Corruption of Modern Physics 9: Misuse of Chaotic Systems

Waterfall as partially predictable chaotic system

The idea that global climate is a chaotic system and as such cannot be predicted, because of sensitivity to small perturbations, is often presented as an expression of deep insight into mathematical modeling. But it may hide a common misunderstanding of the nature of a chaotic system. The basic example of a chaotic system is turbulent flow. The nature of turbulent flow is to be unpredictable pointwise in space and time (because of sensitivity) while being predictable in a mean-value sense (because of insensitivity). 

This is developed in detail in Computational Turbulent Incompressible Flow and Computational Thermodynamics recommended for download. The combination of mean-value predictability and pointwise unpredictability is expressed by the fact that the drag of a car as total resistance to motion through air, is computable/predictable while the pressure at specific points on the car body cannot be computed/predicted. The reason mean-values are predictable is the fluctuating nature of turbulence with high pressure followed by low pressure forming stable mean-values. This is the reason nature can function as a more ot less ordered system even if being a chaotic system, which can be seen as a form of order in chaos.  

The Earth climate system can be described as a turbulent thermodynamic ocean-atmosphere system which forms weather local in space and time and global climate as mean-values over space and time. Experience shows that local weather acts as a chaotic system which is unpredictable pointwise in time over more than a week. The question is then to what extent climate as mean-value weather is computable/predictable? 

If all the equations (Navier-Stokes equations and more) modeling the Earth system were known, we would be able to compute/predict for example global mean temperature year 2100 or the onset of the next Ice Age, because of the fluctuating nature of turbulent flow. But we do not know all the parameters entering in the equations nor the initial conditions. Therefore such computation/prediction for now is impossible, but not because the system in principle is chaotic, rather because present climate models contains unknowns. 

This means that with better climate models it could be possible to predict e.g. the onset of the next Ice Age, or on shorter time scales the Winther weather over Europe depending on jet streams and La Nina and more. Even without climate model we can predict the global mean temperature 2023 to be about the same as 2022. 

In short, global ocean-atmosphere weather system is a chaotic system which as global climate is computable/predictable to a certain degree. Work on better climate models is not meaningless.

What is remarkable is the stability of Earth climate without runaway global warming yet with global cooling into repeated Ice Ages,   

Corruption of Modern Physics 8: Equivalence Principle

In Dialogue Concerning the Two Chief World Systems Galileo lets Salviato explain to Simplicius why different bodies with different masses show the same free fall (in vacuum without air resistance) thus with the same acceleration subject to a gravitational force, in other words that inertial mass scaling with  acceleration is the same as gravitational mass scaling with gravitational force. 

Galileo demonstrated this fact by dropping different objects from the Tower of Pisa. Galileo argued that this must be so because if different parts of a body in free fall would fall differently, bodies would be ripped apart by internal forces and the World could not exist. This is called Galileo's Equivalence Principle and is a cornerstone of Newtonian Mechanics. It says that there is only one type of mass, namely inertial mass, which manifests itself as force resistance to acceleration expressed by Newton's 2nd Law.  If you want to find the mass of a body, measure the force required to put it into motion.  

It is now reported from Institute of Theoretical Physics, University of Paris-Saclay, France, that 
the 

• MICROSCOPE Satellite Experiment has tested the equivalence principle with an unprecedented level of precision.

This is simply Galileo's experiment again now with higher precision. No surprise. So what is the meaning of this apparently ground breaking experiment? Well, it is presented as evidence that Einstein's General Theory of Relativity with a new explanation of gravitation, is correct. 

How can that be when the Equivalence Principle is a cornerstone of Newton's theory of gravitation? How can an experiment confirming Newton's theory be used to show that also General Relativity supposed to be different from Newton's theory, is correct? How can the same evidence be used to support both a basic theory like Newton's and a generalisation thereof like Einstein's supposed to be different? 

Experimentally evidence that Einstein's theory is better than Newton's, would require an experiment which agrees with Einstein's theory but not Newton's. An experiment confirming Newton's theory cannot serve this purpose. Yet the objective of the MICROSCOPE Satellite Experiment is just this! As an example of what modern physicists in the spirit of Einstein do today to advance physics.  

Corruption of Modern Physics 7: Collapse (of the Wave Function)

Niels Bohr brainwashed a whole generation of theorists into thinking that the job (interpreting quantum theory) was done 50 years ago. (Murray Gell-Man Nobel Prize in Physics 1969)

The stated objective of Standard Quantum Mechanics according to Bohr, is to make probabilistic predictions of outcomes of experiments with atomic systems expressed in terms of wave functions satisfying Schrödinger's equation as systems mathematical model, and compare with observations/measurements of actual outcomes. The idea is that a system prior to measurement is in a state of superposition of possible outcomes with different probabilities given by the corresponding wave function, and that in the measurement process one of the possible outcomes becomes real and then is expressed as a collapse of the wave function. 

The mantra is that predictions always agree with observations even if predictions are probabilistic and repeated experiments give the same result as if the wave function can only collapse in one way to the same outcome. The validity of this mantra can be questioned in many ways, in particular because the wave function for a many-electron system is uncomputable and thus cannot offer any prediction at all, but then in particular of course, never any incorrect prediction. This is viewed as evidence that the Schrödinger equation is a complete model without need of any further precision through "hidden variables", in particular cannot be falsified.  

If you feel that this sounds strange, your are not alone, since this has been a source of bitter quarrel between physicists for nearly 100 years without ever any reconciliation.  Questions add up: 

• Is the measurement device included in the system model?
• How does the measurement influence the outcome?
• Does "collapse of the wave function" have a physical meaning? 
• Can a theoretical non-prediction be falsified?  
• Is this a "collapse of QM"? 
• Can it be true that nothing exists until it is measured?
• Does the Moon not exist when it has disappeared behind a cloud? 
• For the young child closing eyes Mom does not exist anymore, but for a physicist?
• Typical measurements can concern atomic spectra and they are deterministic cut in stone.

Corruption of Modern Physics 6: Mathematization

Recent posts recall that the accepted canon/standard of Quantum Mechanics QM as Schrödinger's equation for an atomic system with $N$ electrons, is a linear partial differential equation in terms of a multidimensional complex-valued wave function $\Psi (x1,x2,...,xN,t)$ depending on $N$ three-dimensional space variables $x1, x2,...,xN$ and a time variable $t$. The equation arises as an ad hoc mathematical generalisation of Schrödinger's equation for a Hydrogen atom with one electron ($N=1$), which can be given a direct physical meaning with the wave function representing an electron density. 

The basic question QM concerns the physical meaning of the wave function for $N>1$. The accepted answer coined as the Copenhagen Interpretation CI imprinted into the canon by Born followed by Bohr, is that $\vert\Psi (x1,....,xN,t)\vert^2$ represents a probability density for an electron configuration described by the coordinates $(x1,...,xN,t)$. But a probability density does not describe any state of physics and QM still after 100 years remains a mystery as acknowledged by all prominent physicists. 

To a mathematical mind the ad hoc generalisation is direct, and so physicists impressed by mathematics have been forced to accept it as true physics, although mysterious. So instead of searching for a generalisation with physical meaning (see Real Quantum Mechanics), all efforts have gone into loading the multi-dimensional wave function $\Psi (x1,x2,...,xN,t)$ with (some) physical meaning. 

To this end physicists have come up with the idea to distinguish between wave functions which are symmetric in the variables $(x1,...,xN)$ (augmented by a two-valued spin variable) supposed to represent boson (photon) and anti-symmetric supposed to represent fermion (such as electron and proton), with any particle being either a boson or fermion. Anti-symmetry was crafted so as to prevent two electrons with the same spin to be at the same place in space-time, expressed as Pauli’s Exclusion Principle.

With this perspective a God creating the world of physics must have been mathematician and not physicist. First He created multidimensional wave functions, which is a very rich Universe, and then He decided that only symmetric or anti-symmetric wave functions would represent actual physics, asking systems of particles to keep track of symmetry or antisymmetry. But a mathematician cannot create physics, only at best model physics in terms of mathematics and computation. God must have been also physicist with richer tools for creation than mathematical symbols on a paper. And then He would not have been satisfied with a purely mathematical Universe designed by mathematicians like the CI of QM...

To sum up: Standard QM for a many-electron system is based on a linear wave equation for a multi-dimensional complex-valued wave function arising from a generalisation of Schrödinger's equation for a Hydrogen atom according to purely mathematical principles. The following questions present themselves as the fundamental conundrums of modern physics: 

• Why is the wave equation for a system scalar-valued and not vector-valued?
• Why is the equation linear and thus allowing superposition? Physics is rarely linear.
• What physics is captured by the multi-dimensional wave function?  Do electrons play dice? 

Read what famous physicists have to say about Standard QM. 

Listen to this revelation by Roger Penrose.

      

Corruption of Modern Physics 5: Microscopic Statistics

The number of births, deaths or murders in say Sweden do not vary much from year to year and so are more or less predictable, while it is impossible to predict exactly which person will die from a natural cause or get murdered. This does not say that deaths/murders are completely random as if decided by throwing a dice. In all cases there are very specific conditions which predictably lead to a particular outcome as predictable microscopics of a macroscopic event such as death/murder. If the predictable microscopics was known in full detail, then the macroscopic event would also be predictable. A killed B because of a specific reason.

But with unknown microscopics as hidden variables, macroscopics appear random. This is how a roulette table works.   

This connects to the basic unsolved problem of modern atom physics as the statistical/random nature of the Copenhagen Interpretation CI of quantum mechanics, which Bohr imprinted into the minds of all modern physicists with strong support from Born and Heisenberg, except a few like Schrödinger (inventor of quantum mechanics) and Einstein protesting with his famous God Does Not Play Dice.  

CI postulates that quantum mechanics can only make microscopic predictions of statistical nature such as the probability that an electron as a particle will be at a specific point is space and time. In other words, in CI there can be no hidden variables allowing prediction of microscopics.  In CI an electron really plays dice, something Einstein never accepted. 

Bohr supported CI by the observation that in the decay of radioactive atoms the half-life, as the time after which half of the atoms have decayed, is predictable, while it is impossible to predict precisely which atoms will decay and when. The basic CI conviction is that atoms play roulette to decide to decay or not. There can be no hidden variables, to be compared with the deaths/murders in a population containing hidden variables. 

But random microscopics is is an awkward idea from scientific point of view. Conceptually macroscopics can be complex as an agglomeration of microscopics, while the very idea of microscopics is that it is something simple. Complex microscopics must build on microscopics of microscopics and so on in an endless regression. Thus microscopics as an elementary piece of something bigger must be simple, and simple in general means predictable. When Bohr speaks about an electron playing roulette as random microscopics, it appears self contradictory or at least confusing and mystical as the signum of quantum mechanics: 

• How does single electron play roulette? 
• What is the origin of this strange idea?

An answer is given in Corruption of Physics 3. There we recall that quantum mechanics was created in 1920s when Schrödinger formulated a new model for the Hydrogen atom as a negatively charged electron cloud attracted by a positively charged kernel. The model takes the the form of a partial differential equation named Schrödinger's equation in terms of a wave function $\Psi (x,t)$ depending on a three-dimensional space variable $x$ and a time variable $t$ with $\vert\Psi (x,t)\vert^2$ representing electron density at $(x,t)$. 

This model is fully predicatble/computable and produces an atomic spectrum in direct correspondence with observation as the first model of predictable microscopics of atom physics in parity with Newton's predictable model of the motion of celestial objects. 

That was a wonderful achievement of rational thinking, but what would a Schrödinger equation look like for an atom with more than one electron? It was far from obvious how to generalise from one to many. and Schrödinger hesitated. Of course, a direct formal generalisation could be made with a pen stroke into a wave function $\Psi (x1,x2,....,xN,t)$ depending on $N$ three-dimensional space variables $x1, x2,...,xN$ for an atom with $N$ electrons, thus into a wave function depending on $3N$ space variables, however without direct physical meaning for $N>1$. The only way out was to give this multi-dimensional wave-function a statistical meaning as a probability. That was what Born did followed by Bohr, while Schrödinger protested, and that ended the search for a generalisation of Schrödinger's equation with direct physical meaning. Modern physics was stuck with multi-dimensional Schrödinger equation without physical meaning, which in addition was uncomputable for a multi-electron atom as pointed out by Nobel Laureate Walter Kohn when receiving the Prize. 

There modern physics stands today. Electrons play roulette. Atom microscopics is random with self-contradictory microscopics upon microscopics. Hidden variables are forbidden like the fruits of Knowledge in Paradise. Bohr dictates that physics is not what is, but what we can say. The multi-dimensional Schrödinger equations without hidden variables contains everything that can be said, which however is not much since it is uncomputable. 

A way out of this dead end is opened by Real Quantum Mechanics presenting a different generalisation of Schrödinger's one-electron equation into a computable many-electron wave equation in three space dimensions with physical meaning. With such a model it would in principle be possible to predict which atom would decay because of specific conditions of its nucleus and surrounding electron configuration, although in practice they would appear like hidden variables. 

One thing is to say like Bohr that there can be no hidden variables, only microscopic roulettes without physics, another to say that they may exist and may be revealed into deterministic physics. 

Corruption of Modern Physics 4: Nobel Prize to Spooky Action at Distance

The Nobel Prize in Physics 2022 was awarded to Alain Aspect, John F. Clauser and Anton Zeilinger for

• Experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science.

In other words, the Prize was awarded for showing that Einstein was wrong when questioning the idea of entangled photons with spooky action at distance, as if two photons/particles could be in instant contact/communication even if widely separated in space (thus seemingly violating Einstein's basic relativity postulate of the speed of light as maximal speed of propagation of physical effects).  

Einstein never accepted the canon of the Copenhagen Interpretation CI of the new quantum mechanics dictated by Bohr and Born in the 1920s and still dominating, and so was expelled from the physics community along with Schrödinger as the inventor of the Schrödinger equation for the Hydrogen atom. 

Einstein could not accept spooky action at distance nor the statistical interpretation in CI expressed with his famous God does not play dice. Schrödinger could not give up local reality or Anschaulichkeit as a reality existing in three space dimensions even if not observed by a human being or instrument. 

The controversy between Bohr/Born and Einstein/Schrödinger, that has never be reconciled, has had catastrofical consequences for the development of modern physics through the 20th century into our days.  The 2022 Prize is an expression of the resulting collapse of reality behind string theory, extra dimensions, multiversa, dark matter/energy and black holes occupying the minds of physicists today with lofty promises of quantum computers from superposition and entanglement always far from realisation. 

Quantum mechanics started in 1925 with Schrödinger's equation for the Hydrogen atom as a real physics continuum wave equation for a negatively charged one electron cloud under Coulomb attraction from a positively charged pointwise kernel/proton, expressed in a wave function $\Psi (x,t)$ depending on a three dimensional space variable $x$ and a time variable $t$, with the square of the wave function expressing charge density. This model showed precise agreement with the spectrum of Hydrogen as a formidable stunning success of theoretical physics and Schrödinger instantly rocketed to fame.

But the trouble started already with the Helium atom with two electrons. A quick solution directly presented itself as a direct mathematical generalisation to an atom with $N>1$ electrons simply by formulating a linear multi-dimensional wave equation in a wave function $\Psi (x1,x2,..xN,t)$ depending on $N$ three-dimensional space variables $x1,x2,...,xN,$ as if each electron occupies its own three-dimensional space. A mathematician could make such a generalisation with a stroke of a pen, just like extending the real line into a space of any dimension in linear algebra. With such a wave function electrons are entangled unless the multi-dimensional wave function is a product of one-dimensional wave functions, which is too simple to work. Electron entanglement is thus directly ingrained ad hoc by definition through a truly multi-dimensional wave function, as well as superposition by linearity.  

The direct question confronting Schrödinger was if such an ad hoc formal mathematical generalisation could have any physical meaning? Schrödinger concluded that a wave depending on $3N$ space variables cannot be Anschaulich or represent any reality, and he could not accept Born's resort to a statistical interpretation, and so Schrödinger left quantum mechanics already at its start, or rather like Einstein was kicked out. It is the statistical interpretation of the wave function forced upon science from a multi-dimensional wave function, which is the root of all the unresolved troubles. 

There we stand today: The holy grail of quantum mechanics is a linear multi-dimensional wave equation/function without local reality but with entanglement and spooky action at distance ingrained by construction, claimed to always be in exact agreement with observation, although uncomputable by multi-dimensionality. This is not something, whether you are physicist or not, which you can question, and it is then ironic that the 2022 Prize is given to experimental work initiated in the 1970s supposedly showing that Einstein was wrong, that is showing something which was a truth already 90 years ago. It is as if Einstein's ghost is still haunting physics, by asking questions which again and again have to be dismissed as being silly, without ever being answered satisfactorily.

The state of quantum mechanics today as witnessed by all prominent physicists is that quantum mechanics is weird, with weirdness increasing with prominence. As an example let us just listen to what 2022 Nobel Laureate Anton Zeilinger, named the Quantum Pope, has to say in the concluding words of his book Dance of the Photons with title What Does It All Mean?: 

• We have learned that the idea that the world exists in all its properties independent of us, independent of the kinds of observations we perform, is in trouble.
• It now becomes clear why Einstein had to criticize quantum mechanics, why he called entanglement “spooky.” His picture of the real, factual reality that exists in its essential properties independent of us, this picture of a separation of reality and information, does not seem to be tenable in quantum physics.
• We also learned that a specific philosophical view has been definitely ruled out by the experiment. This is the concept of local realism. Local realism is the point of view that whatever we observe is defined in some way by a real physical property of the observed systems, a property that exists before and independently of our observation. 
• We also learned that the quantum world is governed by a qualitatively new kind of randomness. The individual measurement result is purely random, without any possibility of detailed causal explanation. It is not just that we do not know what the cause is. This is probably the most fascinating consequence in quantum physics. Just imagine: centuries of scientific research, centuries of the search for causes, and attempts to explain why things happen just the way they happen lead us to a final wall. 

What Zeilinger says is that the idea of factual reality is in trouble and does not seem tenable and attempts to explain why things happen the way they happen has led to a final wall, all based on a very tricky photon experiment saying very little about the real world. For this he is awarded the Nobel Prize. The hype is huge: Quantum Manifesto and The Universe Is Not Locally Real, and the Physics Nobel Prize Winners Proved It

To be more precise, the Prize is awarded to experimental work showing that model predictions by solving a multi-dimensional linear Schrödinger equation, although uncomputable, exactly agree with certain very specific very tricky experiments with photons without physical reality, from which it is concluded that any search for a model describing physical reality in the spirit of Einstein is fruitless. In other words, modern physics is settled and the Nobel Prize in Physics has no more role to play.       

If you do not think that science is ever settled, you may be interested in a realist approach to the atomic world: Real Quantum Mechanics.