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Are we missing a subtle anthropomorphism here? Objects don't know from beans about forces, accelerations or anyone named Newton. They just do what they do, and, as has been pointed out, we construct models to help us understand how to predict what it is that they will do under various conditions. No causality is implied in the motion itself. It is only our anthropomorphic prejudices that infer some form of causality. But that impulse to infer causality is very strong in humans, for better or for worse. So perhaps, if we have this overwhelming urge to apply causal laws to our physics, maybe we need to follow John's prescription and not write NSL as an equality, but as an implication: F => ma, and not the converse, although we could use the converse to figure out what the imputed force might have been that "caused" the observed ma. John has stated that a causal relationship cannot be inferred if the statement of the law is mathematically symmetric, and that is certainly correct. But it also seems to me that one might, in principle, conduct an experiment that could distinguish between the symmetry of a mathematical equality and the causal implication, and that is to look for the inevitable time delay that must exist between a cause and its effect. Admittedly, for close encounters detecting this time delay may be beyond our current technological capability, but certainly if one thinks about it for a while it may be possible to come up with a suitable experiment. If so, and if it does demonstrate a causal relationship, then that would imply that we have been writing NSL wrong all these many centuries.
It is a truism that we deal in models.
It is a truism that most (perhaps all_ of these models are imperfect.
The problem with truisms is that even though they are true, they are
not very informative. And to phrase the argument in Manichaen terms
(right versus wrong, black versus white) is to throw judgement to the
winds.
The crucial point is that some models are much, much better than others.
It is not our job to choose models versus no models; our job is to choose
better models over worse models.
So the issue is whether
"F causes ma (and not vice versa)" [a]
is better/same/worse compared to
"F equals ma" [b]
As far as I can see, every limitation and every correction that must
be applied to [b] must also be applied to [a]. I see absolutely no
logical or physical reason why anyone should prefer [a] over [b].
In contrast, there is every reason to believe that the physical
relationship between F and ma is symmetric, and is therefore better
modelled by a symmetric statement than an unsymmetric statement.
Equality is symmetric; causality is not.