanics only in utterly extreme situations, such as black holes or space ships approaching the speed of light, so extreme that even SR/GR falls short.
SR/GR is incompatible with quantum mechanics, and thus makes modern physics into non-physics without a GUT.
SR/GR is understood by very few, if any, and so its practise is sparse, while Newton's Mechanics is understood and practised by many.
Presented experimental evidence concern detection of extremely weak signals from extremely massive violent large scale cosmological phenomena, such as gravitational waves from the merger of two black holes in the LIGO experiment.
In this light the following questions come up:
Is it necessary to replace Newton by Einstein?
Is GUT in the form of Newton+Maxwell+Schrödinger impossible?
A modern physicist would answer Yes! to both questions, even at the cost of giving up the idea of GUT. A modern physicist will then have to motivate why Newton must be replaced by Einstein, even if it means a collapse of physics as science.
Einstein is famous for his "thought experiments" as a chain of arguments within a theory such as SR, twisted to serve as external/experimental confirmation of the correctness of the theory. In particular, the constancy of the speed of light (in vacuum) is an agreement resulting from the thought experiment of agreeing to use the Lorentz transformation, which allows SR to prove itself to be true or allowing Einstein with 100% confidence to proclaim that nothing can prove SR to not be true! Because it is an agreement!
But agreements can be broken, and what happens if the agreement to coordinate observations in different inertial systems according to the Lorentz transformation, is given up? What compels observers to follow such a dictate?
The previous post took a look at the proclaimed mass defect in chemical and nuclear reactions releasing energy: A mass defect or loss of mass exactly corresponding to the energy release is to be computed from $E=mc^2$. This showed a flavor of agreement/definition instead of actual real physics with mass defect in contradiction to conservation of mass (1) as a basic principle of physics. We also exhibited the origin of mass as reactivity to a gravitational potential.
We may compare with conservation of energy (2) as the other basic principle of physics. Here energy is seen as potential to do work and can take the form of potential (e g chemical) energy or kinetic energy connected to motion. If now according to Einstein's $E=mc^2$ energy is "equivalent" to mass, then the two conservation laws (1) and (2) can be replaced by simply conservation of mass + energy (3), which is what Einstein had in mind, presumably: Mass can be converged to energy and vice versa, while the sum mass + energy remains constant. Fair enough. Clearly (3) follows from (1) + (2) and so cannot be disputed.
But (1) and (2) do not follow from (3) in the presence of mass defect. If mass is really converted to energy, then neither mass nor energy is conserved, only their sum mass+energy.
So here we stand. Two entities of different origin, mass as reactivity to gravitation, and energy as potential to do work, have been made “equivalent” as an expression of some deep modern physics expressing that mass+energy is conserved, but not both mass and energy separately.
Is this a step forward to a deeper understanding of the Universe? This connects to the biggest flaw of modern physics which is to not offer a consistent theory including both gravitation and quantum mechanics, despite tremendous efforts by the sharpest minds over more than 100 years. Quantum Mechanics and General Relativity of Gravitation are Incompatible!! What can be the reason? After all, the Universe is built from the (a) quantum mechanics of atoms + (b) gravitation. How could (a) and (b) be incompatible? What would a Universe look like if being formed from incompatible physics? An Incompatible Universe?
Is it so that we if we insist that (a) and (b) are the same corresponding to energy being "equivalent" to mass according to $E=mc^2$, then we seem to be led into a dead end where everything is confused or "incompatible". It is like claiming than man = woman, a principle which is causing a lot of confusion in society. For sure there are shared aspects but if two different concepts are made "equivalent" by agreement/definition, then confusion is created.
It may well be that if gravitation/mass is kept different from atoms/energy, then process can be made, while if confusion is allowed to reign, then no progress is possible. Ready to try? Take a look at the listed labels on the blog: new quantum mechanics and extended Newtonian gravitation which are certainly compatible!
In the next post I will investigate what concrete evidence there is that $E=mc^2$ is true physics, and not just an agreement. To prepare recall that Einstein somehow "derived" this relation in his Special Theory of Relativity to be a consequence of a postulate stating that all observes independent of inertial motion will have to measure the speed of light so that they get the same value named constancy of the speed of light. In other words, they have to use clocks and meter sticks to meet this end. More precisely, since 1983 all observers are demanded to use the SI Standard meter stick as the distance traveled by light over a certain length of time. The SI Standard thus commands all observers to agree on the same value of the speed of light: one light second/second = 1.
But a command, or agreement if no observer objects, is just an agreement and as such is void of true physics. That the Earth is round is not an agreement, but a true physical fact. The agreement before was that the Earth is flat, and it is only recently that this agreement has evaporated. It would today be silly to say that Earth is round because we have agreed that it is. It is not agreement that makes the World go around. It goes around even if there is disagreement. But it is very difficult to get a modern physicist see the difference between agreement and physical fact, definition and theorem in mathematics.
Modern physicists all agree that the Standard Model is correct, and so this is the way Nature is even if very strange...but understanding that real science boils down to showing that something is not so strange...
Here is an article leading into the next post: 103 years Later. Einstein Proven Correct. So it took modern physicist 103 years to come up with some real experimental evidence of $E=mc^2$. But the experiment is very tricky and so can be questioned. If $E=mc^2$ is indeed correct physics as the incarnation of modern physics, why has it been so difficult to verify experimentally? It would seem more likely that since it is so difficult to demonstrate, it cannot be true physics. Only an agreement that the Earth is flat, which you can argue is true in some sense agreed upon, but which is not really the whole story.
Leibniz as the greatest polymath of all times would have had a hard time to swallow the modern physics of the standard version of quantum mechanics here referred to as stdQM, because it violates his Principle of Identity of Indescernibles PII stating that:
No two objects have exactly the same properties.
That PII is valid in the macroscopic world is non-disputable: A set of objects even if identical as concerns intrinsic properties maintain descernibility/individuality by occupying different regions of physical space as an expression of Exclusive Occupancy.The stars in the sky, even if they all look alike, are discernible by their position. The red balls of snooker billiard game even if all alike, are descernible by their position. No big deal.
But things are supposed to be different in the microscopic world described by stdQM, where electrons are not supposed to occupy specific regions in a physical space and time and so have a physicality which is fundamentally different from macroscopics. In other words, electrons (modulo spin) are viewed to be indescernible by having all the same properties (modulo spin) including no specific location in space and time. Yet the electrons are not viewed to be identical because in the wave function of stdQM they are assigned different coordinates.
In other words, stdQM violates PII, which means that stdQM is not physics according to Leibniz.
On the other hand, in RealQM electrons are discernible by Exclusive Occupancy, and so could be embraced by Leibniz.
This connects to the question if the microscopic world must be conceptually different from the macroscopic world: stdQM says yes, and RealQM no.
Leibniz expresses his view on the microscopic world in his theory of monads as mind-like simple substances with individuality endowed with perception and appetite from which bodies, motion and everything else is derived. This closely connects to RealQM with protons and electrons as non-overlapping charged clouds interacting by Coulomb forces as expression of perception and appetite.
Individuality is important because it makes a distinction between one specific body/monad/electron and other bodies/monads/electrons, and thus takes care of theproblem of self-interaction, which if present can be lethal like an auto-immune reaction. This is the case in quantum field theory riddled with infinites from self-interaction.
It is possible that control of self-interaction is a necessary capability in physics as well as in chemistry, biology and sociology. If we as human beings cannot make a distinction between our own mind/body and the minds/bodies of others, then we have a problem as well as society.
Physics Is Wrong, From String Theory to Quantum Mechanics.
This is a funny situation, unprecedented in the history of science, and it has been like that for now
more than 100 years.
A restart is obviously needed and my contribution is Real Quantum Mechanics. Take a look! And think! See also recent posts.
But Sabine Hossenfelder is a physicist and thus must seek to rescue the hopeless situation in one way or the other:
And whatever your misgivings are about quantum mechanics, there is no denying that it is useful.
So quantum mechanics is wrong, but it is nevertheless useful? That does not make sense. A theory which is wrong cannot be truly useful, because from something which is wrong cannot come something which is right. Only if the theory is right in some sense, can it be useful. But no physicist has any clue to what is right about quantum mechanics, only what is wrong!
Sabine Hossenfelder resorts to the common trick of referring to yet a more incomprehensible theory in the form of Quantum Field Theory, when basic Quantum Theory is questioned. This was used by
Einstein when he increased the bet to general relativity when his special theory of relativity was questioned on most rational grounds. This
A physical theory should clearly and forthrightly address two fundamental questions: what there is, and what it does.
The answer to the first question is provided by the ontology of the theory, and the answer to the second by its dynamics.
The ontology should have a sharp mathematical description, and the dynamics should be implemented by precise equations describing how the ontology will, or might, evolve.
The Copenhagen Interpretation, in contrast, does not. There is little agreement about just what this approach to quantum theory postulates to actually exist or how the dynamics can be unam- biguously formulated. Nowadays, the term is often used as short-hand for a general instrumentalism that treats the mathematical apparatus of the theory as merely a predictive device, uncommitted to any ontology or dynamics at all.
Sometimes, accepting the Copenhagen Interpretation is understood as the decision simply to use the quantum recipe without further question: Shut up and calculate. Such an attitude rejects the aspiration to provide a physical theory, as defined above, at all.
Hence it is not even in the running for a description of the physical world and what it does. More specific criticisms could be raised against this legacy of Bohr, but our time is better spent presenting what is clear than decrying what is obscure.
The Copenhagen Interpretation is the text book interpretation of quantum mechanics, which Maudlin thus refutes as meaningless. I agree totally.
What does then Maudlin offer in the book instead of the Copenhagen Interpretation? Very little: pilot wave theory and many worlds theory, both failed attempts to give meaning to Schrödinger's wave function. The book thus gives yet another account of the mystery of quantum mechanics 100 years after its creation.
The whole problem comes from the multi-dimensionality of Schrödinger's equation asking for a statistical unphysical interpretation. How many new books will be written on the theme that physicists do not understand the quantum mechanics they preach?
Physics deals with the most fundamental laws of nature, those from which everything else derives. These laws are, to our best current knowledge, differential equations. Given those equations and the configuration of a system at one particular time, you can calculate what happens at all other times.
That is for what the universe without quantum mechanics is concerned. Add quantum mechanics, and you introduce a random element into some events. Importantly, this randomness in quantum mechanics is irreducible. It is not due to lack of information. In quantum mechanics, some things that happen are just not determined, and nothing you or I or anyone can do will determine them.
Taken together, this means that the part of your future which is not already determined is due to random chance. It therefore makes no sense to say that humans have free will.
This is an expression of the monumental confusion of modern physicists caused by the idea that atoms play games of roulette attributed to quantum mechanics as being based on Schrödinger's multidimensional wave equation, something which Einstein and Schrödinger never accepted.
I have followed a different line of thought viewing physics as forms of analog computation with finite precision, which can be simulated by digital computation with finite precision presented atThe World as Computationincluding anew approach to quantum mechanics asReal Quantum Mechanicswithout games of roulette.
In this world there is room for humans with free will, although you cannot control everything in your life, due to lack of precision. If you are not an addicted gambler this may be the world for you.
Determined or Random??
PS The idea that atoms play games of roulette has corrupted modern physics into incomprehensible voodoo-science. Macroscopics as complex systems of simple microscopics can express random behavior, but random microscopics destroys cause-effect and demands contradictory microscopics of microscopics. Contradictory science is voodoo-science, even if it is text book modern physics.
Scientists have been using quantum theory for almost a century now, but embarrassingly they still don’t know what it means.
Some physicists just shrug and say we have to live with the fact that quantum mechanics is weird.
But some researchers want to dig deeper.
If these efforts succeed, it’s possible that all the apparent oddness and confusion of quantum mechanics will melt away, and we will finally grasp what the theory has been trying to tell us.
There’s no guarantee of success — no assurance that quantum mechanics really does have something plain and simple at its heart, rather than the abstruse collection of mathematical concepts used today.
offering a new approach based on classical physical principles, which is not weird and can be understood, presented in the upcoming book Real Quantum Mechanics.
Here are results for the first excitation of Helium ground state into a 1S2S state with excitation energy = 0.68 = 2.90 -2.22, to be compared with observed 0.72:
Concerning the ground state and ground state energy of Helium the following illumination can be made:
Standard quantum mechanics describes the ground state of Helium as $1S2$ with a 6d wave function $\psi (x1,x2)$ depending on two 3d Euclidean space coordinates $x1$ and $x2$ of the form
with $Z =2$ the kernel charge, and $C$ a normalising constant. This describes two identical spherically symmetric electron distributions as solution of a reduced Schrödinger equation without electronic repulsion potential, with a total energy $E =-4$, way off the observed $-2.903$.
To handle this discrepancy between model and observation the following corrections in the computation of total energy are made, while keeping the spherically symmetric form (1) of the ground state as the solution of a reduced Schrödinger equation:
1 . Including Coulomb repulsion energy of (1) gives $E=-2.75$.
2. Changing the kernel attraction to $Z=2 -5/16$ claiming screening gives $E=-2.85$.
3. Changing Coulomb repulsion by inflating the wave function to depend on $\vert x1-x2\vert$ can give at best $E=-2.903724...$ to be compared with precise observation according to Nist atomic data base $-2.903385$ thus with an relative error of $0.0001$. Here the dependence on $\vert x1-x2\vert$ of the inflated wave function upon integration with respect to $x2$ reduces to a dependence on only the modulus of $x1$. Thus the inflated non spherically symmetric wave function can be argued to anyway represent two spherically symmetric electronic distributions.
We see that a spherically symmetric ground state of the form (1) is attributed to have correct energy, by suitably modifying the computation of energy so as to give perfect fit with observation. This kind of physics has been very successful and convincing (in particular to physicists), but it may be that it should be subject to critical scientific scrutiny.
The ideal in any case is a model with a solution which ab initio in direct computation has correct energy, not a model with a solutions which has correct energy only if the computation of energy is changed by some ad hoc trick until match.
The effect of the fix according to 3. is to introduce a correlation between the two electrons to the effect that they would tend appear on opposite sides of the kernel, thus avoiding close contact. Such an effect can be introduced by angular weighting in (1) which can reduce electron repulsion energy but at the expense of increasing kinetic energy by angular variation of wave functions with global support and then seemingly without sufficient net effect. With the local support of the wave functions meeting with a homogeneous Neumann condition (more or less vanishing kinetic energy) of the new model, such an increase of kinetic energy is not present and a good match with observation is obtained.
Once Schrödinger had formulated his equation for the Hydrogen atom with one electron and with great satisfaction observed an amazing correspondence to experimental data, he faced the problem of generalising his equation to atoms with many electrons.
The basic problem was the generalisation of the Laplacian to the case of many electrons and here Schrödinger took the easy route (in the third out of Four Lectures on Wave Mechanics delivered at the Royal Institution in 1928) of a formal generalisation introducing a set of new independent space coordinates and associated Laplacian for each new electron, thus ending up with a wave function $\psi (x1,...,xN)$ for an atom with $N$ electrons depending on $N$ 3d spatial coordinates $x1$,...,$xN$.
Already Helium with a Schrödinger equation in 6 spatial dimensions then posed a severe computational problem, which Schrödinger did not attempt to solve. With a resolution of $10^2$ for each coordinate an atom with $N$ electrons then gives a discrete problem with $10^{6N}$ unknowns, which already for Neon with $N=10$ is bigger that the total number of atoms in the universe.
The easy generalisation thus came with the severe side-effect of giving a computationally hopeless problem, and thus from scientific point meaningless model.
To handle the absurdity of the $3N$ dimensions rescue steps were then taken by Hartree and Fock to reduce the dimensionality by restricting wave functions to be linear combinations of products of one-electron wave functions $\psi_j(xj)$ with global support:
to be solved computationally by iterating over the one-electron wave functions. The dimensionality was further reduced by ad hoc postulating that only fully symmetric or anti-symmetric wave functions (in the variables $(x1,...,xN)$) would describe physics adding ad hoc a Pauli Exclusion Principle on the way to help the case. But the dimensionality was still large and to get results in correspondence with observations required ad hoc trial and error choice of one-electron wave functions in Hartree-Fock computations setting the standard.
We thus see an easy generalisation into many dimensions followed by a very troublesome rescue operation stepping back from the many dimensions. It would seem more rational to not give in to the temptation of easy generalisation, and in this sequence of posts we explore such a route.
PS In the second of the Four Lectures Schrödinger argues against an atom model in terms of charge density by comparing with the known Maxwell's equations for electromagnetics in terms of electromagnetic fields, which works so amazingly well, with the prospect of a model in terms of energies, which is not known to work.
The standard computational form of the quantum mechanics of an atom with N electrons (Hartree or Hartree-Fock) seeks solutions to the standard multi-dimensional Schrödinger equation as linear combinations of wave functions $\psi (x1,x2,...,xN)$ depending on $N$ 3d space coordinates $x1$,...,$xN$ as a product:
where the $\psi_j$ are globally defined electronic wave functions depending on a single space coordinate $xj$.
The new model takes the form of a non-standard free boundary Schrödinger equation in a wave function $\psi (x)$ as a sum:
$\psi (x)=\psi_1(x)+\psi_2(x)+....+\psi_N(x)$,
where the $\psi_j(x)$ are electronic wave functions with local support on a common partition of 3d space with common space coordinate $x$.
The difference between the new model and Hartree/Hartree-Fock is evident and profound. A big trouble with electronic wave functions having global support is that they overlap and demand an exclusion principle and new physics of exchange energy. The wave functions of the new model do not overlap and there is no need of any exclusion principle or exchange energy.
PS Standard quantum mechanics comes with new forms of energy such as exchange energy and correlation energy. Here correlation energy is simply the difference between experimental total energy and total energy computed with Hartree-Fock and thus is not a physical form of energy as suggested by the name, simply a computational /modeling error.
This connects to the homogeneous Neumann boundary condition identifying separation between electrons of the new model under study in this sequence of posts.
Atoms in Molecules is focussed on the role of atomic kernels in molecules, while the new model primarily (so far) concerns electrons in atoms.
Below are results for the $H^-$ ion with two electrons and a proton. The ground state energy comes out as -0.514, slightly below the energy -0.5 of $H$, which means that $H$ is slightly electro-negative and thus by acquiring an electron into $H^-$ may react with $H^+$ to form $H2$ (with ground state energy -1.17), as one possible route to formation of $H2$. Another route is covered in this post with two H atoms being attracted to form a covalent bond.
The two electron wave functions of $H^-$ occupy half-spherical domains (depicted in red and blue) and meet at a plane with a homogeneous Neumann condition satisfied on both sides.
Standard quantum mechanics of atom is based on the eigen functions of the Schrödinger equation for a Hydrogen atom with one electron, named "orbitals" being the elements of the Aufbau or build of many-electron atoms in the form of s, p, d and f orbitals of increasing complexity, see below.
These "orbitals" have global support and has led to the firm conviction that all electrons must have global support and so have to be viewed to always be everywhere and nowhere at the same time (as a basic mystery of qm beyond conception of human minds). To handle this strange situation Pauli felt forced to introduce his exclusion principle, while strongly regretting to ever have come up with such an idea, even in his Nobel Lecture:
Already in my original paper I stressed the circumstance that I was unable to give a logical reason for the exclusion principle or to deduce it from more general assumptions.
I had always the feeling and I still have it today, that this is a deficiency.
Of course in the beginning I hoped that the new quantum mechanics, with the help of which it was possible to deduce so many half-empirical formal rules in use at that time, will also rigorously deduce the exclusion principle.
Instead of it there was for electrons still an exclusion: not of particular states any longer, but of whole classes of states, namely the exclusion of all classes different from the antisymmetrical one.
The impression that the shadow of some incompleteness fell here on the bright light of success of the new quantum mechanics seems to me unavoidable.
In my model electrons have local support and occupy different regions of space and thus have physical presence. Besides the model seems to fit with observations. It may be that this is the way it is.
Here are results for two hydrogen atoms forming an H2 molecule at kernel distance R = 1.4 at minimal total energy of -1.17 and a non-bonded molecule for larger distance approaching full separation for R larger than 6-10 at a total energy of -1. The results fit quite well with table data listed below.
The computations were made (on an iPad) in cylindrical coordinates in rotational symmetry around molecule axis on a mesh of 2 x 400 along the axis and 100 in the radial direction. The electrons are separated by a plane perpendicular to the axis through the the molecule center, with a homogeneous Neumann boundary condition for each electron half space Schrödinger equation. The electronic potentials are computed by solving a Poisson equation in full space for each electron.
PS To capture energy approach to -1 as R becomes large, in particular the (delicate) $R^{-6}$ dependence of the van der Waal force, requires a (second order) perturbation analysis, which is beyond the scope of the basic model under study with $R^{-1}$ dependence of kernel and electronic potential energies.
%TABLE II. Born–Oppenheimer total, E
%Relativistic energies of the ground state of the hydrogen molecule
%L. Wolniewicz
%Citation: J. Chem. Phys. 99, 1851 (1993);
for two hydrogen atoms separated by a distance R bohr
The modern physics of quantum mechanics born in 1926 was a towering success for the Hydrogen atom with one electron, but already Helium with two electrons posed difficulties, which have never been resolved (to be true).
The result is that prominent physicists always pride themselves by stating that quantum mechanics cannot be understood, only be followed to the benefit of humanity, like a religion:
I think I can safely say that nobody understands quantum mechanics. (Richard Feynman, in The Character of Physical Law (1965))
Text books and tables list the ground state of Helium as $1S^2$ with two spherically symmetric electrons (the S) with opposite spin in a first shell (the 1), named parahelium. The energy of a $1S^2$ state according to basic quantum theory is equal to -2.75 (Hartree), while the observation of ground state energy is -2.903. To handle this apparent collapse of basic quantum theory, the computation of energy is changed by introducing a suitable perturbation away from spherical symmetry which delivers the wanted result of -2.903, while maintaining that the ground state still is $1S^2$.
Of course, this does not make sense, but since quantum mechanics is not "anschaulich" or "visualisable" (as required by Schrödinger) and therefore cannot be understood by humans, this is not a big deal. By a suitable perturbation the desired result can be reached, and we are not allowed to ask any further questions following the dictate of Dirac: Shut up and calculate.
New Quantum Mechanics resolves the situation as follows:
The ground state is predicted to be a spherically (half-)symmetric continuous electron charge distribution with each electron occupying a half-space, and the electrons meeting on at plane (free boundary) where the normal derivative for each electron charge distribution vanishes. The result of ground state energy computations according to earlier posts shows close agreement with the observed -2.903:
Notice the asymmetric electron potential and the resulting slightly asymmetric charge distribution with polar accumulation. The model shows a non-standard electron configuration, which may be the true one (if there is anything like that).
Below are sample computations of ground states for Li1+, C1+, Ne1+ and Na1+ showing good agreement with table data of first ionisation energies of 0.2, 0.4, 0.8 and 0.2, respectively.
Note that computation of first ionisation energy is delicate, since it represents a small fraction of total energy.
The result presentation continues below with alkaline and alkaline earth metals Na (2-8-1), Mg (2-8-2), K (2-8-8-1), Ca (2-8-8-2), Rb (2-8-18-8-1), Sr (2-8-18-8-2), Cs (2-8-18-18-8-1) and Ba (2-8-18-18-8-2):
The presentation of computational results continues below with the noble gases Ar (2-8-8), Kr (2-8-18-8), Xe (2-8-18-18-8) and Rn (2-8-18-32-18-8) with the shell structure indicated.
Again we see good agreement of ground state energy with NIST data, and we notice nearly equal energy in fully filled shells.
Note that the NIST ionization data does not reveal true shell energies since it displays a fixed shell energy distribution independent of ionization level, and thus cannot be used for comparison of shell energies.
Inlägg
