Centrifugal and Other Inertial Forces

Will there ever be a stable definition for centrifugal force?

Centrifugal force is the most obvious, and is usually the first mentioned of the so-called "inertial" forces. But from my earliest years as a student, I can remember that there has always been controversy over what centrifugal force is, and is not.

When I was in my first year at university, back in the 1960s, the textbook we used for Applied Mathematics I was An Introduction to the Theory of Mechanics by K. E. Bullen M.A., ScD., F.R.S., who was Professor of Applied Mathematics at the University of Sydney, Australia.  Prof. Bullen always had an appropriate quotation to introduce each chapter of his book, often "tongue-in-cheek", and from unexpected sources. I can't resist giving a few now:—

For Chapter XI, Centers of Mass and Moments of Inertia

"One should be concerned not merely with the weight of one's body, but with how this weight is distributed."
— Australian Women's Weekly

At the end of Chapter XVII, on the page headed Advice to Examinees

"But though they wrote it all by rote
   They did not write it right."
— "Louisa Caroline", The Vulture and the Husbandman

Getting back to the topic of this post, here is the quotation introducing Chapter VII, Dynamics of a Particle Moving in a Circle:

"Instead of debating whether it (centrifugal force) is a force 'seeking the centre' or 'fleeing from the centre', we should expedite its 'flight' from the subject of (elementary) mechanics altogether."
— E. G. Phillips, Mathematical Gazette, Feb. 1946.

Wikipedia

If we turn to the modern "fount of all knowledge" the internet, and specifically Wikipedia, we find that its definition of centrifugal force has inched forward slightly over the last decade, from total denial to minimal recognition:—

In 2004, we were told that "Centrifugal force is actually not a force..." 

Five years later, it was no longer "not a force", but had become a "fictitious" force and was "one of several pseudo-forces..."

Earlier this year it had changed from "fictitious" to "apparent", and as this is posted it is "apparent" and "fictitious" a.k.a. "inertial," and also a reaction force corresponding to centripetal force. See http://en.wikipedia.org/wiki/Centrifugal_force.

Whether it's labelled "fictitious", "pseudo" or "apparent", some force expels water from the clothes when my washing machine goes into its spin cycle. Some force caused those high-revving flywheels/clutches to explode in the early days of drag-racing, causing serious injury and damage before scattershields became mandatory. Surely we are entitled to recognize and name it as a true force?

Once Wikipedia has finished assuring us about how "fictitious" it is, I don't really have a problem with its current explanation(s) of centrifugal force.

Other inertial forces

There is a lot more about the inertial forces, once again labelled "fictitious", at http://en.wikipedia.org/wiki/Fictitious_force. However, for general readers this is quite a lengthy and complex discussion. The best short account of the inertial forces that I've seen is on p82 of Prof. Andre Assis' book Relational Mechanics. Setting out the orthodox view, he says:—

"In an inertial frame S we can write Newton's second law of motion as  m(d²r/dt²) = F  where r is the position vector of the particle m relative to the center O of S.

Suppose now we have a non-inertial frame of reference S' which is located by a vector h with respect to S (r = r' + h, where r' is the position vector of m relative to the origin O' of S'), moving relative to it with translational velocity dh/dt and translational acceleration d²h/dt². Suppose, moreover, that the axes x', y', z' rotate relative to the axes x, y, z of S with an angular velocity ω. In this frame S' taking into account the complete "fictitious forces" Newton's second law of motion should be written as ... 

m(d²r'/dt²) = F'  -  mω × (ω × r')  -  2mω × (dr'/dt)  -  m(dω/dt) × r'  -  m(d²h/dt²)

The second term on the right is called the centrifugal force, the third term is called the Coriolis force, the fourth and fifth terms have no special names."

Recently the fourth term above has been named the "Euler force".

Why orthodox science doesn't like inertial forces

There is a deep-seated reason for the problems with defining centrifugal force, and by extension, all of the inertial forces, although orthodox science is unlikely to admit it. The following quote explains it well:—

"Possibly due to the fact that the inertia forces are so uniform and also that a search for their source implies the currently unfashionable non-local interaction principle, they have been treated differently from the other forces in modern textbooks and are often only described as "pseudo-forces". Part of the problem with the image of inertial forces is that nobody has yet proposed a Newtonian non-local force law which can give the inertial force the same "true-force" status as the laws of gravitation, electrostatics, and electrodynamics. Such a law is proposed in Chapter 12 of this book. Like its predecessors, the laws of Newton, Coulomb and Ampère, it makes no assumptions regarding the mechanism of non-local interaction, but simply aims to fit the observed acceleration measurements."

Reference: In the Grip of the Distant Universe — The Science of Inertia, Peter Graneau and Neal Graneau, p19.

As I understand it, the "non-local interaction principle" mentioned above really implies IAAAD, (= instantaneous action at a distance). It apparently asks too much of modern orthodox scientists to accept IAAAD, but it would still be more honest for them to give the inertial forces their "true-force" status, and to admit that there is currently doubt and/or controversy over their origin. The option chosen instead, of pretending that they (sort of) don't exist, seems a bit puerile.