Abstract
Causality in physics has had bad press in philosophy at least since Russell’s famous 1913 remark: “The law of causality, I believe, like much that passes muster among philosophers, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm” (Russell 1913, p. 1). Recently Norton (2003, 2006) has launched what would seem to be the definite burial of causality in physics. Norton argues that causation is merely a useful folk concept, and that it fails to hold for some simple systems even in the supposed paradigm case of a causal physical theory – namely Newtonian mechanics.
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Notes
- 1.
Both space-invader examples and the so-called supertasks (involving an infinite number of particles) may be argued to be less troublesome for determinism in Newtonian mechanics e.g. since they involve non-conservation of energy (see, e.g., Alper and Bridger cited in Norton 2006, p. 13) and, in the space-invader case, non-conservation of particle number (and hence an ambiguity in the very specification of the physical system), see, e.g., Malament (2007).
- 2.
- 3.
See also the Note added in proof at the end of the paper.
- 4.
As far as I can see, this point also accounts for why Norton’s “time reversal trick” (Norton 2003, p. 16) does not support that the acausal mass on the dome is a Newtonian system. The ‘reversed motion’ in which a mass point with a precisely adjusted initial velocity slides up the dome and halts exactly at the apex is consistent with Newtonian mechanics. In this reversed case, at t=T the net force on the mass point vanishes, and for all t>T the mass point is at rest and in uniform motion, and so no conflict arises with (NI). But insofar as forces should be first causes we cannot generate Norton’s motion from this allowed reversed case (when time is “run backwards” from some t>T, (N1) – understood as including the constraint that forces must be first causes – demands that the mass remains at rest for all t).
- 5.
Note that the third derivative of the position is non-vanishing at the moment when the harmonic oscillator passes through the origin. In the mass on the dome case, the fourth derivative is ill-defined at t=T. Uniform motion would seem to require, then, the vanishing also of higher (>2) order time derivatives of position.
- 6.
- 7.
One could perhaps argue that Newton’s second law could likewise be understood as an existence claim concerning inertial frames or that both laws of motion (or all three) jointly assert the existence of inertial frames (see, e.g., DiSalle 2008, p. 6). Still, the connection between the first law and inertial frames might be more fundamental, e.g., because free particles can be used, at least in principle, to construct such frames (“We must define an inertial system as one in which at least three non-collinear free particles move in noncoplanar straight lines; then we can state the law of inertia as the claim that, relative to an inertial system so defined, the motion of any fourth particle, or arbitrarily many particles, will be rectilinear” [DiSalle 2008, p. 5]).
- 8.
- 9.
The close relation between (N1) and absolute time in Newtonian mechanics has been emphasized also e.g. by Barbour: “… the law of inertia [N1] itself has two quite distinct parts: the rectilinearity of the motion and the uniformity of the motion. These correspond, respectively, to absolute space and absolute time” (Barbour 1989, p. 28).
- 10.
This point is closely related to one made earlier, namely that Norton’s instantaneous form of Newton’s (first or) second law in which F=ma=0 is not a sufficient condition for uniform motion. In consequence, one cannot define absolute time from this special case of Newton’s second law (since a time interval, in which the acceleration is constantly equal to zero, must be presupposed when integrating up F=ma=0 to get uniform motion).
- 11.
Right after stating the first law, Newton writes: “A top, whose parts by their cohesion are perpetually drawn aside from rectilinear motions, does not cease its rotation, otherwise than as it is retarded by the air. The greater bodies of the planets and comets, meeting with less resistance in more free spaces, preserve their motions both progressive and circular for a much longer time” (Newton 1729, p. 14).
- 12.
When the “turning on” is modelled by a series of discrete forces, the first (or indeed any) non-vanishing discrete force in the series can be identified with a first cause, and my point is that in standard cases – but not in Norton’s – we can use both the continuously varying force approach and that of a series of discrete (first cause) forces.
- 13.
If one takes r(t+Δt)=r(t)+v(t)Δt; v(t+Δt)=v(t)+r(t)1∕2 Δt; and r(0)=v(0)=0, the difference equation for the mass on the dome is found to be (r(t n+2)−2r(t n+1)+r(t n ))∕h 2=(r(t n ))1∕2 in which h=Δt (step size) and t n =nh. Since r(t 0)=r(t 1)=0, this equation has the unique solution r(t n )=0 for all n (and thus the same solution in the limit h→0). I first saw this equation on an anonymous internet forum post by a user named “jason1990”. Hans Henrik Rugh points out (in private discussion) that there are many ways to “discretize” a differential equation, and in this sense the differential equation quoted here is not unique for the dome. However, the difference equation approach is arguably the more fundamental one for Newton and, as far as I can see, the demand of forces as first causes acting at the beginning of each segment does in any case single out the quoted difference equation.
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Acknowledgements
It is a pleasure to thank Carl Hoefer and Svend Rugh for comments and discussion. I also thank the audiences at the “Singular causality, counterfactuals and mental causation” workshop in Granada and at the I EPSA Madrid conference for comments during presentations of this work. Financial support from the Spanish Ministry of Education and Science (project HUM2005–07187-C03–03) is gratefully acknowledged.
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Zinkernagel, H. (2010). Causal Fundamentalism in Physics. In: Suárez, M., Dorato, M., Rédei, M. (eds) EPSA Philosophical Issues in the Sciences. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3252-2_29
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