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.