The Linear Scalar MultiD Schrödinger Equation as Pseudo-Science

If we are still going to put up with these damn quantum jumps, I am sorry that I ever had anything to do with quantum theory. (Erwin Schrödinger)

The pillars of modern physics are quantum mechanics and relativity theory, which both however are generally acknowledged to be fundamentally mysterious and incomprehensible to even the sharpest minds and thus gives modern physics a shaky foundation. The mystery is so deep that it has been twisted into a virtue with the hype of string theory representing maximal mystery.

The basic trouble with quantum mechanics is its multi-dimensional wave function solution depending on 3N space coordinates for an atom with N electrons,  as solution to the linear scalar multi-dimensional Schrödinger equation, which cannot be given a real physical meaning because reality has only 3 space coordinates.

The way out to save the linear scalar multidimensional Schrödinger equation, which was viewed to be a gift by God and as such was untouchable, was to give the multidimensional wave function an  interpretation as the probability of the N-particle configuration given by the 3N coordinates. Quantum mechanics based on the linear scalar Schrödinger equation was thus rescued at the cost of making the microscopic atomistic world into a game of roulette asking for microscopics of microscopics as contradictory reduction in absurdum.

But God does not write down the equations describing the physics of His Creation, only human minds and if insistence on a linear scalar (multidimensional) Schrödinger wave equation leads to contradiction, the only rational scientific attitude would be to search for an alternative, most naturally as a system of non-linear wave equations in 3 space dimensions, which can be given a deterministic physical meaning. There are many possibilities and one of them is explored as Many-Minds Quantum Mechanics in the spirit of Hartree.

It is well known that macroscopic mechanics including planetary mechanics is not linear, and there is no reason to expect that atomistic physics is linear and allows superposition. There is no rational reason to view the linear scalar multiD Schrödinger equation as the basis of atomistic physics (other than as a gift by God which cannot be questioned), and physics without rational reason is unreasonable and thus may represent pseudo-science.

The linear scalar multiD Schrödinger equation with an incredibly rich space of solutions beyond reason, requires drastic restrictions to represent anything like real physics.  Seemingly out of the blue, physicists  have come to agree that God can play only with fully symmetric (bosons) or antisymmetric (fermions) wave functions with the Pauli Exclusion Principle as a further restriction. But nobody has been able to come with any rational reasons for the restrictions to symmetry, antisymmetry and exclusion. According to Leibniz Principle of Sufficient Reason, this makes these restrictions into ad hoc pseudo-science.  
  
  

Welcome Back Reality: Many-Minds Quantum Mechanics

The new book Farewell to Reality by Jim Baggott gets a positive reception on Not Even Wrong (and accordingly a negative by Lubos). The main message of the book is that modern physics (SUSY, GUTS, Superstring/M-theory, the multiverse) is no longer connected to reality in the sense that experimental support is no longer possible and therefore is not considered to even be needed.

But science without connection to reality is pseudo-science, and so how can it be that physics classically considered to be the model of all sciences, in modern times seems to have evolved into pseudo-science? Let's take a look back and see if we can find an answer:

My view is that the departure from reality started in the 1920s with the introduction of the multi-dimensional wave function as solution to a linear scalar Schrödinger equation, with 3N space dimensions for an atom with N electrons. Such a wave function does not describe real physics, since reality has only 3 space dimensions and the only way out insisting on the truth of the linear Schrödinger equation as given by God,  was to give the wave function a statistical interpretation. But that meant a non-physical and non-real interpretation, since there is no reason to believe that real physics can operate like an insurance company filled with experts doing statistics, in Einstein's words expressed as "God does not play dice".  The statistical interpretation was so disgusting to Schrödinger that he gave up further exploration of the quantum mechanics he had invented. 

Schrödinger believed that the wave function had a physical meaning as a description of the electron distribution around a positive kernel of an atom. A non-linear variant of the Schrödinger equation in the form of a system of N equations in 3 space dimensions for an N-electron atom was early on suggested by Hartree as a method to compute approximate solutions of the multi-dimensional Schrödinger, an equation which cannot be solved, and the corresponding wave function can be given a physical meaning as required by Schrödinger. I have explored this idea a little bit in the form of Many-Minds Quantum Mechanics (MMQM) as an analog of Many-Minds Relativity.

MMQM seems to deliver a ground state of Helium corresponding to the observed minimal energy E = - 2.904,  with the 2 electrons of Helium distributed basically as two half-spherical shells (blue and green patches) filling a full shell around the kernel (red) as illustrated in the left picture. This configuration is to be compared with the spherically symmetric distributions of Parahelium 1s1s (hydrogenic orbital) in the middle with E = -2.75 and Ortohelium 1s2s with even bigger energy to the right:

Classical quantum mechanics based on a multi-dimenisonal wave function satisfying the linear Schrödinger equation (QM) presents Parahelium as the ground state of Helium with the two electrons sharing a common spherically symmetric orbit in accordance with the Pauli Exclusion principle (PEP).  But the energy E = -2.75 of Parahelium is greater than the observed E = -2.904 and so Parahelium cannot be the ground state.

QM with PEP thus does not describe even Helium correctly, a fact which is hidden in text books, while the non-spherical distribution of MMQM appears to give the correct energy.

MMQM does not require any PEP and suggests a different explanation of the electronic shell structure of an atom with the numbers of 2, 8, 8, 18, 18... of electrons in each shell arising as 2 x n x n, with n=1,  2, 2, 3, 3, and the factor 2 reflecting the structure of the innermost shell as that of Helium, and n x n the two-dimensional aspect of a shell.

The Farewell to Reality from modern physics was thus initiated with the introduction of the multi-dimensional wave function of the linear Schrödinger equation of QM in the 1920s, and the distance to Reality has only increased since then.  Once the connection the Reality is given up there is no limit to how far you can go with your favorite theory.

QM is cut in stone as the linear multidimensional Schrödinger equation with wave function solution being either symmetric or antisymmetric and satisfying PEP, but QM in this form lacks real physical interpretation.

The exploration of non-linear Schrödinger equations in 3 space dimensions with obvious possibilities of physical interpretation, has been pursued only as a way to compute approximate solutions to the multi-dimensional linear Schrödinger equation, but may merit attention also as true models of physical reality.   

Gomorron Sverige Ärende hos Academic Rights Watch

Academic Rights Watch har nu tagit upp mitt ärende "Gomorron Sverige", som inom kort kommer att behandlas av Kammarrätten i Stockholm. Den större frågan är om KTH har brutit mot Yttrandefrihetsgrundlagen, eller inte.

Essence of Dynamics 1

                           Computed turbulent flow around an airplane represents Case 3. below.

The dynamics of a physical system can typically be described as an initial value problem of finding a vector function U(t) depending on time t such that

• dU/dt + A(U) = F  for t > 0 with U(0) = G,

where, A(U) is a given vector function of U,  F(t) is a given forcing and G is a given intial value at t = 0. In the basic case A(U) = A*U is linear with A = A(t) a matrix depending on time, which is also the linearized form of the system describing growth/decay of perturbations characterizing stable/unstable dynamics.

An essential aspect of the dynamics is the perturbation dynamics described by the linearized system which is determined by the eigenvalues of its linearization matrix A, assuming for simplicity that A is diagonalizable and independent of time:

1. Positive eigenvalues: Stable in forward time; unstable in backward time.
2. Negative eigenvalues : Unstable in forward time; stable in backward time.
3. Both positive and negative eigenvalues: Both unstable and stable in both forward and backward time.
4. Imaginary eigenvalues: Wave solutions marginally stable in both forward and backward time.
5. Complex eigenvalues: Combinations of 1. - 4.         

Here Case 1. represents a dissipative system with exponential decay of perturbations in forward time making long time prediction possible, but backward time reconstruction difficult because of exponential growth of perturbations. This is the dynamics of a diffusion process, e.g. the spreading of a contaminant by diffusion or heat conduction. 

Case 2. is the reverse with forward prediction difficult but backward reconstruction possible. This is the dynamics of a Big Bang explosion. 

Case 3. represents turbulent flow with both exponential growth and decay giving rise to complex dynamics without explosion, with mean-value but not point value predictability in forward time. The picture above shows the turbulent flow around an airplane with mean-value quantities like drag and lift being predictable (in forward time). This case represents the basic unsolved problem of classical mechanics which is now being uncovered by computational methods including revelation of the secret of flight (hidden in the above picture).  

Case 4 represents wave propagation with possibilities of both forward prediction and backward reconstruction, with the harmonic oscillator as basic case. 

There is a further limit case with A non-diagonalizable with an incomplete set of eigenvectors for a multiple zero eigenvalue, with possibly algebraic growth of perturbations, a case arising in transition to turbulence in parallel flow. 

The Dog and the Tail: Global Temperature vs CO2, continuation.

This is a continuation of the previous post.

Consider the following special case with T(t) = T_0 for t < 1970, T(t) increasing linearly for 1970 < t < 1998 to the value T_1 with T(t) = T_1 for t > 1998. The corresponding solution C(t) of the equation dC/dt increases linearly for t < 1970, quadratically for 1970 < t < 1998  and again linearly for t > 1998 as sketched by the solid lines in the following graph:

We see that after 1998 the temperature stays constant while the CO2 increases linearly. The solid lines could picture reality.

On the other hand, if you want to create a fiction of CO2 alarmism, you would argue as follows: Look at the solid lines before 1998 representing recorded reality and simply make an extrapolation until 2020 of the simultaneous increase of both T and C during the period 1970 - 1998, to get the dotted red line as a predicted alarming global warming in 2020 resulting from a continued increase of CO2. The extrapolation would then correspond to using a connection between T and C of the form T ~ C with T determined by C, instead of the as in the above model dC/dt = T with C determined by T.

This shows the entirely different global warming scenarios obtained using the model T ~ C with T determined by C, and the model dC/dt = T with C determined by T.

The Dog and the Tail: Global Temperature vs CO2

Prof. Murry Salby's presentation in Hamburg in April is a showcase of effective scientific communication based on mathematics. Salby gives strong evidence based on observation that the offset of concentration C(t) of atmospheric CO2 as a function of time t is determined by the offset of global temperature T(t) by an equation of the form

• dC/dt  = T   for all t > 0, C(0) = 0,

after suitable scaling of C(t). In other words, C(t) is the integral of T(t), so that if T(t) = cos(t) then C(t) = sin(t) with a time lag of a quarter of a period.  

The fact that in the equation dC/dt = T the concentration C(t) is determined by T(t), comes out as an aspect of stability (or wellposedness): Integration is a stable or well posed mathematical operation in the sense that small variations in the integrand T(t) gives small variations in the integral C(t). 

On the other hand, differentiation is a an unstable or ill posed mathematical operation: small variations dC(t) in C(t) can give rise to large variations in dC(t)/dt as a result of division by a small dt. This means that viewing T(t) in the relation dC/dt = T to be determined by C(t) corresponds to an unstable mathematical operation. 

To make a connection from cause to effect in physics, requires stability and thus in the observed relation dC/dt = T, it is C(t) which is determined by T(t) as the cause and not the other way around. Another way of expressing this fact is to say that C(t) lags T(t) with a quarter of a period, so that variations in the cause T(t) precedes the effect as variations C(t). 

This is the observation from ice core proxies showing that temperature changes before CO2 and thus temperature is the dog and CO2 the tail with the dog wagging the tail, and not the other way around as the basic postulate of CO2 alarmism:

   

Need of Education in Mathematics - IT

Images des Math issued by CNRS reports on a proposal by L'Academie des Sciences to strengthen school education in Information Science and Technology (IT), and expresses the concern that while  the proposal identifies the strong impact of IT in physics, chemistry, biology, economy and social sciences, the connection between IT and mathematics is less visible.

The reason L'Academie des Sciences forgets the fundamental connection between mathematics and IT, is that school mathematics is focussed on a tradition of analytical mathematics, where the IT-revolution of computational mathematics is not visible.

This connects to my proposal of a reform of school mathematics into a new school subject named Mathematics - IT combining analytical and computational mathematics with the world of apps as the world of applications of mathematics using IT. Without such a reform school mathematics will follow the fate of classical latin and greek once at the center of the curriculum but now gone. This is not understood by mathematicians paralyzed by the world of apps based on computational mathematics.

The strength of the (aristochratic) tradition of analytical mathematics is preventing a marriage with (newly rich) computational mathematics, which would serve as the adequate school mathematics of the IT age. As often, a strength can be turned into a fatal weakness when conditions change but strong tradition resists reform.

Milestone: Direct Fem-Simulation of Airflow around Complete Airplane

The first direct computational simulation of the flow of air around a complete airplane (DLR F11 high-lift configuration) has been performed by the CTLab group at KTH led by Johan Hoffman in the form of Direct Fem-Simulation (DFS). The simulation gives support to the new theory of flight developed by Hoffman and myself now under review by Journal of Mathematical Fluid Mechanics after initial rejection by AIAA. The milestone will be presented at 2nd AIAA CFD High Lift Prediction Workshop, San Diego, June 22-23 2013.

DFS is performed by computational solution using an adaptive  residual-stabilized finite element method for the Navier-Stokes equations with a slip boundary condition modeling the small skin friction of air flow. DFS opens for the first time the possibility of constructing a realistic flight simulator allowing flight training under extreme dynamics, beyond the vision of AIAA limited by classical flight theory.

For more details browse my upcoming talk at ADMOS 2013.