fredag 22 februari 2019

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.

1 kommentar:

  1. I comment here because I came to a bit similar conclusion. However, from a bit different angle : the Hilbert space is big. Not Hilbert space (which is what you refer to as finite computation) is countable. Hilbert space is uncountable.

    The problem might be not in finite vs infinite but in "countable" vs "uncountable".

    The probability of picking a rational number randomly from R vs an irrational, is zero.

    Now the quesiton is : what are the equations of motions that describe our universe are "made of"?

    Is it a finite turing machine ? => rational number picked
    Or an infinite turing machine => not rational number picked.

    If we assume that our universe is infinite (the Hilbert space really "exist"), then we assume that we are living in an universe who's laws might or might not be decideable/undecideable algorithms, if they are undecideable (turing machine never halts), then it means, that it is possible that the 2nd law of thermodynamics is "really true".

    Furthermore, if you want to pick a "universe" randomly, from all possible universes. Then that essentially means that you pick a single number from R (real numbers) and this number represents the "algorithm" that we call "physics". Now, the funny part is that the probability of living in such an universe is ZERO.