From: roland.franzius@uos.de   
      
   Am 11.03.2017 um 03:24 schrieb edprochak@gmail.com:   
   > On Thursday, March 9, 2017 at 1:04:34 PM UTC-5, pora...@gmail.com wrote:   
   >> On Wednesday, February 8, 2017 at 5:52:01 PM UTC+2, pora...@gmail.com wrote:   
   > []   
   >>> ============================   
   >>> does the Feynman diagram explain why  the change in direction   
   >>> (after collision )   
   >>> is in angle say ''x''   
   >>> and not angle ''y ''   
   >>> iow   
   >>> why just the angle he is suggesting ??   
   >>> ==========================   
      
   >>>   
   >>> [[Mod. note --   
   >>> * 9 excessively-quoted lines snipped here.   
   >>> * To answer the poster's question, this depends on how precisely the   
   >>>    initial conditions are specified.  If they are specified sufficiently   
   >>>    precisely [so that the impact parameter of the incoming particle   
   >>>    (i.e., the lateral offset of its incoming trajectory with respect   
   >>>    to a collision) is known; obviously the uncertainty principle imposes   
   >>>    restrictions on just how well this can be done] then yes, the particle's   
   >>>    future trajectory (including the change in direction) can be computed.   
   >>>   
   >>>    But in the usual case the impact parameter is completely unspecified   
   >>>    (we *don't* know the incoming particle trajectory's lateral position   
   >>>    to ultra-high accuracy) and in this case even classical mechanics can't   
   >>>    do what you ask.   
   >> ==============================   
   >> in other words   
   >> my above  question  has no answer   
   >> in current science !!  ??   
      
   >   
   > I would say:   
   > current science says there is a limit to how   
   > precisely we can calculate the trajectory.   
      
   Current science has a simple tool to check for the precision of a   
   dynamical theory: Statistics.   
      
   If a dynamical theory comes up with a canonical system of equations of   
   motion as known from classical or quantum mechanics, the solution to the   
   equations is expressed in the form of a tranformation law mapping the   
   start values of a set of position and momentum observables at time of   
   laboratory preparation to its values at later times   
      
   Classically a canonical mapping   
   LiouvilleMap_(t,t_0) : L_t f(x_t0,p_(t0)))  ->  f(L_t(x_t0, p_t0)   
   =f(x_t,p_t)   
      
   with the Hamiltonion as the short time evolution map.   
      
   In simple words, any function of the variables and independent of time   
   separately transforms simply by the canonical time evolution of its   
   arguments.   
      
   The same is true for the quantum time evolution by unitary map on   
   operators   
      
   U_(t,t0) : f(X_t0, P_t0, spin_t0) ->   
   f(U^-1 X U, U^-1 P U, U^-1 spin U)  )   
      
   So one can simply test a rich enough set of statistical ditributions of   
   start values and check if they transform into the distributions at later   
   times. There is no need for sharp delta-like distribtions of the start   
   values necessary representing the trajectories of Newtons celestial   
   mechanics.   
      
   The statistics of canonical time evolution in statistical mixed   
   ensembles is the topic of classical and quantum statitistical mechanics,   
   part IV of the course of theoretical physics.   
      
   Significant differences in time evolution of statistical ensembles are   
   easily detected by thermal properties of matter and light at low   
   temperatures.   
      
   The most spectacular example of detection of a new dynamical framework   
   of time evolution is Max Plancks statistics of thermalized radiation   
   photon frequency distribution in black body radiation.   
      
   Plancks idea sparked Einsteins idea of single photon states in vacuum   
   replacing the classical wave picture of Maxwell, at 1907 a completely   
   unfounded idea with respect to experiments except the independence of   
   enery levels from intensity in the photoelectric effect.   
      
   Physicist began to understand photons and electrons only 50 years later   
   in the framework of QED and relativistic quantum field theory.   
      
   Nevertheless the Bose-Einstein and Fermi-Dirac statistics were   
   established in the first years following development of QM in 1925 by   
   the detection of thermal properties radiation, gas and matter.   
      
   So today, any model of dynamical evolution in natural sciences,   
   finanancial market observables, signal processing in complex systems or   
   genetic evolution is tested on sets of statistical distributions of a   
   (more or less) complete set of variables at time of preparation and a   
   set of statistical tests if the distribution follows the time evolution   
   of the variables in a numerical testable model.   
      
   Of course there are other models of time evolution too, that allow of   
   statistical mixing and an evolution of states in the time direction of   
   encrising entropy like the Boltzmanns equation.   
      
   There is a severe epistemological gap still today in canonical   
   statistical mechanics, both classical and quantum:   
      
   All  canonical theories that simply transform function ba transforming   
   the arguments of the functions in time preserve the state entropy.   
      
   They cannnot be used to explain the universal evolution trend into the   
   uniform state of thermal equilibrium and the increase of entropy to the   
   possible maximum in the family of statistical states.   
      
   --   
      
   Roland Franzius   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)