PSE and the quark modelThe standard model of particle physics is the undisputed measure of all things. How can anyone be so stupid and challenge even parts of it ? It's because theoretical physics is stuck on a level where theoretical chemistry was in the 19th century.
The 19th century witnessed a major breakthrough in chemistry. A symmetry scheme was discovered allowing to order chemical elements, predict new ones and their properties. The Periodic System of the elements has been a cornerstone of chemistry ever since. The cause of this specific order has been unknown until in 1926 Erwin Schrödinger set up its famous equation for the H-atom. With this simple differential equation (+ the Pauli principle) it is possible to describe the features of the PSE exactly, completely and most of all with no need for additional parameters except for natural constants. Computational chemistry today is capable of calculating ever more complicated molecules, their properties and reactions based on this single equation and some very well defined approximations. The cornerstone of the standard model of particle physics is the quark model and QCD. The properties of the quarks are chosen to match symmetry properties of particles as deduced from scattering experiments. This has proved to be very useful for predicting additional particles and their properties. (There is a long tradition of predicting particles not to be observed as well.) However the second step gone in case of the PSE, i.e. deriving the ordering system from a simple underlying principle has not been taken. On the contrary the model will become more complex if neutrino mass will be incorporated driving the number of input parameters far beyond the 19 used by now.
There is no guarantee that Ockham's razor provides a simple solution for any problem in science yet most people in particle physics seem too complacent to even try and prefer to further stride away from Ockham in from of strings and other stuff.
Is there reason apart from the quark model to be enthusiastic about the standard model ?
If you take Wikipedia (on 14.11.2018 Standard Model, Physics beyond the SM) as representative for the major points of critique on the SM you will find as the most important points:
- ad hoc and inelegant, requiring 19 numerical constants
- model does not explain gravitation
- inconsistent with the emerging model of cosmology
- neutrino mass
Let's start with the last one, neutrino mass. This one essentially falsifies the SM. Good, time proven theories like e.g. those of Newton may be degraded to a special case of a broader theory but they do not get falsified.
The second and third are the same problem: you should not expect to be able to get a consistent cosmological model unless one of its most important components, gravitation, is fully understood.
The first point, ad hoc, inelegant, many parameters, in my interpretation:
The model is not only ad hoc but lacks coherence as well.
The very name "standard model" covers the fact, that its a grab bag of theories, QED, QCD, Higgs-mechanism, low mass particles who can not be made fit in the quark-scheme are treated completely separate*, and once again, the fundamental force of gravitation needs a complete separate theory, etc. .
Like in the case of neutrino mass the SM has a history of requiring work-arounds for problems not covered by the original model: ß-decay and flavor change of quarks required an additional force, some decays required to drop parity and other long-cherished conservation laws. Bosons with mass require the Higgs, which does not give mass to neutrinos etc. etc. => inelegant
Accuracy: The precise calculation of the electron anomalous g-factor in QED is the poster boy of accuracy of the SM with precison in the 1E-10s. Yet in spite of the 19+ parameters QCD, relevant for quarks / hadrons, is struggeling with 0.01. Much worse in the case of leptons.
Last not least the standard model of particles is centered around particles. It replaced the "old" particles by new ones, calculating their properties by some interaction mechanism (or not at all if they are leptons). Though this being a successful approach in QED it should be fundamentally questionable if a description of the properties of elementary objects via interaction with other objects is the only way to go.
By and large, the standard model is a useful umpteen parameter fit, lacking a coherent theoretical base. No reason not to try to simplify|.
What I have to offer might not be the "Schrödingergleichung", but maybe the "Bohrsche Atommodell" implying Schrödinger will follow. Naturally it does not cover all aspects processed by the SM in the course of some 60 years though it obviously covers aspects like gravitation or lepton mass left out by the SM .
Last not least:
[(hc α)2 / (e 2/(4π r) )] 2 Ψ(r)/dr2 - (e 2/(4π)) ß r -3 dΨ(r)/dr + (e 2/(4π)) ß r -4 Ψ(r) = 0
*The rigid distinction between leptons and hadrons implies that a set of physical objects characterized by an almost identical set of experimental observables - such as mass, charge, spin, magnetic moment, well defined mean life time and the effects of electromagnetism, weak interaction and gravitation - is based on completely different physical principles. This is quite an extraordinary claim, is it covered by extraordinary evidence ?
The postulate of leptons not being subject to strong interaction is not verifiable beyond experimental accuracy. Neutrino mass is a precedent for the fallacy to confuse a very small value with zero.
The three generation model, attributing a neutrino to each charged lepton, looks like a more solid argument. However, the total number of neutrinos is not beyond doubt (MiniBoone, cosmic neutrinos) and neutrino oscillation obscures the earlier assumption of clearly distinct particles. Last not least, a distinctive interaction of neutrinos with the charged leptons might simply be due to the very weak strong interaction of the particles involved not requiring any assumption beyond that.