if and only iff
Time as a concept is something that we are all familiar with but that is not precisely defined. This quick reference will list every detail relating to the definition of time that I can find.
Farr, Matt (2016) Causation and Time Reversal. [Preprint] – http://philsci-archive.pitt.edu/12658/
“A theory is invariant under time reversal if and only if the time reverse of every motion allowed by the theory is also a motion allowed by the theory.” (Page 4)
Newtonian physics is time invariant, but velocity vector and such must be reversed and time reversed (Page 5).
Farr, Matt and Reutlinger, Alexander (2013) A Relic of a Bygone Age? Causation, Time Symmetry and the Directionality Argument. [Preprint] – http://philsci-archive.pitt.edu/9561/
“The C series is contrasted by McTaggart with the B series in terms of its lack of directionality” (Page 9)
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McTaggart, J. M. E. (1908). The unreality of time. Mind 17(68), 457–474.[T]he C series, while it determines the order, does not determine the direction. If the C series runs M, N, O, P, then the B series [. . . ] can run either M, N, O, P (so that M is earliest and P latest) or else P, O, N, M (so that P is earliest and M latest). And there is nothing [. . . ] in the C series [. . . ] to determine which it will be. (McTaggart, 1908, p. 462, my emphasis.)
McTaggart, J. M. E. (1927). The Nature of Existence, Volume II. Cambridge: Cambridge University Press.
The Directionality Argument
Basically a summary of Bertrand Russell’s argument against causation.
1. If the fundamental physical theories are time-symmetric then they are not
2. The fundamental physical theories are time-symmetric.
3. Therefore, the fundamental physical theories are not causal
Reference: Field (2003), Ney (2009), Frisch (2012) and Farr and Reutlinger (2013)
Robert G Sachs
Sachs, R. G. (1987). The Physics of Time Reversal. Chicago: University of Chicago
This source goes into great detail about the ways of reversing equations in physics. There is some complexity here as Farr points out, for instance, that in electrodynamics the field needs to be inverted and in quantum mechanics the spin inverted.
Aristotle mover, act and acted upon argument thing.
Principle of sufficient reason