Comments on the Culture of the Force

All the English-language accounts ton’s idea that force is a primary, taught in a typical fluid mechanics we could find mentioned the original nonderived concept, which was pur- course. The stress has also been bridge construction in the 1840s and sued steadfastly by Leonhard Euler,1 given a microscopic interpretation in the reconstruction after World War II. led to the greatest successes in con- kinetic theory and in more general We don’t doubt Marton’s additional tinuum mechanics in the two cen- statistical mechanics. historical elements about the reconstruc- turies immediately following publica- Wilczek mentions some assump- tion in 1913–1915, but we couldn’t find tion of Newton’s Principia. That tions about forces. Newton regarded an English account of them. period culminated in the 1820s in mechanics as “the science of motions Augustin-Louis Cauchy’s stress prin- that result from any forces what- References ciple,1 which unified the seemingly ever.”1 Thus, he did not exclude con- 1. R. T. Wetherald, S. Manabe, Science disparate fields of fluid mechanics tact forces, the dominating concept 37, 1485 (1980); 45, 1397 (1988). and elasticity. This approach, com- in continuum mechanics. Nor did he 2. See, for example, the website of the monly attributed to Newton rather demand that all forces be central, Program for Climate Model Diagnosis than to Euler or Cauchy, is chosen which has particular relevance to the and Intercomparison at http:// over its main competitor, the varia- derivation of the angular momentum www-pcmdi.llnl.gov/ipcc/about_ipcc.php. tional formulation of Lagrange, to be principle. 3. See, for example, http://weather.gov/ organization.php, http://seaboard.ndbc .noaa.gov, and http://www.wmo.ch. 4. For more information, see http://www .dynapred.com and http://www.cpc.ncep .noaa.gov/products/analysis_monitoring/ lanina. 5. L. Hatton, IEEE Comput. Sci. Eng. 4(2), 27 (1997). 6. R. B. Laughlin, A Different Universe: Reinventing Physics from the Bottom Down, Basic Books, New York (2005). Douglass E. Post ([email protected]) US Department of Defense High Performance Computing Modernization Program Arlington, Virginia Lawrence G. Votta ([email protected]) Sun Microsystems Inc Menlo Park, California

Comments on the Culture of the Force ne of Frank Wilczek’s main Othemes in “Whence the Force of F ⊂ ma? I: Culture Shock” (PHYSICS TODAY, October 2004, page 11) ap- pears to be that although the force is, in Wilczek’s words, “vaguely defined,” it “continues to flourish” because the microscopic details it conceals are not really relevant for the scale of the phenomena it serves to describe. Fur- ther, it “survives the competition” be- cause “it is much easier to work with.” To this second point one might add that nothing succeeds like suc- cess. Let me explain. The concept of force had been under attack much before the com- ments of Peter Tait and Bertrand Russell. Even some of Isaac Newton’s immediate successors, most notably Joseph-Louis Lagrange and Jean Le Rond d’Alembert, were critical of the concept. D’Alembert regarded it as “useless to mechanics” and said that it “ought therefore to be banished from it.”1 However, the use of New-

August 2005 Physics Today 15 www.pt.ims.ca/6085-10 or Circle #10 Albert Einstein to Max Born1 In 1776, Euler, guided by his re- search on elasticity, came to regard Translated by Irene Born Newton-John the balance of angular momentum In this letter to his old friend, now at Edinburgh University, Einstein as an independent, second principle first responds to Born’s description of a local physician “who wouldn’t of mechanics,1 the first principle hurt a fly, but [states] that no sacrifice is too great [for] the realization of being the balance of linear momen- Marxist ideals, not even the destruction of millions of human lives.” And then it’s tum. When Euler arrived at the back to the old quarrel about quantum mechanics. (See Born’s comment below.) rigid-body equations of motion in Princeton, 15 September 1950 1752 using the first principle, he Dear Born, had to invoke hypotheses about in- . . . People such as your Bolshevik doctor come by their fantastic attitude as ternal forces. However, once he saw a result of their objection to the harshness, injustice and absurdity of our own so- the balance of the moments as an cial order (escape from reality). If he happened to be living in Russia, no doubt independent principle, he had no he would be a rebel there as well, only in that case he would take care not to tell need of such hypotheses. In special you about it. Nevertheless it seems to me that our own people here [in the US] cases such as that of a perfect fluid, make an even worse job of their foreign policy than the Russians. And the idiotic the second principle follows from the public can be talked into anything. And they really are very shortsighted, for first. In fact, the second principle technological superiority is transitory, and if it comes to an all-out conflict, the leads to the symmetry of the stress decisive factor is sheer numerical superiority. tensor when all torques may be ob- There is nothing analogous in relativity to what I call incompleteness of de- tained as moments of forces.2 The scription in the quantum theory. Briefly it is because the c-function is incapable status of the third law has been of describing certain qualities of an individual system, whose “reality” none of us clarified by the work of Walter Noll, doubt (such as a microscopic parameter). Take a (macroscopic) body that can ro- who gives a precise mathematical tate freely about an axis. Its state is fully determined by an angle. Let the initial interpretation of Newton’s verbal conditions (angle and angular momentum) be defined as precisely as the quan- statement of the law.3 tum theory allows. The Schrödinger equation then gives the c-function for any Even in applications of quantum subsequent time interval. If this is sufficiently large, all angles become (in prac- mechanics, Richard Feynman em- tice) equally probable. But if an observation is made (e.g. by flashing a torch), a phasized the importance of forces.4 definite angle is found (with sufficient accuracy). This does not prove that the He commented that “many of the angle had a definite value before it was observed—but we believe this to be the problems of molecular structure are case, because we are committed to the requirements of reality on the macro- concerned essentially with forces,” scopic scale. Thus, the c-function does not express the real state of affairs per- that “forces are almost as easy to fectly in this case. This is what I call “incomplete description.” calculate as energies are,” and that So far, you may not object. But you will probably take the position that a com- “the quantities are quite as easy to plete description would be useless because there is no mathematical relationship interpret.” Another application of for such a case. I do not say that I am able to disprove this view. But my instinct the concept of force is found in non- tells me that a complete formulation of the relationships is tied up with complete equilibrium statistical mechanics. description of its factual state. I am convinced of this although, up to now, suc- Just as the contact force had to be cess is against it. I also believe that the current formulation is true in the same found as the appropriate force to de- sense as e.g. thermodynamics, i.e. as far as the concepts used are inadequate. I scribe the dynamics of the contin- do not expect to convince you, or anybody else. I just want you to understand uum, the physically realistic short- the way I think. time force derived from the mean I see from . . . your letter that you, too, take the quantum theoretical descrip- instantaneous potential had to be tion as incomplete (referring to an ensemble). But you are, after all, convinced discovered as the force that de- that no (complete) laws exist for a complete description, according to the posi- scribes typical chemical dynamics in tivistic maxim: esse est percipi [to be is to be perceived]. Well, this is a pro- liquids,5 in contrast to the tradi- grammatic attitude, not knowledge. This is where our attitudes really differ. For tional concept of the potential of the time being, I am alone in my views—as Leibniz was with respect to the ab- mean force, which is more appropri- solute space of Newton’s theory. ate for slow or diffusion processes. . . . I have not changed my attitude to the Germans, which, by the way, dates not just from the Nazi period. All human beings are more or less the same from References birth. The Germans, however, have a far more dangerous tradition than any of 1. C. Truesdell, in Essays in the History the other so-called civilized nations. of Mechanics, Springer-Verlag, New Kind regards, York (1968). 2. R. Aris, Vectors, Tensors and the Yours, Equations of Fluid Mechanics, Dover, A. E. New York (1962). Born’s 1969 comment:1 This is probably the clearest presentation of Einstein’s 3. W. Noll, in The Axiomatic Method with Special Reference to Geometry philosophy of reality.... He calls my way of describing the physical world “in- and Physics, North-Holland, Amster- complete.” In his eyes, that is a flaw which he hopes to see removed, while I am dam (1959), p. 266. prepared to put up with it. I have in fact always regarded it as a step forward, be- 4. R. P. Feynman, Phys. Rev. 56, 340 cause an exact description of the state of a physical system presupposes that one (1939). can make statements of infinite precision about it, and this seems absurd to me. 5. S. Adelman, R. Ravi, Adv. Chem. Phys. 115, 181 (2000). Reference Ramamurthy Ravi 1. M. Born, The Born–Einstein Letters 1916–1955: Friendship, Politics and Physics in ([email protected]) Uncertain Times, Macmillan, New York (2005), p. 184. Original letter © Hebrew Uni- Indian Institute of Technology, Madras versity of Jerusalem. Chennai, India

16 August 2005 Physics Today http://www.physicstoday.org think Frank Wilczek is too harsh frames contradict later teaching that ilczek replies: Ramamurthy I when he implies that the use of physics can be used in any coordi- WRavi’s letter is an excellent, equations like F ⊂ ma is a matter of nates. Perhaps the first law was just scholarly supplement to my October intellectual inertia. In practical a political device to start discussion, column, which emphasizes that some terms, in engineering, and even in and to divide Newton’s detractors. classical masters of mechanics had the design of physics instruments, The third law is necessary for begin- logical and aesthetic misgivings we are interested in the values ning physics of ropes and pulleys, about the force concept, even before taken by certain variables x and the i but is wrong as “principle”: Momen- modern physics began to push us known dependence is in the form of tum conservation via translational ⊂ strongly toward different ones. differential equations dxi/dt vi and symmetry has myriad solutions. The ⊂ Regarding Brent Meeker’s letter, dvi/dt f(xi, vi). When xi is some po- second law is okay, but it is indefen- sition, the last is a form of F ⊂ ma. my critique was meant to be di- sible to promote Newton’s emphasis rected at foundational issues includ- Many physicists—David Bohm and on “force” as primary, only later to ing, specifically, which principles John Stewart Bell, for example— revise it with Hamilton’s equations should be regarded as primary, and have argued that position is the fun- of greater scope. Eventually I which as derived. There are some damental variable . . . hence the im- evolved a refreshing approach to ⊂ significant problems with using F ⊂ portance of F ma. non-calculus physics with energy Brent Meeker and conservation laws as primary, ma as a primary principle, as I dis- ([email protected]) and it works well. cussed. They could be avoided, per- Naval Air Warfare Center Students happily accept that haps advantageously, by focusing on Point Mugu, California Newton sometimes guessed wrong. A momentum and energy. Of course, in timid teaching culture and careless that approach it would still be ap- rank Wilczek’s column exposes a propriate and extremely useful to delicate point in physics teaching. textbook writing create the intellec- F have F ⊂ ma as a derived equation, Good teachers avoid implanting mis- tual inertia Wilczek observes. Good with its limitations indicated. Some conceptions to be overwritten later. physics teachers need to demon- Yet Newtonian mechanics courses do strate critical thinking, distribute intellectual inertia isn’t necessarily just that! During 20 years teaching their own notes, and have the a bad thing, if it keeps you moving I’ve maintained that Newton’s three courage not to brainlessly repeat in the right direction and allows laws are neither good laws nor inde- what is written in the book. you to remain in sync with long- pendent. Students enjoy hearing the John Ralston established flows. first law is just as circular as it ([email protected]) Frank Wilczek seems. Textbook apologies that University of Kansas Massachusetts Institute of Technology falsely limit physics to inertial Lawrence Cambridge ᭿

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