torsdag 20 mars 2014

Principle of Least Action vs Adam Smith's Invisible Hand

                                     Violation of the PLA of the capitalistic system in 1929.

The Principle of Least Action (PLA) expressing
  • Stationarity of the Action (the integral in time of the Lagrangian), 
with the Lagrangian the difference between kinetic and potential energies, is cherished by physicists as a deep truth about physics: Tell me the Lagrangian and I will tell you the physics, because a dynamical system will (by reaction to local forces) evolve so as to keep the Action stationary as if led by an invisible hand steering the system towards a final cause of least action.

PLA is similar to the invisible hand of Adam Smith supposedly steering an economy towards a final cause of maximal effectivity or least action (maximal common happiness) by asking each member of the economy to seek to maximize individual profit (individual happiness). This is the essence of the capitalistic system. The idea is that a final cause of maximal effectivity can be reached without telling the members the meaning of the whole thing, just telling each one to seek to maximize his/her own individual profit (happiness).

Today the capitalistic system is shaking and nobody knows how to steer towards a final cause of maximal efficiency. So the PLA of economy seems to be rather empty of content. It may be that similarly the PLA of physics is void of real physics. In particular, the idea of a smallest quantum of action as a basis of quantum mechanics, may well be unphysical.

  

26 kommentarer:

  1. The difference being that a dynamical law derived from a Lagrangian can be tested, while the invisible hand theory are neither well defined or testable.

    It may be that similarly the PLA of physics is void of real physics

    What exactly is real physics in this context?

    SvaraRadera
  2. Real physics is physics without interference from human observer.

    SvaraRadera
  3. But if the situation is such that knowledge about a system is limited so that interference is inevitable, then any claim about real physics (in the context you advocate) whould be unscientific since it is untestable. Do you disagree?

    SvaraRadera
  4. Yes, it may be physically untestable microscopically, but macroscopic outputs from microscopic computational simulation may be physically testable, while the microscopic simulation is open to non-invasive inspection.


    SvaraRadera
  5. But a simulation is based on a model.

    If a model produces results close to observations, within some accuracy, can not have the meaning that the model has been prooved. That is faulty logic. Do you dissgree?

    SvaraRadera
  6. Detailed direct inspection of microscopics is impossible, but not necessary, since anyway only macroscopics is of interest. However detailed simulation of microscopics is possible and if macroscopic outputs agree with observation then there is no reason to not use the model as a representation of what you anyway cannot see.

    SvaraRadera
  7. Then what is the difference with conventional quantum mechanics from this view of yours?

    SvaraRadera
  8. The problem is that conventional quantum mechanics is uncomputable because of the high dimension of the wave function, and thus is beyond meaning. What is needed is a computable version of quantum mechanics.

    SvaraRadera
  9. What is needed is a computable version of quantum mechanics.

    One mayor flaw with this reasoning is that quantum mechanical systems just may be intractable for computation by any means available to us. It doesn't mean that the underlying theory is wrong, just that we unfortunately can not test it with any good precision. Approximations can still be made, but requires a lot of skill, experience and analytic reasoning to be any good.

    Another is that when the system is computable, lighter atoms for instance that do have a multidimensional wave function in this treatment, conventional quantum mechanics has an extreme accuracy when compared to experiment. The helium ground state can be computed to 14 significant digits if I remember it right (it's around there at least, may be better).

    And still there are a lot of bizarre experimental results, especially in different experiments within quantum informatics. If you claim to have a microscopic theory that represents "real physics" (in your earlier defined context), the theory needs to reproduce those experiments of course.

    Do you think that you can set up a simulation, using only real physics as you define it, that predicts the result of the delayed choice quantum eraser for instance?

    SvaraRadera
  10. Experiments like that seem to me to be meaningless since they involve single photons for which a physically meaningful model is lacking. There are no photon particles and "all is wave" as Schödinger said.

    SvaraRadera
  11. That is just ignoring uncomfortable facts/experiments.

    Dropping slogans lite "all is wave" is not constructive. You can also say "all is quantum fields" and then we are back at the experiments again since this is models that give a physically meaningful model.

    What makes "all is wave" even weaker is that Schrödinger died 1961, at the same time as the laser was realized. Experiments made later would of course have influence. The same point goes to Einstein who didn't live to see experiments related to the views he had about quantum mechanics.

    SvaraRadera
  12. No: "all is wave" is not a slogan. If you understand that there are no particles then the basic contradictions of quantum mechanics disappear and science can progress.

    SvaraRadera
  13. So why can't it be quantum fields? There is no need to distinct between particles and waves then and the theory has one of the best predictive powers out there.

    SvaraRadera
  14. Maybe, but is QED computable? Less than QM which is uncomputable.

    SvaraRadera
  15. But not even Newtonian mechanics is computable in a realistic calculation of microscopic systems!

    Molecular Dynamics is a great tool for physicists besides that, even if it is not tractable to overcome the Lyapunov instability. You start to evolve a path in state-space and it will quickly deviate from the true one, ending up with a similar path, but not the true one. Still usable to sample for statistics though, so there is a meaning through statistical mechanics.

    SvaraRadera
  16. Uncomputable models have no meaning, including the linear multidim Schrödinger equation, according to Nobel Laureate Walter Kohn.

    SvaraRadera
  17. That is not exactly what Kohn said, if you are referring to his Nobel lecture.

    In general the many-electron wavefunction \Psi(r_1,..,r_N) for a system of N electrons is not a legitimate scientific concept, when N>=N_0, where N_0 \approx 10^3.

    So, the many body wave-function, according to Kohn does have meaning for cases where the number of electrons are limited to a number that he estimates to be of the order of a thousand. And why shouldn't he believe that? The theory that he got the Nobel prize for relies on there being a many body wave function!

    SvaraRadera
  18. The N =10^3 electrons is a safe estimate. The trouble starts already with Helium with N = 2.

    SvaraRadera
  19. Could you be more specific in exactly what those troubles are?

    Using QED (sometimes not necessary) it is possible to calculate systems more complicated than helium within spectroscopic accuracy. Isn't that accuracy good enough for you?

    What do you then demand?

    SvaraRadera
  20. What is needed is a computable model for atomistic physics, which is lacking because Schrödingers' eq is uncomputable because of high dimensionality.

    SvaraRadera
  21. But there are tons of computable models for atomistic physics using different approximations (you referred to Kohn so I guess you at least know that there is something called dft, wich is one among many others).

    SvaraRadera
  22. Of course, but DFT is viewed to be some sort of expert system and as such is questionable science.

    SvaraRadera
  23. Expert system?

    SvaraRadera
  24. Yes atomistic physics based on Schrödinger's multidim wave equation depends on clever choices of orbitals based on knowhow.

    SvaraRadera
  25. But ones you have the "clever choice" the verification isn't that complicated or hard to grasp at all. Some bases are just a better representation than others. Even plane waves can work.

    If you find some theory hard to grasp should not have bearing on the merit of that theory, don't you agree?

    SvaraRadera
  26. It is not hard to grasp that a multidimensional wave function does not represent real physics, that statistics requires microscopics and that electrons jumping around like roullette balls is improbable.

    SvaraRadera