This is an intro to a live video talk I will give on Febr 3 2024 on John Chappell's channel Natural Philosophy: Where Critical Thinking Challenges Theory (directly connecting to the slogan of this blog). If you feel that this must be crackpot science, take a look at my arguments before deciding and remember that established physics can be crackpot science.
Digital computation, with AI (or even AGI) as latest achievement, is today reshaping human conditions and it is natural to ask if also the science of physics as the inner core of existence is transformed.
Classical physics is based on mathematical models in the form of differential equations expressing balance (of forces) in some system, such as Euler’s equations for fluid mechanics and Maxwell’s equations for electro-magnetics, while modern atomic physics is based on Schrödinger’s equation.
The equations express system forces while solutions of the equations represent evolution in time of systems under given conditions. The task of determining solutions is thus central and here digital computation opens entirely new perspectives with computational complexity or computability as key element.
Uncomputable systems keep their information hidden to inspection, with prime example Schrödinger’s equation which in its standard multidimensional form is beyond the capacity of any thinkable digital computer. On the other hand, computing solutions to Euler’s equations resolves the enigma of turbulence, as will be shown in the talk.
It is natural to view the evolution in time of a physical system as a form of analog finite precision computation as the action of forces takes the system over small time steps from one state to the next, which can be modeled by finite precision digital computation:
- Physics as Analog Computation as Digital Computation.
The key elements of computability are (i) finite precision and (ii) stability/wellposedness as a measure of precision required to make computational model output reliable. Forward-in-time evolution then shows to be computable because it is stable, while backward in time evolution is uncomputable because it is unstable, which can be seen to be the essence of the 2nd Law.
Physics as Computation offers solutions to open problems of (i) turbulence and (ii) atomic physics through new computable forms of Euler's and Schrödinger’s equations, which are the subjects of the talk:
Real here directly connects to computability. A real physical system computes its own evolution forward-in-time and so is analog computable and a mimicing digital computable model can be viewed to be a real model:
- Real models are digital computable because reality is analog computable.
The standard multidimensional Schrödinger equation is an uncomputable model without real physical meaning (only statistical). RealQM is computable and has a real physical meaning as a collection of non-overlapping interacting charge densities.
Real Euler computes real turbulent flow, and RealQM computes real atoms/molecules, which opens entirely new perspectives on physics: Physics as Computation.
Real Euler gives an explanation of the 2nd Law (Computational Thermodynamics) as forward-in-time computability and backward-in-time uncomputability. See the book The Clock and the Arrow for a general audience.
There is a connection to Wolfram’s Computational Foundations for the Second Law of Thermodynamics in the sense that computation is central, but the essence is different: For Wolfram it is computational irreducibility, while I favor finite precision+stability.
Inlägg
Inga kommentarer:
Skicka en kommentar