Rather, Newton's Second Law can be derived from the conservation of momentum, which itself is a consequence the spatial homogeneity of physical laws. As such, in the context of causality, a force does not cause a mass to accelerate nor vice versa. Causality in this context is not associated with definitional principles such as Newton's second law. The word causality in this context means that all effects must have specific physical causes due to fundamental interactions. See also Chronology protection conjecture.ĭeterminism (or, what causality is not) For example, the notion that events can be ordered into causes and effects is necessary to prevent (or at least outline) causality paradoxes such as the grandfather paradox, which asks what happens if a time-traveler kills his own grandfather before he ever meets the time-traveler's grandmother. However, the principle of locality is disputed: whether it strictly holds depends on the interpretation of quantum mechanics chosen, especially for experiments involving quantum entanglement that satisfy Bell's Theorem.ĭespite these subtleties, causality remains an important and valid concept in physical theories. In those two theories, causality is closely related to the principle of locality. New subtleties must be taken into account when we investigate causality in quantum mechanics and relativistic quantum field theory in particular. In the theory of general relativity, the concept of causality is generalized in the most straightforward way: the effect must belong to the future light cone of its cause, even if the spacetime is curved. For this reason, special relativity does not allow communication faster than the speed of light.
On the other hand, if signals could move faster than the speed of light, this would violate causality because it would allow a signal to be sent across spacelike intervals, which means that at least to some inertial observers the signal would travel backward in time. If a timelike interval separates the two events, this means that a signal could be sent between them at less than the speed of light.
This is equivalent to the statement that the cause and its effect are separated by a timelike interval, and the effect belongs to the future of its cause. Consequently, the relativistic principle of causality says that the cause must precede its effect according to all inertial observers. The insights of the theory of special relativity confirmed the assumption of causality, but they made the meaning of the word "simultaneous" observer-dependent. In modern physics, the notion of causality had to be clarified. This requirement has been very influential in the past, in the first place as a result of direct observation of causal processes (like pushing a cart), in the second place as a problematic aspect of Newton's theory of gravitation (attraction of the earth by the sun by means of action at a distance) replacing mechanistic proposals like Descartes' vortex theory in the third place as an incentive to develop dynamic field theories (e.g., Maxwell's electrodynamics and Einstein's general theory of relativity) restoring contiguity in the transmission of influences in a more successful way than in Descartes' theory.
In quantum field theory, observables of events with a spacelike relationship, "elsewhere", have to commute, so the order of observations or measurements of such observables do not impact each other.Īnother requirement of causality is that cause and effect be mediated across space and time (requirement of contiguity). These restrictions are consistent with the constraint that mass and energy that act as causal influences cannot travel faster than the speed of light and/or backwards in time. Similarly, a cause cannot have an effect outside its front (future) light cone. In both Einstein's theory of special and general relativity, causality means that an effect cannot occur from a cause that is not in the back (past) light cone of that event. In classical physics, an effect cannot occur before its cause which is why solutions such as the advanced time solutions of the Liénard–Wiechert potential are discarded as physically meaningless. 2 Determinism (or, what causality is not).
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