Editing Causality (physics) (section)

== Determinism (or, what causality is ''not'') ==
The word ''causality'' in this context means that all effects must have specific physical causes due to fundamental interactions.<ref name=":0">"Causality." Cambridge English Dictionary. Accessed November 18, 2018. https://dictionary.cambridge.org/us/dictionary/english/causality</ref> Causality in this context is not associated with definitional principles such as [[Second law of motion|Newton's second law]]. As such, in the context of ''causality,'' a force does not ''cause'' a mass to accelerate nor vice versa. Rather, Newton's second law can be derived from the [[conservation of momentum]], which itself is a [[Noether's theorem|consequence of the spatial homogeneity of physical laws]].

The empiricists' aversion to metaphysical explanations (like Descartes' vortex theory) meant that scholastic arguments about what caused phenomena were either rejected for being untestable or were just ignored. The complaint that physics does not explain the ''cause'' of phenomena has accordingly been dismissed as a problem that is philosophical or metaphysical rather than empirical (e.g., Newton's "[[Hypotheses non fingo]]"). According to [[Ernst Mach]]<ref name=":1">Ernst Mach, ''Die Mechanik in ihrer Entwicklung, Historisch-kritisch dargestellt'', Akademie-Verlag, Berlin, 1988, section 2.7.</ref> the notion of force in Newton's second law was [[Pleonasm|pleonastic]], tautological and superfluous and, as indicated above, is not considered a consequence of any principle of causality. Indeed, it is possible to consider the Newtonian equations of motion of the gravitational interaction of two bodies,

:<math> m_1 \frac{d^2 {\mathbf r}_1 }{ dt^2} = -\frac{m_1 m_2 G ({\mathbf r}_1 - {\mathbf r}_2)}{ |{\mathbf r}_1 - {\mathbf r}_2|^3};\; m_2 \frac{d^2 {\mathbf r}_2 }{dt^2} = -\frac{m_1 m_2 G ({\mathbf r}_2 - {\mathbf r}_1) }{ |{\mathbf r}_2 - {\mathbf r}_1|^3}, </math>

as two coupled equations describing the positions <math> \scriptstyle {\mathbf r}_1(t) </math> and <math> \scriptstyle {\mathbf r}_2(t) </math> of the two bodies, ''without interpreting the right hand sides of these equations as forces''; the equations just describe a process of interaction, without any necessity to interpret one body as the cause of the motion of the other, and allow one to predict the states of the system at later (as well as earlier) times.

The ordinary situations in which humans singled out some factors in a physical interaction as being prior and therefore supplying the "because" of the interaction were often ones in which humans decided to bring about some state of affairs and directed their energies to producing that state of affairs—a process that took time to establish and left a new state of affairs that persisted beyond the time of activity of the actor. It would be difficult and pointless, however, to explain the motions of binary stars with respect to each other in that way which, indeed, are [[Time reversibility|time-reversible]] and agnostic to the [[arrow of time]], but with such a direction of time established, the entire evolution system could then be completely determined.

The possibility of such a time-independent view is at the basis of the [[deductive-nomological]] (D-N) view of scientific explanation, considering an event to be explained if it can be subsumed under a [[scientific law]]. In the D-N view, a physical state is considered to be explained if, applying the (deterministic) law, it can be derived from given initial conditions. (Such initial conditions could include the momenta and distance from each other of binary stars at any given moment.) Such 'explanation by determinism' is sometimes referred to as [[Determinism#Varieties|causal determinism]]. A disadvantage of the D-N view is that causality and determinism are more or less identified. Thus, in [[classical physics]], it was assumed that all events are caused by earlier ones according to the known laws of nature, culminating in [[Pierre-Simon Laplace]]'s claim that if the current state of the world were known with precision, it could be computed for any time in the future or the past (see [[Laplace's demon]]). However, this is usually referred to as Laplace ''determinism'' (rather than 'Laplace causality') because it hinges on [[Determinism#In mathematical models|determinism in mathematical models]] as dealt with in the mathematical [[Cauchy problem]].

Confusion between causality and determinism is particularly acute in [[quantum mechanics]], this theory being acausal in the sense that it is unable in many cases to identify the causes of actually observed effects or to predict the effects of identical causes, but arguably deterministic in some interpretations (e.g. if the [[wave function]] is presumed not to actually collapse as in the [[many-worlds interpretation]], or if its collapse is due to [[hidden variable theory|hidden variables]], or simply redefining determinism as meaning that probabilities rather than specific effects are determined).