Modern Physics as Chaos

Connection between Entropy and Death.

In Greek mythology Gaia as Mother Earth and Heavens emerged from Chaos in a process from disorder to order. 

The science of physics seeking to describe this process in mathematical terms is split into classical physics in the names of Newton, Euler and Maxwell before 1900, and modern physics in the names of Einstein (relativity) and Schrödinger and Bohr (quantum mechanics) after 1900. 

The split is expressed by a shift from determinism of classical physics to indeterminism of modern physics as a process from order to disorder. 

How could this happen? Isn't science about order rather than disorder? Isn't life about order rather than disorder? Isn't true that disorder/death can be created in one single blow without precision, while building order/life requires both time and precision?

The reason for the shift was the 2nd Law of Thermodynamics first formulated by Clausius in 1867 as follows:

• It is impossible to construct a device which operates on a cycle and whose sole effect is the transfer of heat from a cooler body to a hotter body. 

The 2nd Law in this form states that heat energy cannot without losses be transformed into mechanical work, which directly connected to the efficiency of steam engines booming in the 19th century. 

The task of physicists was to rationalise Clausius rather cryptic formulation into an explanation/proof in quantitative physical terms, which was taken on by Boltzmann in a long struggle and eventually made him end his life when realising that he had failed. Boltzmann aimed at expressing the 2nd  Law in terms of microscopic mechanics of colliding gas molecules, which however showed to require an assumption about collision statistics, which was a form of surrender. 

But nobody was able to come up with something better and so Boltzmann's proof came to be the accepted explanation by modern physicists, who carried Boltzmann's statistics into quantum mechanics as if it had a fundamental meaning, albeit a different. But resorting to statistics is a form of surrender and failure of rationality.

So the world is still waiting for a proof of the 2nd Law after more than 100 years which has motivated Stephen Wolfram to step in with his New Kind of Science based on computation, as discussed in recent posts. 

I have also presented a proof of the 2nd Law based on computation, but fundamentally different from that of Wolfram, as also discussed in recent posts. The essence of my argument concerns the relation between order and disorder, between Gaia and Chaos. 

As a basic example I consider the expression of the 2nd Law captured in computational solutions of Euler's equations for a slightly viscous fluid such as compressible air or incompressible water, showing an unavoidable appearance of turbulence transforming ordered kinetic motion/energy into disordered kinetic energy in the form of heat. This transformation is irreversible because the precision required to coordinate disordered kinetic motion into ordered kinetic motion cannot be fully met in physical terms: there is always some loss. Necessarily appearing turbulence thus appears as a loss which cannot be fully retrieved, which is the essence of Clausius 2nd Law formulated without reference to statistics.  

This is analysed in mathematical detail in the books  Computational Turbulent Incompressible Flow and Computational Thermodynamics and in popular form in earlier posts. The analysis in particular describes how ordered swirling structures can develop in a cascade from large to small scales with increasing velocity gradients, which on some smallest scale have to be destroyed into heat to prevent blow-up. 

The result is a Physical 2nd Law expressed in the physical concepts of kinetic energy, work and turbulent dissipation, which does not require the evasive concept of entropy nor any statistics. I believe that both Clausius and Boltzmann could have been pleased with this form. Recall that Boltzmann used a dilute gas as his mathematical model in the form of Boltzmann's equation with his $H-theorem$ expressing his 2nd Law assuming that two particles about to collide are statistically uncorrelated, which is impossible to verify experimentally nor is very likely. 

Returning to greek mythology we find that the 2nd Law in this form expresses and interplay between Chaos/disorder and Gaia/order, where ordered structures emerge form disordered at the expense of energy as a loss, and ordered fine-scale structures are destroyed into disordered heat to prevent blow-up, all described in a mathematical analysis of fluid flow as a basic feature of the World. As a result time is moving forward as explained in catching terms in The Clock and the Arrow.

Statistics was introduced by Boltzmann in a desperate effort to give the 2nd Law a mechanical meaning and so created statistical mechanics, picked up by Planck in 1900 in an equally desperate attempt to explain blackbody radiation in mechanical terms, which opened Pandoras box to quantum mechanics as statistics leading to the disorder/Chaos of the "crisis of modern physics".  

For a derivation of blackbody radiation without statistics, see Computational Blackbody Radiation.  

For a version of quantum mechanics without statistics, see Real Quantum Mechanics. 

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. 

 

Boltzmann 175 vs 2nd Law by Finite Precision Computation

Ludwig Boltzmann 1844-1906

Lubos on the Reference Frame recalls the 175th birthday of Ludwig Boltzmann:

• Yesterday, Ludwig Eduard Boltzmann would have had a chance to celebrate his 175th birthday if he hadn't killed that chance by hanging himself at age of 62...
• Boltzmann's reason powering the suicide were intellectually driven frustrations.
• If he were resurrected and if he were around, he would probably ask me whether there's a reasonable chance that the people will get more reasonable when it comes to the ideas required for his new statistical picture of thermodynamics and physics in general. I would probably answer "No" and he would hang himself again. 

Lubos then enters into a defence of Boltzmann's 2nd law based on statistics and the related
Copenhagen interpretation of quantum mechanics with electrons randomly jumping around atom kernels, something which Einstein and Schrödinger never accepted. 

The problem Boltzmann tried to solve, with its tragic ending, is how formally reversible systems can show to have irreversible solutions. Boltzmann showed that you can hang yourself, but he could not un-hang himself, and he sought the explanation in statistics. Unsuccessfully according to Lubos, because still today people cannot understand what he was saying, about entropy and a 2nd law based on nonsensical statistics saying that something with a higher probability is more likely to happen.  I think this is not because people/scientists are stupid, which Lubos claims, but because what Boltzmann says makes sense only to Lubos.

I have presented a different explanation based on finite precision computation. This says that the reason that you cannot un-do things is lack of precision, and that all physics as well as digital computation is realised in finite precision. This means that you can enter a labyrint (the woods/world) with finite precision, like taking a step forward in time, but you cannot find your way out of the labyrint or retrace your path through the woods, go back in in time, because your are limited by finite precision. The arrow of time is an expression of finite precision computational physics. This is meaningful physics and different from Boltzmann's empty idea that the world moves form less probable to more probable states or from more ordered to less ordered states (with a start/bigbang as most ordered state inexplicable). 

I thus offer an explanation of the 2nd law of thermodynamics presented in many earlier blog posts 

and the book Computational Thermodynamics explaining that finite precision solutions of formally reversible system like the Euler equations of fluid mechanics can show to be irreversible, e.g. by the emergence of turbulence. This directly connects to a resolution of the Clay Navier-Stokes Problem reported in previous posts. 

The catch is that formally reversible systems can have irreversible solutions if precision is finite, and of course precision cannot be infinite, not in digital computation and neither in the physical world.