On Mon, 23 Jun 2008, Bill Miller wrote:
>
> "Timo A. Nieminen" <timo@[EMAIL PROTECTED]
> wrote in message
> news:Pine.WNT.4.64.0806221102300.656@[EMAIL PROTECTED]
>> On Sat, 21 Jun 2008, Bill Miller wrote:
>>
>>> One of the fundamental laws of mechanics is Newton's law of action and
>>> reaction, usually stated as : "Whenever a body exerts a force (action)
on
>>> a
>>> second body, the second body exerts an equal and opposite force
>>> (reaction)
>>> on the first body."
>>>
>>> Suppose that a stationary mass is located in the gravitational field
of
>>> another, distant stationary mass.The two m***** exert equal and
opposite
>>> forces on each other. (Action and reaction) Let us now allow one mass
to
>>> move under the action of the field of the other mass. ut the second
mass,
>>> being far away, does not yet "know
>>> that the first mass has moved. (gravity -- like light -- cannot
propagate
>>> instantaneously.) The second body continues to experience the same
force
>>> as
>>> before.
>>>
>>> In other words, the forces are now unequal in magnitude and direction
and
>>> Newton's action/reaction law no longer holds! Further, this situation
>>> also
>>> is in conflict with the very basic law of conservation of momentum.
>>
>> Hmm. Newton's 3rd law of motion (along with Newton 2, to relate force
and
>> transfer of momentum) is basically a statement that momentum is
conserved.
>
> Correct. And as long as the interaction is of a contact nature, then
> eveything is OK. But when there is a delay between the action and the
> reaction, then *for that delay period* momentum is not conserved. But we
> know that momentum MUST be conserved, so we must look at Newton with an
eye
> to modifying it to deal with what amounts to a time dependency.
>
> This is not a new idea. We have long recognized, for EM that
electrostaic
> representations break down when time dependency is present.
>
> Heaviside suggested this in 1893 but never took it all the way to its
> logical conclusion.
Heaviside's Maxwellian gravitation? There is no modification of Newton's
laws of motion in it. Newton's law of universal gravitation, describing
gravitational forces as interactions between distant bodies, is replaced
by a field theory, wherein all interactions are local - body interacts
with local field, not body with distant body.
As for Newton's laws of motion, Newton 1 and 2 are pretty much just
definititions of inertial motion and force, while Newton 3 is (as above)
conservation of momentum. How can these be modified sensibly?
>> Yes, if we consider two m***** as above (or two electric charges) to be
>> interacting with each other, we have exactly the problem you point out.
>>
>> Does this mean Newton 3 is wrong? Does this mean momentum is not
>> conserved? I would say that it means that we simply don't have a
situation
>> where there are two objects interacting at a distance, but two objects
>> each interacting with a field. Perhaps the interaction really is as
>> described by field theory, a local interaction between field and body,
and
>> we should throw away the classical mechanics idea of interaction at a
>> distance rather than Newton 3.
>
> That's one way of dealing with it. I believe that a better way would be
to
> recognize that Newton's work is not applicable to time dependency.
That's no
> different, conceptually, from Maxwell's expansion of Ampere's Law to
include
> The rate of Change Of E field in order to deal with magnetic fields in a
> time-dependent environment.
I think it is different conceptually. One is a conservation law, and the
other describes a limited set of experimental observations. If the limited
set of observations are static, then modifications for time-dependent
cases shouldn't be surprising. But conservation of momentum works for
time-dependent cases too - consider a bunch of colliding particles in a
box. Consider a collision between two elastic bodies - the collision
itself is time dependent, and Newton's laws work well. How can we modify
conservation of momentum to become time-dependent? Momentum is only
conserved in an average sense? Momentum is not conserved?
Yes, Newton's laws of motions describe observations too, but not in an
obvious or straightforward way (which is why students often have
difficulty).
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
|
