By the way, what model are we assuming for this debate? The mantra **centrifugal force is not a force** is usually used when teaching Newtonian mechanics in inertial reference frames.

I don't know where you got that idea. Typically it's undergrad courses which some teach that, i.e. Physics I, II, III. Not in more advanced courses. See

More modern teachings give the following

http://home.comcast.net/~peter.m.brown/gr/inertial_force.htmMost notably,

From

**Gravitation**, by Misner, Thorne and Wheeler, Box 6.1, page 164

A tourist in a powered interplanetary rocket feels "gravity." Can a physicist by local effects convince him that this "gravity" is bogus? Never, says Einstein's principle of the local equivalence of gravity and accelerations. But then the physicist will make no errors if he deludes himself treating true gravity as a local illusion caused by acceleration. Under this delusion, he barges ahead and solves gravitational problems by using special relativity: if he is clever enough to divide every problem into a network of local questions, each solvable under such a delusion, then he can work out all influences of any gravitational field. Only three basic principles are invoked: special-relativity physics, the equivalence principle, and the local nature of physics. They are simple and clear. To apply them, however, imposes a double task: (1) take spacetime apart into locally flat pieces (where the principles are valid), and (2) put the pieces together into a comprehensible picture. To undertake this dissection and reconstruction, to see curved dynamic spacetime inescapably take form, and to see the consequences for physics: that is general relativity.

From

**Introducing Einstein's Relativity**, by Ray D'Inverno, Oxord/Clarendon Press, (1992) page 122

Notice that all inertial forces have the mass as a constant of proportionality in them. The status of inertial forces is again a controversial one. One school of thought describes them as apparent or fictitious which arise in non-inertial frames of reference (and which can be eliminated mathematically by putting the terms back on the right hand side). We shall adopt the attitude that if you judge them by their effects then they are very real forces.

From

**Nature**, Albert Einstein, February 17, 1921 issue

Can gravitation and inertia be identical? This question leads directly to the General Theory of Relativity. Is it not possible for me to regard the earth as free from rotation, if I conceive of the centrifugal force, which acts on all bodies at rest relatively to the earth, as being a "real" gravitational field of gravitation, or part of such a field? If this idea can be carried out, then we shall have proved in very truth the identity of gravitation and inertia. For the same property which is regarded as inertia from the point of view of a system not taking part of the rotation can be interpreted as gravitation when considered with respect to a system that shares this rotation. According to Newton, this interpretation is impossible, because in Newton's theory there is no "real" field of the "Coriolis-field" type. But perhaps Newton's law of field could be replaced by another that fits in with the field which holds with respect to a "rotating" system of co-ordinates? My conviction of the identity of inertial and gravitational mass aroused within me the feeling of absolute confidence in the correctness of this interpretation.

A.P. French - Inertial force is defined as the force on a body that results solely from observing the motion of the body from a non-inertial frame of reference. This in addressed in

**Newtonian Mechanics**, A.P. French, The M.I.T. Introductory Physics Series, W.W. Norton Pub. , (1971) , page 499. After describing the inertial force as seen from an accelerating frame of reference French writes

From the standpoint of an observer in the accelerating frame, the inertial force is actually present. If one took steps to keep an object "at rest" in S', by tying it down with springs, these springs would be observed to elongate or contract in such a way as to provide a counteracting force to balance the inertial force. To describe such force as "fictitious" is therefore somewhat misleading. One would like to have some convenient label that distinguishes inertial forces from forces that arise from true physical interactions, and the term "psuedo-force" is often used. Even this, however, does not do justice to such forces experienced by someone who is actually in the accelerating frame of reference. Probably the original, strictly technical name, "inertial force," which is free of any questionable overtones, remains the best description.

Cornelius Lanczos - The subject of inertial force is also addressed in The Variational Principles of Mechanics - 4th Ed., Cornelius Lanczos, Dover Pub., page 98.

Whenever the motion of the reference system generates a force which has to be added to the relative force of inertia I’, measured in that system, we call that force an “apparent force.” The name is well chosen, inasmuch as that force does not exist in the absolute system. The name is misleading, however, if it is interpreted as a force which is not as “real” as any given physical force. In the moving reference system the apparent force is a perfectly real force, which is not distinguishable in its nature from any other impressed force. Let us suppose that the observer is not aware of the fact that his reference system is in accelerated motion. Then purely mechanical observations cannot reveal to him that fact.

From

**Cosmological Physics**, John A. Peacock, Cambridge University Press, (1999), page 6-7 (See URL, last quote at bottom)

One last comment - It seems like a very common thing that is done on discussion forums that when someone uses the term

*maths* (not the "s" at the end of math) it seems to come from someone who doesn't know math very little or at all. If you want to give the impression that you know math then I recommend that you don't use the term "maths" or if you need to then leave the "s" off the end of maths.

Pete