The Deep Secret of $E=h\nu$ Uncovered = 0

The value of Planck's constant $h$ is supposed to carry a deep secret of the atomic physics captured in the Schrödinger Equation SE of Quantum Mechanics QM as the foundation of modern physics. A deep secret of a microscopic world which is fundamentally different from the macroscopic world we can fathom by direct experience. A strange world of the modern physics emerging in the beginning of the 20th century, which "nobody understands" including the physical meaning of Planck's constant $h$. 

In the new 2019 SI standard of units, the value of $h$ is specified to be exactly $h=6.62607015\times 10^{−34}$ Joule-seconds, which is a very small number viewed to hide a deep secret, while appearing as an arbitrary unit conversion factor. 

Let us seek to untangle the secret in detail. We recall the message of modern physics of the existence of a smallest quantum of energy $h\nu$ associated to a wave of frequency of $\nu$ showing that the microscopic world is discrete and not continuous like the macroscopic world so well described by continuum mechanics. More precisely, light as a wave phenomenon is viewed to consist of a stream of light particles named photons each one carrying exactly the energy $h\nu$. Mind boggling, suggesting some deep secret.

Let us now trace the connection to SE for the Hydrogen atom taking the form: 

• $ih\frac{\partial\psi}{\partial t} + H\psi =0$                (SE)

where $\psi (x.t)$ is a complex-valued wave function depending on a 3d spatial coordinate $x$ and a time variable $t$ and $H$ is a (Hermitian) operator acting on $\psi$ with a discrete spectrum of real eigenvalues $E$ representing energies of normalised eigenfunctions $\Psi (x)$ satisfying $H\Psi =E\Psi$, which give wave solutions to (SE) of the form 

• $\psi (x,t)=\exp(i\frac{E}{h}t)\Psi (x)=\exp(i\nu t)\Psi (x)$ with
• $\nu =\frac{E}{h}$ or $E=h\nu$.  

We thus see a direct connection between the smallest quantum of energy $h\nu$ and energies $E=h\nu$ of eigenstates/functions of a Hydrogen atom, as a direct reflection of the form of (SE) including a first time derivative: Energy $E$ scales linearly with frequency $\nu$. 

The other way around, one can see (SE) as being formed by Schrödinger to include the connection $E=h\nu$ between energy $E$ and frequency $\nu$ (as a linear dispersion relation), because that fits with observed spectrum of the Hydrogen atom. Mathematical modeling to fit observation.   

More precisely, the spectrum of a Hydrogen atom comes out from differences of eigenvalues/energies $\Delta E$ translated to frequencies by $\Delta E =h\nu$. 

The basic heuristic idea of Einstein in 1905 was that  the energy of the electron of a Hydrogen atom can "jump" from one energy level to another by receiving/delivering exactly one photon of energy $\Delta E =h\nu$ in radiative equilibrium with light of frequency $\nu$: 

• Transition from one energy level to another with an energy jump $\Delta E$ of the electron of a Hydrogen atom involves receiving/delivering exactly the energy $\Delta E=h\nu$ of one photon of frequency $\nu =\frac{E}{h}$. 

This idea is supposed to convince us that the world of a Hydrogen atom is discrete operating with discrete chunks of energy $h\nu$ carried by discrete light particles/photons.

But this is an invented discreteness: SE is a continuum model of classical form in a wave function $\psi$ with $\vert\psi (x,t)\vert^2$ representing charge density, which has a discrete set of eigenvalues just like a vibrating string. The association of energy to frequency by $E=h\nu$ is simply a scaling of between energy and frequency with a scaling factor of $h$ with a value depending on choice of units.

From (SE) it follows that size of a Hydrogen atom scales with $h^2$ which connects to the discreteness of a Hydrogen atom with its only electron, which is described by the continuous model (SE) of classical continuum form. 

We thus find nothing fundamentally different from classical continuum mechanics point of view in the (SE) model of a Hydrogen atom in terms of a charge density. The association of an energy jump $\Delta E =h\nu $ to exactly one photon of frequency $\nu$ lacks real physical meaning and is just a convention which appeared as a heuristic idea in Einstein's mind in 1905. Planck's constant $h$ does not say that the microscopic world is discrete making it fundamentally different from a continuous macroscopic world. Planck's constant has a meaning as setting the physical scale of a Hydrogen atom, but not as a deep secret about the world. Of course atoms have spatial size just as specific macroscopic material objects with specific spatial extension. A Hydrogen atom is a like a continuous string of a violin of certain length and tension. No quantum.

In short, the quantum world of a Hydrogen atom can be understood in terms of classical continuum mechanics. 

The split appears when generalising (SE) to atoms with $N>1$ electrons following the route of Standard QM by Born-Bohr-Heisenberg into a linear wave equation in $3N$ spatial dimensions, with the wave function given a probabilistic unphysical meaning which makes StdQM "not understandable".

RealQM offers a fundamentally different generalisation without split away from classical continuum mechanics, which is understandable.  

Summary: 

1. Planck's constant $h$ serves as a formal conversion factor between energy $\Delta E$ and frequency $\nu$ with $\Delta E=h\nu$ in the setting of a radiating  Hydrogen atom. The size of a Hydrogen atom scales with $h^2$ which gives the specific value of Planck's constant $h$ a physical meaning, which is not some deep secreted of smallest quantum of energy. 
2. The generalisation to any atom by StdQM leaves classical continuum mechanics into a probabilistic quantum world "nobody can understand" where Planck's constant appears as a deep secret.
3. RealQM offers a generalisation staying within the form of classical continuum mechanics which "everybody can understand" where Planck's constant remains the simple conversion factor of 1. = No Secret = 0.
4. RealQM appears as "Quantum Mechanics without Quantum" which opens to unification with electromagnetics-Newtonian gravitation into a Unifies Field Theory as unfinished dream of Einstein. Let's get to work! 

The World is Continuous Not Discrete

Calculus was invented to solve a problem of "quadrature" of computation of the total distance $D$ covered when walking with varying step size in space $dx=v(t)\times dt$ with $v(t)$ representing velocity at time $t$ and $dt$ the time required for each step, starting from $t =0$ and ending at $t=T$. The total distance appears as the sum over all steps which takes the form of an integral : 

• $D(T)=\int_0^T v(t)dt$

The "trick" was to find a primitive function $x(t)$ satisfying $\dot x(t) =v(t)$ with $\dot x=\frac{dx}{dt}$ the derivative or $dx=v(t)dt$ to find 

• $D(T)=\int dx = \sum dx = x(T)-x(0)$

allowing $D$ to be computed from knowing a primitive function thus avoiding laborious summation.  For example, if $v(t)=2t$ as increasing velocity with time, then $D(T)=T^2$.

Calculus allowed tedious summation to be replaced be smart analytical mathematics: A tremendous success initiating the scientific revolution in the late 17th century also named the dot-age referring to $\dot x =\frac{dx}{dt}$.

Calculus showed to be more than "quadrature" by allowing a description the world in terms of differential equations depending on continuous space and time variables varying over a continuum of real numbers formalised in the late 19th century. So was continuum physics including electromagnetics formed allowing a description of the world we could fathom with our senses. 

The foundation was a model of space and time as a continuum of real numbers without a smallest scale. It was a world described by fields $\psi (x,t)$ depending on continuous space-time variables $(x,t)$ without smallest scale. 

Such field-models could be discretised  by introducing a smallest scale to allow finitary computation with finite number of digits connecting to "quadrature" performed simply as massive summation. The smallest scale could be refined to resolve increasingly fine details. 

Today this technique in the form of Computational Continuum Physics has been perfected into simulation of increasingly complex phenomena of the macroscopic world. Continuum models allow compact formulation and discretisation makes them computable. This is a world of classical physics made alive by computation. Classical physics as continuum physics.

But it is not the world of modern physics where Quantum Mechanics QM has replaced the continuum of no smallest scale, with a world of quanta of smallest scale $h\nu$ with $h$ Planck's constant and $\nu$ a frequency supposed to be the nature of the microscopics of atoms and molecules. 

This presents a world split into continuous macroscopics and discrete microscopics which comes with many difficulties now manifested in a crisis of modern physics. 

Let us follow the emergence of the split according to this time line:

1. In 1900 Planck introduced quanta of energy $h\nu$ to theoretically explain blackbody radiation. It gave him fame.
2. In 1905 Einstein introduced quanta of light energy $h\nu$ in a heuristic explanation of the photoelectric effect. It gave him the Nobel Prize in Physics in 1921. 
3. In 1915 Bohr introduced quantised discrete energy levels of a Hydrogen atom.
4. In 1925 Schrödinger formulated a model of a Hydrogen atom in the form of classical continuum mechanics.
5. In 1925 Heisenberg introduced a discrete matrix model. 
6. In 1926 Schrödinger's model was extended to atoms with more than one electron as  anew form of multi-d model beyond classical continuum mechanics, which was forcefully sold by Bohr-Heisenberg as Standard Quantum Mechanics StdQM according to the Copenhagen Interpretation. 
7. In 1928 Schrödinger left QM because it did not have the form of classical continuum mechanics.
8. Today the non-classical multi-d model as StdQM dominates completely. 
9. RealQM is a new model in the form of classical continuum mechanics. 

Today physicists speak about "quantisation" as the magic element separating modern physics from classical physics, which has brought so many wonders to the modern world. The idea goes back to the atomists of the Democritus school as smallest building elements of the world today carried in all sorts of particle physics. It appeared in Newton's corpuscular view of light, replaced by Maxwell's wave mechanics in the 19th century to return with Einstein's photons in 1905.  

Is then the split between continuous macro-physics and discrete micro-physics really necessary? Is it impossible to explain blackbody radiation and the photoelectric effect within classical continuum physics? 

No, it is in fact possible as shown in Computational Blackbody Radiation. This was also the message of Willis Lamb Nobel Laureate in Physics in 1955:  

• It should be apparent from the title of this article that the author does not like the use of the word "photon", which dates from 1926. In his view, there is no such thing as a photon. Only a comedy of errors and historical accidents led to its popularity among physicists and optical scientists.

The split has led to many difficulties. If the split can be avoided keeping both macro and micro within a continuum model, it may help out of the present crisis. Why not give continuum physics a new try to cover also microphysics without "quantisation".

The enigma of modern physics is presented as: How to quantise gravitation into a unified quantised theory? No answer in sight. Wrong question. 

A better idea is to de-quantise atom physics into a unified continuum model with gravitation. 

The late Einstein: These days, every Tom, Dick and Harry, thinks he knows what a photon is, but he is wrong. But nobody listened. 

I am pretty sure that Schrödinger would have welcomed RealQM since it follows his basic idea, which was overpowered by Bohr.

Mathematics: Calculus replaced discrete quadrature by understandable analysis, which returned in the form of digital computation giving power to understandable analysis.  

Physics: Calculus allowed classical physics to describe the world as a continuum open to understanding. Modern physics returned to Democritus atomism as a discrete world beyond understanding.   

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.    

Non-Physical Nature of Energy Quanta of Light or Photons

Photons are elementary particles of the Standard Model viewed to be mediators of electromagnetic interaction carrying energy. But what is the physical nature of these little packets of energy named photons? Fiction or reality? 

Let us compare with the harmonic oscillator as the basic model of physics (in non-dimensional form):

•  $\ddot x = - x $    (H)

where $x(t)$ is the elongation of a spring with one end attached to $x=0$ and the other end to a body of unit mass, $-x(t)$ is the spring force, $\dot x =\frac{dx}{dt}$ is the body velocity and (H) expresses Newton's 2nd Law. 

The physics of this model is the spring with its spring force depending on spring elongation $x(t)$ and the acceleration or dynamical force $\ddot x$ balanced by the spring force $x(t)$. Energy serves no role in the specification of the model. 

Energy can formally be introduced my multiplying (H) by $\dot x$ to find that the total energy

• $E(t) = K(t) + P(t)$,
• with $K(t)= \frac{1}{2}\dot x(t)^2$ as kinetic energy,
• and $P(t)=\frac{1}{2} x(t)^2$ as potential energy, 

stays constant during harmonic oscillation. We understand that mulitplication of (H) expressing force balance by the velocity $\dot x$, gives a balance of work per unit time as force times velocity with work a form of energy with thus energy constance over time the same as zero net work per unit of time. 

We understand that multiplication of (H) with $\dot x$ is a formal operation which lacks physical realisation. Therefore energy/work arising from this formal operation has no physical realisation. 

Energy/work does not consist of little packets of energy/work with physical presence. Energy/work are fictional quantities as abilities which can be associated with (H), but do not carry a definite physical shape. 

  

This gives perspective to photons as little packets or quanta of energy: They have no physicality and thus should better be removed from specifications of models of physics like (H) and then also from generalisations to atomic physics. 

We are thus led to a form of quantum physics as continuum physics without quanta as RealQM.     

Phlogistons and Photons as Non-Physics

Phlogiston Theory proposed in 1667 by Becher followed by Stahl postulated the existence of a fire-like element named phlogiston (flame, burning) within combustible bodies being released during combustion/oxidation as heat energy. Phlogistons were thus thought to be carriers of energy released during burning. 

The theory was dismissed when Lavoisier in 1772 showed that phosphorous increased weight by combining with oxygen from air during burning thus increasing weight. This showed that if phlogistons were real as elements being released during burning, then they had negative weight/mass, and so could not be physical elements, only fiction.  

In 1905 Einstein suggested that light of frequency $\nu$ heuristically could be thought of as a stream of little elements of energy or energy quanta later named photons of size $h\nu$ with $h$ Planck's constant, which could be released when hitting a metal surface thus producing electric energy as photoelectricity. The physical nature of a photon has remained elusive. 

The photon is an element of the Standard Model of particle physics as a carrier of electromagnetic interaction/energy at the speed of light in vacuum, a carrier without mass and charge. 

The phlogiston and the photon are both seen as carriers of little elements or packets of energy. A phlogiston has negative mass, while a photon has no mass. Both have zero charge. 

What about then the idea of an element or quanta of energy? Is this physics? 

We know that the energy released in combustion comes from a recombination of atomic structure. Phlogistons as little elements of energy are not needed. 

I agree with Schrödinger to see electromagnetic interaction/transfer of energy as an electromagnetic wave resonance phenomenon described by Maxwell's equations. This is the way an antenna works. It can be seen as a recombination of wave structures. There is here no need of photons as little elements of energy to explain communication over distance by radio waves. 

Phlogistons have been discarded as fiction without any role to serve. More generally, there can be no elements of pure energy. 

It may well be that also photons can be discarded as fiction without any role to serve. 

In quantum field theory there is place for both particles and fields with a particle seen as a local perturbation of the field. But if a particle is nothing but a perturbation of a field, why not use Ockham's razor to be satisfied with only fields? 

 

The Real Essence of Quantum Mechanics

Essential Real Elements of Schrödinger's Life as a Scientist.

1. Theory 

Quantum Mechanics QM grew out a need to explain observations that (i) an atom has a stable ground state without interaction with the environment and (ii) an atom can interact with light to exhibit an absorption/emission line spectrum. Next step was to explain molecules formed by atoms. There was no need to explain light since that was already done by Maxwell’s wave equations.

Since light is known to consist of electromagnetic waves of different frequencies $\nu$ and an atom is seen to interact with light, it is natural to seek an atomic wave equation for a function $\Psi (x,t)$ depending on a space variable $x$ and a time variable $t$ of the form of a harmonic oscillator (in non-dimensional form): 

• $i\frac{\partial\Psi}{\partial t} = H\Psi$   (S)

where $H$ is a Hamiltonian operator with a set of real-valued eigenfunctions $\psi_j(x)$ with eigenvalues $E_j$ satisfying $H\psi_j=E_j\psi$ where $E_1<E_2<E_3...$, forming the following representation:

• $\Psi (x,t) =\sum_{j\ge 1}\exp(-iE_jt)c_j\psi_j(x)$, 

with certain coefficients $c_j$. It is natural to associate $\vert\Psi (x,t)\vert^2$ with electronic charge density and $E_j$ with atomic energy. 

The charge density of the pure eigenstates $\exp(-iE_jt)\psi_j (x)$ including the ground state with $j=1$ is independent of time and so naturally can be seen as non-radiating states. 

Consider now a superposition of two eigenstates such as 

• $\exp(-iE_t)\psi_1(x)+\exp(-iE_2t)\psi_2(x)$
• $=\exp(-iE_1t)(\psi_1(x) + \exp( -i(E_2-E_1)t)\psi_2(x))$

for which the charge density is varying in time with the "beat frequency" $\Delta E=E_2-E_1$ as the difference of atomic energy between two eigenstates.  We thus see that superposition of two eigenstates generates a time varying charge density with frequency $\Delta E$ as difference in atomic energies. 

We know that an electric charge oscillating in space generates radiation/electromagnetic waves and it is natural to expect the same from oscillation in time with the frequency of the radiation set by the frequency of the oscillation. 

We can thus naturally connect the above superposition to radiation of frequency $\Delta E$ in interaction with light of the same frequency thus with  $\nu =\Delta E$, or $h\nu =\Delta E$ with $h$ Planck's constant defining space and time dimensions. 

Now, a prediction of atomic spectrum can thus be made from the eigenvalues of $H$ which can be compared with observation. For the Hydrogen atom with one electron Schrödinger formed by the Hamiltonian in non-dimensional form: 

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

with $\Delta$ the Laplacian, which gave very close agreement with observations. Schrödinger very happily concluded that he had created a mathematical model of the Hydrogen atom in a wave function representing charge density, and he was rocketed to fame. Notice that in this wave model there is no need to speak about energy quanta $h\nu$, only frequencies which can be observed, as macroscopic spectral lines.

What then about atoms with more than one electron? The standard procedure is to make a formal extension into multi-dimensional configuration space with a probabilistic non-physical interpretation of the wave function named Copenhagen Interpretation CI made into a canon by Bohr/Hesienberg/Born but never accepted by Schrödinger arguing that the CI interpretation of the wave function as a probability to find an electron as particle at a particular spot was void of meaning.

A different generalisation in physical terms is presented as Real Quantum Mechanics RealQM.  

Recall that Planck introduced energy quanta $h\nu$ to derive his law of black body radiation, which was then picked up by Einstein to (heuristically) explain the photoelectric effect, which lacking anything better gave him the Nobel Prize in Physics in 1921. 

RealQM and Computational Black Body Radiation show that energy quanta are not needed to explain these phenomena, and so loose their role and can be removed from the discussion, which brings a relief since nobody knows what an energy quanta is. In particular, the idea of explaining light as a stream of energy quanta or “photons” lacks physical basis.

CI comes with many problems which have never been resolved (see shocking review). RealQM offers a new start in the spirit of Schrödinger. 

The beauty of (S) for the Hydrogen atom is that it has clear physical meaning as an electronic cloud subject to Coulomb attraction from the kernel with spectrum in agreement with observation. Observe that electron cloud density itself is not observable, only the atomic spectrum as this is what reflects interaction with the environment, recalling that observation/measurement requires interaction.

Compare with the state of affairs as expressed by John Bell:

• Nobody knows what quantum mechanics says exactly about any situation, for nobody knows where the boundary really is between wavy quantum systems and the world of particular events.

But the boundary is clear as concerns atomic spectra.  Maybe RealQM opens to a resolution of the basic open question: The Measurement Problem. 

2. Theory vs Observation 

Let is now confront the eigenstates of (S) with observation of line spectrum for Hydrogen.

We observe a frequency of $2.469\times 10^{15}$ Hz corresponding to the ground state vs 1st excited state as lowest frequency in the Lyman (ultra-violet) series.   

We compute from (S) the energy level eigenvalues $-\frac{1}{2n^2}$ for $n=1,2,3,..$ with smallest $\Delta E = 3/8$ in Hartree or $10.2$ electronVolts eV. 

From the equation $\Delta E =h\nu$ with $\Delta E$ computed and $\nu$ observed, we can now compute Planck's constant $h$ to find the value given in physics books $h=4.136\times 10^{-15}$ eV.

We see that Planck's constant can be seen as a constant determined to make the model (S) fit with observation of the Hydrogen spectrum, thus as a form of model calibration (setting the relation between kinetic and potential energy) in (S). The wavelength of the lowest frequency in the Lyman series is $121.56701x10^{-9}$ meter which gives a connection to dimensional reality. 

Note the idea of energy quanta or photons $h\nu$ with some kind of physical realisation connects to the idea of phlogiston ("fire of the Earth") as carrier of energy in chemical reactions. The phlogiston theory was found to lack physical reality and so was abandoned before the end of the 18th century, while energy quanta has survived. Energy is a measure of the state of a system but is not a physical substance. 

(S) as a model of atoms and molecules does not need energy quanta, just continuum physics, which can help to demystify QM. It is the application of QM to light as a stream of photons which has brought the main mystery. It is time to let photons meet the same fate as phlogistons. 

Interaction between matter (atoms) and light can be modeled by QM for atoms and Maxwell's equations for light, and there seems to be no need to extend QM to light with all its complications. Yet this has become the objective of foundational quantum mechanics occupying the minds of philosophers of quantum mechanics or explorers of quantum computing.

3. Formality without physics  

Note that in the standard formulation of Schrödinger's equation in dimensional form the Laplacian $\Delta$ is multiplied with the factor $\frac{{\bar h}^2}{2m}$ with $\bar h =\frac{h}{2\pi}$ Planck's reduced constant and $m$ the mass of the electron. 

The appearance of the mass of electron here is strange, since it plays no role in the electro-magnetics of the Hydrogen atom captured by Schrödingers equation. It comes from a formal similarity to the kinetic energy $\frac{p^2}{2m}$ with $p=mv$ and $v$ velocity of classical mechanics, formally replacing $p$ by ${\bar h}^2\frac{\partial}{\partial x}$ without physics rationale. 

The energy associated with the Laplacian $\Delta$ is given by 

• $\int\frac{{\bar h}^2}{2m}\vert\nabla\psi\vert^2dx$, 

which motivated by the above formality is referred to as "kinetic energy". But this is a misnomer since kinetic refers to motion and here nothing is moving. Better would to refer this energy to a form of "elastic energy" or "compression energy" since it measures $\vert\nabla\psi\vert$.  

4. Physical size of Hydrogen atom ground state 

If we change the non-dimensional spatial coordinates $x$ in (1) into physical coordinates $\bar x=a_0x$, where $a_0=5.3\times 10^{-11}$ meter is the Bohr radius, then the Hamiltonian $H$ takes the following standard form in physical dimensions: 

• $\bar H = -\frac{{\bar h}^2}{2m}\bar\Delta - \frac{e^2}{4\pi\epsilon_0}\frac{1}{\vert\bar x\vert}$,

where $m$ here is (reduced) electron mass, $e$ electron charge and $\epsilon_0$ dielectric constant with $a_0=\frac{4\pi\epsilon_0h^2}{me^2}$. The Bohr radius gives the size of the electron cloud of the Hydrogen ground state in the range of 0.05 nanometers.   

5. Electron Mass?

The appearance of the electron mass in the coefficient $\frac{{\bar h}^2}{2m}$ of the Laplacian is strange since the electron mass $m$ is not part of the quantum physics of the Hydrogen atom building on electrostatic Coulomb attraction on the electron cloud balanced by the "compression force" from the Laplacian term. As said above the presence of the mass comes from a formal similarity to the kinetic energy $\frac{p^2}{2m}$ of classical mechanics. The value assigned to $m$ is $0.511$ MeV  based Einstein's formula $m=\frac{E}{c^2}$ translating energy to mass, to be compared with $10.2$ eV corresponding to the lowest frequency in the Lyman spectral sequence. The presence of the electron mass in the standard formulation of Schrödinger's equations (apparently) lacks rationale and the assigned large value of millions of eV appears to be ad hoc. 

In the 2019 redefinition the unit of mass 1 kg $\approx 8.98\times 10^{16}$ Joule as the energy of a collection of photons with frequencies summing to $1.356\times 10^{50}$, that is mass is defined in terms of energy, as a tribute to $E=mc^2$ showing Einstein's influence on modern physics. 

But mass is according to Newton's 2nd Law $m=\frac{F}{a}$ or $a=\frac{F}{m}$ a measure of resistance to motion with $F$ force and $a$ acceleration. This is inertial mass which is equal to gravitational mass. You discover the mass of your body by weighing it on a scale without any connection to energy. 

The $E=mc^2$ equivalence of energy is maybe Einstein's biggest mistake, and that is huge! 

   

What Is a Photon?

This is a continuation on previous posts on the concept of photon.  It was Einstein who in 1905 introduced the idea of a photon as a little packet of energy or light quanta of size $hf$ with $h$ Planck's constant and $f$ a frequency, to give a heuristic explanation the photoelectric effect. The idea was picked up by leading physicists elevating the photon to be an elementary particle of the Standard Model of particle physics as a gauge boson as force carrier of the electromagnetic force. 

But Einstein did not get along on that train and confessed in 1954 just before his death:

• All these fifty years of conscious brooding have brought me no nearer to the answer to the question, "What are light quanta?" Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken.

So what is then a photon? What properties does it have? We read:

1. A photon is stable.
2. A photon has zero mass.
3. A photon has zero charge:
4. A photon mediates electromagnetic interaction.
5. A photon moves at the speed of light in vacuum. 
6. A photon has spin angular momentum $-h,0,+h$.
7. A photon has orbital momentum $0,1,2,3,...$.

We note that in Maxwell's wave equations describing all of electromagnetics including electromagnetic interaction, there is no role for photons. The properties 1- 5 are thus empty by Ockhams Razor and one may then ask what meaning 6 and 7 can have starting from emptiness. 

Here is a supposedly illuminating picture of photons as little wave packets  traveling SouthEast at the speed of light:

Do you get the idea? Do photons really exist? Does black body radiation consist of a shower of photons?

Check out What, exactly, is a photon or specifically a single photon:

• A photon is the click registered by a single-photon resolving detector.

We learn that a (single) photon is a click of a (single) photon detector, but understand that the click says more about the detector than about the photon, so we are left in mystery. 

An explanation of the photoelectric effect without photons is given on Computational Black Body Radiation.  There you also find the real physical phenomenon of resonance as mediator of electromagnetic interaction instead of unphysical photons.

PS Is there maybe a connection to this picture: