From: jos.bergervoet@xs4all.nl   
      
   On 1/6/2017 5:04 PM, Roland Franzius wrote:   
   > Am 06.01.2017 um 05:07 schrieb Rich L.:   
   >> On Wednesday, January 4, 2017 at 2:14:30 PM UTC-6, SEKI wrote:   
   >>> ...   
   >>> My basic point is as follows:   
   >>> Without any cohesive force or some sort   
      ...   
   >> There is no mechanism in QM that provides any "cohesive force" or   
     ...   
   > In classical physics the distribution function for one particle is a   
   > function of six canonically chosen variables   
     [ ... snip ]   
   > What is different in quantum mechanics?   
   >   
   > Not so much.   
      
   I would say at least these two things:   
     1. Those six variables cannot simultaneously be chosen   
        independently at the start.   
     2. The evolution for the members of the distribution slightly   
        differs from Newton's laws (or else the hydrogen atom would   
        still have a radiation dipole in its ground state!)   
      
   To be honest, I think that full QFT needs a wave functional   
   describing distributions over field shapes, not distributions   
   over point particle in phase space, but your analogy at least   
   suffices for simple Schrodinger-like wave functions in QM.   
      
     ...   
   >        the pure states -   
   > classical the trajectories with fixed starting position, momentum and   
   > spin - are replaced with pure states that are eigenstates of some   
   > observables, that can be given sharp values in an experiment dictating   
   > the starting distribution at time zero.   
      
   But they cannot all be given arbitrary sharp values! You   
   essentially only have to specify half of the starting values,   
   compared to the classical case..   
      
   > The apparent difference to canonical mechanics is now, that the pure   
   > quantum states evolving in a given dynmical environment display - as   
   > functions in Hilbert space - a statistical non-delta distribution over   
   > position and momentum variables   
      
   Of course Hilbert space is already described by *only* momentum   
   variables or position variables (the difference is just the kind   
   of basis vectors you construct.) So if you use both simultaneously,   
   then your possible distributions over them are highly constrained.   
   Of course that also applies to then classical case.   
      
   > and that these distributions still seem   
   > to act by conservation of momentum as if they were representing the   
   > position-momentum distribution of a classical swarm of particles.   
      
   If they still do, why are you calling this an "apparent difference?"   
      
   > This picture is naively wrong. The distribution again represents an   
   > ensemble of independent experiment recordings in identical environment   
   > with identical starting conditions at time zero.   
      
   Why do you believe that? Why can't the state in Hilbert space   
   just represent reality, without your additional restrictions?   
      
   > Why is it wrong to think in pure state wave functions as particles?   
      
   On the contrary: it is *exactly equivalent* to a distribution   
   of particles! If you choose the density in your distribution   
   proportional to the wave function squared and use the Schrodinger   
   flux to pilot each of them, as in Bohm's theory (I never understood   
   why he only talked about one particle at a time).   
      
   > Any measurement of any observable is an integral over the whole   
   > configuration space or momentum space. No local pointwise evaluable   
   > state properties can be measured locally only.   
      
   "Measurement" has to be described in QM as an effect of interacting   
   fields, so all you are allowed to use is the unitary time evolution.   
   Unless you invoke the collapse of the wave function or "projection   
   operators" like that. But those are not described by QFT, nor by the   
   Schrodinger equation, so you could mean anything by that. You post   
   becomes meaningless if that is the path you want to take (unless of   
   course you give the altered time-evolution equations you want to   
   use for your distribution, or your wave function, but you don't!)   
      
   > With the one exception: The set of commuting variables that are chosen   
   > to have a sharp set of common values remains so under the unitary time   
   > evolution in Hilbertspace of the set of pure states, wave functions,   
   > that are their common eigenbasis.   
      
   That is also meaningless. It is just your choice of basis, so it   
   will remain your choice. Just like someone else can keep another   
   choice. The state evolution is described by any chosen basis in   
   Hilbert space.   
      
   > And this mathematical phenomenon is used widely in textbooks to   
   > circumvent the apparatus of probability theory in the 3rd theoretical   
   > course 'Quantum Mechanics', because with the introduction to quantum   
   > probability, that follows in course 4, most students drop out from   
   > reaching their personal limit point of aggregated mathematical inabilities.   
      
   This may of course happen, but why do you believe you can introduce   
   "probability"? The unitary time evolution does not make choices   
   (since there is no collapse). And if no-one plays dice, there is   
   no concept of probability. So I think the students do at least   
   have a second reason to reject your concept.   
      
   > Even if energy, angular momentum and spin components  are constantly   
   > delta-sharp in atomic states, people reason much about momentum and   
   > position distributions.   
      
   So what's wrong? Another basis where you need to use a sum over   
   the basis vectors instead of using just one. No big deal, what is   
   your point?   
      
   > It reminds of being astonished as a human that   
   > bees cannot focuse on points in space because their eyes are built to   
   > control motion in 3-space and analyze colors of flowers in the environment.   
      
   OK, if the students are astonished that a different basis requires   
   different coefficients then there are some inabilities...   
      
   > The basic set of canonical observables does not expose itself in atomic   
   > states as an experimentally preparable entity.   
      
   Why not? An experimentalist can prepare atomic states, or plane   
   waves, or Rydberg states with (somewhat) localized particles, so   
   whatever more you want, with some ingenuity it might be prepared.   
   (And if not, it is just an experimental difficulty, mathematically   
   you can describe the state with any complete set of eigenstates or   
   non-eigenstates that you prefer to use as a basis!)   
      
   > On the other hand the set of q,p=-id/dq variables still constitute the   
   > mathematical basis in the construction of the relevant algebra of "good"   
   > quantum observables.   
   >   
   > And this "good" set, a set that is exactly or nearly constant in time   
   > with repect to atomic time scales in a given dynamical environment, is   
   > the only existing set of exactly measurable quantities in priciple.   
      
   Wrong. If you would say "in practice" you might be right, but   
   *in principle* any Hermitian observable is exactly measurable.   
   (Measurable of course meaning that you can 100% entangle it with   
   the output state of some measurement device. You just construct   
   a device having the right interaction with the state under test.)   
      
      
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