Re: Apparent weight

[David Bowman <dbowman@tiger.gtc.georgetown.ky.us>]

A. R. Marlow wrote in part:
> ...        .  Definitions are free, so of course you can do that if
> you wish, but you will pardon me I hope if to me it seems madness.  

Yes, I pardon you.

> ...
> But magnetic fields do work on massive objects.  If Coriolis force is real 
> (as opposed to Coriolis acceleration which is certainly real) but does no
> work on masses, what *does* Coriolis force work on?

I said that magnetic fields do no work on *charges* not on objects.  The
magnetic force on a charge is always perpendicular to the direction of
motion of that charge and thus can do no work on that charge.  If an
object possesses multiple charges and those charges are held together via
some other (nonmagnetic) forces (or if a particle possesses an intrinsic
magnetic moment) then an inhomogeneity in a magnetic field can do work on
the magnetic dipole moment of the object as a whole even though it does no
work on the charges themselves. In this case the work done on the
constituent charges comes from the internal forces on constraint among the
object's charged particles.  Coriolis forces *don't* do work on masses.  I
credited you with an exception for Coriolis forces.  The Coriolis force on
a mass is perpendicular to the motion of the mass and, hence, can do no
work on it.  But other so-called inertial, fictitious, pseudo, etc. forces
*do* do work on masses (in the frames in which they arise), among these:
centrifugal force, gravitational force, other forces arising from the
translational acceleration of a given frame's origin, etc.

> Again, the notion that forces can appear and disappear at the whim of the 
> frame choser seems to be at the nub of our disagreement.  There is no
> dispute about forces not transforming as scalars (has anyone made a claim
> otherwise?)  --  I claim that if a force is zero (tensor) in one frame it
> will be zero in all frames.

Forces (I'm using the term 'force' to refer ordinary 3-vector forces) do
not necessarily transform as tensors under general transformations among
variously accelerated frames.  Since they are not tensors they may appear
in one frame and they vanish in another. (BTW, forces do transform as
vectors, i.e. rank 1 tensors under Galilean transformations among
inertial coordinate systems, but such transformations are not
characteristic of the accelerated frames of interest here.)  The actual
transformation law that the forces obey depends somewhat on the kind of
transformation being made.  For instance, the transformation behavior
under general canonical transformations is different from the behavior
under more restricted contact transformations which is different than more
restricted time-independent coordinate transformations, etc., etc.

> You apparently claim otherwise, and validate
> your claim by decreeing  arbitrary accelerations as forces.  ....

I think the problem here is that you may attribute more "reality" to
forces generated by physical interactions between particles than I do.  I
tend to see all kinds of forces, whether frame generated, or interaction
generated, as essentially convenient mathematical constructions which
are equally 'real' and/or equally 'fictitious'.  To me, the component of
force acting on a given coordinate of a particle is just the partial
derivative of the system's Lagrangian wrt that coordinate (or,
equivalently, the negative of the partial derivative of the system's
Hamiltonian wrt the coordinate).  The Euler-Lagrange equations also allow
us to consider a given force component to be whatever expression it takes
to equal the time derivative of the corresponding momentum component,
where that momentum component is the partial derivative of the Lagrangian
wrt the corresponding velocity (time derivative of the appropriate
coordinate) component, or equivalently, the partial derivative of the
system's action wrt the corresponding coordinate.  The resulting force
component so-defined can be frame generated, interaction generated, or a
complicated mixture of both.  For instance, in a uniformly rotating frame
the Lagrangian possesses a centrifugal potential term generated from the
frame's noninertial motion which had its origin in the kinetic energy of
the Lagrangian when written in an inertial frame.  In the rotating frame
the negative of the gradient of this centrifugal potential wrt the
coordinates of a given particle is the centrifugal force on that particle.
If the Lagrangian contains other contributions giving other spatial
dependences among the particles' coordinates, then there are other
contributions to the forces on those particles.  If some of these position
dependences happen to come from an interaction among the particles
represented by a given type of potential energy term, then so be it.

> Limiting the question for the moment to the case of the experiences in the
> 747, may I ask why there is a necessity of reporting any other force than
> the one that is felt on your back, exerted by the seat?  Imagining  
> another force that you don't feel seems to me weird, and the fact that the
> new "force" has no third law counterpart would seem to complicate teaching
> students an understanding of Newton's laws.  How do you handle that
> aspect?    
 
I think a necessity of reporting another force is in order to accurately
account for energy changes in the system.  If the 747 is in a state of
uniform acceleration during takeoff, then in the frame for which the plane
is at rest there is a ("fictitious") force field that determines a
potential energy used to account for energy conservation among the
various objects in the plane.  Moving an object toward the back of the
plane lowers the potential energy of the object and moving it toward the
front raises that potential energy.  When an object is released from
rest and allowed to respond to the "fictitious" force without outside
interference, then the action of that force is to do work on the object
increasing that object's kinetic energy and decreasing its potential
energy.  If the released object was not initially at rest, then the
action of the force is to still cause the object to accelerate in a
direction away from the high potential energy region toward the lower
potential energy region.  The energy of the system in this frame is
determined by the system's Hamiltonian written in that accelerated frame.
If the 747 takeoff profile is not one of uniform acceleration then the
Hamiltonian for objects referred to a frame in which the plane is at rest
has an explicit time dependence and the energy of systems of such objects
is then not conserved.  But the forces acting on the objects from the
(now time-dependent) force field are still calculated the same way by
differentiating the time-dependent Hamiltonian or Lagrangian wrt the
appropriate coordinates and the equations of motion for the objects is
still determined as Euler, Lagrange and Hamilton would wish.

I don't think it is weird to imagine a force that I can't feel, since I
don't think I can feel any forces of any kind anyway.  What I feel are
the neurological impressions left in my brain from nerve impulses sent
from parts of my body that are distorted (strained) in some way from their
usual relative configuration.  If a particular force is a body force that
causes no such localized strain, then I do not feel its effects.  If a
force is applied locally to a relatively small surface region of my body,
then such strains occur and I can feel the strain effects as consequences
of the inhomogeneity of the force's application.

>  ...                                      .  The acid test, then, for a
> *real* force is "Does it cause deviation from local inertial motion?"  If
> it does it is a force; if it doesn't it is not a force.  And this holds in
> both Newtonian and Einsteinian physics.

Given your defining acid test above for a force everything you have been
saying seems to be consistent.  I just don't choose to use this criterion
to define what I mean by a force.  According to your definition of force
frame generated influences on the motion of a body in a given reference
frame cannot be called forces, and hence you call them fictious.  Only
interaction-generated forces pass your (very low pH) acid test.  My, much
weaker, test for a force is that if, in a given frame, it mathematically 
functions as a force as far as its role in the equations of motion and in
its relationship to various integrals of the motion (action, Lagrangian, 
Hamiltonian, etc.), then it is a force regardless the mechanism of its 
ultimate generation (physical interaction or frame acceleration).  I prefer
the duck test to an acid test.

David Bowman
dbowman@gtc.georgetown.ky.us