Certain differential equations can be found, which ... given the configuration and velocities at one instant, or the configurations at two instants, render the configuration at any other earlier or later instant theoretically calculable. That is to say, the configuration at any instant is a function of that instant, and the configurations at two given instants. this statement holds throughout physics and not only in the special case of gravitation.
The laws 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
A law L is time-reversal invariant just in case, for every trajectory (S_i, S_1, S_2, s_3 ... S_f) there is a history (S_f, S_f-1, S_f-2 ... S_i) which reverses the sequence, that is also compatible with L. If L is not time-reversal invariant, then there are physically possible trajectories whose time-reversal is physically impossible. But this does not help us recover causality into physical law, or an intrinsic direction of determination in nature. We still are unable to declare whether the nomological predecessor, or successor that determines the other.
Russell gave two main reasons for rejecting the causal interpretation of the dynamical laws:
1. Causal relations incorporate temporal asymmetry - dynamical laws do not.
2. Causal beliefs relate to localised events - dynamical laws relate global system states. — tom
Yes, but "laws" are a calculational machinery and so they have to represent the holism of nature indirectly. You get time-reversal because time itself has to be taken for granted as a backdrop dimension not accounted for by law. — apokrisis
General relativity tells us that reality is a static 4D block - quite a feat for a mere calculating machine, I think you'll agree. — tom
But this does not help us recover causality into physical law,
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