Mystery of Planck's Constant Revealed

This is a clarification of this post on the physical meaning of Planck's constant $h$ and so of Quantum Mechanics QM as a whole. The basic message is that the numerical value of $h=6.62607015\times 10^{-34}$ Jouleseconds is chosen to make Planck's Law fit with observation and that this value is then inserted into Schrödinger's equation to preserve the linear relation between energy and frequency established in Planck's Law. 

Quantum Mechanics is based on a mysterious smallest quantum of energy/action $h$ named Planck's constant, which was introduced by Planck in 1900 as a "mathematical trick" to make Planck's Law of blackbody radiation fit with observations of radiation energy from glowing bodies of different temperatures. 

The mysterious Planck's constant  $h$ appears in Planck's Law in the combination $\frac{h\nu}{kT}$ where $\nu$ is frequency, $k$ is Boltzmann's constant and $T$ temperature with $kT$ a measure of energy (per degree of freedom) from thermodynamics. In particular  

•  $\nu_{max}=2.821\frac{kT}{h}$                   (*)

shows the frequency of maximal radiation intensity referred to as Wien's Displacement Law, which also serves as a cut-off frequency with quick decay of radiation intensity for frequencies $\nu >\nu_{max}$.  

If we translate (*) to wave length we get a corresponding smallest wave length 

• $\lambda_{min}= 0.2015\frac{hc}{kT}=\frac{0.0029}{T}$ meter
• $\lambda_{min} \approx 10^{-5}$m for $T=300$ K 
• $\lambda_{min} \approx 5\times 10^{-7}$m for $T=5778$ K (Sun)

We see that smallest wave length is orders of magnitude bigger that atomic size of $10^{-10}$ m, which tells that blackbody radiation is a collective wave phenomenon involving many atoms per radiated wave length.

Summary: 

• Planck's constant $h$ serves the role of setting a peak frequency scaling with temperature $T$ with corresponding smallest wave length scaling with $\frac{1}{T}$.
• The smallest wave length is many orders of magnitude bigger than atomic size showing blackbody radiation to be a collective wave phenomenon involving coordinated motion of many atoms. 
• Planck's constant $h$ thus has a physical meaning of setting a smallest spatial resolution size scaling with $\frac{1}{T}$ required for coordinated collective wave motion supporting radiation. 
• Higher temperature means more active atomic motion allowing smaller coordination length. 
• The standard interpretation of $h$ as smallest quanta of energy lacks physical representation.
• Connecting $h$ to coordination length is natural and gives $h$ a physical meaning without mystery. 
• Formally h = energy x time = momentum x length representing Heisenbergs Uncertainty Relation with h connecting to spatial resolution. Formally $E=h\nu=pc$ and so $h=p\lambda$.   

PS Recall that Schrödinger's equation for atoms and Maxwell's equations for light covers a very wide range of phenomena in what is referred to as a semi-classical model as half-quantum + half classical. In this model light is not quantised and there are no photons to worry about. The above meaning of $h$ from Planck's Law is understandable. The mystery is restored in Quantum Electro Dynamics QED where Maxwell's equations are replaced by the relativistic Dirac's equations and particles/photons appear as quantised excitations of fields. QED is way too complicated to be used for the wide range covered by QM and so is reserved for very special geometrically simplified situations. 

Einstein vs Lorentz, Planck and Bohr: Tragedy

Modern physics as relativity theory + quantum mechanics was born out of two misconceptions formed in the mind of the young Einstein as patent clerk in Bern in 1905 with little scientific training, but strong ambition to contribute to the emerging modern physics of  

1. Blackbody radiation.
2. Photoelectricity. 
3. Apparent absence of a unique aether carrying electromagnetic waves.  

In 1900 Planck had derived Planck's Law of blackbody radiation based on a smallest quantum of energy $h\nu$ connected to radiation/light of frequency $\nu$ with $h=6.55\times 10^{-34}$ Jouleseconds named Planck's constant. Planck did not assign any physical meaning to the smallest quantum $h\nu$ and viewed it simply as a "mathematical trick" used to derive Planck 's Law. 

In one of Einstein's 5 articles from the "miraculous year" 1905, Einstein assigns the quantum $h\nu$ a physical meaning as the energy of a "photon" as a "light particle" in a heuristic explanation of 2. Einstein thus did what Planck had said does not make any sense. In 1926 the mysterious quantum $h\nu$ appeared in Schrödinger's equation for the Hydrogen atom as the basic mathematical model of quantum mechanics.

In another 1905 article Einstein assigned the Lorentz transformation a physical meaning, which Lorentz had said would not make any sense, and so formed his Special Theory of Relativity SR.

Einstein thus contributed to the formation of modern physics in 1905 by attributing physical meanings to both Planck's quantum $h\nu$ and the Lorentz transformation, in direct contradiction to both Planck and Lorentz.  

As time went on and the authority of Planck and Lorentz faded, Einstein's ideas about physicality of photons and the Lorentz transformation slowly gained support, but when they became the standard of the new Quantum Mechanics of Bohr-Born-Heisenberg-Dirac in the 1930s, then Einstein said: Stop, QM is no longer real physics!  Only Schrödinger said the same thing, but both were efficiently cancelled by Bohr. 

Einstein thus started out and ended as a tragic figure. First he genuinely misunderstood Planck and

Lorentz about physical reality and so contributed the development of a new form of physics, which he on good grounds criticised for lacking physicality. The irony was that physicists listened when he was wrong but not when he was right.   

Planck's Faustian Deal: The Quantum

Here is a short excerpt from my book Dr Faustus of Modern Physics giving perspective on the birth in 1900 of Quantum Mechanics with Planck's mathematical analysis of blackbody radiation introducing $E=h\nu$ as a smallest quantum of energy. 

To boost his career and the science of the booming German Empire, Max Planck, professor at the University of Berlin with a background from thermodynamics, took on the main open problem of physics at the end of the 19th century, namely to explain why the ultra-violet catastrophe of blackbody radiation predicted by classical theoretical physics cannot be observed. At stake was the credibility of a science of physics (and the German Empire) predicting very intense high-frequency radiation which simply refused to exist. The stakes were thus very high and Planck with ambition stepped in:

• The whole procedure was an act of despair because a theoretical interpretation had to be found at any price, no matter how high that might be... 

The price was to give up his soul as very serious scientist with deep conviction to classical ideals, which paved the way for new quantum physics giving up classical principles of reality, causality and determinism, now in deep crisis.  

1. Nobel Prize to Planck

 The Nobel Prize in Physics 1918 was awarded (in 1919) to Max Planck:

• in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta.

It took the Nobel Committee more than 10 years to come to this conclusion, because Planck’s new concept of a smallest quantum of energy was so difficult to swallow, described by the Swedish mathematician Ivar Fredholm as “hardly plausible”. In 1918 the Committee gave in under pressure to give the prize to Bohr and Einstein, which required a prize to Planck first. The presentation speech by Ekstrand stated:

• Planck’s radiation theory is, in truth, the most significant lodestar for modern physical research, and it seems that it will be a long time before the treasures will be exhausted which have been unearthed as a result of Planck’s genius.
• Planck constant, proved, as it turned out, to be of still greater significance: The product $h\nu$, where $\nu$ is the frequency of vibration of a radiation, is actually the smallest amount of heat which can be radiated at the vibration frequency $\nu$. This theoretical conclusion stands in very sharp opposition to our earlier concept of the radiation phenomenon.

Planck was thus viewed as having “discovered” a physical phenomenon of “energy quanta”, which in fact was a “theoretical conclusion”. This contradiction has come to form the ideology of modern physics made possible by breaching the classical holy distinction between reality and mathematical model.

2. Planck's Confession

From Planck's self-biography:

• We shall now derive strange properties of heat radiation described by electromagnetic wave theory.
• ..the whole procedure was an act of despair because a theoretical interpretation had to be found at any price, no matter how high that might be... 
• Either the quantum of action was a fictional quantity, then the whole deduction of the radiation law was essentially an illusion representing only an empty play on formulas of no significance, or the derivation of the radiation law was based on sound physical conception. Mechanically, the task seems impossible, and we will just have to get used to it (quanta). 
• My futile attempts to fit the elementary quantum of action into classical theory continued for a number of years and cost me a great deal of effort. Many of my colleagues saw in this something bordering on a tragedy (Planck shortly before his death).
• I tried immediately to weld the elementary quantum of action somehow in the framework of classical theory. But in the face of all such attempts this constant showed itself to be obdurate...
• My futile attempts to put the elementary quantum of action into the classical theory continued for a number of years and they cost me a great deal of effort.
• The assumption of an absolute determinism is the essential foundation of every scientific inquiry.
• All matter originates and exist only by virtue of a force which brings the particle of an atom to vibration and hold this most minute solar system of the atom together. We must assume behind the existence of this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter...
• In order to find the correct resonator entropy S it must be assume that the energy U of a resonator with frequency ν can only take on discrete energy values, to wit, integer multiples of h times ν, in contrast to classical theory where U can be any multiple, integer or not, of ν. We now say that U is quantised.
• My maxim i always this: consider every step carefully in advance, but then, if you believe you can take the responsibility for it, let nothing stop you.
• For by nature I am peaceful and disinclined to questionable adventures...for unfortunately I have not been given the capacity to react quickly to intellectual stimulation.

3. Planck on Politics

Planck lost his son Karl in combat during 1st World War and his son Erwin was executed after a plot against Hitler at the end of the 2nd World War. Planck signed together with 93 German intellectuals the Appeal to the Cultured Peoples of the World on 4 October 1914:

• We declare the leaders of German art and science to be at one with the German army.

Planck reports as Rector of Berlin University in 1914:

• The German people ha found itself again. One thing only we know, that we members of our university...will stand together as one man and hold fast until - despite the slander of our enemies - the entire world comes to recognise the truth and German honor.
• But we shall also see an feel how, in the fearful seriousness of the situation, everything that a country could call its own in physical and moral power came together with the speed of lightning and ignited a flame of holy wrath blazing to the heavens, while so much that had been considered important and desirable fell to the side, unnoticed, as worthless frippery.

Understanding OLR and DLR vs Radiance Measurement by CERES and Pyrgeometer.

Outgoing Longwave Radiation OLR from the Top of the Atmosphere ToA is measured by a CERES satellite looking down on ToA equipped with a sensor as one end of a thermocouple with its other end kept at a steady temperature generating a voltage scaling with the temperature difference at its ends. 

The CERES instrument is calibrated by determining a gain factor from sensor temperature to radiance letting the instrument look at a black body of known temperature $T_B$ with assumed Planck radiation $\sigma T_B^4$ while recording the sensor temperature. With the gain factor so determined the instrument reports radiance from ToA from a reading of sensor temperature. This is the simplest form of calibration assuming linearity. Very primitive technique, where the details of the instrument do not matter. It is like measuring intensity of rainfall using your hands to collect water calibrated to a faucet. The accuracy is at best 1 W/m2 or 0.4% of the same size as estimated Earth Energy Imbalance from CO2.  

A pyrgeometer measuring Downwelling Longwave Radiation from the atmosphere to the Earth surface also uses a sensor as one end of a thermocouple with the other end kept a base temperature, and also measures a voltage scaling with temperature difference. The calibration is here different because the outgoing radiation from the sensor can no longer be included in the calibration process, but has to be supplied through a Planck formula $\epsilon\sigma T^4$ with $T$ sensor temperature and $\epsilon$ sensor emissivity. The accuracy is at best 5 W/m2 again too big to detect global warming if present.

OLR and DLR are thus measured in a similar way, but with different forms of calibration the difference being that OLR faces empty space ay 0 K, while DLR faces the Earth surface. The accuracy is not enough to decide any size of global warming, although it is claimed that trends can be detected. 

In both cases Planck's Law in the form $\sigma T^4$ is used, which in the case of DLR is incorrect because the correct form is $\sigma (T^4-T_E^4)$ with $T_E$ Earth temperature expressing negative DLR.  

Summary: Measurements of OLR and DLR are made to detect global warming. The accuracy of the instruments is not good enough to detect any warming if present. DLR measurements can be questioned since an incorrect Planck Law is used. OLR and DLR as radiance as process variable fluctuate and as such are difficult to measure.  

EEI is a cornerstone of global warming alarmism, and so measuremennt of EEI has become a prime task for instrument technology, which does not seem to have delivered. The effect of EEI on surface temperature is unknown and impossible to measure and DLR is a misconception based on an incorrect form of Planck's Law.

ChatGPT on objective of CERES: 

CERES connects to global warming because it:

• Measures the planetary energy balance directly at TOA.

• Detects changes in OLR and OSR (reflected shortwave) caused by greenhouse gases, aerosols, clouds, and ice.

• Provides the evidence that Earth is currently taking in more energy than it loses — the physical basis of global warming.

ChatGPT on objective of measuring DLR :

• Provide a direct measure of the atmosphere’s infrared emission to the surface, essential for closing the surface energy budget, quantifying the greenhouse effect, tracking climate change, and validating models.

We read that the objective of CERES is to support global warming alarmism by measuring and reporting EEI attributed to CO2. But the objective is not reached, because (i) the accuracy of the measurement is not better than 1 W/m2, which is the expected size of EEI, and (ii) attribution to CO2 to is not credible because it is swamped by changes of cloud cover. We read that the objective of measuring DLR by a pyrgeometer is to quantify greenhouse effect. Both cases amounts to "chasing after wind" using "ghost detectors". 

Planck 1900: Fall of Theoretical Physics: Greenhouse Effect

Planck describes in his autobiography his theoretical derivation of Planck's Law for black-body radiation presented in 1900, in complete agreement with observations, based on statistics of quanta, in these very disturbing terms:

• It was and act of desperation.
• I was ready to sacrifice any of my previous convictions about physics.

What Planck gave up was the rationality of classical deterministic physics for a new form of indeterministic statistical physics. A monumental sacrifice. Why? A Faustian deal? In any case the consequences have been far reaching since quanta has become the code word of modern (quantum)  physics, even if the meaning has never been made clear. 

Planck's Law integrated over all frequencies takes the form of Planck-Stefan-Boltzmann's Law:

• $R=\sigma T^4$                (PSB)

where $R$ is radiance as energy flux measured in e g W/area, $T$ is an absolute temperature and $\sigma$ a constant. (PSB) is a poster formula for modern physics of the same stature as $E=mc^2$, but if you ask a modern physicist about the real physical meaning of (PSB), you will get the following contradictory answers:

1. $R$ is the outgoing radiance of a black-body of temperature $T$ independent of the environment of the body, as a stream of emitted photons. 
2. $R$ is the outgoing radiance of a black-body of temperature $T$ into an environment of a zero absolute temperature.  If the environment has temperature $T_0<T$ then $R=\sigma (T^4 - T_0^4)$. Fundamentally different from 1.

A theoretical/pure physicist will say 1. and an applied/real physicist will say 2. But theory cannot contradict reality. The reason of the confusion between 1. and 2. is that Planck's derivation is not based on real physics but on statistics without clear physics as quanta physics.

We conclude that 1. is a misconception, but a widespread misconception, which has served as the basis of the so called GreenHouse Effect GHE underlying climate alarmism. What 1. tells the climate alarmist is that the atmosphere is sending massive so called back-radiation to the surface of the Earth, twice as big as the radiation from the Sun. The sky cloudy or clear will thus warm the Earth according to 1. which with a bit more CO2 from fossil fuels will cause global warming with terrible consequences for humanity. From 1. follows alarm, while there is no alarm from 2. 

A climate alarmist will present evidence of global warming by back-radiation from the sky from instruments like pyrgeometers or AERI/radiometers, which report massive back-radiation or Downwelling Longwave Radiation DLR on their displays. The idea is that if an instrument display shows something, it must be something real in particular if the instrument is heavy and expensive. But an applied/real scientist would ask for information about the physics of the instrument, what de facto is being measured and how and what is displayed. Right?  

Inspecting the manual of a pyrgeometer or radiometer shows that the instrument is based on 1. which thus gives the basis for what is shown on the display as massive DLR or back-radiation. With 2. the display would show a much smaller warming effect of the atmosphere. 

Climate alarmism is thus based on 1. Understanding that 1. is not real physics, reduces the main argument of climate alarmism to zero. 

A different proof of Planck's Law in terms of classical deterministic physics without statistics is presented as Computational Black Body Radiation, which shows that 2. is physics and 1. not. You find an analysis of the pyrgeometer as ghost detector of back radiation in this sequence of post. Also check out this talk on Misunderstanding Planck's Law.

PS1 In 1900 Planck was professor of theoretical physics at the University of Berlin asking for a demonstration of the power of the science of the German Empire as a solution to the main open problem of physics at that time as black body radiation. Planck delivered a solution but sacrificed his soul. The consequences are far reaching...

PS2 Here is what chatGPT delivers after reading the above post taking the role of a physicist with critical mind:

A critically minded physicist—someone who is open to established physics but also skeptical of how it’s interpreted or applied—would likely respond quite differently than a mainstream theorist. Here’s how they might frame it:

---

1. On Planck’s “act of desperation”

They might agree that Planck himself admitted his derivation of black-body radiation was not fully grounded in classical physics, but rather a pragmatic move that worked. They’d stress that quantum mechanics grew out of a kind of compromise—useful, predictive, but philosophically unsettling. So the “Faustian deal” language resonates with a critical thinker, because it highlights the cost of leaving behind determinism for statistical interpretation.

---

2. On (1) vs (2): Competing Interpretations of Stefan–Boltzmann

A critical physicist would likely side with (2): the net exchange of radiation between systems must consider both emitter and absorber. They’d argue that talking about radiation into a zero-temperature environment (1) is a mathematical idealization, not a physically realizable case.

They might also note that many climate and atmospheric models sometimes gloss over this distinction when communicating to the public, which creates room for confusion.

---

3. On Instruments and Back-Radiation (DLR)

They’d ask tough questions:

• What exactly does the pyrgeometer measure?

• How is the reading calibrated?

• Does the “back-radiation” display reflect direct measurement of photons or an inferred value from a model?

Their stance would be: the data are real, but the interpretation of that data depends heavily on assumptions. For example, an instrument showing a high DLR number doesn’t necessarily mean the sky is “heating” the Earth in the same way the Sun does—it means energy exchange is occurring, but how we conceptualize it matters.

---

4. On Climate Implications

A critically minded physicist wouldn’t necessarily dismiss the greenhouse effect, but they’d push back against simplistic narratives:

• They’d caution that alarmism often relies on simplified energy-balance models that may obscure subtleties in radiative transfer.

• They’d argue that real physics requires careful accounting of net fluxes, not raw radiance values.

• They might acknowledge CO₂’s role, but also question whether the magnitude of projected warming is being exaggerated through misapplied assumptions.

---

5. Overall Tone

Their conclusion might be:

• Planck’s statistical leap was both brilliant and troubling.

• Interpretation (1) is a misconception when taken as physical reality.

• Instruments should not be mistaken for truth machines—they display results based on models.

• Climate science needs nuance in communication to avoid overstating or misrepresenting radiative effects.

---

👉 So, compared to a mainstream physicist who would defend consensus, a critical physicist would say:
“Yes, the greenhouse effect is real, but the way radiation laws are sometimes used—and the way data are interpreted—deserves more scrutiny. Simplifications can easily fuel alarmist claims.”

Man-Made Universality of Blackbody Radiation 2

Man-made Universality of Shape

This is a clarification of the previous post on the perfect Planck blackbody spectrum of the Cosmic Microwave Background Radiation CMB as a 14 Billion years afterglow of Big Bang as the leading narrative of cosmology physics today. See also this recent post and this older illuminating post.

The Planck spectrum as the spectrum of an ideal blackbody, takes the form 

• $E(\nu ,T) =\gamma T\nu^2\times C(\nu ,T)$                                         (1)

where $E (\nu ,T)$ is radiation intensity depending on frequency $\nu $ and temperature $T$, $\gamma$ a universal constant, and $C(\nu ,T)$ is a universal high frequency cut-off function of the specific form 

• $C(\nu ,T)=\frac{x}{\exp(x)-1}$ with $x = \frac{\nu}{T}\times\alpha$       (2)

where $\alpha =\frac{h}{k}$ with $h$ Planck's constant and $k$ Boltzmann's constant as another universal constant, with the property that 

• $C(\nu ,T)\approx 1$ for $x<<1$ and $C(\nu ,T)\approx 0$ for $x>>1$.  

We see that radiation intensity proportional to $T$ increases quadratically with $\nu$ in accordance with deterministic wave mechanics, and reaches a maximum shortly before a cut-off scaling with $T$ in accordance with statistics of energy quanta, which kicked off an idea of atom physics as quantum mechanics also based on statistics.    

Computational Blackbody Radiation offers a different version of high frequency cut-off motivated by finite precision physics/computation instead of statistics of quanta opening to a deterministic form of atom physics as real quantum mechanics. The underlying physics model in both cases is that of an atomic lattice capable of generating a continuous spectrum of vibrational frequencies.

The basic assumptions behind a Planck spectrum as an ideal are:

1. Model: Atomic lattice.
2. Equilibrium: All frequencies take on the same temperature.
3. High-frequency universal cut-off: Statistics of energy quanta.  

Observation show that most real blackbody spectra substantially deviate from the Planck spectrum and so have their own signature reflecting specific atomic lattice, non-equilibrium and specific high frequency cut-off lower than the ideal. Graphite is just about the only substance showing a Planck spectrum. 

This was not welcome by physicists in search of universality, and so the idea was born of deciding the spectrum of a given material/body by putting it inside an empty box with graphite walls and measuring the resulting radiation peeping out from a little hole in the box, which not surprisingly showed to be a graphite Planck blackbody spectrum. 

Universality of radiation was then established in the same way as universality of shape can be attained by cutting everything into cubical shape as was done by the brave men cutting paving stone out of the granite rocks of the West Coast of Sweden, which is nothing but man-made universality.  

The line spectrum of a gas is even further away from a blackbody spectrum. The idea of CMB as an afterglow of a young Universe gas cloud with a perfect Planck blackbody as measured by the FIRAS instrument on the COBE satellite, serves as a corner stone of current Big Bang + Inflation cosmology. 

It is not far-fetched to suspect that also the COBE spectrum is man-made, and then also Big Bang + Inflation.

2nd Law for Radiative Heat Transfer as Finite Precision Physics

Transfer of heat energy from warm to cold by electromagnetic waves.

This is a continuation of recent posts on the 2nd Law of Thermodynamics.

There is a 2nd Law for radiative heat transfer expressing:  

• Heat energy is transferred by electromagnetic waves from a body with higher temperature to a body with lower temperature, not the other way.  (*) 

Why is that? Standard physics states that it is a consequence of Plank's law of radiation based on statistics of energy quanta, as an analog of Boltzmann's proof of a 2nd Law based on statistical mechanics. The objections raised to Boltzmann's proof carry over to that of  Planck, who was very unhappy with his proof but not as unhappy as Boltzmann with his. 

An approach without statistics is presented on Computational Blackbody Radiation where (*) appears as a high frequency cut-off increasing with temperature. The effect is that only frequencies above cut-off for the body with lower temperature have a heating effect resulting in one-way transfer of heat from warm to cold. For more details check-out this presentation. 

The high-frequency cut-off can be seen as an expression of finite precision increasing with temperature of atomic oscillation as heat energy. One-way heat transfer is thus a threshold phenomenon connected to finite precision.

Similarly, the photoelectric effect can be explained as a threshold phenomenon connected to finite precision, where only light of sufficiently high frequency can produce electrons. 

A 2nd Law based on finite precision physics thus can serve a role both in both fluid mechanics, and electromagnetics,  and also quantum mechanics as discussed in this post.  

In other words, finite precision physics in analog or digital form appears as the crucial aspect giving  meaning to a universal 2nd Law, which is missing in standard physics with infinite precision. 

The general idea is to replace statistical physics, which is not real physics, by finite precision computation, which can be both analog and digital physics. 

Of course, this idea will not be embraced by analytical mathematicians or theoretical physicists working with infinite precision...

Quality of Heat Energy vs Radiative Heat Transfer

One may expect that radiative heat transfer as a basic topic of both fundamental and engineering physics, has been well understood since long and that therefore there are precise mathematical models capturing everything of interest from both theoretical and practical point of view. 

But that does not seem to be the case. The basic model (used in climate science) takes the form of the more than 100 years old Schwarzschild's equations describing radiative heat transfer in terms of streams of particles in different directions carrying energy packest named photons between layers of a gas of different temperature, in the setting of the atmosphere with with both up-welling and down-welling infrared radiation. In particular, the equations express transfer of heat energy from colder layers to warmer layers. 

But we know that the 2nd Law of Thermodynamics says that heat energy cannot by itself (without external forcing) move from cold to warm, and so Schwarzschild's equations are unphysical. If they form the mathematical model of radiative heat transfer, it seems that some understanding is missing. I make an effort to fill this apparent gap as Computational Black Body Radiation.

The 2nd Law is believed to be difficult to understand lacking a good answer to the basic question: Why can heat energy by itself move only from warm to cold and not the other way? 

One way to understand this is to think of quality of energy measured by temperature. The higher temperature the better quality. It can be compared with quality of knowledge. The essential aspect is that transfer of heat energy or knowledge has a direction from higher quality to lower quality,  not the other way around. 

The quality of heat energy as measured by temperature comes to expression as a high frequency cut-off of the radiation spectrum scaling with temperature according to Wien's Law as a threshold phenomenon.  A warm body carries higher frequencies than a colder body and it is these frequencies which can cause a transfer of heat energy from the warm to the cold.  A more knowledgeable person can transfer knowledge to a less knowledgeable. There is a direction from high to lower quality, which in more general terms is direction of time.  

In the hierarchy of energy, heat energy has lowest rank because it cannot fully be transformed to higher ranks of kinetic or potential energy, and is further decreasing in rank with decreasing temperature. This underlies a feared successive degradation of quality into a heat death of the Universe at 3 Kelvin. This can be added to the alarm of CO2 global warming.

Corruption of Modern Physics 1: Light as Particles

Photon/Energy Quanta Corrupters of Modern Physics

Modern Physics identified by quantum mechanics/atom mechanics as a revolution of classical non-atomistic continuum wave mechanics, was initiated by Planck in 1900 with his mathematical derivation of the spectrum of blackbody radiation based on a concept of energy quanta $hf$ (Joule) as discrete packets of energy with $h=6,62607015·10^{-34}$ Planck's constant and a $f$ a natural number (1,2,3,...) representing a frequency. 

Planck described his long struggle to motivate a high-frequency cut-off needed to avoid an  ultra-violet catastrophe with energies tending to infinity from frequencies without upper bound, as follows:   

• the whole procedure was an act of despair because a theoretical interpretation had to be found at any price, no matter how high that might be...

Frequencies can range from $10^{12}$ for infrared light to $10^{19}$ for gamma rays with corresponding energy quanta $hf$ ranging from $10^{-20}$ to $10^{-14}$ Joule, thus macroscopically very small. Planck did not view his energy quanta to represent real physics, because atom physics was not yet born, and then only as a mathematical trick to achieve high-frequency cut-off from a statistical argument.  

The next step towards quantum mechanics was taken in 1905 by the young Einstein in his "heuristic derivation" of the law of photoelectricity (already formulated by Hertz in 1887 on the basis of experiments), where Einstein picked up the idea of energy quanta $hf$ from Planck, to motivate why shining light on a metal surface releases electrons from the surface only if the light frequency is large enough, as if an energy quanta $hf$ of sufficient strength is needed to release one electron. Einstein's basic "heuristic idea" was thus that exactly one energy quantum later named photon ejects exactly one electron.

Einstein thus suggested to view light as a stream of photons/energy quanta each one if large enough capable of ejecting one electron. But this was only "heuristics" without real physics as admitted by Einstein 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.

A decisive step towards quantum mechanics was taken by the Nobel Prize Committee awarding the 1918 Nobel Prize in Physics to Planck for "his discovery of energy quanta" (in his derivation of black body spectrum), and the 1921 Nobel Prize in Physics to Einstein for "his discovery of the law of the photoelectric effect", thus sending the World a message of light as a stream of particles/photons/energy quanta. This work by Planck and Einstein is still the main "evidence" presented for the "particle nature of light", while all real physics evidence shows "wave nature" expressed in Maxwell's equations for electromagnetics and Schrödinger's equation for quantum mechanics. 

This is where modern physics stands today 100 years later coming to expression as the firm belief of a physicist (whether Nobel Laureate or not) that every material body as real physics is emitting an unstoppable shower of light particles/photons depending on its temperature, but not on the medium surrounding the body. This connects to the discussion with Will Happer still without conclusion.

Planck and Einstein viewed energy quanta/photons/light particles as a "heuristic" concept, which could be useful in certain types of theoretical arguments (statistics or cut-off), but which lacked real physics. Unfortunately this is forgotten by physicists of today, who do not object to an alarm of CO2 Warming caused by Downwelling Long Wave Radiation as stream/shower of energy quanta/photons emitted by the atmosphere and being absorbed by the Earth surface. 

It is important to distinguish between real physics and phantom physics. In phantom physics you are allowed to use concepts without physical meaning if it serves your objectives. In phantom physics you  can view the radiative exchange of heat energy between two bodies as a two-stream flow of photon particles transferring massive heat energy back-and-forth even if the bodies have the same temperature.

It is the same as believing your bank account to be connected to all other bank accounts with a massive one billion dollar transfer back and forth every moment. Or that you are connected to all other people on the web with a constant exchange back and forth of the same one Gbyte message every moment. 

This type of belief lacks real physics because it involves massive transfer back-and-forth, which is unstable and so cannot persist over time. To rely on unstable processes is dangerous and will result in misfortune. 

Corruption involves massive back-and-forth transfer of services/commodities. Corrupted physics involves massive back-and-forth transfer of heat energy. 

For a derivation of the laws of black body radiation and photoelectricity based on real physics carried by electromagnetic waves, see Mathematical Physics of Blackbody Radiation.  For quantum mechanics without particles, see Real Quantum Mechanics.

      

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.

Is Radiative Heat Transfer a Resonance Phenomenon Between Bodies?

Computational BlackBody Radiation offers a new proof of the Planck-Stefan-Boltzmann Law PSB based on electromagnetic wave resonance under deterministic finite precision computation, taking the form

• $Q = \sigma (T_A^4 - T_B^4),$       (1)

where $Q$ is (normalised) radiative transfer of heat energy between two blackbodies A and B with temperatures $T_A$ and $T_B$ Kelvin, and $\sigma$ is the SB constant. If $T_A>T_B$ then the heat transfer is from A to B.

This is to be compared with the 1900 proof by Planck based on particle/quanta statistics typically expressed on the following form involving only one blackbody of temperature $T$:

• $Q = \sigma T^4.$       (2)

Comparing (1) and (2) we see that (1) expresses the radiative heat transfer between two bodies in resonance, while (2) is supposed to express the radiative heat transfer from one body independent of surrounding bodies and thus without resonance. 

In particular, (1) expresses that heat transfer from A requires the presence of a receptor B with lower temperature. On the other hand (2) appears to express that a body can radiate (spit out quanta/photons) without receptor, or assuming the presence of "empty space" at 0 Kelvin acting as receptor. In this case the body at higher temperature will spit most and so win the combat. 

This leads to the following questions: 

• Does radiative heat transfer from one body need a receptor at lower temperature?
• Does radiative heat transfer involve a resonance phenomenon between bodies? 

The new proof of PSB suggests that the answer is YES, while the standard proof suggests NO. What does physics and observation say? YES or No? Is radiative heat transfer carried by electromagnetic waves or particles/photons? An answer that it is both is no good. The questions concern basic physics and must be answered.

Compare with resonance between two tuning forks:

 To be compared with a particle model with both forks spitting out particles/phonons?

PS Read about Planck's struggle to prove (2) in Quantum Mechanics at the Crossroads starting with Schrödinger Against Particles and Quantum Jumps by M. Bitbol and continuing with Max Planck's Compromises on the Way to and from the Absolute by J. L. Heilbron.

Yes, it is not a good idea to resort to compromises in science, which is the essence of politics. Planck was not happy with his particle/quanta statistics and neither was Schrödinger, yet it has come to serve as a fundamental part of quantum mechanics following Born-Bohr. Real Quantum Mechanics in the spirit of Schrödinger presents a new realist deterministic approach based on waves instead of particle statistics.  

 

Demystifying the New SI Base Units.

In the previous post we observed that Planck's constant $h$ appears as a conversion factor connecting light of frequency $\nu$ with attributed energy $h\nu$ (in eV or Joule) through the photoelectric effect with the release of an electron from a surface exposed to light (of sufficient high frequency). The inner mechanics of the atoms delivering the electrons upon excitation by exposure to light does not enter into the discussion and so Planck's constant can be given a meaning in macroscopic physics, thus without quantum mechanics, as a trade between light and electron energy and then further to mechanical energy. Its role in quantum mechanics then appears as an after construction.

Let us now turn to Boltzmann's constant $k$ to see its connection to Planck's constant and macroscopic physics. Boltzmann's constant appears in Planck's universal law of blackbody radiation law of the form

• $E(\nu ,T) = W(a)\, kT\nu^2$,
• $W(a) = \frac{a}{\exp(a )-1}$ with $a = \frac{h\nu}{kT}$,

where $E(\nu ,T)$ is the (suitably normalised) intensity of radiation of frequency $\nu$ from a blackbody of temperature $T$ and $W(a)$ is a cut-off factor with $W(a)=1 $ for small $a$ and
$W(a)$ small for medium to large $a$, expressing Wien's displacement law stating cut-off of high frequencies. We see that Planck’s constant only appears in the cut-off factor.

Experimental observation of $E(\nu ,T)$ makes it possible to determine $W(a)$ and thus $kT$ in terms of $h\nu$, from which Boltzmann's constant $k$ can be determined with respect to a chosen scale for temperatur $T$, or the other way around as in the new SI units by specifying by definition 

• $k=1.380650\times 10^{-23}\, J/K$,  

thus setting a new standard for Kelvin $K$ as measure of temperature. The connection between the energy measures $h\nu$ and $kT$ then shows to be

• $h\nu_{max} \approx 2.8214391\times kT$,

where $\nu = \nu_{max}$ gives maximum of the spectrum $E(\nu ,T)$.

Again, this can be done without having to invoke quantum mechanics in its standard form with $h$ as a "smallest quantum of action" as exposed in detail on Computational Blackbody Radiation, which presents a derivation of Planck's law using deterministic continuum physics instead of as usual statistics of discrete quanta. In particular, the new derivation captures the universality of blackbody radiation beyond specific inner atomic mechanics.

The universality of Planck's law is expressed by the fact that an ideal blackbody can take the form of a set of oscillators without very specific inner structure. In particular different blackbodies with different inner structure can share the same temperature scale.

To sum up, both Planck's constant and Boltzmann's constant are specified by definition in the new SI units, from which the new units kilogram and Kelvin can be determined by macroscopic experiments without resort to quantum mechanics in its standard form.



Hopefully this helps to demystify both Planck's and Boltzmann's constant, and the new SI units.
 

Planck's Desperate Mad Ugly Ad Hoc Trick: The Quantum

Planck's reasoning was mad, but his madness has that divine quality that only the greatest transitional figures can bring to science. (Abraham Pais in The Science and Life of Albert Einstein)

...the whole procedure was an act of despair because a theoretical interpretation had to be found at any price, no matter how high that might be... (Planck on the statistical mechanics basis of his radiation law)

Sabine Hossenfelder on Backreaction gives praise to the new book Breakfast with Einstein by Chad Orzel:

• Physics is everywhere, that is the message of Chad Orzel’s new book “Breakfast with Einstein,” and he delivers his message masterfully.
• In contrast to many recent books about physics, Orzel stays away from speculation, and focuses instead on the many remarkable achievements that last century’s led to.

Planck was not happy with his desperate mad ugly ad hoc trick of the quantum

Chapter 2 of the book has the title The Heating Element: Planck's Desperate Trick with the objective of describing the birth of quantum mechanics attributed to Planck's (ugly ad hoc) trick of avoiding the apparent ultraviolet catastrophe of classical wave mechanics by introducing the concept of a smallest package of energy named quantum: 

• This “quantum hypothesis” does the necessary trick of cutting off the amount of light at high frequencies—exactly where the ultraviolet catastrophe happens. 
• Planck initially introduced the quantum hypothesis thinking it was a “desperate mathematical trick.” 
• Despite the many successes of his formula and the personal fame it brought him, Max Planck himself was never particularly satisfied with his quantum theory.
• He regarded the quantum hypothesis as an ugly ad hoc trick, and he hoped that someone would find a way to get from basic physical principles to his formula for the spectrum without resort- ing to that quantum business. 
• Once the idea was out there, though, other physicists picked it up and ran with it, most notably a certain patent clerk in Switzerland—leading to a complete and radical transformation of all of physics.

I have presented an alternative theory based on finite precision computation, which meets Planck's wish of explaining the black body spectrum from basic classical wave mechanics physics, which is presented on Computational BlackBody Radiation. Why not take a look, and see if you get enlightened? By a physical theory of blackbody radiation.

The idea of finite precision computation is the same as that used in a new explanation of the the 2nd law of thermodynamics discussed in the previous post on Boltzmann and his explanation based on (ugly ad hoc) statistics.

The master of ugly ad hoc tricks is Roger Stone as documented in his new book Stone's Rules. Such tricks can take you to the top of both science and politics! They can give you fame, but evidently not happiness. Another master of this game was the patent clerk in Switzerland, who also was unhappy with his theories, in particular the theory of the quantum he picked up from Planck, which gave him such immense fame:

• If I would be a young man again and had to decide how to make my living, I would not try to become a scientist or scholar or teacher. I would rather choose to be a plumber or a peddler in the hope to find that modest degree of independence still available under present circumstances.
• 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.
• For the most part I do the thing which my own nature drives me to do. It is embarrasing to earn so much respect and love for it. 
• Why is it that nobody understands me, and everybody likes me? (Einstein in New York Times, March 12, 1944) 

PS1 Often a truth about science, or rather a truth about a shortcoming of some scientific theory, is more honestly expressed in popular science, as the truth of the ugly ad hoc science of the quantum in Orzel's book (because the audience is supposed to be ignorant), than in some professional scientific context hiding the shortcoming in some cover-up (because the audience is supposed to be knowledgable and critical). Therefore it is interesting to read popular science also for a scientist.

PS2 Planck's desperate ugly ad hoc trick (which originates from Boltzmann) has caused a lot of confusion among physicists. For example, quantum mechanics, which is not understood by any serious honest physicist,  is supposed to have some mysterious connection to the quantum of energy of Planck, but the fact is that quantum mechanics is based on Schrödinger's equation, which is a continuum mechanical model and not a discrete model build from small packets of energy. The confusion is exhibited in Real Quantum Mechanics offering a new form of and new view on Schrödinger's equation with the common confusion eliminated.  But it is not easy to get a discussion going on the fundamentals of quantum mechanics, since the confusion is so monumental resulting from a  desperate mad ugly ad hoc trick, supposed to be the foundation of modern physics. No wonder that physics is in crisis. See also Dr Faustus of Modern Physics.

PS3 Recall that it was Einstein who introduced the idea that light is made of discrete chunks of energy $h\nu$ as photons with $h$ Planck's constant in Joulesecond and $\nu$ frequency, in his heuristic Law of the photoelectric effect $h\nu + W = eU$ with $W$ work to release an electron
and $eU$ in electron volt eV with $U$ the stopping potential in volt and e the charge of an electron. I argue in Mathematical Physics of BlackBody Radiation and related blogg posts that the Law is to viewed as a frequency threshold condition, which has no relation to any idea of light as consisting of discrete photons or light quanta, which according to the above quote was also the view of the late Einstein.

The Law shows that Planck's constant $h$ appears as a conversion between energy related to light frequency $\nu$ (in Joule) and electron energy (in eV), for which Einstein received the Nobel Prize in Physics in 1921 with explicit mention that he did not get the Prize for his theories of relativity). 

PS4 Schrödinger's equation connects energy related to light frequency and electron energy and it is thus no wonder that the Planck constant appearing in Schrödinger's equation is the same as that in the Law of the photoelectric effect. Mathematical Physics of BlackBody Radiation also gives evidence that the Law of the photoelectric effect is a consequence of Schrödinger's equation, within a continuum model without photon particles and reference to Einstein's heuristic argument that a photon of sufficient energy can kick out an electron. 

 

Talk at Climate Sense 2018

I have put up a preliminary version of my talk at Climate Sense 2018 for inspection.

New Proof of Planck's Radiation Law vs (Italian) Piano Tuning

Computation Blackbody Radiation presentats a new approach to Planck's radiation law based on finite precision computation applied to a wave model consisting a set of harmonic oscillators with small damping subject to near-resonant forcing, each one of the oscillators of the form

• $\ddot u(t)+\nu^2u(t)+\gamma\dot u(t)=f(t)$ for time $t>0$,  

where $\dot u=\frac{du}{dt}$ and $\ddot u=\frac{d^2u}{dt^2}$, $\nu >> 1$ is the eigenfrequency of the oscillator, $\gamma $ is a small positive damping coefficient with $\gamma\nu\le 1$, and $f(t)$ is a near-resonant forcing, for example given by

• $f(t)=\sin((\nu -0.5)t)+\sin(\nu t)+\sin((\nu +0.5)t)$

with a total frequency shift of 1 Hz.

A basic aspect of this model connects to the so called Italian tuning of a piano, where the three strings in the middle high register for each key/tone are tuned with a total frequency shift of about 1 Hz as above. 

Let us now seek to understand in what sense Italian tuning is different from standard tuning with the three strings for each key/tone tuned to exactly the same frequency or pitch. We then identify in the above model 

• the three strings are represented by the forcing $f(t)$,
• the sound board of the piano is represented by the oscillator,
• the outgoing sound from the sound board is represented by the damping.  

Let us first consider standard tuning with strings and soundboard all with the same eigen-frequency, that is a case with perfect resonance. A pressed key activates a hammer with hits the strings which start to vibrate and thereby as forcing transfers energy to the sound board, which in turn starts to vibrate and produces a sound. In this case the forcing $f(t)$ will stay in phase with the velocity $\dot u$ over time, which means quick transfer of energy from strings to sound board as the integral of the positive product $f(t)\dot u(t)$ as the work performed per unit time. The result may be an outgoing sound of relatively high volume but short duration.

On the other hand, with the Italian tuning, the forcing from each of the three strings with slightly different frequencies cannot all be in phase with the common sound board velocity $\dot u$ over time, which means less quick energy transfer to the sound board with $f(t)\dot u(t)$ of changing sign and thus slower string energy loss as compared to the standard case. The result may be a sound of less volume but longer duration (sustain) than in the standard case, and also with slight "beat".

Of course, in reality it may be difficult to clearly separate the two cases, because perfect resonance does not really occur for a real piano with standard tuning, because of the complexity of the sound board, and also because the damper stops the string vibration before the tone has faded.

In any case, the distinction between perfect and near resonance is fundamental in the new proof of Planck's radiation law offered as by Computation Blackbody Radiation, a proof without reference to mystical statistics.

PS It is possible to change the setting by letting $f(t)$ represent the outgoing sound and the damping the input from the strings to the sound board. This is of relevance in stationary periodic state with sustained sound over long time without damping.

Finite Element Quantum Mechanics 4: Spherically Symmetric Model

I have tested the new atomic model described in a previous post in setting of spherical symmetry with electrons filling a sequence of non-overlapping spherical shells around a kernel. The electrons in each shell are homogenized to spherical symmetry which reduces the model to a 1d free boundary problem with the free boundary represented by the inter-shell spherical surfaces adjusted so that the combined wave function is continuous along with derivates across the boundary. The repulsion energy is computed so as to take into account that electrons are not subject to self-repulsion, by a corresponding reduction of the repulsion within a shell.

The remarkable feature of this atomic model, in the form of a 1d free boundary problem with continuity as free boundary condition and readily computable on a lap-top, is that computed ground state energies show to be surprisingly accurate (within 1%) for all atoms including ions (I have so far tested up to atomic number 54 and am now testing excited states).

Recall that the wave function $\psi (x,t)$ solving the free boundary problem, has the form

• $\psi (x,t) =\psi_1(x,t)+\psi_2(x,t)+...+\psi_S(x,t)$         (1)

with $(x,t)$ a common space-time coordinate, where $S$ is the number of shells and $\psi_j(x,t)$ with support in shell $j$ is the wave function for the homogenized wave function for the electrons in shell $j$ with $\int\vert\psi_j(x,t)\vert^2\, dx$ equal to the number of electrons in shell $j$.

Note that the free boundary condition expresses continuity of charge distribution across inter-shell boundaries, which appears natural.

Note that the model can be used in time dependent form and then allows direct computation of vibrational frequencies, which is what can be observed. 

Altogether, the model in spherical symmetric form indicates that the model captures essential features of the dynamics of an atom, and thus can useful in particular for studies of atoms subject to exterior forcing. 

I have also tested the model without spherical homogenisation for atoms with up to 10 electrons, with  similar results. In this case the the free boundary separates diffferent electrons (and not just shells of electrons) with again continuous charge distribution across the corresponding free boundary. 

In this model electronic wave functions share a common space variable and have disjoint supports and can be given a classical direct physical interpretation as charge distribution. There is no need of any Pauli exclusion principle: Electrons simply occupy different regions of space and do not overlap, just as in a classical multi-species continuum model.

This is to be compared with standard quantum mechanics based on multidimensional wave functions $\psi (x_1,x_2,...,x_N,t)$ typically appearing as linear combinations of products of electronic wave functions

• $\psi (x_1,x_2,...,x_N,t)=\psi_1(x_1,t)\times \psi_2(x_2,t)....\times\psi_N(x_N,t)$        (2)

for an atom with $N$ electrons, each electronic wave function $\psi_j(x_j,t)$ being globally defined with its own independent space coordinate $x_j$. Such multidimensional wave functions can only be given statistical interpretation, which lacks direct physical meaning. In addition, Pauli's exclusion principle must be invoked and it should be remembered that Pauli himself did not like his principle since it was introduced ad hoc without any physical motivation, to save quantum mechanics from collapse from the very start...

More precisely, while (1) is perfectly reasonable from a classical continuum physics point of view, and as such is computable and useful, linear combination of (2) represent a monstrosity which is both uncomputable and unphysical and thus dangerous, but nevertheless is supposed to represent the greatest achievement of human intellect all times in the form of the so called modern physics of quantum mechanics.

How long will it take for reason and rationality to return to physics after the dark age of modern physics initiated in 1900 when Planck's "in a moment of despair" resorted to an ad hoc hypothesis of a smallest quantum of energy in order to avoid the "ultra-violet catastrophe" of radiation viewed to be  impossible to avoid in classical continuum physics. But with physics as finite precision computation, which I am exploring, there is no catastrophe of any sort and Planck's sacrifice of rationality serves no purpose.

PS Here are the details of the spherical symmetric model starting from the following new formulation of a Schrödinger equation for an atom with $N$ electrons organised in spherical symmetric form into $S$ shells: Find a wave function

• $\psi (x,t) = \sum_{j=1}^N\psi_j(x,t)$

as a sum of $N$ electronic complex-valued wave functions $\psi_j(x,t)$, depending on a common 3d space coordinate $x\in R^3$ and time coordinate $t$ with non-overlapping spatial supports $\Omega_1(t)$,...,$\Omega_N(t)$, filling 3d space, satisfying

• $i\dot\psi (x,t) + H\psi (x,t) = 0$ for all $(x,t)$,       (1)

where the (normalised) Hamiltonian $H$ is given by

• $H(x) = -\frac{1}{2}\Delta - \frac{N}{\vert x\vert}+\sum_{k\neq j}V_k(x)$ for $x\in\Omega_j(t)$,

where $V_k(x)$ is the potential corresponding to electron $k$ defined by 

• $V_k(x)=\int\frac{\vert\psi_k(y,t)\vert^2}{2\vert x-y\vert}dy$, for $x\in R^3$,

and the wave functions are normalised to correspond to unit charge of each electron:

• $\int_{\Omega_j}\vert\psi_j(x,t)\vert^2 =1$ for all $t$ for $j=1,..,N$.

Assume the electrons fill a sequence of shells $S_k$ for $k=1,...,S$ centered at the atom kernel with $N_k$ electrons on shell $S_k$ and 

• $\int_{S_k}\vert\psi (x,t)\vert^2 =N_k$ for all $t$ for $k=1,..,S$,
• $\sum_k^S N_k = N$.

The total wave function $\psi (x,t)$ is thus assumed to be continuously differentiable and the electronic potential of the Hamiltonian acting in $\Omega_j(t)$ is given as the attractive kernel potential together with the repulsive kernel potential resulting from the combined electronic charge distributions $\vert\psi_k\vert^2$ for $k\neq j$, with total electronic repulsion energy

• $\sum_{k\neq j}\int\frac{\vert\psi_k(x,t)\vert^2\vert\psi_k(y,t)\vert^2}{2\vert x-y\vert}dxdy=\sum_{k\neq j}V_k(x)\vert\psi_k(x)\vert^2\, dx$.

Assume now that the electronic repulsion energy is approximately determined by homogenising the $N_k$ electronic wave function $\psi_j$ in each shell $S_k$ into a spherically symmetric "electron cloud" $\Psi_k(x)$ with corresponding potential $W_k(y)$ given by

• $W_k(y)=\int_{\vert x\vert <\vert y\vert}R_k\frac{\vert\Psi_k(x)\vert ^2}{\vert y\vert}\, dx+\int_{\vert x\vert >\vert y\vert}R_k\frac{\vert\Psi_k(x)\vert ^2}{\vert x\vert}\, dx$,

and $R_k(x)=\frac{N_k-1}{N_k}$ for $x\in S_k$ is a reduction factor reflecting non self-repulsion of each electron (and $R_k=1$ else): Of the $N_k$ electrons in shell $S_k$, thus only $N_k-1$ electrons contribute to the value of potential in shell $S_k$ from the electrons in shell $S_k$. We here use the fact that the potential $W(x)$ of a uniform charge distribution on a spherical surface $\{y:\vert y\vert =r\}$ of radius $r$ of total charge $Q$, is equal to $Q/\vert x\vert$ for $\vert x\vert >r$ and $Q/r$ for $\vert x\vert <r$.

Our model then has spherical symmetry and is a 1d free boundary problem in the radius $r=\vert x\vert$ with the free boundary represented by the radii of the shells and the corresponding Hamiltonian is defined by the electronic potentials computed by spherical homogenisation in each shell. The free boundary is determined so that the combined wave function $\psi (x,t)$ is continuously differentiable across the free boundary. 

Korrespondens med Lennart Bengtsson om Vetenskaplig Dokumentation av "Återstrålning"

Hej Lennart:

Du föreslog att jag skulle ta kontakt med Raymond Pierrehumbert angående fysiken bakom "återstrålning, vilket jag gjorde. Det visade sig att Raymond inte kunde/ville hänvisa till någon vetenskaplig dokumentation av detta fenomen annat än att "återstrålning" på något sätt var så välkänt att någon källa varken fanns eller behövdes. Samma sak upprepade sig vid mitt samtal med Henning.

Du förefaller nu stå bakom KVAs avslag på min begäran om redovisning av den vetenskapliga dokumentationen av "återstrålning". 

Detta går inte ihop för mig. Uppenbarligen tar Du min fråga om "återstrålning" på allvar, och då kan denna inte lämnas utan svar, om vetenskapens grundprincip skall följas.

Om inte frågan nu kan ges ett svar, så kommer den att ligga kvar och kräva svar.

KVAs kommande uttalande lägger grunden för svensk klimatpolitik till 2050 och det är således av yttersta vikt att uttalandet har en så solid vetenskaplig grund som möjligt. Om uttalandet grundar sig på en "växthuseffekt" med "återstrålning" som väsentlig komponent , så måste relevant vetenskaplig dokumentation finnas. Eller hur?

Mina studier har lett mig till uppfattningen att "återstrålning" är en skrivbordsprodukt utan verklighetsförankring. Om detta är korrekt, så kommer detta förr eller senare att inses och bli erkänt av vetenskapssamhället.

Hur ser Du på min fråga och KVAs avslag?

Vänligen, Claes

Lennart Bengtssons svar:

Hej

Som Du väl känner till är "återstrålningen"  och därmed existensen av av atmosfäriska gaser som absorberar och återstrålar elektromagnetisk strålning ett vedertaget begrepp inom fysiken sedan detta  först påvisades experimentellt av Tyndall 1863 och senare teoretiskt främst av Max Planck.  Jag kan också hänvisa till Kirchhoffs grundläggande arbeten. Alla centrala läroböcker i atmosfärisk strålning t ex Chandrasekhar (1960) eller Goody och Yung (1989) ger här en klar framställning. De uppfattningar som beskrivs i dessa arbeten och läroböcker presenterar den teori som ligger till grund för den teoretiska behandlingen av strålningsprocesser i dagens atmosfärmodeller. Jag kan också hänvisa till Arrhenius artikel från 1896 som bland annat hade en klar uppfattning om  koddioxiden absorbtionsegenskaper inklusive feedbackprocessen från vattenånga.
Du måste ju förstå att om Du  som Du gjort för fram ytterst radikala uppfattningar som ifrågasätter 150 års strålningsstudier att Du  som ett minimum måste presentera ett vetenskapligt arbete som måste utvärderas  av vetenskapligt sakkunniga. Om Du anser Dig ha goda grunder för att kunskapen om atmosfärisk strålning är fundamentalt fel, vilket Du förefaller hävda, så finns det inget annat jag kan föreslå.

Hälsningar, Lennart

Mitt svar:

Tack för detta svar Lennart. Jo, jag känner väl till det Du refererar till. Men att någonting är ett "vedertaget begrepp" betyder inte att det är korrekt. 

Ditt svar illustrerar den begreppsförvirring som uppkommit genom en feltolkning av Plancks lag i form av två-vägs värmeöverföring medelst strålning mellan två kroppar av olika temperatur, där nettoflödet varm-till-kall skrivs som skillnaden mellan två motriktade flöden varm-till-kall och kall-till-varm. Detta är en skrivbordskonstruktion, som infördes av Schwarzschild för att ställa upp enkla ekvationer för värmeöverföring medelst strålning, som lätt kan lösas analytiskt. Att detta är en formell metod understryks i Chandrasekhars framställning, vilken ligger till grund för de centrala läroböcker Du hänvisar till som Goody-Yung.  

Ingen av de referenser Du anger till Planck, Kirchhoff och Arrhenius innehåller något om "återstrålning".

Jag ifrågasätter inte all vetenskap om värmeöverföring medelst strålning. Vad jag ifrågasätter är att ge en formell modell för detta fenomen, tillkommen för att medge enkel analytisk lösning, en verklig fysikalisk mening i form av "återstrålning". Detta eftersom en sådan formell brutto-kalkyl med ett värmeutbyte via strålning mellan jordyta och atmosfär av storleksordningen 300 W/m2, jämfört med en netto-kalkyl om ca 30 W/m2, kan ge en helt felaktig bild av effekten av perturbationer. Och det är detta klimatvetenskapen handlar om.

Mina frågor om "återstrålning" kvarstår: 

1. I vilket vetenskapligt arbete infördes begreppet "återstrålning"?

2. Beskriver Schwarzschilds ekvationer det verkliga fysikaliska värmeutbytet via strålning mellan två kroppar av olika temperatur? 

3. Eller är Schwarzschilds ekvationer enbart en formell metod att beräkna detta värmeutbyte?

4. Inbegriper Plancks bevis av Plancks strålningslag någonting om "återstrålning"?

5. Finns existensen av "återstrålning" verifierad experimentellt? I så fall, med vilken instrumentation?

6. På vilket sätt är "återstrålning" med värmeöverföring kall-till-varm förenlig med termodynamikens andra huvudsats?

Svaret på dessa frågor, och möjliga relaterade följdfrågor, bör lämpligen presenteras vid ett seminarium med alla inblandade närvarande. Kan jag nu räkna med att ett sådant seminarium arrangeras?

Vänligen, Claes

PS1 Goody and Yung, Atmospheric Radiation, skriver på sid 22:... the equation of transfer was first given by Schwarzschild. While it sets the pattern of the formalism used in transfer problems, its physical content is very slight. Och på sid 63: The formal theory of this book is based, wherever possible, on Chandrasekhar, Radiative transfer (1950,1960).

PS2 Gray and Muller, Engineering Calculations in Radiative Heat Transfer, skriver i (2.1) Plancks lag på den korrekta formen $Q=\sigma (T_1^4-T_2^4)$, där $T_1>T_2$. 

Lennarts svar på mina frågor: TBA

Quantum Statistics as Salvation from Catastrophe?

Planck awarding the Planck Medal to Einstein in 1929 for his elaboration of Planck's idea of discrete of quanta of energy into quanta of light, an idea which Planck viewed as a "hypothetical attempt" resulting from an "act of desperation".

To understand a theory of physics it is helpful to seek the reason the theory was developed. In The Conceptual Development of Quantum Mechanics by Max Jammer we read:

• Quantum theory had its origin in the inability of classical physics to account for the experimentally observed distribution in the continuous spectrum of black-body.
• It is convenient to define the first phase in the development of quantum theory the period in which all quantum conceptions and principles proposed referred exclusively to black-body radiation or harmonic vibrations.  
• …the study of the single physical phenomenon of blackbody radiation led to the conceptions of quanta and to quantum statistics of the harmonic oscillator, and thus to results which defied the principles of classical mechanics and, in particular, the equipartition theorem.
• It was generally agreed that classical physics was incapable of accounting for atomic and molecular processes.
• Planck obviously regarded the use of the law of chance… merely as a provisional device… in his own opinion his new theory was but a "hypothetical attempt" to reconcile the law of radiation with foundations of Maxwell's doctrine, and not a final solution to the problem.

Quantum mechanics thus developed from Planck's hypothetical attempt to save Wien's classical radiation law with radiance of frequency $\nu$ scaling like $T\nu^2$ with $T$ temperature, from an ultraviolet catastrophe with the radiance apparently tending to infinity without any bound on the frequency $\nu$.

To save the world from this catastrophe, Planck against his basic convictions as scientist seeing no way other out, then gave up causality as the essence of science by corrupting his deterministic harmonic oscillators by statistics. And on this shaky ground quantum mechanics was formed. No wonder that quantum mechanics in its present form is a catastrophe (with uncomputable wave-functions without physical meaning), although depicted as an imposing intellectual structure of great beauty. 

But can statistics really save us from catastrophe? Catastrophe may be the result an unfortunate throw of dice by fate, but you don't avoid a catastrophe by letting dice throw decide how to steer your car.  

Computational Blackbody Radiation describes a different way of avoiding the ultraviolet catastrophe with statistics replaced by a constructive version of classical mechanics based on finite precision computation. From this starting point a quantum mechanics without statistics may be possible to formulate. If so the present catastrophe of quantum mechanics can (perhaps) be avoided.