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Anatol Feldman
12-14-2000, 03:15 AM
Dear all,
Surprisingly, a lively chat on centrifugal force continues despite
Gottlieb’s opinion that such a force is a dead thing and is not worthy
of “scientific discussions”.
I would like to reiterate some points expressed in other comments and
add a new one, which relate the topic of inertial forces with another
thing that, in Gottlieb’s opinion expressed in his numerous
publications, is also dead - the equilibrium-point hypothesis. In other
words, I am going to make a bridge between the notion of inertial forces
and that of motor control, which may be most interesting for students
and specialists in biomechanics.
Sorry, Gerry, if at some turns of my thoughts, I centrifugally hit
your judgment. The purpose of my comments, in addition to what I said
above, is not to convince Gottlied that he is wrong but rather to warn
some students (and professors) who might be inclined to take his or a
similar opinion seriously.

1. To teach or not to teach students about inertial (in particular,
centrifugal) forces and about different coordinate systems? Mitnitski’s
comments correctly imply that the notion of inertial forces and frames
of reference is a part of the fundamental knowledge of physics. This
knowledge should be in the list of basic tests offered not only to
students of mechanics or biomechanics but also to professors who teach
them. Unlike professor Gottlieb, students cannot afford to be
wishy-washy about this subject. Also, I would advise, for safety
reasons, not to sit in a car with the driver who is ambivalent about the
physical reality of centrifugal forces (the real consequences of such
forces were nicely illustrated in Bogert’s comments).
2. Gottlieb’s statement that “the thing called "centrifugal" force is a
confection of physics and lay terminology that probably should be
avoided in scientific discussions” advises us to become, in a sense,
handicapped by forgetting “about the unity of the nature of inertia and
gravitation” (Einstein 1922) resulting, according to the general theory
of relativity, from the curvature of the 4-dimensioal space-time
continuum. We should also forget that the equivalency of inertial and
gravitational masses directly follows from this theory (see also
Bogert’s and other messages on this toppic).
3. The terminology that inertial forces are fictitious or pseudo-forces
came to us historically since physics initially focused on inertial
frames of reference in which these forces are non-existent. I think that
from the present state of knowledge, the terminology referring to
inertial forces as fictitious is misleading: in non-inertial frames,
these forces, like gravity, are experimentally measurable and therefore
are as real as other forces. Examples are plenty (again, see Bogert’s
message).
4. What causes inertial forces? The acceleration of a mass is determined
with respect to a physical body with which a frame or system of
coordinates is associated. In other words, accelerations and forces are
not absolute quantities. Therefore, if the referent frame, i.e., the
referent body accelerates, it affects the relative acceleration of the
mass. The part of the force resulting from the motion of the referent
frame is called inertial force. There is no mystic in it.
At this point, I can explain why the notions of frame of reference
and inertial forces are related to the equilibrium-point hypothesis.
5. The idea that motor actions are produced by the nervous system by
shifting spatial frames of reference associated with the environment or
body parts is a key notion of the most recent formulation of the
equilibrium-point hypothesis (Feldman & Levin 1995). Specifically, it
suggests that neural control levels are responsible for the
specification of parameters that determine the origin, orientation,
metrics and geometry of the spatial frames of reference for perception
and action. Changes in neural and muscle activity and, eventually,
movement or isometric force production emerge from changes in these
parameters by control levels. Recently, this hypothesis has offered an
explanation of how multiple skeletal muscles are controlled globally, as
a coherent whole. The appropriate predictions were verified for several
movements in humans and monkeys (Feldman et al. 1998; Lestienne et al.
2000; for references and an illustration of the basic idea, see my web
site with the address below). Simultaneously, in a set of recent
studies, especially those from Ostry’s group from McGill, it has been
demonstrated that the claims of falsification of the equilibrium-point
hypothesis (including those of Gottlieb’s) are largely flowed. See, for
example, Feldman et al. (1998) on how the effects of Coriolis force on a
pointing movement in a rotating room are explained in the framework of
the EP hypothesis.
Thus, if control levels change parameters of spatial frames of
reference for motor actions (which was experimentally established for
parameter lambda) then muscle forces emerging from this control process
are all, in essence, inertial. My feeling is that this idea relating the
motor control and inertial forces is non-trivial, worthy of discussion
and further elaboration.

Wishing you Happy Holidays, without problems associated with centrifugal
forces on snowy and icy road turns,


--
Dr. Anatol Feldman
Professor
Neurological Science Research Center
Department of Physiology
University of Montreal and
Rehabilitation Institute of Montreal
6300 Darlington, Montreal, Quebec, Canada H3S 2J4
feldman@med.umontreal.ca
Tel (514) 340 2078 ext. 2192
Fax (514) 340 2154
Web Site: http://www.crosswinds.net/~afeldman/

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