fredag 3 februari 2023

Newton's Cosmic Model: Irony of Modern Physics

  • From the same principles, I now demonstrate the frame of the System of the World. (Newton)

This is a continuation of the previous post on the primordial role of a gravitational potential $\phi (x)$ as giving gravitational mass $\rho (x)=\Delta\phi$ to matter through the Laplacian operator $\Delta$ as instant local action by differentiation with $x$ a 3d Euclidean space coordinate. This is Newton's Law of Gravitation describing gravitational force.  

We obtain a model of cosmic interaction as a set of point masses represented by $\rho (x,t)$ moving according to Newton's 2nd Law of Motion $F=am$ connecting inertial force $F$ to acceleration $a$ and mass $m$, subject to gravitational force $\nabla\phi (x,t)$ with $t$ a time coordinate. You can follow the dynamics by starting  Cosmic Interaction on Leibniz World of Math and clicking in point masses. 

Combining Newton's Law of Gravitation and 2nd Law of Motion we thus have a mathematical model capable of describing cosmic interaction on any scale as point masses all "falling freely" with gravitational and inertial forces balancing to net zero force. This is the weightless zero-stress state so happily experienced by Stephen Hawking when visiting Virgin Galactic

We understand that it is the gravitational potential/force which creates the dynamics of cosmos through the key creative steps of 

  1. Giving gravitational mass to matter through $\rho =\Delta\phi$ according to Newton's Law of Gravitation. 
  2. Stipulating that inertial mass = gravitational mass to invoke Newton's Law of Motion.    

This is Newton's Cosmic Model describing cosmic interaction on all scales. It is a computable model of extreme simplicity with only one parameter $G$ connecting gravitational force to mass and distance, yet with a universal scope. This is a triumph of classical physics which has not been matched by modern physics. 

We can compare with the Standard Model of particle physics as an uncomputable model of extreme complexity including 19 parameters with a very limited scope:

Newton's Cosmic Model is not a part of modern physics based on the Standard Model without gravitation and Einstein's General Theory of Relativity with gravitation viewed to be incompatible. The unmatched triumph of classical physics is thus not a part of modern physics. This is deeply ironic. It does not help that Einstein ask for mercy: Newton forgive me! It is a travesty.

tisdag 31 januari 2023

The Gravitational Potential Gives Mass to Matter

In previous posts I have presented a non-standard view on the connection between mass density $\rho (x)$ and gravitational potential $\phi (x)$ connected by Poisson's equation

  • $\Delta \phi = \rho$   
where $\Delta $ is the Laplacian differential operator with respect to the spatial coordinate $x$ in 3d Euclidean space and the gravitational force is given by $\nabla\phi (x)$ as the gradient of $\phi$.

The standard view is to consider the mass density $\rho (x)$ somehow creating the gravitational potential and so the gravitational force, through the formula
  • $\phi (x) = \frac{1}{4\pi}\int \frac{\rho (y)}{\vert x-y\vert}dy$,
that is, the gravitational potential/force is created by global summation over the global presence of mass as an instant action at distance. The appearance is that the gravitational potential/force at the position $x$ is the instant effect of the total presence of mass at all points $y$ different from $x$. 

The trouble with this standard view is that generates questions which have never been satisfactorily answered:
  1. How can action be instantly transmitted over arbitrarily large distances?
  2. Is there self-interaction between a point mass and the gravitational potential/force it creates? 
In the Standard Model of fundamental/particle physics, forces are transmitted by force carrying particles but no such particle (named graviton) for gravitational force has been found. It seems that the standard view has reached a dead end.

In the non-standard view the roles of mass density and potential are switched: The potential $\phi (x)$ is then viewed to endow matter with mass density $\rho (x)$ through the formula
  • $\rho (x) = \Delta\phi (x)$  (*)
that is, $\rho (x)$ is created by differentiation of $\phi (x)$.  This is a local instant operation which does not require instant action at distance and thus eliminates questions 1. Further, there is no self-interaction because the flow of information is one-way from $\phi (x)$ to $\rho (x)$. 

The dynamics of a Newtonian Universe can thus be described by (*) combined with Newton's 2nd Law, more precisely in the form of the Euler equations for a compressible gas in terms of gravitational potential, momentum and internal energy as shown in detail here.  

To see the role of a potential, let us we compare with what we see on weather maps as rotational flow around high and low pressure zones with the pressure acting like a potential (click on arrow to start simulation)

We see the trace of air particles moving around high and low pressure zones driven by pressure/Coriolis and inertial forces, in a way similar to planets moving around Suns subject to gravitational and inertial forces, with pressure and gravitational potential playing the same role. 

The power of the gravitational potential is to supply matter with the quality of mass as the capability to react to gravitational force according to Newton's 2nd Law, and then in a next step react the same way subject to inertial forces as an expression of equality of gravitational and inertial mass. 

In this non-standard view, the gravitational potential thus supplies matter with mass and so opens to motion under gravitational force from the potential. The gravitational potential is thus primordial, while it changes according to the dynamics it creates, which can be seen as a form of feed-back. The non-standard view avoids the unresolved problems of the standard view with matter/mass as primordial, with further rationale here.  

The fact that we can see celestial bodies move subject to gravitational force, while we cannot see the gravitational potential, only feel its gravitational force, can give us the impression of the standard view that it is the celestial bodies, which creates the gravitational force by Newton's Law of gravitation. If we could see the gravitational potential we would be led to the non-standard view with the gravitational potential somehow giving mass to matter.  

Ultimately motion is created by the gravitational potential giving gravitational mass to matter to react to gravitational force and then to inertial force with inertial mass equal to gravitational mass. The origin of dynamics as motion in space is thus the gravitational potential.  

PS The gravitational potential vs mass is a hen vs egg problem, with the gravitational potential playing the role of the hen laying an egg by local action, which is in a way understandable. On the other hand the creation of a hen out of an egg is more mysterious as a creation seemingly out of nothing, and so is the original creation of the gravitational potential. 

However it is possible to think of the source as a local oscillation $\bar\phi$ of an original null state $\phi_0 =0$ satisfying $\Delta\phi_0 =0$ with $\Delta\bar\phi =\bar\rho$ where $\bar\rho (x)$ has variable sign representing positive and negative mass, which by gravitational dynamics repel each other and so separate into two Universa with no further contact, where we happen to live in the Universe with positive mass. The creation of the gravitational potential would thus result from a perturbation in an original null state $\phi_0$ satisfying the equation  $\Delta\phi_0 =0$ serving as a laboratory ready for perturbation, like a violin string before the stroke by a bow. The creation miracle is then reduced to the stretching of a string. 

Notice that by the nature of the differentiation action of the Laplacian $\Delta$ a small localised perturbation $\bar\phi$ will give an amplified mass density $\bar\rho =\Delta\bar\phi$ output as an apparent creation out of nothing.

torsdag 26 januari 2023

Hydrogen as Two-Density Schrödinger Equation

This is a continuation of the previous post with a Hydrogen Atom modeled according to Real Quantum Mechanics RealQM  in terms of two spatial charge densities, $\phi (x)$ for the proton $\psi (x)$ for the electron as functions of a Euclidean space coordinate $x$, assuming $\phi$ and $\psi$ have non-overlapping supports filling space meeting at a common boundary $\Gamma$ with some boundary conditions to be specified, starting for simplicity with zero charge density for both proton and electron. 

We start with the ground state with the proton occupying a fixed sphere of diameter $d$ with the electron filling the exterior volume. We characterise the ground state as the state of minimal total energy 

  • $E(\phi ,\psi ) = PE(\phi ,\psi ) + KE(\phi ,\psi)$
  • $PE(\phi ,\psi ) = -\int\frac{\phi^2(x)\psi^2(y)}{\vert x-y\vert}dxdy$
 is mutual potential energy, and  
  • $KE(\phi ,\psi )=\int\frac{d^2}{2}\vert\nabla\phi (x)\vert^2dx+\int\frac{1}{2}\vert\nabla\psi (x)\vert^2dx$
is the sum of proton and electron compression energies (also referred to as "kinetic energies"under the normalisation 
  • $\int \phi^2(x)dx =1$ and $\int \psi^2(x)dx =1$.
Here the coefficient $d$ sets the size of the proton compared to the electron of unit size and we assume that $d$ is small. 

The proton charge density is given by a spherical harmonic as a "blob" of diameter $d$ centered at $x=0$, while for small $d$ the electron charge distribution is close to the standard Hydrogen ground state with $\psi (x)\sim\exp(-\vert x\vert )$. The total energy comes out as the standard electron compression/potential energy $-\frac{1}{2}$ plus proton compression energy as a constant independent of $d$. Letting $d$ tend to zero and neglecting the proton energy makes the proton into a point source as in the Born-Oppenheimer approximation in terms of only electron density, compare PS below.  

Eigenstates of higher energies emerge as stationary points of $E(\phi ,\psi )$ in a variational setting. 

We see that for small $d$ the two-density model thus reduces to the standard electronic wave function with a constant shift of total energy, which does not affect the spectrum since it corresponds to energy differences. Thus the two-density model for Hydrogen may be seen as a trivial extension of the electronic one-density model, but allowing $\Gamma$ to be a free boundary included in the variational setting may open new views on the interaction between proton and electron. One can then ask if the presence of the electron around the proton affects the proton density, as well as ponder different boundary conditions. 

We note that in RealQM the combined density comes out as the sum of proton and electron densities in 3-dimension physical space, while in standard QM it is the product in 6-dimensional configuration space, which is not physical. 

Altogether, we find that RealQM naturally can be extended beyond electronic interaction. One can then address the question why the proton appears to be so much smaller than the electron in e.g. the Hydrogen atom. It reflects that the proton has a much smaller "resistance to compression" than the electron, which can be accepted as a physical fact asking for deeper analysis.   

Note that it is more natural to connect the compression/kinetic energies to spatial size rather than mass, since the quantum mechanical model concerns electromagnetic interaction without effects of inertia/gravitation. More precisely, the coefficient $\frac{d^2}{2}$ in RealQM corresponds to $\frac{1}{2m}$ in stdQM with $m$ the proton inertial/gravitational mass, which is strange since standard QM primarily concerns electromagnetics. Only in molecular modeling using the Born-Oppenheimer approximation with kernel dynamics treated by classical mechanics, does kernel masses enter. In any case, $d$ appears to scale with $\sqrt{m}$ which with the table value $m=1836$ gives $d\approx 0.02$ to be compared with 1 as atom size. 

Returning to the idea of a neutron as an "inverted Hydrogen atom" with the electron at the center surrounded by a proton of size $d$ will give a large increase of electron compression energy which can be released when the neutron decays observed to be around 1 MeV, which suggests an electron size of $10^{-3}$ which may again suggest a proton size $d\approx 0.02$  

Note that we here speak about "electromagnetic" size, which may be different from a smaller inertial/gravitational size as measured in collision experiments. 

PS1 The article On the hydrogen atom beyond the Born–Oppenheimer approximation considers a two-density model in the spirit of stdQM with a combined wave function as a product of proton and electron densities. Model computations suggest that in RealQM one can assume both proton and electron densities to vanish on the common boundary. 

PS2 The two-density model in the above form contains one parameter $d$ which connects proton mass to electron charge/mass with a direct coupling to the non-dimensional fine structure constant $\alpha\approx\frac{1}{137}$ as expressed here.  

onsdag 25 januari 2023

Neutron as Inverted Hydrogen Atom?

Is this a proton charge density surrounded by an electron charge density. Or is it the other way around? 

The Hydrogen atom consisting of a positively charged proton and a negatively charged electron can in Real Quantum Mechanics RealQM  be mathematically modeled in terms of two spatial charge densities, $\phi (x)$ for the proton $\psi (x)$ for the electron as functions of a Euclidean space coordinate $x$, assuming $\phi$ and $\psi$ have disjoint supports (filling space) meeting at a boundary $\Gamma$ signifying that the proton and the electron do not overlap. 

The ground state of Hydrogen is then characterised as the state of minimal total energy 

  • $E(\phi ,\psi ) = PE(\phi ,\psi ) + KE(\phi ,\psi)$
  • $PE(\phi ,\psi ) = -\int\frac{\phi^2(x)\psi^2(y)}{\vert x-y\vert}dxdy$
 is mutual potential energy, and  
  • $KE(\phi ,\psi )=\int\frac{1}{2m}\vert\nabla\phi (x)\vert^2dx+\int\frac{1}{2}\vert\nabla\psi (x)\vert^2dx$
 is the sum of proton and electron compression energies under the normalisation 
  • $\int \phi^2(x)dx =1$ and $\int \psi^2(x)dx =1$.
Here $m\approx 1836$ is the ratio of proton to electron mass. Eigenstates of higher energies emerge as stationary points of $E(\phi ,\psi )$. Further, $\Gamma$ is a free boundary included in the minimisation with specific boundary conditions to be decided. 

A proton-electron configuration which agrees with observations is given by a proton charge density of small radius centered at $x=0$ surrounded by an electron charge density of large radius. In the limit with the proton modeled as a constant charge distribution of vanishing radius, this gives the standard Schrödinger equation for the Hydrogen atom with Hamiltonian
  • $H = -\frac{1}{2}\Delta -\frac{1}{\vert x\vert}$
in terms of the electron charge distribution $\psi (x)$ alone, with $\psi (x)\sim \exp(-\vert x\vert)$ as ground state.  

Now, a neutron is viewed to also consist of a proton and an electron, and so it is natural to ask if the above model can also describe a neutron? That would correspond to a switch of roles with now the electron at the center surrounded by a proton charge density. The compression energy would now be that of the proton resulting in a change of scale with the neutron radius about $\frac{1}{1836}$ of that of a Hydrogen atom.  

In RealQM the size of an electron, in an atom with electrons organised into shells, increases with distance to the kernel, and so electron size is variable. We may expect the same property of a proton with thus increasing size if harbouring an electron inside in the formation of a neutron. The size of a free proton  is estimated to about $10^{-15}$ meter. We compare with a Hydrogen atom of size $5\times 10^{-11}$  which with the above 1836 scaling, gives a proton size of about $10\times 10^{-15}$ when surrounding an electron in a neutron, about 10 times as big as when free.

These are speculations suggested by RealQM as a classical continuum model in terms of non-overlapping charge densities. RealQM can be seen as a form density functional theory which is different from that pioneered by Walter Kohn and Pierre Hohenberg (Nobel Prize in Physics 1998) formed by averaging in a standard multi-dimensional Schrödinger equation. 

Recall that a free neutron is unstable and decays with mean lifetime of 14 minutes into a proton, an electron and an antineutrino (but not a Hydrogen atom), while neutrons are formed in the fusion process of Hydrogen into Helium in a star like the Sun.  

tisdag 24 januari 2023

Quantum Mechanics as Classical Mechanics can be Understood

Feynman: think I can safely say that nobody understands quantum mechanics

The crown jewel of the modern physics of Quantum Mechanics QM is the Schrödinger equation for the Hydrogen atom. Complete Success. Schrödinger rocketed to Fame in 1925.

It is possible to view this model also in terms of classical continuum mechanics as an electron charge density $\psi (x)$ in a potential field $-\frac{1}{\vert x\vert}$ generated by a proton kernel at $x=0$ with the electron charge density resisting "compression" like an elastic body. In this setting the ground state $\psi (x)$ minimises the total energy

  • $E(\psi ) = PE(\psi ) + KE(\psi)$
  • $PE(\psi ) = -\int\frac{\psi^2(x)}{\vert x\vert}dx$ is potential energy 
  • $KE(\psi )=\int\frac{1}{2}\vert\nabla\psi (x)\vert^2dx$ is compression energy
under the normalisation 
  • $\int \psi^2(x)dx =1$. 
More generally, states with larger energy emerge as stationary points of $E(\psi )$ with corresponding eigenvalues and form the spectrum of the Hydrogen atom in full agreement with observations. 

The connection to the spectrum is realised by extending the real-valued $\psi (x)$ into a complex-valued function $\Psi (x,t)=\exp(-iEt)\psi (x)$ also depending on a time variable $t$ with $E$ an eigenvalue, satisfying Schrödinger's equation in the form 
  • $i\frac{\partial\Psi}{\partial t}=H\Psi =E\Psi$ 
  • $H = -\frac{1}{2}\Delta -\frac{1}{\vert x\vert}$
is the Hamiltonian differential operator with eigenvalue $E$. All of this makes perfect sense with the Hydrogen atom modeled by classical continuum mechanics with a static electron distribution around a kernel. In particular, nothing is moving fast and so the Dirac equation with all its complexity from being relativistically correct has no role to play.

The novelty of QM came from viewing the electron compression energy instead as a form of "kinetic energy" arising from a purely formal association of classical Newtonian momentum as mass times velocity, with the differential operator $i\nabla$ with respect to $x$, which generates the Laplacian in the Hamiltonian $H$. 

The terminology "kinetic energy" connects to the Bohr model of the atom with electrons as particles orbiting around a kernel like planets around a Sun. But the Bohr model cannot explain the stability of the ground state since orbiting electrons radiate and loose energy.  The "kinetic energy" attributed to a static electron charge density is the root of the mystery of standard QM obsessed with "electron orbitals". 

A further step away from classical mechanics is taken in stdQM as the standard extension of Schrödinger's equation to atoms with mor than one electron, which is also performed as a formality replacing physical space with configuration space without physical meaning, and as a result resorting to statistics. 

RealQM gives a different extension as classical continuum mechanics in terms of non-overlapping electron charge densities subject to mutual Coulomb repulsion but no self-repulsion.

With the Schrödinger equation for the Hydrogen atom cashed in as a complete success, the main question is how to extend it to atoms with more than one atom while keeping the success. 

In stdQM the extension is made as a formality without real physical rationale into a new form of physics as quantum mechanics conceptually different from classical mechanics, thus creating mystery upon mystery.

RealQM makes the extension within classical continuum physics and thus keeps physical rationale without mystery. 

There is a clear choice: Either the atom can be understood, and then in terms of classical physics, or the atom cannot be understood at all.  

    måndag 23 januari 2023

    KlimatUpplysningen och Cancel Culture 2

    Jag har begärt att Styrelsen för KlimatUpplysningen tar upp den avstängning som utfärdats av Ingemar Nordin, ansvarig för kommentarer till inlägg, vilken jag tidigare rapporterat om,  och specifikt preciserar  vilka av mina kommentarer som motiverat denna drastiska åtgärd. Jag har fått följande svar på min begäran:

    Hejsan Claes!

    Under styrelsens senaste sammanträde diskuterades ärendet angående din avstängning från att kommentera på Klimatupplysningen. Styrelsen är enig om att du har brutit mot kommentarsreglerna och att avstängningen därför är korrekt.

    Alla som vi anser bryta mot kommentarsreglerna får först en varning och om denna inte hörsammas stängs personen av. Så har även skett i detta fall.

    Magnus Cederlöf
    Ordförande föreningen Klimatrealisterna

    Jag läser att jag "brutit mot kommentarsreglerna" men inget alls sägs om vad jag uttryckligen begärt, nämligen precisering av vilka av mina kommentarer som avses.  Jag har upprepat begäran om att detta måste redovisas, om det finns någon rim o reson, och kommer att rapportera svaret. 

    Annars kan vi idag på KlimatUpplysningen läsa vad Ann L-H i sin recension av Elsa Widdings senaste bok har att säga om Ingemar Nordin: 

    Ingemar Nordin, professor i filosofi och vetenskapsteori har ett kort men kärnfullt inlägg om Yttrandefrihet, demokrati och vetenskap (del 2). Han går tillbaka till John Stuart Mills bok, Om Friheten med citatet:

    ”…det utmärkande för den skada som vållas genom att man undertrycker en åsikt ligger däri att man sålunda begår en stöld från mänskligheten, från de efterkommande såväl som från de nu levande, från dem som avviker från åsikten ännu mer än från dem som hyser den.”

    Utebliven öppen information är med andra ord en stöld från mänskligheten en stöld som kan orsaka ödesdigra konsekvenser…Dagens politik liknar alltmer den styrmodell som övergavs av folket i det forna Sovjetunionen för trettio år sedan, skriver Elsa.

    Både Ann L-H och Ingemar Nordin uttrycker mycket hårda ord om den som undertrycker en åsikt, särskilt vad gäller vetenskap kan man förmoda. 

    Men detta gäller uppenbarligen inte mina åsikter som matematiker och vetenskapsman. Inte heller besvaras min begäran om Upplysning om vilken av dessa mina åsikter som inte får yppas, inte ens som kommentar till ett inlägg begärd av Gösta Petterson i egenskap av inläggets författare. Har Ingemar något att säga som kommentar här, om skälet till sitt beslut och i vad mån det är en "stöld från mänskligheten"? 

    söndag 22 januari 2023

    The World is Continuous not Discrete?

    Double pendulum as Lagrangian mechanics in generalised angular coordinates as two discs modeled as particles of finite size carrying mass. 

    The old question if the World on small scales is (i) continuous (fields) or (ii) discrete (particles) is handled by modern physicists by saying that it is both: fields create particles which create fields and so the World is both continuous and discrete. Both fields and particles. Very clever, but is it illuminating and more importantly, can it be true? 

    An example of a continuum is the set $\Re$ of real numbers as digital (decimal o binary) expansions without limit on the number of digits. We may say that $\Re$ offers infinite precision, to be compared with finite precision if a limit is set to the number of digits. 

    We may compare with the resolution of analog photo with no clear smallest size and a digital photo with a smallest pixel, and we may say that with the resolution of today it is difficult to distinguish between analog and digital.  We know that the Digital World is a world of finite precision, but what about the Real World?  

    We know that the physical world has a range of scales from very large cosmological scales to very small atomistic or subatomic scales. It is a natural to believe that there is a biggest scale as the scale of the Universe, but we do not know its size. Atom physics is physics on small scales and it is natural to ask if there is a smallest scale. In quantum mechanics as the physics of small scales, Planck's constant $h$ serves the role of smallest scale of energy and also determines smallest scales in space and time. On the other hand, the mathematical models of quantum mechanics like Schrödinger's and Dirac's equations take the form of differential equations over the continuum of real numbers as continuum mechanics models.  

    The Real World consists, roughly speaking, of matter with mass subject to gravitation and light as electromagnetic waves in a vacuum. It is natural to view a vacuum as a continuum without smallest scale and thus allow light as waves to arbitrarily short wave length/high frequency, even if there are limits because power increases quadratically with frequency. 

    Concerning matter with mass the situation is less clear and has invited to use the concept of particle as something without extension in space yet capable of carrying mass, then as a concept borrowed from macroscopic continuum mechanics modeled as discrete systems of point masses to allow digital computation with finite precision as in the finite element method used in engineering. Here the continuum model remained as the starting point for discretisation for computation. 

    Classical mechanics was perfected in Lagrangian mechanics in generalised coordinates of particle positions and velocities with equations of motion derived from a Principle of Least Action. This was extended to the Hydrogen atom by Both and Rutherford in 2013 with a Hydrogen atom viewed as a little planet system with an electron orbiting around a kernel. But this model could not explain the stability of the ground state and so was replaced in 1925 by Schrödinger's equation for a wave function as a continuum mechanics model. However, in extensions to atoms with more than one electron the particles of Lagrangian mechanics reappeared to serve the statistical interpretation required by the multi-dimensionality of the wave function. 

    Atom physics thus took the form of classical Lagrangian particle mechanics rather than continuum mechanics of solid/fluid mechanics and electromagnetics, although Schrödinger's equation is a continuum mechanics model. Planck's constant $h$ then emerged as the smallest possible action.         

    We find no compelling reason to insist that atom physics is particle physics, nor that an elastic body is the same as the mass-spring system effectively used in (finite element) computation.  

    RealQM offers a continuum model of atoms with the electrons of an atom appearing as non-overlapping continuous charge distributions. See lecture on Structural Mechanics of the Atom.

    Summary: Macroscopic particles of finite small size have physical meaning, while microscopic particles of no size does not seem to make much sense. Microscopics as continuum wave mechanics makes sense. There is no fundamental difference between macroscopic continuum wave mechanics and microscopic continuum wave mechanics, which opens to human understanding of microscopics from experience of macroscopics. Like a Hydrogen atom as a cloud of negative charge attracted by a positive kernel with minimal total energy as kinetic and potential energy.  

    To be compared with the standard view that quantum mechanics cannot be understood, only used as a black box to predict outcomes of experiments.

    torsdag 19 januari 2023

    Self-Interacting Electron: QED Horror

    Audio Feed Back Can Ruin Your Loud Speakers

    Schrödinger's equation (S) describes the Hydrogen atom as a negative electron charge density $\phi (x)$ in the Coulomb potential field $\frac{1}{\vert x\vert}$ generated by a positively charged point kernel at $x=0$, with electron potential energy (combined with "kinetic energy" measured by $\vert\nabla\phi\vert^2$)

    • $\int\frac{\phi^2(x)}{\vert x\vert}dx$     
    of finite size. This is a prefect model of an electron bound in a Hydrogen atom, as basic building block of the Universe. 

    In classical electrostatics the electrical field $E$ generated by a point charge (scaling like $\vert x\vert^{-2}$) appears to have infinite total energy in the sense that the integral 
    • $\int \vert E\vert^2 dx$
    diverges. This is viewed with suspicion because it suggests that an electron as a point charge has infinite energy. The troubling question without answer is to what extent the electron interacts with the electric filed it has generated, so called self-interaction or feedback. 

    Even worse, infinite electron energy is a feature of both Dirac's equation (D) and Feynman's Quantum ElectroDynamics QED both supposed to describe the electron as the ultimate achievement of modern physics. Both Dirac and Feynman viewed this to be a deeply troubling aspect, but to save modern physics from collapse Feynman invented a technique of "renormalisation" getting rid of the infinities captured in Feynman diagrams. 

    We know the phenomenon of audio feedback and its dangers, as with feedback in general. The system my go berserk. Electrons do not go berserk.

    Real Quantum Mechanics RealQM extends (S) to atoms with more than one electron as a system of non-overlapping electron charge densities interacting by Coulomb potentials without self-interaction. Each electron has an individuality by occupying a specific domain in space, and as such is interacting with the kernel and the other electrons through Coulomb potentials. 

    There is no self-interaction. This is like a group of people interacting with each other without anyone interacting with her/himself.

    So we have two theories for the electron. (S) extended to RealQM for electrons bounded in atoms without infinities. QED for "free electrons" with self-interaction and infinities. 

    The electrons in an atom can by shifting configuration back and forth interact with electromagnetics of light outside the atom through the Abraham-Lorentz recoil force and so generate an absorption/emission radiation spectrum as described here. There is no feedback in this system, only balance like in a good audio system. 

    QED seems to say nothing about atoms and atomic radiation and so may be overrated as the jewel of modern physics. 
    Also listen to Wolfgang Pauli in his Nobel Prize Lecture in 1946 about his Exclusion Principle: 
    • At the end of this lecture I may express my critical opinion, that a correct theory should neither lead to infinite zero-point energies nor to infinite zero charges, that it should not use mathematical tricks to subtract infinities or singularities, nor should it invent a 'hypothetical world' which is only a mathematical fiction before it is able to formulate the correct interpretation of the actual world of physics.
    • From the point of view of logic, my report on Exclusion Principle and Quantum Mechanics has no conclusion. I believe that it will only be possible to write the conclusion if a theory will be established which will determine the value of the fine structure constant and will thus explain the atomistic structure of electricity, which is such an essential quality of all atomic sources of electric fields actually occurring in nature.
    Pauli died in 1958 and did not live to experience QED with its infinite zero-point energies and mathematical tricks.

    Connecting to the previous post on the concept of self-energy of an electron as particle, recall that in Newton mechanics there is no self-gravitation, only gravitational between different masses as in RealQM. 

    onsdag 18 januari 2023

    The State of Modern Physics

    Alexander Unzicker gives in his last book Make Physics Great Again: America Has Failed a very critical evaluation of the state of modern physics:

    • All in all physicists have developed a system that keeps itself alive by detaching from observations, by abandoning comprehensible mechanisms and clean mathematics, by postulating arbitrary concepts and by weawing a "theoretical explanation" for every thinkable phenomenon, which amounts to nothing other than fitting fantasy products to measuring values.
    These are tough words, but probably very true and as such cannot be directly refuted and so will be met by total silence by the physicists setting the agenda of contemporary physics. 

    A main theme on Unzicker's Real Physics youtube channel is the question if all constants ultimately can be reduced to a few fundamental physical constants like the gravitational constant $G$, the speed of light in vacuum $c$ and Planck's constant $h$. The Standard Model of fundamental/particle  physics includes 29 constants, which adopting Unzicker's view means that it is not fundamental physics. 

    The value of physical constants directly connects to the specification/definition of units used in experimental or observational physics. The definitions reflect specifications to make measurements. In the new 2019 SI standard 
    • Time in seconds is measured in terms of number of oscillations of a certain Cesium atom.
    • Length in meter is measured in lightseconds as the distance traveled by light in vacuum per second.
    • Mass $m$ in kilo is measured in terms of h and c assuming that Einstein's Law $E=mc^2$ and Planck's Law $E=hf$ with $f$ frequency, are valid.     
    What is of special interest here is that by definition the speed of light is set to be exactly = 1 lightsecond per second or $c=1$, which thus by definition makes the speed of light constant. With a common unit of time for all observers, the choice of length unit for all observers (possibly moving with different speeds) is to be such that the speed of light is exactly = 1. 

    Einstein's postulate that the speed of light is constant stated as a physical fact, which could be wrong, is thus turned into a definition which cannot be wrong. It is just an SI standard to be adopted by all observers: $c=1$.

    We meet the same phenomenon with the kilo defined assuming $E=mc^2$ and $E=hf$. This means that $E=mc^2$ is made into a definition just like $c=1$, by adjusting the definition of kilo so that $E=mc^2$.

    We meet here a confusing mixing of physical fact and definition, typical of Einstein's physics, which makes it possible for Einstein and all followers to be 100% sure that the speed of light is constant and that energy is equivalent to mass according to $E=mc^2$. 

    But mixing a proposed physical law, which may false, with a definition, which cannot be false, can give you the false impression that the physical law is a true physical law. 

    This aspects are very difficult to discuss with physicists who have been trained that Einstein's postulates that the speed of light is constant and energy is equivalent to mass, really are true postulates about physics, which in addition to being physically true are ideal as standard. This is like mixing analytical and synthetic truths in logical positivism which is an endless source of confusion making modern physics into a true mystery.

    More on this theme in Many-Minds Relativity. There is a limit to the confusion.

    By definition all humans are equal, but we know that this is not really so. 

    tisdag 17 januari 2023

    Accelerating Expanding Universe: Reality or Illusion?

    Hubble's Law collects observations of redshifts of the light from galaxies suggesting that the Universe is expanding away from the Earth at speeds proportional to the distance from the Earth. The Nobel Prize in Physics was awarded work showing larger expansion suggesting an Accelerating Universe with redshifts seemingly corresponding to superluminal speeds at the edge of the observable Universe. 

    Speculations about an enormous amount of dark energy as driver of the acceleration expansion were made but, nothing is known about this type of energy supposed to make up 68% of the total energy of the Universe. 

    Other speculations seek to solve the mystery generated by the observations of large redshifts by suggesting they are just illusions resulting from measurement techniques. Like the apparent decrease of size with view distance.

    Let us make a connection to Many-Minds Relativity where velocities are computed from observed Doppler effects and includes a law of adding two velocities $v$ and $w$ from composite Doppler effects of the form 
    • $v+w+vw$ 

    as a variant of Einstein's velocity addition law of Special Relativity. Here $v+w+vw$ is the velocity perceived by an observer X moving with velocity $v$ with respect to another observer Y observing the velocity $w$. 

    The computed velocity is seen to be larger than the standard $v+w$, and will increase with increasing number of composite Doppler shifts, which could be connected to increasing distance. In the limit that gives from a nominal real velocity $v$ a computed velocity $\exp(v)$ suggesting an expansion of the Universe which is exponentially increasing with distance. We understand that this is an illusion depending on the way we compute velocities from composite Doppler shifts.

    So, we have two possibilities of explaining observations of an expanding Universe: 

    1. dark matter
    2. illusion. 

    Which is more reasonable? To believe in 1. requires a massive addition to the total energy of the Universe, a big deal. To believe in 2.  requires simply some understanding of how velocities are computed from redshift observations, no big deal. Your choice.