Physics as Computation

Upcoming Saturday Febr 3 at 10 am EST I will give a live presentation at John Chappell Natural Philosophy Society CNPS channel with title:

         PHYSICS as ANALOG COMPUTATION as DIGITAL COMPUTATION 

stating MAIN IDEA:

• REAL WORLD - CONTINUUM MECHANICS MODEL - COMPUTABLE
• REAL QUANTUM MECHANICS - CONTINUUM MODEL - COMPUTABLE
• STANDARD QM: HIGH-DIMENSIONAL SCHRÖDINGER EQ - UNCOMPUTABLE.
• REAL WORLD - COMPUTABLE
• MICROSCOPICS = MACROSCOPICS

  with the following references:

• REAL QUANTUM MECHANICS  REALQM
• TURBULENCE
• THERMODYNAMICS: 2ND LAW     DIRECTION of TIME
• RADIATIVE HEAT TRANSFER: PLANCK'S LAW

with remarks on: 

• SPECIAL RELATIVITY = LORENTZ TRANSFORMATION = UNPHYSICAL 
• GRAVITATION: NO ACTION AT DISTANCE: $\rho =\Delta\Phi$

Key aspect: 

• REAL PHYSICS - ONTOLOGY - WHAT IS - WHAT CAN BE COMPUTED

in opposition to 

• EPISTEMOLOGY - WHAT WE CAN SAY - COPENHAGEN QM

with key ingredients:

• COMPUTABILITY 
• STABILITY - WELLPOSEDNESS 
• FINITE PRECISION 

connecting to: 

• STANDARD QUANTUM MECHANICS = UNCOMPUTABLE
• REALQM = COMPUTABLE 
• TURBULENCE = COMPUTABLE = EULER'S EQUATIONS

modeled by:

• CLASSICAL CONTINUUM MECHANICS MATHEMATICAL MODELS 

including:

• NEWTON'S LAWS MOTION + GRAVITATION
• EULER EQ
• MAXWELL EQ
• REAL SCHRÖDINGER EQ

The mantra of John Chappell Natural Philosophy is 

• WHERE CRITICAL THINKING CHALLENGES THEORY

which connects to the mantra of this blog: 

• TOWARDS UNDERSTANDING BY CRITICAL CONSTRUCTIVE INQUIRY

I look forward to a constructive discussion with free-thinking physicists, in a situation where leading physicists insist on "Shut-up and Calculate". 

PS1 Einstein's No-Aether Special Relativity with its unphysics/paradoxes has attracted much debate recently on CNPS to which I can contribute Many-Minds Relativity as an alternative with physical meaning connecting back to Ebenezer Cunningham's Many-Aethers concept. 

Here different observers moving with different constant velocities are locked to different moving aethers as different Euclidean coordinate systems for expression of Maxwell's equations. The key question is to what extent different observers can agree. 

PS2 Some high-lights:

• Instant local action - explicit time stepping: local force-acceleration-velocity-position: add-mult

• Radiative heat transfer: Not 2-way stream of photons. Instead: resonance mediated by Maxwell. 

• New theory of flight - turbulent Euler: drag lift computable/predictable with slip boundary condition. 

• Quantum mechanics: Deterministic continuum mechanics = physical. Statistics = unphysical.

• Solution concept: Pointwise/strong vs meanvalue/weak. 

RealQM Molecules with Valence Electrons

Standard Quantum Mechanics stdQM teaches that the electrons of an atom successively fill an expanding system of shells around the kernel, with 2 electrons in the 1st shell, 8 in the 2nd, 18 in the 3rd, more generally with (at most) $2m^2$ electrons in shell $m$.

RealQM is classical 3d space continuum mechanics model of atoms and molecules based on non-overlapping electron densities subject to Coulomb interaction. In particular, RealQM gives a rationale for the shell system as a packing problem. For an atom with kernel charge $Z$  electrons successively fill a sequence of non-overlapping spherical shells $S_m$ of radius $r_m\sim \frac{m^3}{Z}$ of thickness $dS_m\sim \frac{m^2}{Z}$ with $\sim m^2$ electrons of width $de_m\sim \frac{m^2}{Z}$ in each shell, for $m=1,2,...,M,$ with $M^3\sim Z$, which gives the sequence $2, 8, 18, 32, 50,..$. Compare with previous post connecting to charge density $\psi^2(r)\sim \frac{Z}{r^2}$ as function of kernel distance $r$. 

Check out by running Atom Simulator giving support to $\psi^2(r)r^2$ approximately constant as  emergent design principle revealed by RealQM, with in particular the total energy in $S_m$ dropping off as $\frac{1}{m+1}$.

In reality outer shells are filled with slower progression and the outermost shell is filled with valence electrons which determine interaction with other atoms as chemistry based on valence bonds. The number $K$ of valence electrons shows to range from 1 to 4 representing different columns in the periodic table,  while noble gasses have 8. 

To reduce computational cost all electrons except the valence electrons can be homogenised into a reduced form of RealQM with the valence electrons interacting with a Z-kernel surrounded by a charge density of total charge $Z-K$, thus effectively involving only $K+1$ electron densities. You can test 2-atom chemistry here: 

• Valence +2+2  (MgO, SO and MgS)
• Valence +1+2  (LiO, NaO)     

with good agreement of atomisation energy. This shows promise that RealQM can simulate complex chemistry in computations involving only valence electrons, thus with computational cost for a molecule with $N$ atoms scaling as $N^2$, way smaller than the exponential cost for multidimensional stdQM.  

  

The 2nd Law vs Progress of Physics

The 2nd Law of Thermodynamics is the main enigma of classical physics left unresolved by modern physicists thus leaving the scene to other scientists. After a 50-year struggle Stephen Wolfram presents a  resolution in the form of computational irreducibility explained in the recent podcast Did Stephen Wolfram Finally Prove the 2nd Law of Thermodynamics?

The role of the 2nd Law is to explain irreversibility in macroscopic processes ultimately based on microscopical processes which are reversible in time. From where does the irreversibility come? Why is there an arrow of time pointing forward as an expression of increasing entropy or disorder?

Wolfram seeks an answer viewing physical processes as forms of analog computation subject to speed/cost limitations, which connects to my own explanation explained in the books Computational Thermodynamics and The Clock and the Arrow.  

The common idea is that the evolution of a physical system over a time step from one time instant to a next, can be viewed as a form of analog computation or processing of information subject to certain limitations forcing destruction of information which cannot be retrieved. 

I complement this general idea by offering a reason why necessarily physics evolves into more complex configurations beyond computational resolution and so require destruction of information, with turbulent fluid flow as key example. 

In fluid flow velocity differences/gradients can increase by advection as form of instability, while sharp gradients are smoothed by viscosity as a stabilising effect.  If the viscosity is small, like in air and water, the resulting flow becomes so complex that computational resolution is no longer possible as feature of turbulence, which forces destruction of information into irreversibility. 

The 2nd Law can thus be given a meaning in terms of computation of finite precision + complexity arising from instability, which can be made precise in mathematical terms with turbulent dissipation replacing the role of the mysterious concept of entropy as a measure of disorder or randomness. This is a meaning not asking for any observer, which still lingers in Wolfram's computational irreducibility.  

It is often heard that there has been no/little progress in modern fundamental physics since 1973, when string theory took over, and of course no/little progress in classical physics since 1900 when modern physics took over. 

It took 2000 years for Pythagoras to take over from Euclide with the development of Calculus forming the scientific revolution. 

Da Vinci pondering the nature of turbulent fluid flow as an expression of the 2nd Law, 

  

QED with Self-Interaction vs RealQM vs Resonance

Quantum Electro Dynamics QED underlying the Standard Model of atom physics, while presented as the most successful scientific theory ever, comes along with a concept of self-interaction stating that an electron can interact with itself through emission and absorption of photons, more precisely virtual photons as a form of "ghost particles" without physical presence expressed symbolically in Feynman diagrams of the form: 

supposed to describe an electron emitting a photon to the left and absorbing it again to the right after a short detour. Very illuminating. Compare with this video and: 

 

But self-interaction can drive a system by instability into infinite energy blowup and this is what happens in QED, which to survive has to be subject to renormalisation cancelling infinities. 

QED thus first introduces self-interaction and then cancels its effect by renormalisation, and by Ockham it would seem to be better to eliminate self interaction from the theory. Selling QED as "most successful theory ever" may be seen as form of self-promotion into infinity.

RealQM presents a quantum theory based on electrons with physical identities without self-interaction. 

As an elementary particle an electron cannot suffer from hazardous self-interaction, but a system can be subject to a form of system self-interaction in the form of resonance with different components of the system interacting with each other. This is the nature of a mass-spring harmonic oscillator, where the energy swings back and forth between kinetic and potential energy, as a form of stable resonance, captured in the equation

• $\frac{dx}{dt} = ax$   

with $a=i$ imaginary. We may compare with a blow-up to infinity if $a=1$, and decay to zero if $a=-1$ in a chemical reaction system. In both cases the two terms in the equation represent different physics. A configuration with only one component is not system and supplying it with self-interaction is contradictory physics which cannot exist over time.  

Compare with previous posts and recall Feynman's frank confession: 

• What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school... It is my task to convince you not to turn away because you don't understand it. You see my physics students don't understand it... That is because I don't understand it. Nobody does.

         

Absolute Rotation: Newton or Mach?

The development of modern physics in the form of relativity theory and quantum mechanics came out from an idea that classical Newtonian mechanics must be wrong because it appears to ask for both absolute space/position and absolute time/change and so absolute motion. 

But this is a misconception since it is clear from Newton's laws of motion that both space/position and time/change is relative. In particular Newton's 2nd Law for inertial motion with $v$ velocity and $t$ time 

• $\frac{dv}{dt} =  0$          (or more generally a 2nd Law of the form $\frac{dv}{dt} =  f$ with $f$ force/unit mass)

is invariant under shifts to $v+v_0$ and $t+t_0$ with constants $v_0$ and $t_0$, referred to as Galilean invariance. Inertial motion is thus relative, which means that some outside reference is required. Traveling in a car you cannot determine speed without looking outside (or on a speedometer setting the reference). The essence of the 2nd Law is to connect material motion to force.

So Newton was full aware that inertial motion is relative, but he took a step further and asked if non-inertial motion such as rotation can be detected in an absolute sense without outside reference? He then used his famous rotating water bucket experiment to argue that a curved water surface indicates rotation without outside reference. This was questioned by Mach who suggested that in fact an outside reference must be involved as the totality of all celestial objects. 

Who is then right Newton or Mach? Check out this recent video by Alexander Unzicker.

Other examples showing that rotation of a system can be detected within the system without outside reference build on the Coriolis force creating winds in a rotating Earth atmosphere (below) and mysteriously appearing when seeking to change radial distance on a carousel. Foucault’s pendulum in Pantheon showed that the Earth is rotating.

A variant of Newton's bucket experiment involves a system of two equal masses joined by a weightless elastic spring for which rotation can be discovered by examining the length of the spring compared to its tensionless rest length, which can be inspected by disassembling the system.  

In the same way it is possible to determine if the whole Universe is rotating and observations show that it is not. 

To me it thus seems pretty clear that Newton was right, and so the key motivation of Einstein that he was wrong, is not valid. More support to this view is given here. I have asked Unzicker about his view and will report.   

The development of quantum mechanics also found motivation from an idea that the physics of atoms could not be captured in terms of understandable deterministic Newtonian mechanics, and so required a whole new form of non-deterministic mechanics beyond understanding and scientific agreement today taking the form of standard quantum mechanics stdQM. RealQM presents an alternative to stdQM in a setting of classical Newtonian continuum mechanics.

Einstein introduced his special theory of relativity based on a principle of Lorentz invariance in contradiction to the Galilean invariance of Newton's 2nd Law, while asking for mercy: Newton, forgive me!

To sum up: Both relativity theory and stdQM are formed as corrections to supposedly incorrect Newtonian mechanics and so loose rationale if after all Newton is not incorrect... 

Recall that Einstein's special relativity came out from an apparent clash between Newtonian material motion and immaterial Maxwellian light propagation with Newton carrying the guilt. An alternative to special relativity is presented as Many-Minds Relativity connecting Newtonian material motion and immaterial propagation of light through a Doppler effect leading to a modified 2nd Law of the form $\frac{dv}{dt}=(1+v)f$ with $v>-1$. 

PS Unzicker says that he believes that Mach is correct, as a working hypothesis without proof (yet).

Max Born on Statistical Interpretation of Quantum Mechanics

Max Born received the Nobel Prize in Physics in 1954 (twenty years after his collaborators Schrödinger, Heisenberg and Dirac) for his statistical interpretation of quantum mechanics. In his Nobel Lecture Born expressed misgivings: 

• The work, for which I have had the honour to be awarded the Nobel Prize for 1954, contains no discovery of a fresh natural phenomenon, but rather the basis for a new mode of thought in regard to natural phenomena. (statistics)
• The work at the Göttingen school, which I directed at that time (1926-1927), contributed to the solution of an intellectual crisis into which our science had fallen...Today, physics finds itself in a similar crisis... - 
• There are some very noteworthy exceptions (to the statistical interpretation), particularly among the very workers who have contributed most to building up the quantum theory. Planck, himself, belonged to the sceptics until he died. Einstein, De Broglie, and Schrödinger have unceasingly stressed the unsatisfactory features of quantum mechanics and called for a return to the concepts of classical, Newtonian physics while proposing ways in which this could be done without contradicting experimental facts.  Such weighty views cannot be ignored.
• How does it come about then, that great scientists such as Einstein, Schrödinger, and De Broglie are nevertheless dissatisfied with the situation? Of course, all these objections are levelled not against the correctness of the formulae, but against their interpretation.
• ....somewhere in our doctrine is hidden a concept, unjustified by experience, which we must eliminate to open up the road.

Today 70 years later the situation is the same: 

• Physics is in a state of (intellectual) crisis.
• Interpretation of quantum mechanics is still without answer.
• There is a hidden doctrine which has to be eliminated. 

If you are dissatisfied with this state of affairs, take a look at RealQM offering an opening to a road forward.  

Where Quantum Mechanics Went Wrong

One of the many traumas of modern physics, maybe the most severe, is the lack of convincing physical meaning of the wave function $\Psi$ of standard quantum mechanics stdQM. Despite 100 years of brooding by Science Titans, it is still a mystery. How can it be? What went wrong?

Let us recall that stdQM arises as a formality without physical meaning starting  from a classical Hamiltonian function for a collection of $N$ unit point masses with positions $x_i$ for $i=1,...,N$, and potential energy $V(x_1,....,x_N)$ of the form

• $\sum_{i=1}^N\frac{1}{2}p_i^2 + V(x_1,...,x_N)$                     (1)

where $p_i=\frac{dx_i}{dt}$ is momentum (velocity), as total energy as kinetic energy plus potential energy. The Hamiltonian thus depends on positions and velocities of a collection of particles roaming over $3N+3N$-dimensional position-momentum configuration space. 

From this classical mechanics model stdQM comes out by formally replacing momentum $p_i$ by the gradient operator $\nabla_i$ acting on $x_i$-coordinates (multiplied by the imaginary unit $i$) to arrive at a quantum mechanical Hamiltonian operator of the form 

• $\mathcal{H} = -\sum_{i=1}^N\frac{1}{2}\nabla_i^2+\mathcal{V} =  -\frac{1}{2}\Delta_i + \mathcal{V}$   (2)

where $\mathcal{V}$ is a potential operator, acting on wave functions $\Psi (x_1,...,x_N)$ depending on $N$ three-dimensional spatial coordinates $x_1,...,x_N$, altogether $3N$ spatial coordinates as a formal analog to configurations space.   

This means that stdQM from its very beginning was formed as a formality without physics since replacing kinetic energy $\frac{p_i^2}{2}$ by the differential operator $-\frac{1}{2}\nabla_i^2$ lacks physics.  Thus the physics of (2) remained to be invented, and that showed to be beyond human capacity.  Even worse, $\Psi$ is uncomputable on present day computer for $N>3$ and on any thinkable computer for $N>10$.

RealQM presents a different story with a different wave function representing a sum of non-overlapping electronic charge densities with direct physical meaning depending on a common single spatial coordinate, thus computable for any $N$.

This simply means that the non-overlapping point masses of (1) are replaced with distributed non-overlapping (charge) densities in a common 3d Euclidean space $R^3$carrying a form of compression energy measured by the gradient $\nabla$ acting on $R^3$. This makes perfect sense from a classical continuum physics sense, while introducing $\nabla_i$ lacks physical meaning and so poses unresolvable questions blocking progress.

If physical meaning of the wave function $\Psi$ of stdQM is still evading, and in addition $\Psi$ is uncomputable, why not start from computable physics instead of magical formality, as in RealQM?  

PS Listen to Peter Woit giving his view on what is wrong with modern physics including in particular string theory, which despite the fact that it does not work still is propagated by leading theoretical physicists like Ed Witten. If leading modern physicists are not willing to accept the fact that string theory does not work, maybe the situation is the same with stdQM? If the $\Psi$ of stdQM is uncomputable, then it is impossible to decide between right and wrong, and then wrong must be rule in science.    

Åsa Wikforss och Monstren

Åsa Wikforss, professor i teoretisk filosofi samt ledamot av Svenska Akademien, har tagit som sin uppgift att varna svenska folket för faktaresistens i sina böcker:

• Därför demokrati : Om kunskapen och folkstyret
• Filosofiska klarlägganden i en grumlig tid
• Alternativa fakta : om kunskapen och dess fiender

samt i sitt Vinterprat i P1 25 dec 2023, med följande budskap:

• När förnuftet sover vaknar monstren.
• Vi tycks leva i en tid då förnuftet somnat och monstren väller fram. 
• Kunskapen är hotad, det offentliga samtalet förgiftat, anti-demokratiska krafter är på frammarsch...
• Demokratins fiender gör vad de kan för att spä på berättelsen. 
• Vi människor har den mest avancerade tankeförmågan av alla djur men vår förmåga är inte obegränsad.

Men vilka "monster" är det då Åsa pratar om? En ledtråd är kanske:

• Tidiga varningssignaler är inskränkningar i yttrandefriheten och mediefriheten, begränsningar av den akademiska friheten .... försvagningar av civilsamhällets organisationer.

Vilka anti-demokratiska krafter är det då som vill inskränka yttrandefriheten och begränsa den akademiska friheten samt försvaga civilsamhället med alla sina alternativa media? 

Jag ställer denna fråga till Åsa och kommer att meddela svaret här. Åsa’s bok om alternativa fakta delas ut gratis till alla gymnasieelever, vilket gör att vad Åsa säger har stort genomslag! Kanske då Åsa borde svara på min fråga?

PS Åsa kan naturligtvis inte själv vara faktaresistent och jag har därför bett Åsa att ge sin syn på en sammanställning av fakta om jordens klimat.