Abstract
Do component forces exist? I argue that the answer lies in the affirmative, on historical and operational grounds.
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Notes
- 1.
Papers addressing the issue, or closely related issues to do with causality and scientific realism, include Creary (1981), Forster (1988), Bigelow et al. (1988), Spurrett (2011), Corry (2006), Schmidt-Petri (2008), A. Wilson (2009), J. Wilson (2009), Massin (2009), and Schrenk (2011). Cartwright’s discussion of component forces is situated in a larger project, in which she argues against taking fundamental laws in physics to be literally true. I am sympathetic with her conclusions on this matter – see Rowbottom (2011a, 2015, Manuscript) – and will not challenge them. As will become apparent, I am mainly interested in whether there are observable entities (and/or effects on entities) that we may associate with component forces in some circumstances.
- 2.
We will later touch on whether it is reasonable to ascribe this law to Newton. I use a momentum representation because this is an easy way to link classical mechanics with quantum mechanics and relativistic mechanics. In short, this definition of force has been retained, although the definition of momentum has changed. (In the former case, force and momentum are operators rather than vectors. In the latter case, momentum is defined in terms of relativistic mass.)
- 3.
Massin (In Press: §4.3) argues for this conclusion. Moreover, Blay (2001) understands Newton’s verbal precursor to the modern version of the second law to state a sufficient condition. We would expect the modern version to follow suit in this respect (and therefore for an impulse on a body to be sufficient to change the body’s momentum). We will discuss Newton’s formulation in more detail in due course.
- 4.
‘Act’ is in scare quotes because its use is metaphorical. The talk is of representations in a class of physical models.
- 5.
I use these two laws for presentational reasons, e.g. to enable easier quotation of Cartwright (1983) at later points in the paper; it’s possible, of course, to consider three bodies and just one of these laws. For instance, two of the bodies could exert equal but opposite attractive forces on the third.
- 6.
See also Massin (2009: §1.2).
- 7.
There’s also a third way, which is to take both kinds of law to have definitional relevance. I think that this is the correct view, as will become apparent.
- 8.
From my pragmatic perspective, very roughly, mechanics is primarily about understanding how to arrange objects such that they stay still or move in particular ways. Derivatively, this gives understanding of how objects will behave when in particular arrangements. For my more detailed views on scientific progress, see Rowbottom (2015, Manuscript).
- 9.
This is one sense in which Kuhn’s (1996) emphasis on shared exemplars (of puzzle solving), within a discipline, is important; see Bird (2004) and Rowbottom (2011b: §3) for more on this. Any physicist worth her salt will have cut her teeth by solving many problems in elementary mechanics involving the equations cited previously, as well as derivative constant acceleration equations. Even elementary two-dimensional problems solved before vector formulations are learned, e.g. concerning projectile motion, involve resolving motion into independent perpendicular components.
- 10.
This is not to presume that they co-exist in all mechanical scenarios.
- 11.
Not all component forces are natural. I also agree with Creary (1981, p. 151–152) that:
A distinction is made between natural component forces, which arise directly from the action of various real physical causes, and mathematical component forces, which arise merely from the artificial resolution of vectors, and thus lack physical existence.
I will argue for the existence of natural component forces.
- 12.
In classical mechanics, it is a consequence of the third law that these have the same value. But the distinction is not easy to spot, because the third law is expressed in terms of forces. We’ll return to this distinction in relation to the third law a little later, in Sect. 5.
- 13.
See, for example, http://www.livescience.com/46560-newton-second-law.html and http://physics.info/newton-second/.
- 14.
See, for instance, http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law.
- 15.
Stevinus is best known for his ingenious derivation of the principle of the inclined plane. For a presentation and discussion of his thought experiment, see Rowbottom (2014). As Mach (1892, p. 23) points out, however, the principle of the inclined plane can be derived from the principle of the lever (although I think this derivation depends on thinking of tensions and weights as both being kinds of force).
- 16.
Bridgman (1927, p. 28) mentions expressions too, and implicitly endorses a similar principle concerning these. Appeal to concepts may be required in order to extend the present principle to cover these. For example, Bridgman presumably intended that an expression is meaningless if it involves at least one meaningless concept; and that the same goes for questions and statements, mutatis mutandis.
- 17.
The images from Luna 3 were rather indistinct, and could, at best, only very weakly verify such a statement on Ayer’s view; Apollo 8 might be substituted, if this is a concern.
- 18.
Bridgman imagines a laboratory in distant space, in order to avoid some of these difficulties. But this is not required. Or if it is, this difficulty is in no way peculiar to the concept of force. There are no closed systems, strictly speaking, although physics often proceeds, in its definitions and derivations, as if there are.
- 19.
Naturally, the motion may be retarded by the use of multiple springs instead. This fits with the idea, discussed below, that whether multiple component forces are present may, in some situations, be difficult or impossible to determine.
- 20.
This is not to deny that ‘deformed’ (and ‘deformation’) are theory-laden terms. They are. Thus we must be aware that not all changes in shape constitute deformations in the relevant sense; springs might change size due to changes in temperature, or become permanently deformed after exposure to high (or repeated) stresses, for example. Similarly, the use of ‘spring balance’ is an abstraction in so far as it doesn’t specify any particular type of concrete spring balance. (However, it is possible to restrict the definition to a concrete type and still show that component forces exist.) For more on abstractions and idealizations, see Cartwright (1989).
- 21.
It’s conceivable for there to be n parallel springs having the same effect, for any integer n, subject to the appropriate physical constraints on spring size being obeyed.
- 22.
Besides, I don’t think we ‘experience’ forces in the way that Wilson appears to think that we do. I contend instead that that the observation statements we take to be true concerning our bodily sensations are theory-laden, and that the theories we are inclined to employ are often false (e.g., folk physical theories). It’s also possible to argue that we can experience accelerations, but not forces.
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Acknowledgements
Thanks to Martin Hardcastle, Olivier Massin, Julian Reiss, and an anonymous referee for comments on an earlier version of this piece. Thanks also to an audience at Hong Kong University, and especially Malcolm Forster, Alyssa Ney, John T. Roberts, and Peter Simons. This research was supported by the UGC, Hong Kong (‘The Instrument of Science’, Humanities and Social Sciences Prestigious Fellowship).
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Rowbottom, D.P. (2017). On Component Forces in Physics: A Pragmatic View. In: Chao, HK., Reiss, J. (eds) Philosophy of Science in Practice. Synthese Library, vol 379. Springer, Cham. https://doi.org/10.1007/978-3-319-45532-7_7
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