Quantum Mechanics Without Quantum

Recent posts have identified the roots of  textbook Standard Quantum Mechanics StdQM, as the essence of modern atomic physics, in the works by Planck in 1900 on blackbody radiation and by Einstein in 1905 on photoelectricity. 

Let us retrace how StdQM as based on Schrödinger's Equation SE from 1925 for the Hydrogen atom, connects back to the early work by Planck-Einstein who did not know of atoms.  

We recall that in an act of desperation Planck introduced the concept of smallest quantum (chunk) of energy $E=h\nu$ of a wave with frequency $\nu$ and $h$ a constant later named Planck's constant, in order to explain why the ultra-violet catastrophe of blackbody radiation does not take place, as the prime challenge to theoretical physics in 1900. Planck as leading physicist of the German Empire simply had to come up with an explanation. In a Faustian deal Planck gave up his soul deeply rooted in classical physics for statistics of quanta and saved the day to the German Empire, which he deeply regretted but could not reverse.

Einstein followed in 1905 by connecting the smallest quantum of energy $h\nu$ to an idea of light as consisting of particles later named photons carrying exactly the energy $h\nu$. Einstein used this idea to come up with an explanation of photoelectricity in his position as patent clerk in Bern, in desperate need of scientific publications to open the door to a university position.

So was a smallest chunk or quantum of energy $h\nu$ and a light particle/photon supposed to carry that quantum of energy, introduced into physics in desperate attempts to gain attention, but the scientific community remained skeptical. 

The SE of a Hydrogen atom of 1925 took the form of classical continuum wave mechanical model in terms of an electron charge density $\psi (x)$ depending on a 3d spatial coordinate $x$ in Coulomb interaction with a kernel, while carrying a certain energy measured by $\vert\nabla\phi (x)\vert^2$ named kinetic energy. The observed spectrum of Hydrogen as a certain set of discrete frequencies $\nu$ showed to fit very precisely with differences of eigenvalues of SE representing differences of energy levels of the electron representing beat frequencies of an electron oscillating between levels. This connected energy to frequency in the same way as Planck's energy quantum $E=h\nu$ and Einstein's photon of energy $h\nu$.

So was a connection created between (i) a concept of smallest quantum of energy $h\nu$ and (ii) the discrete spectrum of a classical continuous wave equation without presence of any smallest quantum of energy. 

So was stdQM born to form the essence of modern physics as radically new form of physics based on a radically new idea of a smallest quantum of energy, which was based on a mathematical model of classical form as SE where the smallest quantum of energy had no role to play.  

The result is a mismatch between classical continuum physics in the form of SE without quantum, and a proclaimed new form of physics with quantum. No wonder that StdQM is surrounded by confusion expressed as "nobody understands QM". 

RealQM is an alternative to StdQM in the form of classical continuum physics without quantum. Computational Blackbody Radiation explains blackbody radiation and photoelectricity without quantum.The mismatch is gone. 

  

 

Why "Nobody Understands Quantum Mechanics"

This is a continuation of recent posts on the present crisis of modern physics. 

The essence of classical physics as a science is that it can be understood as a theory about the real world that makes sense to a human mind asking for logic and rationality. 

In 1900 a shift was initiated by Planck in his study of blackbody radiation followed by Einstein in his 1905 study of the photoelectric effect, which 20 years later was used to motivate a new form of physics named Quantum Mechanics QM, which became the trade mark of modern physics into present time. 

The trouble with QM is that all leading physicists say and have said for 100 years that "nobody understands QM". The result is a crisis of a modern physics based on QM.

But science is about understanding and so the fact that QM is not understandable, asks for an explanation. 

One way of forming a theory qualifying for not being understandable is to take some triviality and in the spirit of Einstein "elevate it to a Postulate" as a very deep truth about the world. The apparent clash between triviality and deep truth will cause confusion coming out as "nobody understands". This is like viewing 1+1=2 to be a deep truth of mathematics (instead of trivial definition), which if believed would express "nobody understands mathematics"? 

Let us see if this is in fact what happened with a QM growing out from Einstein's "heuristic explanation of the photoelectric effect" in 1905. Einstein started with the following observations made long before 1905:

• Light of frequency $\nu$ impinging on a metallic surface generates a current of electrons only if $\nu$ is bigger than a threshold value characteristic of the metal.
• The energy of electrons scales linearly with the frequency above the threshold, with energy identified with a stopping potential.    

It was believed that this could not be explained within the classical understandable wave theory of light by Maxwell, simply because that theory was not viewed to include the interaction between light and matter manifested in the photoelectric effect. 

Something more appeared to be needed and that was what Einstein offered in his "heuristic explanation" of the form "one incoming photon ejects one electron" or "one photon = one electron" or "one person = one vote":

• Energy balance gives "photon energy  = electron energy + electron release energy". 
• Define "photon energy" =$h\nu$ with $h$ a constant. 
• Conclude "$h\nu$ = electron energy + electron release energy" as the Law of Photoelectricity.  

Einstein here introduced the idea of a photon as "quanta of light" with an energy $h\nu$ picked from Planck. The essence was the scaling of energy with frequency $\nu$ and not amplitude of light, which connected to the nature of the threshold as a demand on frequency and not amplitude.

Einstein thus gave a "heuristic explanation" of the already observed Law of Photoelectricity, which gave him the 1921 Nobel Prize in Physics "for his discovery of the Law of Photoelectricity" as a misconception from "not understanding".

What Einstein did was to associate the energy $h\nu$ to something named "photon", which could be anything and still is not identified as to physical reality, but with the definite ability to kick out an electron from a metallic surface with the same energy $h\nu$ minus a release energy. For sure this was a "heuristic explanation" where the physics of "kicking out an electron" was hidden. It was thus a triviality made into a deep truth, and as such causing confusion ultimately leading to "nobody understands QM".

Is it then impossible to explain the Law of Photoelectricity in classical terms? If we look at the ingredients of incoming light and outgoing electrical current and stopping potential everything looks classical. Even the threshold on frequency can be accepted as classical as a form wave length precision required to release an electron tied to an atom. The energy of a classical wave of frequency $\nu$ scales with $\nu^2$ thus setting incoming light energy per unit length and time. The observed scaling with $\nu$ can then be obtained by partitioning incoming energy into wave length pieces each with energy scaling with $\nu$ into a totality of $\nu$ incoming pieces per unit of time. 

It is thus possible to give a "heuristic explanation" of the Law of Photoelectricity within classical wave physics, because it only involves classical concepts, which is as good as Einstein's resorting to discrete chunks of energy $h\nu$. 

Einstein did not get the Nobel Prize for explaining the Law of Photoelectricity, because his explanation convinced nobody, only for discovering a law that was already discovered. 

Computational Blackbody Radiation gives an explanation of blackbody radiation and photoelectricity in terms of classical wave mechanics without mystery, which can be understood by a high-school student. 

Altogether a basic reason that "nobody understands QM" is that it starts from a triviality of "quantisation" presented as a deep truth about reality as being discrete chopped up in little "quanta".  See also RealQM as "quantum mechanics without quanta" as understandable physics.

Photoelectricity/Radiation as Threshold Phenomena not Quantum

The previous post reminded that Quantum Mechanics QM as the mark of modern physics, was born when Planck in 1900 introduced a smallest quanta of energy $h\nu$ of frequency $\nu$ with $h$ Planck's constant to explain blackbody radiation, followed by Einstein in 1905 introducing a smallest quanta of light energy $h\nu$ carried by a particle of light later named photon to explain the photoelectric effect.

So was a new theory of physics born based on discrete chunks of energy named quanta as a form of atomistic physics going back to Democritus. The objective of the new theory from the beginning was to explain blackbody radiation and photoelectricity believed to be impossible to explain within classical continuum physics in the form of Newton's mechanics and Maxwell's electro magnetics. The new theory took the form of QM based on Schrödinger's equation forming the core of a modern physics, which now 100 years later is in state of deep crisis from erosion of credibility by a mantra that "physicists know how to use QM but cannot understand it".

Let us then go back to 1900/1905 and ask if it is really true that blackbody radiation and photoelectricity force the idea of quanta with all its mysteries into the mind of the defenseless physicist? 

We recall that the intensity of a classical wave of frequency $\nu$ as energy per unit length and time scales with $\nu^2$, which gives an energy per wave length scaling with $\nu$. 

We recall that the law of photoelectricity supposedly explained by Einstein's photons, reads 

• $E_{kin}+W=h\nu$, 

where $E_{kin}$ is the kinetic energy of an electron ejected by a metallic surface subject to incoming light of frequency $\nu$ and $W$ is the work/energy required to bring an electron from the interior to the boundary for ejection. If $h\nu <W$ no electricity will be generated, and if $h\nu >W$ an electric current as a stream of electrons will be generated according to Einstein's heuristic (brilliant?) idea: Each incoming photon ejects one electron. 

Let us take a step back and see if an explanation in classical terms not requiring light quanta or photons, is possible. What we have is light of frequency $\nu$ impinging on a metallic surface generating an electric current over a certain stopping potential P if $\nu$ is large enough as a threshold condition of the form: 

• $\nu >\frac{W}{h}$ with $W$ depending on the metal and $h$ is a constant,

assuming the following energy balance per electron of unit charge above the threshold:

• $P=h\nu - W$ or $h\nu = P+W$

thus assigning a certain energy to $h\nu$ balancing $P+W$ as energy $W$ to free an electron and to make it climb the potential $P$. Here we do not have to invent a light particle/photon to carry the chunk of energy $h\nu$. It is thus possible to explain photoelectricity by simply assigning a certain amount of energy $h\nu$ per wave length to wave of frequency $h\nu$ scaling with $\nu$ as remarked above. Neither does the threshold condition require any photon. 

We conclude that photoelectricity can be explained without invoking the concept of energy carrying light particle named photon. Classical wave mechanics with a threshold or high-frequency cut-off condition, is enough. The concept of photon is not needed, and by Ockham's razor we can dismiss this idea as irrelevant.

Blackbody radiation also has a threshold condition as a high-frequency cut-off condition limiting radiation to frequencies below a cut-off frequency scaling with $\frac{T}{h}$ with $T$ temperature as Wien's displacement law. Blackbody radiation is therefore also explainable in terms of classical wave mechanics with a threshold condition, see Computational Blackbody Radiation also discussing photoelectricity.

RealQM presents a new Schrödinger equation as the basis of a QM without quanta. Since nobody knows what a quanta is from physical point of view, this may helå to cope with crisis born from introducing this concept, which both Planck and Einstein deeply regretted.

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.    

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:

Photon Foolishness and CO2 Alarmism

Einstein received the Nobel Prize in Physics in 1921 for his 1905 discovery of the Law of Photoelectricity (discovered by Hertz already in 1887) based on an idea of light as a stream of light particles or light quanta later named photons, in a return to an idea of Newton abandoned since the discovery of light as an electromagnetic wave phenomenon captured by Maxwell's equations published in 1873.  

Einstein was not happy with the Prize motivation, since it explicitly stated that he was not awarded because of his theory of relativity, which he considered to be his main work, while he viewed his early work on photoelectricity rather as a misconception, since concerning photons/light quanta he confessed in 1951:

• All these 50 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.

Unfortunately, the Tom, Dick and Harry misconceived idea of light as a stream of photon particles has survived into our days, in parallel with the wave picture, and has come to serve as the basis of CO2 alarmism in the form of Downwelling Long Wave Radiation DLWR of Back Radiation as a stream of photons from the atmosphere to a warmer Earth surface with a massive global warming effect. 

In the spirit of Bohr the particle and wave nature of light are not considered contradictory but simply complementary although behaving differently:  

The Tom, Dick and Harry particle misconception is captured in an incorrect Planck-Stefan-Boltzmann Law PSBL stating that a black body at temperature $T$ Kelvin emits/radiates heat energy in the form of light quanta/photons scaling with $T^4$ (per unit area and time), independent of the surrounding temperature. The radiation has a Planck spectrum scaling with $T\nu^2$ with $\nu$ frequency (modulo high-frequency cut-off scaling with $T$). The misconception is that the radiation is independent of the surrounding temperature based on a primitive idea of radiation as a stream of photon particles being ejected independent of surrounding. This misconception is widely spread and embraced by otherwise very knowledgable physicists and laymen. 

A correct PSBL states black body radiation scaling with $(T^4 - T_s^4)$, where $T_s$ is the surrounding temperature. In this form the radiation can be seen as a wave resonance phenomenon between black body and surrounding, see Computational Blackbody Radiation. 

The Planck spectrum scaling with $T\nu^2$ directly connects with the wave nature of light with the energy of a harmonic oscillator of frequency $\nu$ scaling with $\nu^2$. 

To fit this into a particle idea Einstein suggested to view a photon as a localised wave packet of length scaling with $\frac{1}{\nu}$ and energy scaling with $\nu$ (captured in Planck's formula $E=h\nu$ with $h$ Planck's constant). The total radiation from a a stream of photons would then scale with $\nu^2$ since $\nu$ photons of length $\frac{1}{\nu}$ (traveling with the speed light) would pass in unit time. 

Einstein thus in 1905 associated the energy $E=h\nu$ to a concept of light quanta, which gave him the Nobel Prize in 1921 with the Law of Photoelectricity taking the form $E+P=h\nu$ with $P$ electron release energy and $E$ kinetic energy of an emitted electron upon impact by one photon with energy $h\nu$, but then misled generations of physicists into a misconception of PSBL misused by CO2 alarmism, while his insight in 1951 that light quanta has no physical meaning passed by without notice.  

This post directly connects to the following recent posts:

• Discussion with Will Happer on Back Radiation 
• Radiation as Resonance     

and to a wave analysis of the photoelectric effect (p 97). The idea of light as a stream of photon particles is as misconceived as an idea of sound as a stream of phonon particles which you spit out when you speak, while we all know that sound is transmitted by sound waves as a resonance phenomenon from loud speaker to your eardrums carried by air. 

The idea of light from Proxima Centauri as the closest star to our own as a stream of photon particles traveling at the speed of light one by one all alone 40,208,000,000,000 km on a journey taking 4.37 years without ever getting lost in cosmic dust or atmosphere until finally being captured by a human eye, is to fantastic to be credible. Light as particles is not physics, as Einstein said.

PS Typical misconception of photon particles each one ejecting an electron thus creating photoelectricity:

Compare with Mathematical Physics of Blackbody Radiation describing instead photoelectricity as a wave threshold phenomenon asking for a high enough frequency for electron ejection. See also this post.

Water Dam Analog of Photoelectric Effect

                               Open sluice gates in the Three Gorges Dam in the Yangtze River.

Einstein was awarded the 1921 Nobel Prize in Physics for his "discovery of the law of the photoelectric effect", connecting frequency $\nu$ of light shining on a metallic surface with measured potential $U$:

• $h\nu = h\nu_0 + e\, U$ or $h(\nu -\nu_0) = e\, U$,

where $h$ is Planck's constant with dimension $eVs = electronvolt\,\times second$,  $\nu_0$ is the smallest frequency releasing electrons and $U$ in Volts $V$ is the stopping potential bringing the current to zero for $\nu >\nu_0$ and $e$ is the charge of an electron. Observing $U$ for different $\nu$ in a macroscopic experiment shows a linear relationship between $\nu -\nu_0$ and $U$ with $h$ as scale factor with reference value 

• $h = 4.135667516(91)\times 10^{-15}\, eVs$,

with Millikan's value from 1916 within $0.5\%$.

Determining $h$ this way makes Einstein's law of photoelectricity into an energy conversion standard attributing $h\nu$ electronvolts to the frequency $\nu$, without any implication concerning the microscopic nature of the photoelectric effect.

The award motivation "discovery of the law of the photoelectric effect" reflected that Einstein's derivation did not convince the committee as expressed by member Gullstrand: 

• When it was formulated it was only a tentatively poorly developed hunch, based on qualitative and partially correct observations. It would look peculiar if a prize was awarded to this particular work. 

To give perspective let us as an analog of the law of the photoelectric effect consider a water dam with sluice gates which automatically open when the level of water is $\nu_0$.  The sluice gates will then remain locked as long as the water level $\nu <\nu_0$.  Lock the sluice gates and let the dam fill to some water level $\nu >\nu_0$ and then unlock the sluices. The sluices will then open and water will flow through under transformation of potential energy into kinetic energy. Assuming the work to open the sluices corresponds to a level loss of $\nu_0$, a net level of $\nu -\nu_0$ potential energy will then be transformed into kinetic energy by the water flow through the sluices. 

The dam can be seen as an illustration of the photoelectric effect with the water level corresponding to frequency $\nu$ and the gravitational constant corresponding to $h$ and the width of the dam corresponding to the amplitude of incoming light. If $\nu <\nu_0$ then nothing will happen, if $\nu >\nu_0$ then the kinetic energy will scale with $h\nu$ and the total flow will scale with the width of the dam.

Notice that noting in this model requires the water to flow in discrete lumps or quanta. The only discrete effect is the threshold $\nu_0$ for opening the sluices.

Planck's Constant = Human Convention Standard Frequency vs Electronvolt

The recent posts on the photoelectric effect exhibits Planck's constant $h$ as a conversion standard between the units of light frequency $\nu$ in $Hz\, = 1/s$ as periods per second and electronvolt ($eV$), expressed in Einstein's law of photoelectricity:

• $h\times (\nu -\nu_0) = eU$, 

where $\nu_0$ is smallest frequency producing a photoelectric current, $e$ is the charge of an electron and $U$ the stopping potential in Volts $V$ for which the current is brought to zero for $\nu > \nu_0$. Einstein obtained, referring to Lenard's 1902 experiment with $\nu -\nu_0 = 1.03\times 10^{15}\, Hz$ corresponding to the ultraviolet limit of the solar spectrum and $U = 4.3\, V$ 

• $h = 4.17\times 10^{-15} eVs$

to be compared with the reference value $4.135667516(91)\times 10^{-15}\, eV$ used in Planck's radiation law. We see that here $h$ occurs as a conversion standard between Hertz $Hz$ and electronvolt $eV$  with 

• $1\, Hz  = 4.17\times 10^{-15}\, eV$ 

To connect to quantum mechanics, we recall that Schrödinger's equation is normalized with $h$ so that the first ionization energy of Hydrogen at frequency $\nu = 3.3\times 10^{15}\, Hz$ equals $13.6\, eV$, to be compared with $3.3\times 4.17 = 13.76\, eV$ corresponding to Lenard's photoelectric experiment. 

We understand that Planck's constant $h$ can be seen as a conversion standard between light energy measured by frequency and electron energy measured in electronvolts. The value of $h$ can then be determined by photoelectricity and thereafter calibrated into Schrödinger's equation to fit with ionization energies as well as into Planck's law as a parameter in the high-frequency cut-off (without a very precise value).  The universal character of $h$ as a smallest unit of action is then revealed to simply be a human convention standard without physical meaning. What a disappointment!

This fits with the article Quantum Theory without Planck's Constant ny John P. Ralston:

• Planck's constant was introduced as a fundamental scale in the early history of quantum mechanics. We find a modern approach where Planck's constant is absent: it is unobservable except as a constant of human convention.

Finally: It is natural to view frequency $\nu$ as a measure of energy per wavelength, since radiance as energy per unit of time scales with $\nu\times\nu$ in accordance with Planck's law, which can be viewed as $\nu$ wavelengths each of energy $\nu$ passing a specific location per unit of time. We thus expect to find a linear relation between frequency and electronvolt as two energy scales: If 1 € (Euro) is equal to 9 Skr (Swedish  Crowns), then 10 € is equal to 90 Skr.

Photoelectricity: Millikan vs Einstein

The American physicist Robert Millikan received the Nobel Prize in 1923 for (i) experimental determination of the charge $e$ of an electron and (ii) experimental verification of Einstein's law of photoelectricity awarded the 1921 Prize.

Millikan started out his experiments on photoelectricity with the objective of disproving Einstein's law and in particular the underlying idea of light quanta. To his disappointment Millikan found that according to his experiments Einstein's law in fact was valid, but he resisted by questioning the conception of light-quanta even in his Nobel lecture:  

• In view of all these methods and experiments the general validity of Einstein’s equation is, I think, now universally conceded, and to that extent the reality of Einstein’s light-quanta may be considered as experimentally established. 
• But the conception of localized light-quanta out of which Einstein got his equation must still be regarded as far from being established. 
• Whether the mechanism of interaction between ether waves and electrons has its seat in the unknown conditions and laws existing within the atom, or is to be looked for primarily in the essentially corpuscular Thomson-Planck-Einstein conception as to the nature of radiant energy is the all-absorbing uncertainty upon the frontiers of modern Physics.

Millikan's experiments consisted in subjecting a metallic surface to light of different frequencies $\nu$ and measuring the resulting photovoltic current determining a smallest frequency $\nu_0$ producing a current and (negative) stopping potential required to bring the current to zero for frequencies $\nu >\nu_0$. Millikan thus measured $\nu_0$ and $V$ for different frequencies $\nu > \nu_0$ and found a linear relationship between $\nu -\nu_0$ and $V$, which he expressed as

• $\frac{h}{e}(\nu -\nu_0)= V$,     

in terms of the charge $e$ of an electron which he had already determined experimentally, and the constant $h$ which he determined to have the value $6.57\times 10^{-34}$. The observed linear relation between $\nu -\nu_0$ and $V$ could then be expressed as

• $h\nu = h\nu_0 +eV$    

which Millikan had to admit was nothing but Einstein's law with $h$ representing Planck's constant. 

But Millikan could argue that, after all, the only thing he had done was to establish a macroscopic linear relationship between $\nu -\nu_0$ and $V$, which in itself did not give undeniable evidence of the existence of microscopic light-quanta. What Millikan did was to measure the current for different potentials of the plus pole receiving the emitted electrons under different exposure to light and thereby discovered a linear relationship between frequency $\nu -\nu_0$ and stopping potential $V$ independent of the intensity of the light and properties of the metallic surface.  

By focussing on frequency and stopping potential Millikan could make his experiment independent of the intensity of incoming light and of the metallic surface, and thus capture a conversion between light energy and electron energy of general significance.  

But why then should stopping potential $V$ scale with frequency $\nu - \nu_0$, or $eV$ scale with frequency $h(\nu - \nu_0)$? Based on the analysis on Computational Blackbody Radiation the answer would be that $h\nu$ represents a threshold energy for emission of radiation in Planck's radiation law and $eV$ represents a threshold energy for emission of electrons, none of which would demand light quanta.

   

Why the Same Universal Quantum of Action $h$ in Radiation, Photoelectricity and Quantum Mechanics?

Planck's constant $h$ as The Universal Quantum of Action was introduced by Planck in 1900 as a mathematical statistical trick to supply the classical Rayleigh-Jeans radiation law $I(\nu ,T)=\gamma T\nu^2$ with a high-frequency cut-off factor $\theta (\nu ,T)$ to make it fit with observations including Wien's displacement law, where

• $\theta (\nu ,T) =\frac{\alpha}{\exp(\alpha )-1}$,
• $\alpha =\frac{h\nu}{kT}$, 

$\nu$ is frequency, $T$ temperature in Kelvin $K$ and $k =1.38066\times 10^{-23}\, J/K$ is Boltzmann's constant and $\gamma =\frac{2k}{c}$ with $c\, m/s$ the speed of light in vaccum. Planck then determined $h$ from experimental radiation spectra to have a value of $6.55\times 10^{-34} Js$, as well as Boltzmann's constant to be $1.346\times 10^{-23}\, J/K$ with $\frac{h}{k}= 4.87\times 10^{-11}\, Ks$ as the effective parameter in the cut-off.  

Planck viewed $h$ as a fictional mathematical quantity without real physical meaning, with $h\nu$ a fictional mathematical quantity as a smallest packet of energy of a wave of frequency $\nu$, but in 1905 the young ambitious Einstein suggested an energy balance for photoelectricity of the form 

• $h\nu = W + E$,

with $W$ the energy required to release one electron from a metallic surface and E the energy of a released electron with $h\nu$ interpreted as the energy of a light photon of frequency $\nu$ as a discrete lump of energy. Since the left hand side $h\nu$ in this law of photoelectricity was determined by the value of $h$ in Planck's radiation law, a new energy measure for electrons of electronvolt was defined by the relation $W + E =h\nu$. As if by magic the same Universal Quantum of Action $h$ then appeared to serve a fundamental role in both radiation and photoelectricity.

What a wonderful magical coincidence that the energy of a light photon of frequency $\nu$ showed to be exactly $h\nu \, Joule$! In one shot Planck's fictional smallest quanta of energy $h\nu$ in the hands of the young ambitious Einstein had been turned into a reality as the energy of a light photon of frequency $h\nu$, and of course because a photon carries a definite packet of energy a photon must be real. Voila!

In 1926 Planck's constant $h$ showed up again in a new context, now in Schrödinger's equation

• $-\frac{\bar h^2}{2m}\Delta\psi = E\psi$

 with the formal connection   

• $p = -i\bar h \nabla$ with $\bar h =\frac{h}{2\pi}$,
• $\frac{\vert p\vert^2}{2m} = E$, 

as a formal analog of the classical expression of kinetic energy $\frac{\vert p\vert ^2}{2m}$ with $p=mv$ momentum, $m$ mass and $v$ velocity.

Planck's constant $h$ originally determined to make theory fit with observations of radiation spectra and then by Planck in 1900 canonized as The Universal Quantum of Action, thus in 1905 served to attribute the energy $h\nu$ to the new fictional formal quantity of a photon of frequency $\nu$ . In 1926 a similar formal connection was made in the formulation of Schrödinger's wave equation.  

The result is that the same Universal Quantum of Action $h$ by all modern physicists is claimed to play a fundamental role in both (i) radiation, (ii) photolelectricity and (iii) quantum mechanics of the atom. This is taken as an expression of a deep mystical one-ness of physics which only physicists can grasp,  while it in fact it is a play with definitions without mystery, where $h$ appears as a parameter in a high-frequency cut-off factor in Planck's Law, or rather in the combination $\hat h =\frac{h}{k}$,  and then is transferred into (ii) and (iii) by definition.  Universality can this way be created by human hands by definition. The power of thinking has no limitations, or cut-off.

No wonder that Schrödinger had lifelong interest in the Vedanta philosophy of Hinduism "played out on one universal consciousness".

But Einstein's invention of the photon as light quanta in 1905 haunted him through life and approaching the end in 1954, he confessed:

• 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. 

Real physics always shows up to be more interesting than fictional physics, cf. Dr Faustus ofd Modern Physics.

PS Planck's constant $h$ is usually measured by (ii) and is then transferred to (i) and (iii) by ad hoc definition.

Mystery of Quantum of Photoelectricity Replaced by Non-Mystery of Threshold Value

The deepest mystery of quantum mechanics is the smallest quantum of action introduced by Planck in his proof of Planck's law:

• $h\nu$ 

where $h=6.626\times 10^{-34}\, Js$ is Planck's constant and $\nu$ is frequency. 

The smallest quantum of action $h\nu$ appears in Einstein's celebrated law of the photoelectic effect:

• $h\nu  = W + P$, 

where $W$ is the energy required to liberate an electron and $P$ and the energy of a liberated electron.

Einstein's formula models generation of an electric current corresponding to $P >0$ from input of light of frequency $h\nu$, scaling with the intensity of the light.

Einstein interpreted $h\nu$ as the "smallest packet of energy" of a wave of frequency $\nu$ later named photon with $h\nu - W>0$ required for the generation of an electric current with $P > 0$. We can view

• $h\nu > W$

as a cut-off condition for photo-electricity similar to the cut-off condition in Planck's law with $T$ temperature and $k$ Boltzmann's constant:

• $h\nu > kT$

which according to Computational Blackbody Radiation expresses internal heating from exposure to radiation of frequency $\nu$. 

We can thus view both photo-electricity and internal heating from exposure to radiation as being determined by a high-frequency cut-off condition expressing that no effect occurs for input frequencies below the cut-off, and that the effect scales with the intensity above the cut-off. 

The idea of smallest packet of energy, which is strange as physical concept, can thus be replaced by the concept of threshold value on frequency or wave length, which is not strange from physics point of view. For details, see the book Computational Blackbody Radiation.

Recall that Einstein was awarded the 1921 Nobel Prize in Pbysics for his above law of photoelectricity, but it was explicitly stated in the award motivation that he was not given the Prize because of his derivation of the formula based on photons, only for the "discovery" of the formula as if formulas are laying around waiting to be discovered.

Physics Illusion 13: Light as Stream of Photon Particles

                                      Light as a stream of photon particles or as electromagnetic wave?

Quantum mechanics is supposed to originate from Planck's proof in 1900 of Planck's Law of Black Body Radiation introducing a smallest quantum of action named Planck's constant denoted by $h$ with a value later determined to

• $h = 6.62606957\times 10^{-34}\, J\cdot s$ 

attributing the energy $E=h\nu$ to a wave of frequency $\nu$, as a smallest quantum of energy of the frequency $\nu$. Planck used the quantum of energy $h\nu$ to save the scientific world from the ultra-violet catastrophe of classical electromagnetics with radiation energy scaling with $\nu^2$ without limit for increasing frequency $\nu$,  using a statistical argument suggesting low probability of high frequency, thus effectively introducing a high-frequency cut-off in the radiation spectrum. Planck viewed his quantum as a mathematical trick without physical reality.

Then Einstein entered the game in 1905 with the article giving him the 1921 Nobel Prize in Physics presenting a formula expressing an energy balance for the photoelectric effect with electrons being ejected from a surface when exposed to light:

• $ h\nu = E + P$

where $E$ is the energy of an ejected electron and $P$ the energy required to release the electron from the surface. With this formula, where $h\nu$ would represent a smallest quantum of light of frequency $\nu$, Einstein seemed to explain the basic properties of the photoelectric effect: No electrons are ejected unless $h\nu > P$ independent of light intensity and the number of ejected electrons scale with intensity. The value of $h$ was determined in 1916 by Millikan using Einstein's formula with the objective to falsify Einstein's concept of quantum of light.

Neither did the Nobel Committee buy Einstein's derivation of his formula based on light quanta, but with the appearance of quantum mechanics in 1925 Einstein's idea received momentum and with the name photon by Lewis in 1927 became a trademark of modern physics, although it was basically the same old corpuscular theory of light once suggested by Hobbes but quickly replaced by the wave theory of Huygens. In the Standard Model ruling fundamental physics of today the photon has as a respectable position as the elementary particle carrying the electromagnetic force. Light as a flow $\nu$ photons per unit time then correponds to an energy flux of $h\nu^2$, which we now compare with Planck's Law. 

Let us in particular check out how Planck's constant enters into Planck's Law, which reads

• $R_\nu (T)=\gamma\nu^2T\times \theta(\nu ,T)$,

where $R_\nu (T)$ is radiated energy per unit frequency, surface area, viewing angle and second, $\gamma =\frac{2k}{c^2}$ where

• $k = 1.3806488\times  10^{-23} m^2 kg/s^2 K$

is Boltzmann's constant and $c$ the speed of light in $m/s$, $T$ is temperature in Kelvin $K$, and 

• $\theta (\nu ,T)=\frac{\alpha}{e^\alpha -1}$, 
• $\alpha=\frac{h\nu}{kT}$

is a high-frequency cut-off factor such that $\theta (\nu ,T)\approx 1$ for $\alpha < 1$ and  $\theta (\nu ,T)\approx 0$ for $\alpha > 10$. 

We see that Planck's constant $h$ enters into Planck's law as a high-frequency cut-off for $\frac{\nu}{T} > \frac{10k}{h}$, which reflects the original role of $h$ given by Planck, with the dependence on $T$ reflecting Wien's displacement law.

Computational Black Body Radiation presents an alternative derivation of Planck's law based on wave mechanics with finite precision computation serving as high-frequency cut-off. Maybe after all there is no compelling reason to speak about photons and light particles.