### Fictional force

Frank Wilczek, recent Nobel Laureate, has written an intriguing column in Physics Today about the strangeness of the concept of "Force", which unlike momentum or energy does not have an analogue in the more sophisticated models of reality that physicists have developed since Newton:

Newton's second law of motion, F = ma, is the soul of classical mechanics. Like other souls, it is insubstantial. The right−hand side is the product of two terms with profound meanings. Acceleration is a purely kinematical concept, defined in terms of space and time. Mass quite directly reflects basic measurable properties of bodies (weights, recoil velocities). The left−hand side, on the other hand, has no independent meaning. Yet clearly Newton's second law is full of meaning, by the highest standard: It proves itself useful in demanding situations. Splendid, unlikely looking bridges, like the Erasmus Bridge (known as the Swan of Rotterdam), do bear their loads; spacecraft do reach Saturn.

The paradox deepens when we consider force from the perspective of modern physics. In fact, the concept of force is conspicuously absent from our most advanced formulations of the basic laws. It doesn't appear in Schrödinger's equation, or in any reasonable formulation of quantum field theory, or in the foundations of general relativity.

He spends most of his time discussing what hecalls the "culture" of force, but I was especially struck by this comment which is somewhat tangential to his main point:

Nevertheless it survives the competition, and continues to flourish, for one overwhelmingly good reason: It is much easier to work with. We really do not want to be picking our way through a vast Hilbert space, regularizing and renormalizing ultraviolet divergences as we go, then analytically continuing Euclidean Green's functions defined by a limiting procedure, . . . working to discover nuclei that clothe themselves with electrons to make atoms that bind together to make solids, . . . all to describe the collision of two billiard balls. That would be lunacy similar in spirit to, but worse than, trying to do computer graphics from scratch, in machine code, without the benefit of an operating system. The analogy seems apt: Force is a flexible construct in a high−level language, which, by shielding us from irrelevant details, allows us to do elaborate applications relatively painlessly.

What an interesting analogy! I think however that it can be extended beond the concept of force - to classical vs quantum mechanics as a whole. Classical mechanics itself as a "high-level" language, built upon the "assembly language" foundation of quantum. It occurs to me that much of the elegance of MR physics can be aesthetically understood better in that context.

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