Re: [Phys-l] Phys-l Digest, Vol 37, Issue 22

["Alfredo Louro" <louro.alfredo@gmail.com>]

OK, I agree. It's just that this is precisely where I part ways with
John Denker, who does not accept that a field that you switch on and
off is time-dependent. Regards,

Alfredo

>  Message: 6
>  Date: Fri, 22 Feb 2008 15:33:47 -0600 (CST)
>  From: Jack Uretsky <jlu@hep.anl.gov>
>  Subject: Re: [Phys-l] non-conservative --> non-grady ???
>  To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
>  Message-ID: <Pine.LNX.4.64.0802221527400.2131@theory.hep.anl.gov>
>  Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed
>
>  1.  That the work done around a closed path is zero;
>  2.  That the force is time independent and derivable from a potential.
>
>                                     Reggards,
>                                            Jack
>
>  On Thu, 21 Feb 2008, Alfredo Louro wrote:
>
>  > On Thu, Feb 21, 2008 at 10:04 PM, Jack Uretsky <jlu@hep.anl.gov> wrote:
>  >> Hi all-
>  >>         Since the two statements are mathematically equivalent, as far as
>  >>  I can see, why is either one to be preferred?
>  >>                                         Regards,
>  >>                                                 Jack
>  >>
>  >
>  > Well, I thought earlier I would conclude my correspondence on this
>  > particular thread, but I can't help asking which two statements you
>  > find mathematically equivalent?
>  >
>  > Alfredo
>  >
>  >
>  >>  On Thu, 21 Feb 2008, John Denker wrote:
>  >>
>  >> > On 02/20/2008 09:57 AM, Alfredo Louro wrote:
>  >> >> "Piecewise time-independent" is not time-independent at all. And
>  >> >> whether a force is conservative cannot depend on what the particle is
>  >> >> doing. One way of defining a conservative force is to say the work
>  >> >> done by it around a closed path is zero. For any closed path. At all
>  >> >> times.
>  >> >
>  >> >
>  >> > Do we really want to define "conservative force" that way?
>  >> >
>  >> > I called attention to a situation
>  >> >  http://www.av8n.com/physics/img48/accelerator.png
>  >> > where it was uniformly true that the field /applied to/ the
>  >> > system was
>  >> >  a) independent of time, and
>  >> >  b) the gradient of some potential.
>  >> >
>  >> > This is a statement about the field /applied to the system/
>  >> > at the time and place where the system happens to be.
>  >> >
>  >> >
>  >> > Do we really want to insist that the field be unchanging at
>  >> > all other times and all other places as well?  That seems
>  >> > kinda strict.  Forsooth, it guarantees that the suggested
>  >> > definition is vacuous.  That is, there cannot be any field
>  >> > that satisfies the terms of this definition, because surely
>  >> > there is a non-constant field somewhere in the universe.
>  >> >
>  >> >
>  >> > This example seems to reinforce the point I was making at the
>  >> > beginning of this thread:  The whole business of "non-conservative"
>  >> > force field is just begging to be misunderstood.
>  >> >
>  >> > To summarize:
>  >> > -- If you mean grady, say grady.  Calling a non-grady field
>  >> >  "non-conservative" is asking for trouble.
>  >> > -- Both grady and ungrady force-fields uphold conservation of
>  >> >  energy.  No exceptions have ever been observed.
>  >> > -- Conservation is not the same as constancy.  Local conservation
>  >> >  of XX means that XX is constant /except/ insofar as it flows
>  >> >  across the boundary.
>  >> > -- For an isolated system, conservation would be the same as
>  >> >  constancy, but that's an almost trivial subset of physics.
>  >> >  Physics relies on /local/ conservation laws that can be
>  >> >  applied to non-isolated systems and subsystems.
>  >> >
>  >> >
>  >> > http://www.av8n.com/physics/conservative-flow.htm
>  >> > http://www.av8n.com/physics/non-grady.htm