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.

Compare with Gravitational World Model and Cosmic Interaction on Leibniz World of Math.

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 

• $E(\phi ,\psi ) = PE(\phi ,\psi ) + KE(\phi ,\psi)$

where

• $PE(\phi ,\psi ) = -\int\frac{\phi^2(x)\psi^2(y)}{\vert x-y\vert}dxdy$

 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.  

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 

• $E(\phi ,\psi ) = PE(\phi ,\psi ) + KE(\phi ,\psi)$

where

• $PE(\phi ,\psi ) = -\int\frac{\phi^2(x)\psi^2(y)}{\vert x-y\vert}dxdy$

 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.  

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

• $E(\psi ) = PE(\psi ) + KE(\psi)$

where

• $PE(\psi ) = -\int\frac{\psi^2(x)}{\vert x\vert}dx$ 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 

• $i\frac{\partial\Psi}{\partial t}=H\Psi =E\Psi$ 

where 

• $H = -\frac{1}{2}\Delta -\frac{1}{\vert x\vert}$

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.  

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.

Vänligen,
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"? 

 

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.

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. 

• With quantum physics, who needs drugs? (Richard P. Feynman in QED: The Strange Theory of Light and Matter)

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. 

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. 

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.    

Energy Cannot Be Equivalent to Mass

Identifying Mass with Energy is the same as identifying Being with Doing. Not so Clever.

The most famous formula attributed to the most famous physicist all times is Einstein's Law

•  $E=mc^2$      (1)

apparently stating that energy $E$ is equal or "equivalent" to mass $m$ multiplied by the large coefficient $c^2$, where $c$ is the speed of light in vacuum.  

A modern physicist will inform you that (1) is a consequence of Einstein's Special Theory of Relativity SR, even if the details of such a derivation cannot be recalled. To counter further questions you will be informed that in fact (1) is just a special example of of a more "relativistically correct" Einstein Law of the form 

• $E^2=(pc)^2+(mc^2)^2$,     (2)

where $p$ is momentum, which is supposedly easier to prove even if details of proof cannot be recalled.  You will also be informed that both (1) and (2) have been confirmed by the same experiments. And do not forget that atom bombs build on (1) and so show the amazing "power" of this "equivalence".

First, let us seek to understand the meaning of (1). We recall that in the physics of thermodynamics 

• energy is capacity to do (mechanical) work 
• work = force x distance measured in Joule = Newtonmeter.   

Energy comes in forms of large scale ordered kinetic energy and potential energy and heat energy as small scale unordered kinetic energy. Here the kinetic and potential energies associated with a body are extrinsic or relational quantities i.e. depending on the environment of the body. The energy produced by the decent of the bob of a classical pendulum clock depends on bob weight and decent distance. 

The typical expression of kinetic energy of a body of mass $m$ and and speed $v$ is viewed to be $m\frac{v^2}{2}$ as the work required to bring the body from rest to speed $v$, with the rest state as the reference state. This energy/work can be regained letting the body impact with an environment at rest.

Likewise potential energy is created by lifting an object from some reference level, which can be regained by letting the body return to the reference level. Large scale ordered kinetic and potential energy can be transformed to heat energy as small scale unordered kinetic energy in turbulent dissipation, and the 2nd Law of Thermodynamics puts limits to recovery of large scale energy from heat energy, that is limits on production of work from heat energy. 

We conclude that thermodynamical energy is an extrinsic relational quantity which is measured in terms of what it can do depending on the environment. 

What then is the mass $m$ of a body? Is it an extrinsic or intrinsic quantity/quality? Well, mass is inertial mass which is equal to gravitational mass as resistance to motion induced by a force.  This is expressed in Newton's 2nd Law $m=\frac{F}{a}$, where $F$ is force and $a$ acceleration. This is an intrinsic quantity in terms what it is. All bodies independent of quantity of mass react the same way on gravitational force, that is,  carry an intrinsic property of reacting to inertial or gravitational force. We can think of the mass of a body as being equal to he sum of the masses of the pieces of atoms forming the body. All the atoms react the same way on inertial or gravitational force, and this explains why a body is not ripped apart by such forces. Mass is maybe the most intrinsic quality of all. 

Sum up: Energy is extrinsic (what it can do) while mass is intrinsic (what it is). Is it possible that an extrinsic quantity can be equivalent to an intrinsic quantity as expressed by $E=mc^2$? There seems to be no sufficient reason to insist that  "energy is equivalent to mass", so the answer can only be No. 

Let us now turn to (2) as an "improved version" of $E=mc^2$, keeping the first term, that is let us look at the Law, motivated by Many-Minds Relativity MR:

• $E=pc$,     (3)

where $p=mv$ is momentum $v$ velocity. This Law seems to make a bit more sense since $p$ is both intrinsic thorough $m$ and extrinsic through $v$, but the previous post shows that this only an illusion. There is no sufficient reason to insist that "energy is equivalent to momentum".

When confronted with the above arguments a modern physicist will say that "is is all wrong" without showing what is wrong. 

In any case, the bottomline may well be that the by many witnessed crisis of modern physics ultimately depends on (1) as a foundational relation that does not make sense. More detailed arguments in recent previous posts. 

Photons 

Physicists use (2) with $m=0$ to give momentum to the massless photon with energy $E=h\nu$ through the connection $p=\frac{h}{\lambda}=\frac{h\nu}{c}$ with thus $E=pc$. Magic!

Thermodynamics and Atom Physics 

$E=mc2$ is supposed to be a result of SR which does not describe thermodynamics nor atom physics. 

Basic postulates of thermodynamics say that mass and energy are conserved. This means that $E=mc^2$ in the sense of actual transformation of mass into energy cannot happen in thermodynamics. Unless you say that by definition energy and mass are equal and so $E=mc^2$ is a tautology without physical meaning. 

Can $E=mc^2$ or $E=pc$ have a meaning in atom physics, when SR and MR say nothing about atom physics?  Or is also here $E=mc^2$ a tautology without physical meaning? Probably. MR says that (3) is an illusion. Einstein was a master of double play mixing physical fact with definition/logical truth. SR is filled with this ambiguity: Is time dilation and length contraction real or illusion? Ask your physics professor!

 

E=mc2 and Large Red Shift in Many-Minds Relativity

The Galaxy GN-z11 is seen to recede at 11 times the speed of light with large redshift.

Many-Minds Relativity MR presents and alternative to Einstein's Special Theory of Relativity SR, which gives new light to Einstein's $E=mc^2$ as a fundamental postulate of modern physics as well as an explanation of large red shifts observed in receding galaxies. 

Many-Minds Relativity leads to a modified version of Newton's second law of the form 

• $F=\frac{m}{1+v}\dot v$     (MR1)

where $F$ is force, $m$ is (inertial/gravitational) mass, $v$ is the velocity of a body approaching ($v<0$) or receding ($v>0$) as observed by an observer $O$ equipped with a standard clock measuring time $t$ while sitting still at the origin of a Euclidean coordinate system, with speed of light normalised to 1 and $\dot v=\frac{dv}{dt}$. 

This gives an apparent increase of mass in approach making $v>-1$ and an apparent decrease of mass in recession allowing $v$ to increase without limit from a constant force $F$.

 

A rocket with mass $m=1$ launched by O at time $t=0$ supplied with constant propulsion force $F=1$ would thus with time be seen by O to recede with the velocity $v(t)=t\exp(t)$ as solution to (MR1) thus  with seemingly exponentially increasing velocity and corresponding arbitrarily large Doppler shift.  This connects to the observed large red shift of far away galaxies increasing with distance. 

We recall the velocities in MR are computed from Doppler shifts and that (MR1) is the result of composite Doppler shifts. 

We compare with Einstein's relativistic version of Newton's 2nd Law of the form

• $F=\frac{m}{\sqrt{1-v^2}}\dot v$   (SR1)

with an apparent increase of mass in both approach and recession, seemingly in contradiction to recession velocities larger than the speed of light.

Let us now make a connection between MR and Einstein's $E=mc^2$. Using that $\frac{m}{1+v} = 1-v$ with error scaling with $v^2$, we can reformulate (MR) into

• $F=(m - P)\dot v$

where $P=-mv$ as momentum can be seen as a change of mass $P=\Delta m$, which without normalisation to $c=1$ reads 

• $Pc = \Delta mc^2$.       (MR2) 

as an apparent relation between momentum $P$ and mass change $\Delta m$. This relation closely connects to the following (SR) version of Einstein's $E=mc^2$ viewed to be a more "relativistically correct" version: 

• $E^2 =(pc)^2 + m^2c^4$.   (SR2)

We see that (MR2) is contained in (SR2). 

We understand that (MR2) to O can be seen as a connection of momentum to change of mass in the same spirit as Einstein's $E=mc^2$ connects energy to change of mass, but that this is a consequence of the system of observation used by O. There is no sufficient reason for O to believe that the mass of the body under observation effectively changes in accordance with momentum (or energy). 

To explain the change of mass in (MR2) and (SR2) to the scientific community, $O$ as a smart observer can say that this is no real change of mass only an apparent change or illusion. In addition $O$ can give an explanation of the observed large red shifts in recession for which no convincing explanation is given in standard cosmology. 

The highest-confirmed spectroscopic redshift of a galaxy is that of GN-z11, with a redshift of $\frac{v}{c} = 11.1$ that is with a velocity $11.1$ times the speed of light, see image above.

As concerns apparent dependence of mass on energy, which is not real, we can compare with the apparent shrinking of the size of an object when viewed at distance. Only a person equipped with magical thinking would conceive this as a real shrinking of physical size.

The longer the distance to the tree, the smaller the view angle and apparent size on the retina:

Einstein's 1905 Kick-off of E=mc2: Definition?

Einstein kicks off modern physics in the last of the five articles from his Annus Mirabilis 1905 as a short note starting with the question:

• DOES THE INERTIA OF A BODY DEPEND UPON ITS ENERGY-CONTENT?

and ending with the answer:

• If a body gives off the energy L in the form of radiation, its mass diminishes by $\frac{L}{c^2}$. The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference, so that we are led to the more general conclusion that
• The mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same sense by $\frac{L}{9}\times 10^{20}$, the energy being measured in ergs, and the mass in grammes.
• It is not impossible that with bodies whose energy-content is variable to a high degree (e.g. with radium salts) the theory may be successfully put to the test.
• If the theory corresponds to the facts, radiation conveys inertia between the emitting and absorbing bodies.

This is nothing but $E=mc^2$, which thus to Einstein was only a loose hypothesis in 1905 (If the theory corresponds to the facts), but became a truth after proclaimed experimental conformation to a very high precision, much welcomed by Einstein as you can hear above: 

• It followed from the special theory of relativity that mass and energy are both but different manifestations of the same thing -- a somewhat unfamiliar conception for the average mind. Furthermore, the equation E is equal to m c-squared, in which energy is put equal to mass, multiplied by the square of the velocity of light, showed that very small amounts of mass may be converted into a very large amount of energy and vice versa. The mass and energy were in fact equivalent, according to the formula mentioned above. This was demonstrated by Cockcroft and Walton in 1932, experimentally.

As a 100 year celebration of Einstein's $E=mc^2$ a team at MIT including David Pritchard presented an experimental conformation with improved accuracy of one part of a million, with the following caveats by Pritchard:

• In spite of widespread acceptance of this equation as gospel, we should remember that it is a theory. It can be trusted only to the extent that it is tested with experiments.
• Determining the mass difference requires the individual masses to be measured with the incredible accuracy of one part in 100 billion -- equivalent to measuring the distance from Boston to Los Angeles to within the width of a human hair!
• This doesn't mean it has been proven to be completely correct. Future physicists will undoubtedly subject it to even more precise tests because more accurate checks imply that our theory of the world is in fact more and more complete.

So we still cannot be sure. We should also be aware that if a physical law is confirmed to an extreme precision, then it may be that the law is not something created by Nature, but rather a logical necessity created by human minds as simply a definition. The equivalence of energy and mass may well be true by definition and so exactly true and then there is no wonder if experiments can confirm with extreme precision.

 

It is like experimental confirmation to a very high precision that there 100 centimeters on meter, which certainly can attract funding, although rather meaningless...

The equivalence of inertial and gravitational mass comes with the same ambiguity as definition or physical fact. Why should Nature play with two different notions of mass? Compare with Many-Minds Relativity.

Feynman prides himself of having predicted using his theory of QED, the anomalous magnetic dipole moment of the electron to a precision of better than a part in a billion. Again too precise to be credible as an agreement with real physical fact, rather than definition?

Experimental evidence

Here a neat little experiments which you can do with a pot of water and a kitchen scale: Heat the water allowing it to gain heat energy and check if its mass increases, and report back!

Another is to climb 10 stores and check if your mass has increased, or descend instead if you want loose weight:

Easy way loose body mass, if needed.

 

Weird and Strange Modern Physics based on E=mc2 and E=hf

There is no sufficient reason for the Universe to not be Eternal without beginning and end.

Modern physics is built on the following two postulates formulated by Planck (1900) and Einstein (1905) as essence of quantum mechanics and theory of relativity:

• $E=hf$ where $E$ is energy and $f$ light frequency mediated by Planck's constant $h$.
• $E=mc^2$ expressing equivalence of energy $E$ with mass $m$ mediated by $c^2$ with $c$ the speed of light in vacuum.

In the 2019 SI standard of units the following values of $h$ and $c$ are set by definition:

• $h=1.054571817\times 10^{–34}$ Joule per Herz.   (small)
• $c=299 792 458$ meter per second.     (big)

Einstein's $E=mc^2$ is then used to define kilo as the unit of mass in terms of $h$ and $c$ with details in this post. 

Modern physicists all express that modern physics is strange or more precisely that nature is weird. 

It is strange to insist that energy has to be counted as integer multiples of a smallest chunk or quantum of energy $h$ of light. It is weird that light of frequency $f$ consists of streams of light particles named photons of size $hf$, when it is known that light is an electromagnetic wave phenomenon without smallest scale. 

It is strange to insist that energy as potential to do work can be equivalent to mass as gravitational/inertial mass as resistance to force/motion. It is like insisting that you eat energy/calories and not food. 

The most weird outcome of modern physics is the atomic bomb viewed as the ultimate demonstration of the correctness of Einstein's equivalence of energy and mass. The enormous energy released in the explosion of an atomic bomb from the enormous factor $c^2$ in Einstein's $E=mc^2$, has been exploited by physicists to show the weird power of modern physics thus suppressing any criticism or doubt that modern physics makes sense. But atomic bombs do not make sense...

A consequence of the equivalence of energy and mass, is that mass is lost in exothermic chemical reactions when molecules recombine to release energy, which however can be dismissed as something of no real importance because the loss of mass is so incredibly small, like the mass of the angels on a knives edge of the Scholastics.

But the release of energy in nuclear reactions is so big that a corresponding loss of mass must be made in the best case into an observable fact, when insisting on $E=mc^2$. To start with the loss of mass is referred to as a mass defect indicating something strange, which is computed according to $E=mc^2$ and then cleverly is used as evidence that mass defect is real even if strange, although only computed. Another thing is to measure the mass defect in nuclear reactions, which is not easy because nuclear reactions are delicate to handle and to weigh on a scale to determine gravitational mass. But of course the SI definition of mass in terms of energy can help to show that mass and energy are equivalent, then by definition. 

We have now identified why modern physics is viewed to be both strange and weird: Planck and Einstein.

But is it necessarily so that Nature is weird and modern physics is strange. What if Nature is not really weird, because something that is weird cannot exist over time, and then modern physics would not have to be strange.

The classical view is that both energy and mass is conserved. The number of protons of the Universe is then constant, which means that the Universe has no beginning and no end. This is a simple reasonable cosmological theory, which is hard to dispute, and in addition may be true. A reasonable Universe has a bigger chance of existing than a weird Universe, and also to be more understandable as not being strange. 

     

If you ask a contemporary physicist about the physics of $E=mc^2$ and $E=hf$, you will only get the answer that this is all "in the books" combined with a poodle : Sure,  it is strange and weird, but that is the way it is and everyone asking for some rationality is a crackpot. 

This was not the attitude of Planck, who was very unhappy with his breach from classical continuum physics introducing $h$ as smallest possible chunk of energy. It was Einstein who opened the door to strange and weird modern physics in his quest to trump Newton by opening the door to modernity. Einstein masterfully played the double game of confusing ontology and epistemology allowing strange ideas of human conception to be the same as reality.    

Is Mass Converted to Energy in Fusion/Fission of Atoms?

According the Einstein's $E=mc^2$ the energy released in fusion/fission of atoms corresponds to a decrease of mass. The atoms before fusion/fission have more mass than after, with the mass difference being transformed to energy. 

The process of fusion/fisson of atoms is thus considered to be different from chemical reactions generating energy from recombination of the electronic clouds of molecules/atoms/ions into new energy levels in exotermic reactions producing energy and in endothermic reactions consuming energy. Her the total mass of the molcules/atoms/ions involved does not change, only the total electronic energy level, up or down. 

A molecule/atom/ion is here considered to be one or more positively charged kernels surrounded by negatively charged electrons held together by electromagnetic Coulomb forces with corresponding electronic energies.  

In the same way atom kernels are viewed to consist of collections of protons and neutrons held together by the strong force overriding electromagnetic repulsion between protons with corresponding nuclear energies. In fusion/fission atomic kernels recombine just like electrons clouds of molecules/atoms/ions into new energy levels with corresponding production/consumption of energy. Does here the total mass change?  

In modern physics it does because energy is viewed to be equivalent to mass according to Einstein's $E=mc^2$. 

In classical physics energy mass is inertial/gravitational mass and so is not expected to change under recombination of molecules/atoms/ions, because a sufficient reason in the spirit of Leibniz is lacking. Recombination of electron configurations into new electronic energy levels is enough. This is what is observed. Reorganising a truck load does not change its mass/weight, but possibly its potential energy by putting things on top of each other.  

Why expect anything different when reorganising collections of protons and neutrons with corresponding change of nuclear energy?  Is there any sufficient reason? If not, then what?

But what about experiments? Isn't it true that 0.1% mass is lost in fission energy? Maybe, but measurement of inertial/gravitational mass is very delicate. How do you measure the loss of mass in an atomic bomb explosion? 

The fission mass of Little Boy was about 1 kilo releasing about $64\times 10^{12}$ Joule, to be compared with the $10^{17}$ Joule of the SI standard based on Einstein's $E=mc^2$ discussed in the previous post, with thus a formal loss of mass of less than 0.1%. Was it measured?

We may compare with the discussion of phlogiston theory predicting a loss of mass in chemical reactions into phlogistons of energy, which showed to be wrong because mass showed to be conserved.   

 

Is E=mc2 without Meaning?

As noted in the previous post the new 2019 SI definition of kilo kg as unit of mass is based on Einstein's 

• $E=mc^2$      (E)

stating equivalence of energy $E$ and mass $m$ mediated by the speed of light $c$, which is viewed to be signum of the progress from classical physics to modern physics of relativity and quantum mechanics. 

Endless speculations have been devoted to give meaning to equivalence of energy and mass apparently expressed by (E). But is it really possible to give a meaning or is (E) meaningless? 

Let us consider some basic facts, starting with units. Energy is expressed in Joules with 1 Joule = 1 Newtonmeter as the work performed by force of 1 Newton over a distance of 1 meter. Energy is here viewed as a capacity to do work measured in units of work = force x distance or 

• Joule = Newtonmeter.      (1) 

Next, mass $m$ is classically viewed as a measure of resistance to motion or inertial mass expressed in Newton's 2nd Law

• $m = \frac{F}{a}$

where $F$ is force and $a$ acceleration. When $F$ is gravitational force $m$ is referred to as gravitational mass which is equal to inertial mass with unit 

• $\frac{Newton\times second^2}{meter}$.     (2) 

We see that the units in (1) and (2) are very different and requires the coefficient $c^2$ in $\frac{meter^2}{second^2}$ to harmonise. 

There is classically no relation between energy as capacity to do work and inertial/gravitational mass. 

What Einstein did with $E=mc^2$ was to make energy "equivalent" to mass thus breaking completely with classical physics where there is no relation between energy and mass. This break is viewed to be the main heroic accomplishment of modern physics from the hands of Einstein. Paradoxically, this was never awarded any Nobel Prize, evidently because the Nobel Committee could not understand the meaning of (E).

Einstein thus connected two entirely different aspects of physics, namely work and inertial/gravitational mass, which have no connection whatsoever. No surprise that this caused a monumental confusion which opened modern physics to also other forms of confusion. 

To give perspective on the absurdity of $E=mc^2$ recall from the previous post that transforming 1 kg (of e.g. sea water) per second into energy is "equivalent" to a power of $10^{17}$ Watts, to be compared with the power of 1 nuclear reactor of $10^{9} $ Watts, thus equivalent to the combined power of 100 million nuclear reactors! Can we conclude that (E) lacks meaning?

Recall that $E=mc^2$ is the main result of Einstein's special theory of relativity, which is critically analysed in Many-Minds Relativity.

Recall further that Einstein uses the concept of "rest mass" as the mass of a body at rest (in some coordinate system or with respect to other bodies), carrying the idea that the kinetic energy of a body in motion will add to the "relativistic mass" of the body as being bigger than the "rest mass". If you do not find this confusing, you need to study the question in more depth.  

Not Natural New 2019 SI Definition of Unit of Mass

The Kibble balance is an impressive instrument used to specify a new of unit of mass.

The 2019 SI definition of units gives a new specification of the unit of mass as kilo $kg$ based on Einstein's formula $E = Mc^2$ where $E$ is energy in joule $J$, $M$ is mass in $kg$ and $c$ is the speed of light in meter $m$ per second $s$, with  

•  1 kilo = 89875517873681764 J     (*)

and by SI definition $c=299792458\, \frac{m}{s}$. 

Here second $s$ is defined as the duration of exactly 9192631770 periods of certain radiation from a Cesium atom, and meter $m$ in terms of the distance traveled by light per second assumed to be exactly 299792458 meters. The new choice of units connect to old units but the exact values are assigned by definition. 

Further,  $J$ is defined in terms of jouleseconds $J\cdot s$ by specifying Planck's constant $h$ to be exactly equal to $1.054571817\times 10^{−34}\, J\cdot s$, which by a special electromechanical instrument named Kibble balance gives the value (*). 

We see that the unit of mass is defined in terms of second, meter and Plancks constant $h$ assuming Einstein's formula $E=mc^2$ together with Planck's light/photon energy formula $E=h\nu$ to make a connection through the Kibble balance between (gravitational) mass and electric/light energy. 

Many other possibilities of replacing the International Prototype of the Kilogram (IPK) in Paris, named Le Grand K (The Big K), were discussed before settling on using Planck's and Einstein's formulas arguing that they are the most fundamental relations of all of physics. 

In other words the new SI  definition of unit of mass is a hommage/tribute to Planck and Einstein representing modern physics with Le Grand K simply old physics.

But is it natural? The result is that the energy of a mass of 1 kg is equal to the energy of a collection of photons with frequencies summing to $1.356392489652\times 10^{50}$, which is not very illuminating. 

In other words, insisting on Einstein's $E=mc^2$ has very little to do with actual physics. We know that energy can take different forms as kinetic, potential, chemical energy and nuclear energy with possibly a connection to $E=mc^2$ in nuclear energy. But not else, and so the present SI unit of mass lacks good reason as long as controlled nuclear fusion is far into the future, if ever.  

Further, Planck's key formula $E=h\nu$ for photon energy with $\nu$ a natural number, expresses that energy can only take discrete values as multiples of a smallest quanta of size $h$. Planck did not like this idea, which he used only as a last resort in a hopeless situation as explained in Computational BlackBody Radiation offering a new theory in the form of continuum wave mechanics without smallest quanta. Compare with What, exactly, is a photon?  

A more natural definition of a unit of mass would be in terms of a certain number or atoms (the Avogadro project) of e.g. gold as a new gold standard of physics. But that would be classical physics, which has to be replaced by modern physics, even when it does not make sense, to motivate continued funding...and it seems to work...

 

Empty Mantra of Particle Light Quanta in Photoelectricity

Grand piano as radiating atom

The story of the modern physics of quantum mechanics says that it all started with Einstein's 1905 "heuristic explanation" of the Law of Photoelectrity returning to Newton's particle view of light of frequency $\nu$  as consisting of little lumps or energy or photons of size $h\nu$, with $h$ a certain small constant today normalised to 

• $h=4,135667696\times 10^{-15}$ electronVolts per Hz.   (P)

Einstein's heuristics was met with total skepticism since light was well known to be an electromagnetic wave phenomenon precisely described by Maxwell's equations. Moreover the Law Photoelectricity of the form 

• $E = h\nu + W$          (L)

was well know long before 1905, with here $E$ electron energy in electronVolts and $W$ "release energy". In any case Einstein received the Nobel Prize for the "discovery" of (L) and not for his "heuristic explanation" of (L) based on energy quanta/photons, which nobody then believed in.  

But the Prize gave credibility to Einstein and so his particle idea of light as consisting of little lumps of energy entered as an element of the new quantum mechanics formed in the 1920s. 

Let us now explain (L) as an expression of Schrödinger's equation for Hydrogen discussed in the previous post The Real Essence of Quantum Mechanics, which is a wave equation without particles:

• $i\frac{h}{2\pi}\exp(-i\frac{E}{h}2\pi t)\Psi = H\Psi$,     (S)

where $\Psi (x,t)$ is a wave function depending on a space variable $x$ and time variable $t$ and $H$ is Hamiltonian operator with eigenvalue $E$ representing electron energy. The solution of (S) is a harmonic oscillation with frequency $\nu =\frac{E}{h}$ in Hz, which carries the connection $E=h\nu$ as connection between electron energy and frequency, with a connection to light through the line spectrum of Hydrogen with $E$ as a "beat frequency" as difference between eigenvalues. The value of Planck's constant (P) is determined to make frequency predicted by (S) fit with observation of the line spectrum of Hydrogen, thus as a calibration of (S) to fit observation, effectively determining a relation between kinetic spatial energy and potential electron energy in (S).   

We are thus led to the relation $E=h\nu$ between electron energy and light frequency from Schrödingers wave equation as an expression without need of any particle interpretation. Planck's constant $h$ appears as conversion factor between electron energy and light energy. 

Returning now to (L) we see that modulo the release energy $W$ independent of frequency, (L) is nothing but $E=h\nu$ derived from Schrödinger's equation for the Hydrogen atom, which expresses the conversion of light energy into electron energy realised in photoelectricity. No need here to speak about lumps or energy or photons as having physical realisation. The Mantra of Particle Quanta in Photoelectricity is empty. The wave equation (S) is enough. 

Yes, you can determine Planck's constant $h$ by shining light on a metal surface and observe the "stopping potential" bringing the flow of electrons produced by the light to a stop, thus measuring per electron $E$ in Volts and knowing the frequency $\nu$ determining $h=\frac{E}{\nu}$. 

The line spectrum of Hydrogen shows that a Hydrogen atom acts like a "light piano" generating a discrete spectrum of "light tones" under excitation as wave mechanics of strings. No need to believe a piano as being "quantised" just because it generates a discrete spectrum of tones. No need to believe an atom being "quantised" just because it has a discrete line spectrum. No need of "particles of energy". More on RealQM.   

Einstein as young patent clerk in 1905 with great ambitions to become a name in physics, however with little research experience, simply had to "find something" and he did. 

Planck determined a value of $h$ from assuming a high-frequency cut-off scaling with $\frac{T}{h}$ where $T$ is temperature, in the spectrum of blackbody radiation. Observing the spectrum cut-off for some temperatures $T$, allowed Planck to determine a value of $h$ up to 4 percent. Planck resorted to particle statistics of assumed quanta of smallest size $h$ to motivate the cut-off. 

Computational BlackBody Radiation gives a different view based on wave mechanics free of statistics motivating cut-off by a principle of "finite precision computation".  

Summary

RealQM and Computational BlackBody Radiation show that Planck's constant serves the following roles: 

• Conversion factor between electronic and light energy.
• Cut-off in blackbody radiation.

Nothing here says that atomic physics is particle physics. Continuum wave physics can describe the physics originally motivating introduction of particles/energy quanta. This is a relief resolving the unsolvable artificial problems coming from insisting on discreteness on small scales.    

Microscopics of Macroscopic Continuum Physics

Continuum waves even on smallest scale.

Quantum mechanics as the crown jewel of the modern physics of the 20th century is commonly viewed to be fundamentally different from classical physics reaching full bloom towards the end of the 19th century with Maxwell's equations for electromagnetics. Together with Navier's equations for solid mechanics and Navier-Stokes equations for fluid mechanics this offered a complete picture of the World in the form of continuum physics described by partial differential equations in 3 space dimensions and 1 time dimension.

Quantum mechanics is viewed to describe the microscopics of small scale atom physics while classical continuum physics is viewed to describe macroscopics of bigger scales. A consensus developed to view the microscopic world to be fundamentally different from the macroscopic world, the reason being that the quantum mechanics of microscopics could not be understood in classical terms of continuum physics. 

In short, classical continuum physics could be understood and used as a reasonable model of the macroscopic world, while quantum mechanics could not be understood as a resonable model only used. 

The reason quantum mechanics cannot be understood is that it is based on Schrödinger's equation in a multi-dimensional configuration space without reasonable physical interpretation. Quantum mechanics is unreasonable because Schrödinger's equation is unreasonable. Quantum mechanics is viewed to be fundamentally different from classical continuum physics because Schrödinger's equation is fundamentally different from the models of continuum physics, more precisely no agreement has been reached concerning its physical meaning despite 100 years of dispute. 

Is then Schrödinger's multi-dimensional equation the only thinkable model of the microscopics of atoms? Maybe, but anyway I test as Real Quantum Mechanics RealQM a different model, which has the form of classical continuum physics and as such can be understood in physical terms. 

With RealQM there is no fundamental difference between microscopics and macroscopics since all physics is described as continuum physics. This is not unreasonable since in continuum physics there is no smallest scale, as this is the nature of the continuum like the continuum of real numbers where more decimals always can be added if needed. 

The beauty of continuum physics is that it can handle all scales from microscopics to macroscopics in a unified way. In continuum physics there are no (elementary) particles of zero spatial extension. Everything is waves and matter with spatial extension, which can be captured in the partial differential equations of continuum physics. This is physics without the mysteries of standard QM.