Wood and Spekkens show that faithfulness, the causal Markov condition, and the assumptions that the quantum predictions are correct form an inconsistent set. That a principle of determinism is violated in physics receives support from quantum mechanics-or at least from any interpretation according to which the theory is indeterministic. Näger (2016) explores several alternative ways in which faithfulness might be violated in quantum causal systems. Thus, the usefulness of deterministic causal reasoning might be restricted to some contexts-contexts that may include some theoretical contexts in physics-while there may also be domains in physics in which deterministic causal notions are not applicable. Thus, probabilistic accounts that deny a fundamental causal asymmetry need to be careful to avoid probabilistic arguments for the asymmetry ultimately driven by causal intuitions and presumably have to be content with positing the initial randomness assumption as a fundamental de facto asymmetry that cannot be further justified. Thus, in order to define the direction of causation, the conserved quantity accounts need to be supplemented by probabilistic information. Proponents of conserved quantity accounts take their accounts to contribute to the metaphysical project of determining objective causal structures that serve as truth-makers of causal claims.
Within the descriptive project the argument would aim to show that a certain feature of our common-sense notion of cause does not allow this notion to at least some theoretical frameworks in physics. These problems appear especially pressing from the perspective of the functional project. That is, the most general solution to the wave equation applied to our pond will consist of sums of ripples associated with any pebbles being dropped into the pond plus source-free waves on the pond not associated with any pebble as their "source". For example, the Green’s function associated with the wave equation describes the circular ripples on a pond’s surface after a small pebble was dropped in. While the time asymmetry challenge can be raised for the Green’s function associated with hyperbolic equations, it is worth pointing out that there are also theories or theoretical frameworks in physics with time-asymmetric Green’s functions, chiefly among them linear response theory.
On Woodward’s account the notion of causation is spelled out in terms of so-called "hard" or "arrow-breaking" interventions. A structural causal model provides us with information on how the values of variables change under external interventions into a system, while causal discovery algorithms allow us to construct causal models from information about probability distributions over the values of variables characterizing the system and information about the effects of interventions. Here the question concerning interventions in fundamental physics makes contact with another issue on which there is an active debate: the question on appropriate constraints on allowable interventions and the question to what extent interventions need to be physically or conceptually possible. Neo-Russellians, by contrast, deny that causal notions and causal explanation can play any role in suitably fundamental theories of physics. Maudlin (2007) points out that on reading (ii) premise 2 is false, since not all the fundamental laws of physics are in fact time-reversal invariant. The laws of classical electrodynamics, the Maxwell-Lorentz equations, imply a wave equation, which is a time-reversal invariant hyperbolic equation of motion and is standardly solved using the Green’s functions formalism. By deriving its inspiration from physics, where conservation laws play a central role, conserved quantity accounts promise to be able to meet the neo-Machian and neo-Russellian challenges.
5. Properties or relations that cannot be grounded in features of physical laws cannot play a legitimate role in physics. 4. Therefore, causal relations cannot be grounded in features of physical laws. Most authors exploring the connection between the thermodynamic and causal asymmetries argue that the causal asymmetry is ultimately grounded in some facts about the initial state of the universe. From this observation the time asymmetry challenge concludes that nothing in the mathematical formalism can legitimately distinguish between the different representations to single out one representation as the correct causal representation. Any reason for singling out the short circuit goes beyond a purely physical description of the situation and must be driven by adding context-dependent or pragmatic considerations. This contrast is offered as a reason for why causal relations cannot be a part of physical theorizing. Some authors take the asymmetry between prevailing initial and final conditions to be metaphysically primary and maintain that it is this asymmetry which grounds our ability to reason causally. As a particularly vivid example illustrating common-cause inferences from very limited knowledge of the state of the universe on a final value surface consider the detection of gravitational waves in 2016, which, physicists concluded, were emitted by two colliding black holes.
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