Physics Violations

BUT: All non-Markovian equations in contemporary physics are non-fundamental. They represent simplifications of fundamental equations, such as Maxwell's equations for electromagnetism, Einstein's equations for relativity, and the broader framework of classical field theory in classical physics, or the Klein-Gordon and Dirac equations of Quantum Field Theory. All the fundamental theories are Markovian, and science treats these fundamental theories as a deeper truth closer to the ontological reality.

Non-Markovian equations emerge only as coarse-grained simplifications. Such references to past events are only an 'epistemic' form of memory, where we, as modelers, need to keep track of history because we've averaged out microstates. There is no true ontological memory defined in the equations of contemporary physics, where the universe itself remembers past states. If consciousness is defined via epistemic models, i.e. levels of description relative to some modeler, the theory needs to be made explicitly relational and address concerns about the arbitrariness of choosing a model/modeler or different mutual-modeling possibilities. Perhaps all possible models simultaneously exist, but this risks identifying consciousness in very many systems.

NB. Some interpretations of wave function collapse could constitute a counter-example, but it is unclear how contemporary functionalist theories could exploit this.

BUT: This places a strict constraint on the types of temporal history that functionalists can rely on and types of causal mechanism they can invoke. Systems' present-states do provide information about past trajectories but typically a wide range of past trajectories could lead to the same present-state. Without solutions like a block universe or a metaphysical observer, the present-state cannot know which of those past trajectories created it. Functionalists would need to show that all possible equivalent past trajectores would preserve the motivating intuitive causal mechanism for their theory (e.g. global broadcast, meta-representation etc.). Or that what actually happened does not matter, provided the system interprets its present-state as implying the relevant history. But this requires rejecting the intuitive causal mechanisms with their powerful counterfactuals. It would be enough to falsely believe a mechanism occurred, rather than it actually having occurred.

NB. If we assume deterministic and time-reversible fundamental laws and allow access to the complete physical microstate, then the present state would, in principle, fix a unique past history. But this relies on substantive interpretive commitments — e.g., rejecting fundamental wavefunction collapse — and in any case no actual subsystem (including any conscious system) has access to such a state, since it is itself only a tiny part of it. So uniqueness of the past is a feature of a God's-eye theoretical description rather than of any physically or cognitively available perspective.

PERHAPS, BUT: Such extraordinary claims require extraordinary evidence. Unless consciousness is epiphenomenal and illusory, in which case there isn't anything meaningful to emerge anyway. If consciousness is a meaningful phenomenon, it must find its roots somewhere in the equations of physics or a different sort of world is being posited to our best current understanding. This is an avenue to pursue, but must acknowledge the boldness of its claims and make them explicit, e.g. in what sense a different form of causality or ontology is envisioned vs contemporary physics, what different predictions are made relative to those equations.

PERHAPS, BUT: If this is the argument, functionalists should be explicit that their claims specifically contradict contemporary laws of physics and rely on future novel insights. For instance, if particles carry their history, where do they do this? If they carry information within the framework of physics, then that information must be stored physically. But particles are too simple to store an ever-increasing volume of information describing every single past interaction and too simple to conduct computations over it to look for particular patterns. They are literally too light to encode the weight of this information. If this notion is true, where are the predictions and incredible technologies based on leveraging it for data storage...

PERHAPS, BUT: The preference for Markovian formats is not arbitrary. the added variables in successful physical theories are not generic memory registers but correspond to independently measurable quantities, transform naturally under the theory's symmetry group, and support a local initial-value formulation: these strongly constrain the space of viable options.

One example is the equal footing of position and momentum in the uncertainty theorem in quantum mechanics: neither can be eliminated without loss of structure, and they are related by a duality (Fourier transform) rather than a simple derivation. State-space enlargement can reflect genuine physical structure rather than representational excess.

The Markovian formulation is often the unique fixed point of deep structural constraints (locality, symmetry, variational principles, well-posedness), whereas non-Markovian formulations form a large equivalence class with no canonical internal ordering (you can typically generate other non-Markovian variants by removing different subsets of state-space variables in different orders). That asymmetry gives a non-aesthetic reason to prefer the Markovian formulation even when non-Markovian ones are formally equivalent. Non-Markovianity also brings other worries: temporal non-locality (physicists tend to require particularly compelling motivations to introduce non-localities, e.g. given difficulties reconciling with relativity) and infinite regress needed to determine future trajectories (where is this information stored?).

It might be possible to restructure contemporary physics in non-Markovian formats (and that might ultimately prove a deeper truth, as Nancy Cartwright argued when rejecting simple universal physical laws in The Dappled World, 1999). But this is not a simple motivation - and goes counter to the historical trend where originally non-Markovian formulations have been replaced over time. Functionalists could pursue this path but should be explicit in what type of non-Markovianity meets their needs and why it is better motivated than current Markovian equations.