The Principles of Least Action and Virtual Work

To seek out what Euler was referring to let us consider the basic case of a harmonic oscillator which can be seen as a body attached to one end of a spring the other end being fixed with the body moving back and forth on a frictionless table (along a straight line). The motion of the body satisfies the following differential equation expressing balance of dynamic and spring forces:

• $\ddot x(t) = - x(t) $ for $0<t<T$     (1)

where $x(t)$ is the position of the body being equal to the length of the spring, $\dot x(t)=\frac{dx}{dt}(t)$ is the velocity and $\ddot x(t)$ is the acceleration of the body at time $t$.  Here  $0$ is an initial time with $x(0)$ and $\dot x(0)$ given as initial conditions and $T$ is a final time.

The equation (1) can be solved analytically and with $x(0)=0$ and $\dot x(0)=1$ the solution is $x(t)=\sin (t)$ as a periodic harmonic oscillation. 

Following Euler, let us now formally multiply (1) with an arbitrary function $y(t)$ satisfying $y(0)=0$ and $y(T)=0$ and integrate over $[0,T]$ including integration by parts to get 

• $\int_0^T(-\dot x\dot y + xy) dt = 0$ for all $y(t)$ with $y(0)=y(T)=0$.   (2)

The equation (2) expresses stationarity of the Lagrangian 

• $L(x)=\int_0^T (-\frac{1}{2} {\dot x}^2 +\frac{1}{2}x^2 )dt$

in the sense that $L(x+\epsilon y)$ does not change from $L(x)$ for a perturbation $\epsilon y(t)$ with small $\epsilon$ i.e,  

• $\frac{d}{d\epsilon}L(x+\epsilon y)=0$ for $\epsilon =0$.   (3)

We thus see that:

• The Equation of Motion EoM (1) expresses Stationarity of the Lagrangian (2) or (3).  

The stationarity of the Lagrangian is also named the Principle of Least Action PLA where action or work is force times displacement as expressed by multiplying the force balance equation $\ddot x+x=0$ by the displacement $x$ or $y$ as in (2). The Principle of Least Action in the from (2) is also referred to as the Principle of Virtual Work PVW with $y(t)$ a virtual displacement.

The Principal of Virtual Work is the starting point for the Finite Element Method as a computational method to solve EoM in cases when analytical solution is not feasible.

We can now summarise:

• Physics is modeled by EoM expressing balance of forces. 
• Formally EoM expresses PLA/PVW.
• Computational methods build on PLA/PLW.

We understand that PVW is a formality since virtual work is a formality. 

We can naturally connect to the distinction between ontology (what is) and epistemology (what one can say). What is are the body and spring on the table with dynamic and spring forces. What we can say is PLA or PVW and from that can we construct computational methods. 

What is less natural is to view a physical system to evolve according to PLA or PVW since it is not equipped with any (brain) power to compute action and then seek least action. This is something a a human with computer can do but not the physical system itself. A physical system evolves in order to satisfy EoM but not to satisfy PLA or PVW. 

We know that light is wave phenomenon satisfying certain EoM with a connected PLA expressing quickest path which can used in computation but does not govern the real physics. 

The formalism of PLA was given a prominent role in classical physics because it was useful in computation and so the distinction from the physics of EoM became unclear. The formalism was picked up in modern physics with Lagrangians being the holy grail.  In particular, quantum mechanics was based on formalities without physics, which has led to endless discussions about physicality without resolution as made clear in previous posts. 

The Value of Incorrect Theories of Physics?

Incorrect (or correct?) Theory of the World

This is a return to a previous post on the book 

• Foundations of Quantum Mechanics An Exploration of the Physical Meaning of Quantum Theory  

after a lengthy discussion with its author Travis Norsen. The book presents the three basic problems of  Foundations of Quantum Mechanics QM:

1. Measurement Problem 
2. Locality Problem
3. Ontology Problem 

along with the following attempted “solutions” 70-90 years old: 

• Copenhagen Interpretation 
• Pilot Wave Theory
• Many Worlds Theory
• Collapse Theory

none of which is considered to be satisfactory. Travis favours the Pilot Wave Theory, which apparently does not solve the problem, since the other "solutions" are also given wide attention.

When confronted with RealQM as my attempted solution to all three problems, Travis says that this appears to be a new solution, while stressing that something like that cannot possibly be true!

Fair enough. It is not to be expected that yet another "solution" will be welcomed into the circle of physicists still working on the Foundations of QM despite so little progress over so many years. But I welcome the information that RealQM seems to offer new ideas.  

What can be the scientific value of theories which are incorrect and so cannot be really useful or at least are risky to use? 

Well, you can apparently fill text books and give courses with such material. For the student to learn many incorrect theories may serve to protect from believing in them. But there are infinitely many incorrect theories, so the curriculum will be vast. If there was at least one correct theory, then the curriculum could be shortened to the satisfaction of the student. RealQM may offer something in that direction.

The situation is the same in the classical area of aerodynamics where NASA presents three incorrect Theories of Flight, but no theory claimed to be correct. Also here is there a new theory, which has many signs of being correct as presented on Secret of Flight.

The role of a scientist (and politician) is to have answers to questions and solutions to problems. To not be able to deliver is a sign of weakness resulting in lack of funding or votes, and then a resort to incorrect theories may be the quick "solution" (like printing money or referring to dark energy), even if over time it does not work. 

I have asked Travis about a comment.

How to (Not) Create a Model of (Atom) Physics

The classical method to formulate a mathematical model of some physical phenomena used since ancient time through the 19th century is to combine a set of laws of physics describing some real (or imagined) physical reality. And then use the model to find consequences of the laws of physics and learn about the World.

A prime success example is Newton's model of a system of bodies interacting by Newton's Law of gravitational attraction. Another is Maxwell's equations expressing the Laws of Ampere, Faraday, Gauss and Coulomb.  Both models capture a very wide range of physics. 

In 1913 Bohr together with Rutherford formulated a model for the Hydrogen atom as an electron orbiting a kernel in the spirit of a Newtonian planetary system. But the model was not satisfactory since it ad hoc postulated that only certain electron orbits were allowed without convincing physical rationale. In addition it could not explain why an atom in ground state was stable. In short the model contained ad hoc elements without physics and did not fit with the observation of stable atoms without radiation. 

In 1925 Schrödinger formulated a new model for the Hydrogen atom as an electronic charge density attracted by a kernel according to Coulomb's Law. The model was greeted as an enormous success because it could explain both the stability of ground state and radiation spectrum. The model did not contain any ad hoc non-physics. 

Schrödinger's Hydrogen model opened the new era of atom physics, but the generalisation to atoms with more than one electron was not at all obvious, and so Schrödinger resorted to a formal generalisation into an equation in formal configuration space without physical meaning. This was another ad hoc model formed by a purely formal mathematical procedure without physics, but lacking any alternative it became Schrödinger's equation (S) as the foundation of quantum mechanics of atoms. 

But since (S) was not formed from a physical law, only from mathematical formality, the tasks to give solutions to (S) a physical meaning remained. But that showed to be far from easy troubling the minds of physicists for 100 years until it was agreed that this was not necessary: It was enough to "Shut up and calculate" and not ask about any physical meaning. 

RealQM offers a new atomic model based on laws of physics. This brings atom physics into the classical methodology of forming mathematical models of physics from laws of physics, not from formalities without physical meaning. 

A mathematical model based on laws of physics can say something about physics. This is Wigner's

•  Unreasonable Effectiveness of Mathematics in the Natural Sciences.

which should rather read: 

• Reasonable Effectiveness of Computational Mathematics in the Natural Sciences. 

It is further unreasonable to expect that a mathematical model based on ad hoc laws without physics, can say something about physics.    

Non-Physical Nature of Energy Quanta of Light or Photons

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

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

•  $\ddot x = - x $    (H)

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

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

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

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

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

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

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

  

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

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

Phlogistons and Photons as Non-Physics

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

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

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

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

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

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

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

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

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

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

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

 

The Real Essence of Quantum Mechanics

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

1. Theory 

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

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

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

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

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

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

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

Consider now a superposition of two eigenstates such as 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

2. Theory vs Observation 

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

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

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

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

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

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

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

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

3. Formality without physics  

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

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

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

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

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

4. Physical size of Hydrogen atom ground state 

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

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

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

5. Electron Mass?

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

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

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

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

   

Quantum Mechanics Today: For or Against Measurement?

In the probabilistic Bohr/Heisenberg Copenhagen Interpretation CI of quantum mechanics from 1930s the word measurement plays a key role, because it is the measurement which decides some actuality out of many possibilities, like the observation of a dead or alive Schrödinger Cat upon opening of the Box somehow deciding an actuality from a possibility of a both alive and dead cat before the opening. The key role of measurement was expressed as follows:  

• Bohr: Nothing exists until it is measured. (The Moon does not exist if you are not looking at it)
• Heisenberg: The purpose of quantum mechanics is to predict the outcome of experiments/measurements. 
• Bohr: It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.

John Bell (1990) expresses an opposite view in Against Measurement: 

• When I say that the word "measurement" is worse than the others, I have in mind its use in the fundamental interpretative rules of quantum mechanics. 
• It would seem that the theory is exclusively concerned about 'results of measurement', and has nothing to say about anything else.
• However, the idea that quantum mechanics, our most fundamental physical theory, is exclusively even about the results o f experiments would remain disappointing.

The contradiction between Measurement and Against Measurement has not been resolved. Physicists no longer want to talk about or express belief in CI, like Bell, but have nothing better to offer as concerns the foundations of quantum mechanics, which is left to philosophers pf physics outside physics departments in endless scholastic disputes about the meaning of words without physics as Everett's Many-Worlds and Bohm's Guiding Waves. I wonder what the situation will be 100 years from now. 

The lack of progress as concerns the foundations of quantum mechanics is even more paradoxical as the we now pass inte the Second Quantum Revolution heroically pursued by EU in the grand project The Future is Quantum searching new revolutionary applications of the very foundations of quantum mechanics. If the foundations are not well understood, how can they be turned into wonders of quantum computing?

Recall the previous post with a measurement "click" identified as a photon, like the click of passenger counter making the passenger come alive as being counted:

  but saying very little about the characteristics of the passenger.

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:

Icke-Svar från KVA om Människans Påstådda Påverkan på Global Uppvärmning

Den 4 december begärde jag av Expertgruppen för dokumentet Vetenskapen Säger - om Klimatet på KVAs hemsida, upplysning om vilka direkta vetenskapliga referenser som stödjer det huvudsakliga påståendet:  

• Det är obestridligt att människans påverkan, främst genom utsläpp av växthusgaser, har orsakat en global uppvärmning och andra förändringar i klimatsystemet. 
• De senaste 160 åren har den globala medeltemperaturen stigit med 1,1 grader. 
• Det finns ingen annan vetenskapligt förankrad förklaring till detta än de ökande halterna av växthusgaser, främst koldioxid.

preciserad genom huvudfråga att besvaras av Expertgruppen:

1. Vilken är den vetenskapliga precisa referensen till påståendet att Det är obestridligt att människans påverkan, främst genom utsläpp av växthusgaser, orsakat en global uppvärmning och andra förändringar av klimatsystemet. Jag vill ha ursprungliga referenser i den vetenskapliga litteraturen med precis markering exakt var i referensen vetenskaplig evidens till påståendet står att finna. Jag vill inte ha en allmän referens till IPCC (som inte utför egen forskning utan endast påstår sig sammanställa sådan), utan direkt referens till den vetenskapliga litteraturen med precis markering. 
2. Vad menas här med “obestridligt”?
3. Hur stor global uppvärmning har mänskliga utsläpp av växthusgaser obestridligt orsakat? Precis referens?

Svar har nu inkommit från 5 av Expergruppens 7 medlemmar:

• DELIANG CHEN*, professor, Göteborgs universitet, Göteborg
• SVANTE BJÖRCK*, professor, Lunds universitet, Lund
• ERIK KJELLSTRÖM, professor, SMHI, Norrköping
• THORSTEN MAURITSEN, lektor, Stockholms universitet, Stockholm
• ILONA RIIPINEN*, professor, Stockholms universitet, Stockholm
• HENNING RODHE*, professor emeritus, Stockholms universitet, Stockholm
• ANNA RUTGERSSON*, professor, Uppsala universitet, Uppsala

där * anger att personen är ledamot av KVA. Svaren finns nedan och kan sammanfattas enligt följande:

• DELIANG CHEN: Inget svar.
• SVANTE BJÖRCK: Ingen referens.
• ERIK KJELLSTRÖM: Allmän referens till IPCC (Summary for Policymakers).
• THORSTEN MAURITSEN: Inget svar.
• ILONA RIIPINEN: Allmän referens till IPCC (WG1).
• HENNING RODHE: Allmän referens till IPCC (Summary for Policymakers)
• ANNA RUTGERSSON: Referens till egen rapport om Östersjöområdet.

med följande analys:

• Ingen direkt referens till vetenskaplig litteratur som svar på frågor 1-4. 
• KVAs påståenden är av politisk och inte vetenskaplig natur.   

Att KVA talar politik framgår av följande påstående av Expertgruppen:

• Att begränsa den globala uppvärmningen till 1,5 grader kräver mycket snabba utsläppsminskningar med en halvering av koldioxidutsläppen till omkring 2030, nettonollutsläpp av koldioxid till omkring 2050 samt avlägsnande av koldioxid från atmosfären. 

Slutsatsen kan bara vara är att KVA tillsammans med sin Expertgrupp är ett rent politiskt organ. 

Jag har begärt kommentar till denna post från Expertgruppen: Är KVA numer främst ett politiskt organ med egen politisk agenda?

Inkomna svar:

Ilona Riipinen

Hej Claes,

 

Tack för dina meddelanden. Här kommer mina svar. Ber om ursäkt för min svenska som inte är helt perfekt.

 

Om du vill kräva djupare än Summary for Policymakers (som t.ex. Henning Rodhe redan hänvisade till), hittar du en rad referenser för dina frågor 1-4 från Chapter 3 av IPCC WG1 -rapporten: https://www.ipcc.ch/report/ar6/wg1/chapter/chapter-3/ . För din fråga 5, hittar du referenser inom Chapter 11:https://www.ipcc.ch/report/ar6/wg1/chapter/chapter-11/ . Dessa Chapters innehåller också ganska mycket material om de använda metoderna och är därför bra grundresurser. Det känns inte så meningsfullt (eller bra resursanvändning) att i denna diskussion börja sammanfatta och upprepa arbetet som en stor grupp forskare (som författare och granskare) har redan gjort inom IPCC-processen, och som beskrivs inom IPCC-rapporterna. Allt du behöver att hitta svar på dina frågor finns där. Därför, särskilt som en vetenskapligt litterat människa, kan du gå och läsa de ursprungliga referenserna samt IPCCs sammanfattning av dessa, och baserat på dem, göra din bedömning om du litar på metodiken eller inte. Det har vi gjort, och vår bedömning om kunskapsläget präglas inom ”Vetenskapen säger – om klimatet”. För min del har jag inte mer att tillägga inom detta samtal.

 

Önskar dig en god jul och gott nytt år 2023!

 

Ilona

Svante Björk 

Hej Claes, 

 

detta är ett helt personligt inlägg som jag inte kunde motstå att skriva. Jag menar att du som matematiker och klimatmodellerare bör förstå att påståenden inom klimatrelaterad vetenskap (som IPCC) inte bara baseras på några mkt precisa referenser utan på de samlade indicierna från en stor mängd studier. Som geolog är jag van vid att tolka stora mängder data som behandlar något som hände för x antal år sedan och utan mänsklig närvaro och utan detaljerade insikter och kunskaper om bakomliggande processer när det hände. Detta innebär att ingen kan med 100% säkerhet veta vad som verkligen har hänt men ändå kommer vi fram till det mest troliga scenariot, baserat på så mycket data som möjligt. Visst blir det ett pussel. Vi kan ju inte gå ut i dagens värld och testa våra idéer med lab-försök i naturen om en svunnen värld, men olika modeller kan hjälpa oss att förstå processer och möjliga scenarier. Vi vet väl alla att vi får olika väder-scenarier, vad gäller detaljer, för de kommande veckornas väder när vi går in på olika väder-appar, men de långsiktiga trenderna är desamma. Detta visar ändå att kunskaperna om klimatsystemets processer är relativt goda, men att det finns ingen helig graal för att egentligen förstå klimatsystemets hela komplexitet och hur jordens olika sfärer samverkar. 

Till skillnad från matematiska formler och ekvationer, och kemiska eller fysiska lab-försök, utgör absolut säkra, helt bevisade kunskaper inom geovetenskap (inkl. klimatvetenskap) snarare undantag än regel. Data kan vara helt ovedersägliga och korrekta men hur samverkar t ex olika processer under olika förhålladen. Detta hjälper oss modellerna att försöka förstå, men de är ju inte samstämmiga. Så vad gör vi då, när vi inte kan bevisa vad som är säkert eller helt rätt? Använder det samlade förnuftet hos tusentals forskare som arbetar med dessa frågor inom sin forskning! Det är väl knappast fel att varna mänskligheten om vad som har hänt och vad som kanske väntar om vi inte gör något åt det. Dagens globalt samtidiga uppvärmning har enligt geologiska data inte inträffat tidigare under åtminstone de senaste 20.000 åren, inte ens när senaste istiden avslutades; det skedde 800 år tidigare på södra halvklotet än på norra halvklotet. Så man ställer sig onekligen frågan vad det är som händer med vårt jordklot. Det är ju det vi som forskare (liksom IPCC) försöker förstå, baserat på en mkt stor mängd data. Och är det inte alltid bättre att varna än att underlåta varningar när vi har starka indikationer på vad som kan hända; har vi inte alltför många dåliga erfarenheter av det senare?

Hälsningar

Svante

Hej igen Claes,

självklart har jag ett personligt ansvar för att våra påståenden är riktiga; jag tror nämligen benhårt på det vi har skrivit! Det brukar jag göra när jag skriver något för offentligheten eller kollegor. Och som jag skrev i texten till dig så brukar jag som geolog/geovetare basera mina vetenskapliga påståenden på en stor mängd data/referenser/observationer. Detta är mitt "torftiga" svar, men att redogöra för alla referenser gruppen har diskuterat känns helt meningslöst. Det är ju fråga om tillit mellan forskare! Vi är ju knappast några politiker. Något annat svar kan du inte förvänta dig från mig!!

Hälsn

Svante

Anna Rutgersson

Hej,

 

Gällande extremhändelser (punkt 5) har vi gjort en sammanfattning gällande Östersjöområdet (som också refereras till i dokumentet), där har vi kommit fram till att det skett en viss ökning av extrem nederbörd och värmeböljor (konfidensen uppskattades till medel) ökning av extremt milda vintrar, minskning av extremt kalla vintrar (hög konfidens), förskjutning under året av extrem avrinning.

 

Rutgersson, A., Kjellström, E., Haapala, J., Stendel, M., Danilovich, I., Drews, M., Jylhä, K., Kujala, P., Larsén, X. G., Halsnæs, K., Lehtonen, I., Luomaranta, A., Nilsson, E., Olsson, T., Särkkä, J., Tuomi, L., and Wasmund, N.: Natural hazards and extreme events in the Baltic Sea region, Earth Syst. Dynam., 13, 251–301, https://doi.org/10.5194/esd-13-251-2022, 2022.

 

 

Mvh

Anna

Henning Rohde

Bäste Claes,

Ordet "unequivocal" förekommer i den senaste IPCC-rapportens Summary for Policymakers (AR 6, SPM),  paragraferna A1 och A1.1. (bifogas nedan). Där finns också utförliga referenser. Texten i SPM nagelfars i stor detalj av såväl forskare som representanter för alla världens länder.

Jag hoppas att detta ger svar på din huvudfråga. Jag rekommenderar att du själv söker i den sjätte IPCC-rapporten (AR6) efter svaren på dina övriga frågor.

Henning Rodhe

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"A.  The Current State of the Climate 

Since AR5, improvements in observationally based estimates and information from paleoclimate archives provide a comprehensive view of each component of the climate system and its changes to date. New climate model simulations, new analyses, and methods combining multiple lines of evidence lead to improved understanding of human influence on a wider range of climate variables, including weather and climate extremes. The time periods considered throughout this section depend upon the availability of observational products, paleoclimate archives and peer-reviewed studies.

A.1  It is unequivocal that human influence has warmed the atmosphere, ocean and land. Widespread and rapid changes in the atmosphere, ocean, cryosphere and biosphere have occurred. {2.2, 2.3, Cross-Chapter Box 2.3, 3.3, 3.4, 3.5, 3.6, 3.8, 5.2, 5.3, 6.4, 7.3, 8.3, 9.2, 9.3, 9.5, 9.6, Cross-Chapter Box 9.1} (Figure SPM.1, Figure SPM.2) 

A.1.1  Observed increases in well-mixed greenhouse gas (GHG) concentrations since around 1750 are unequivocally caused by human activities. Since 2011 (measurements reported in AR5), concentrations have continued to increase in the atmosphere, reaching annual averages of 410 parts per million (ppm) for carbon dioxide (CO2), 1866 parts per billion (ppb) for methane (CH4), and 332 ppb for nitrous oxide (N2O) in 2019.6 Land and ocean have taken up a near-constant proportion (globally about 56% per year) of CO2 emissions from human activities over the past six decades, with regional differences (high confidence).7 {2.2, 5.2, 7.3, TS.2.2, Box TS.5}"

Erik Kjellström

Hej Claes,

 

”Unequivocal” används som sagt i summary for policymakers i AR6 och i den underliggande tekniska sammanfattningen (TS). I TS används uttrycket för att i) beskriva människans påverkan på den historiska ökningen av koldioxid i atmosfären (Box TS.5), ii) på observerade förändringar i klimatsystemet på global skala (TS.1.2.3) och iii) i syntesen för alla de olika ändringar i klimatsystemet som kopplats till människans påverkan (TS.2.1). Tabell TS.1 beskriver vad syntesen bygger på genom att lista vilka attributionsutlåtande som görs för observerade förändringar i atmosfären, vattnets kretslopp, haven, kryosfären, kolcykeln och extremer. I samtliga fall finns hänvisningar till resten av AR6 där de olika kapitlen i sin tur pekar på litteraturen som använts. 

 

Artikeln som du nämner i ditt mail här nedan diskuteras i samma tidskrift i en artikel från 2022 av Richardson och Benestad som sitt abstract konstaterar att författarna till den tidigare studien gjort ”a basic error in the choice of statistical methods” och vidare ”The solar-climate linkage is an area of fascinating and ongoing research with rigorous technical discussion. We argue that instead of repeating errors, they should be acknowledged and corrected so that the debate can focus on areas of legitimate scientific uncertainty.”, se https://iopscience.iop.org/article/10.1088/1674-4527/ac981c

 

Erik Kjellström

Real Quantum Mechanics for Atomic Kernels

Helium atom: 2 electron clouds around a kernel consisting of 2 proton and 2 neutron clouds.

In a moment of heavenly inspiration Schrödinger formulated in 1925 a mathematical model of the Hydrogen atom as a negatively charged electron cloud attracted by a positively charged proton point kernel. The ground state of the atom was given in the form of a real-valued wave function $\Psi (x)$ depending on a space variable $x$ with $x=0$ at the kernel and $\Psi (x)^2$ representing charge density, as the minimizer of the total energy cost functional

• $E(\Psi ) = KE(\Psi ) + PE(\Psi )$,

where

• $KE(\Psi ) = \int\frac{1}{2}\vert\nabla\Psi\vert^2dx$ 

is kinetic energy, and 

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

is potential energy expressing Coulomb attraction, under the normalization

• $\int\Psi^2dx =1.$                                  

Qualitatively the minimising charge density representing an eigenstate of minimal energy, concentrates towards the kernel making the negative $PE(\Psi )$ small under the positive gradient cost of $KE(\Psi )$ and takes the analytical form $\Psi (x)=\exp(-\vert x\vert )$ modulo normalisation (with 2d section here), with a charge density dropping off exponential away from the kernel. 

In classical continuum mechanical terms, the kinetic energy can be seen as a form of elastic energy increasing with compression. Real Quantum Mechanics RealQM offers in this spirit a generalisation to atoms with several electrons represented by non-overlapping charge densities. This model has a deterministic physical meaning and is different from the standard Schrödinger equation in configuration space with only probabilistic meaning as stdQM. RealQM thus retains Schrödinger's original conception for the Hydrogen atom of an electron cloud around the kernel with physical meaning, while stdQM already for Hydrogen connects the wave function to the probability of finding an electron particle at a specific location around the kernel (abhorred by Schrödinger).

 

Schrödinger suggested that the atomic kernel similarly possibly could be viewed as a positively charged cloud. For a kernel with several protons to be stable that would require an attractive force named strong force stronger than that of Coulomb repulsion. 

RealQM has a natural extension to a kernel model consisting of non-overlapping positive charge densities with repulsion replaced by attraction from an assumed strong force. In the simplest case with spherical homogenisation this model takes the above form, as a special case of the Cornell potential of Quantum ChromoDynamics QCD. 

RealQM thus can be extended to include also the kernel with the same approach of non-overlapping charge densities interacting by long range Coulomb attraction/repulsion and short range strong force. 

Notice that the contribution to the total energy of positive kinetic energy requires a distributed charge density and thus excludes point particles with infinite kinetic energy, in agreement with Schrödinger's wave mechanics without particles. In the setting of atomic eigenstates, the wave function represents a distributed cloud of charge like the spatial part of a standing wave.

A first challenge would be to model a Helium kernel with 2 protons and 2 neutrons taming the strong force into a stable kernel. Specifically it would give the kernel a small positive radius as required to make RealQM prediction of ground state energy to precisely agree with observation. 

PS Note that the Standard Model of QCD describes interaction of quarks forming hadrons such as protons  mediated by force carrying gluons, both viewed as particles (abhorred by Schrödinger).