Re: Spookiness in physics

From: Bilge (dubious_at_radioactivex.lebesque-al.net)
Date: 09/14/04 

Date: Tue, 14 Sep 2004 19:47:47 -0000

 Patrick Reany:
>dubious@radioactivex.lebesque-al.net (Bilge) wrote:
>> Patrick Reany:
>> >dubious@radioactivex.lebesque-al.net (Bilge) wrote:
>> >> Patrick Reany:
>> >> >Why don't we regard all noncontact forces as "spooky"?
>> >>
>> >> What is a ``contact force?'' Don't give a naive definition.
>> >> Explain what it means for two objects to be in contact. So,
>> >> you need to define what an object is first. You'll need to
>> >> do this such that your definition explains why two objects
>> >> don't pass through each other. I think once you try to deal
>> >> with a contact force, you'll discover it's not very simple to
>> >> make that concept physical.
>> >
>> >I'm referring to the model of the perfectly rigid body to make the
>> >point that there is no reason to think of one type of force as any
>> >more "spooky" than any other kind of force.
>>
>> So, your model of a contact force starts with the force having the
>> form,
>>
>> F(r) = \infty 0 <= r <= R
>> = 0 r > R
>
>You have chosen to model the forces associated to spheres. OK, but
>since these spheres will never intersect in this crude model, we can
>claim:
>
>Assume we have two or more nonintersecting spheres of finite radii (no
>part of any sphere is inside any other sphere). Let S and S' be any
>two such spheres. Let S have of radius R. Let \ell be the line
>containing the centers of S and S'. Let P be the point of intersection
>of S' and \ell. Let r be the distance along \ell from the center of S
>to P.
 
  Neglecting the force you've given for the moment, let me say that
your definition above leads immediately to a number of physical
consequences. We can say a number of things. First, the mean free
path of a particle is equal to the average velocity of the particles
<v>, multiplied by the mean time between collisions, or,

    l_mfp = <v> x T_ave

Defining 1/T_ave as the collision frequency, \nu, I get the relation,

     v = l_mfp \n

That already gives me a rough idea of the speed at which a disturbance
in the medium can propagate. I claim that the most probable speed may
be obtained from a maxwell-boltzman distribution, which is basically
defined by maximizing the probability for a given number of particles
to have a particular speed, i.e., if n is the number of particles
with a speed v and there are N particles, then the probability is
just P(n) = [N!/n!(N-n)!]p^n (1-p)^(N-n), for which P(n) is a maximum.

  From that, I can go on to derive the basic kinetic theory of an ideal
gas, the propagation velocity of a disturbance, etc. In any event, if
you do that, the disturbance can't be light and if you try to use the
permittivity and permeability from maxwell's equations for v, you get
really weird numbers that don't make physical sense. Paul already tried
that with his bulk modulus and density and the result is that light
couldn't propagate in free space if the frequency were larger than
about 1 GHz.

>Then the force on S due to the existence of S' is given by:
>
> F(r) = oo, r = R
> = 0, r > R
>

   You haven't defined the region r < 0.

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