# What was meant by the 'ponderomotive force' as understood by Minkowski?

Skimming through Minkowski's famous 1907 paper, he uses the term ponderomotive force.

What does he mean by this?

-
He just means the Lorentz force on one in response to the field of the other. – Ron Maimon Sep 3 '11 at 2:36
@Ron: That's what I thought too, but Wikipedia has a description of ponderomotive force that's not identical to the Lorentz force. Edit: Although I now wonder if Minkowski really was referring to the Lorentz force and Ponderomotive force is not the correct translation of the German. Unfortunately I don't have Minkowski's paper. – twistor59 Sep 3 '11 at 7:18
@twistor59: I put the comment on after looking at both Wikipedia and Minkowski's paper. – Ron Maimon Sep 3 '11 at 19:07
Minkowski writes "ponderomotorische Kräfte", so there is no translation from German at all, its some kind of Latin in both cases. The gist of this new-latin "creation" is something like "force that causes movement of mass" BTW, Minknowski is a fine typo, one could call it a Freudian typo :=) – Georg Nov 2 '11 at 21:58
@Georg: The "pondermotive force" is explicitly stated to be what we call the Lorentz force today, and there are no two answers here. – Ron Maimon Nov 3 '11 at 16:50

Let's look at some clues as to what it probably meant at the time. The word is ponderomotive rather than pondermotive and is constructed like electromotive, magnetomotive, from ponder-o-motive. The [etymology][1] of ponder is given as

ponder early 14c., "to estimate the worth of, to appraise," from O.Fr. ponderare "to weigh, poise," from L. ponderare "to ponder, to consider," lit. "to weigh," from pondus (gen. ponderis) "weigh" (see pound (1)). Meaning "to weigh a matter mentally" is attested from late 14c.

Therefore as an initial guess, it could mean the line integral between two points of a force that acts upon substance to give it weight; perhaps the line integral of the Newtonian gravitational force?

Book Googling 'ponderomotive' turns up a quote from Energy and Empire: a biographical study of Lord Kelvin

what makes an electrified body move?

In May of 1843 Thomson published in the Cambridge Mathematical Journal a paper of a mere two pages which marks his earliest consideration of ponderomotive forces on electrified bodies. 'On the attractions of conducting and non-conducting electrified bodies' showed that, for a given distribution of electricity on the surface of a body A, the total moving force exerted on A by an arbitary electrical mass M is the same whether A be a conductor or non-conductor.

Hermann von Hermholtz and the foundations of nineteenth-centurey science by David Cahan

For he sought to orientate himself and others in the "pathless wilderness" of competing theories in electrodymanics around 1870; it was in this historical context that he promulgated his own contribution to the ongoing discussion about a fundamental potential for current elements. As already noted, those current potentials were mathematical tools used to derive further equations. Thus, the negative gradient of the potentials (the variation with repsect to changing position) furnished laws of ponderomotive forces, that is laws of mechanical forces between distant linear currents. The time derivative of the potentials furnished the electromotive force induced in systems of time-varint currents.

Page 11 of Eddington's Principle in the Philosophy of Science

In order to generate mechanical momentum, we usually need the action of a pondermotive force. Now a ponderomotive force of electromagnetic origin does act on conduction-current, but there is no conduc-tion-current in the free aether.

Page 165 of a 1922 Bulletin of the National Research Council By National Research Council (U.S.)

According to the Maxwell-Lorentz theory the fundamental equation for the calculation of all ponderomotive forces of electromagnetic origin is $f = q(E + \frac 1 c \vec v \times\vec H)$

So Minkowski meant the electromagnetic force on mass - the Lorentz force.

-
Yes, this is correct, but it requires no long exegesis. – Ron Maimon May 2 '12 at 15:02
I like this answer, except for the last conclusion. In the last quotation, the Lorentz force is mentioned only as a means of explaining the ponderomotive force (which is macroscopic force on bulk) by some fundamental equation, and Minkowski says this too: – Ján Lalinský May 27 '14 at 18:23
Also the fundamental equations for electromagnetic processes in ponderable bodies are in accordance with the world-postulate throughout. I shall also show on a later occasion that even the deduction of these equations, as taught by Lorentz on the basis of the concepts of electron theory, are by no means to be given up. - en.wikisource.org/wiki/Translation:Space_and_Time#14 – Ján Lalinský May 27 '14 at 18:23
Nevertheless, however strange it seems, Minkowski did use the term "ponderomotive force" in the meaning of force acting on a charged particle, not force in bulk. Perhaps he did not see think the difference is important at the time, or who knows. – Ján Lalinský May 27 '14 at 18:27

He just means the Lorentz force. The Lorentz force is called the "pondermotive force" in his paper, for no good reason. Old papers did not have internet to standardize their terminology for them.

-

Ron's responses are incorrect. You can see here that it was Boot and Harvie in 1957. In an inhomogenous plasma all particles regardless of charge will move toward the weaker field. This is much different from Lorentz forces, ie the motion of neutral particles do not generate a magnetic field.

-
If you read the question, I do say Minkowski mentions it in 1907. – Physiks lover Mar 6 '13 at 19:00