Time, Quantum Values, and Whitehead’s Speculative Philosophy

It appears that time in quantum theory operates at the boundary of deterministic evolution but while opening up the discussion of determinacy to more contest because the causality of time appears, on the surface, to be axiomatic. Attempts at constructing arguments on time may appear tautological on the outset.  At a microstate level, the coupling of time to position, momentum, and energy at the quantum level is more hidden than what one might have encountered at the classical level. The visual diagrams produced of the mathematics demonstrating the couplings of these physical states where gauge interactions are effected, such as the Feynman diagram for instance, locate time within a simplified epistemology of graphical vertices.  While there have been discussions concerning the individuality and indeterminacy of quantum events in the arrow of time (Stengers 2011): and on whether the past can be indeterminate, and if such level of determinacy can be worked out from Heisenberg’s Principle (Tanaka 2004), such interrogations do not inform us of the ontology of time, and what are its especial properties that make it amenable to particular developments in mathematical physics, and even the construction of experiments after a fact. Therefore, the properties of time are unstable and speculative despite its unequivocal location in laws of physics.

I am interested in exploring the philosophical implications of quantum states by considering the meaning of speculation in the quantum phenomenology of time. The evolution of time, as embodied by the Schrödinger wave functions, sets time as a pointer on the particularized and discrete elements of the physically observable states, with time at points of contiguity. Hence, I argue that temporality, more so than spatiality, can act as an index, or ‘pointer,’ to physical events situated at multiple timelines, or which are constitutive of multiple timelines, because time can enact a cut through the ambiguity that spatial coordinates contain.

While time is always present, times also obtains a ghost-like (virtual) quality manifested through oscillatory modes and symmetries that are not always explicitly defined and formalized, and could sometimes dropped out from the process involved in the calculations. What does it mean to apprehend time in quantum space and are its detection and perception only possible through the medium provided by sensitive and selective digital apparatuses? These digital instruments mediate the apprehension of wave-particle duality that could be interpreted causally or acausally. How do these digital mediators enact time within the epistemic regime of the trading zone, therefore making our access to its ontology more speculative, thereby enabling different causal/acausal interpretations of time?

I intend to begin by considering first the double slit experiment, examined in tangent with the Aspect experiment, through the interpretive lens of the Bohrian complementarity principle and Bell theorem.  The discussions around the double slit experiment, where the screen behind the slits become the photodetector for each individual photon: every gradation of intensity in the light fringes represent snapshots of time while the time does not stand still, because time moves in accordance to the points of interferences and superpositions. What can one say about how time reacts and interacts at the locus of interference and decoherence, and can we create a rich phenomenology of time when causality is excluded? Or, perhaps one can consider causality as where locality is most determinable, because informational states are deciphered at the local level.

Before we even venture into where time may stand at that point of entanglement of local/non-local states, we may have to return to the beginning of the ‘creation’ of quantum mechanics: from the point when contestation was taking place between the causalist and acausalist camps of quantum physics that Paul Forman documents in his article, “The Reception of an Acausal Quantum Mechanics in Germany and Britain.” We might argue that matrix mechanics and the wave theory are mathematically equivalent, but could we consider time be equivalent, given that the interpretation of physicality is differently bounded.  How does one perceive the category of time should we set the physical events within the framework of the particle and the field? How far can the mathematization of time account for the deterministic gaps in quantum theory, and how can time bridge the experiential with the logic?

I argue that the tracing of time through its multiple operations also means understanding the hybridity of functional, symbolic, and affective facets of temporality that are in simultaneous interactions, occupying spaces of the material and the real, even as it might also operate at an imaginative plane that could be pure physical feeling. Could the positioning of time against a speculative theory for furthering the discourse of theoretical under-determination and hypothetical postulation, settle the realist versus anti-realist debate surrounding physical observables?

The classic double slit experiment can then be compared to the De-Broglie-Bohm delayed-choice experiment. By looking at where the interpositions are, one can magnify the internal and external fields where time marks the spectral of distribution in the wave mechanics, and how time is squished or expanded in the choice of initial experimental setup. Bell, in his collection of essays published in Speakable and Unspeakable in Quantum Mechanics, has written extensively on the question of the measurable through the different versions of the wave-particle problem, which then culminate in the entanglement problem for which the question on the completeness of quantum mechanical epistemology when positioned against an inaccessible ontology.

Time may hold the clue to the traits constituting local beables within the bounds of finitude, and shortcomings involved in the renormalization of divergent behaviors of the quantum field. The renormalization process is able to parameterize time within structure independent terms, and eliminates the structure-dependent terms of the Hamiltonian: data may be deciphered at the temporal level to provide further explication of degenerate quantum behavior.  It is possible to embed time within the symmetries of interactions of the different fields in existence, and I would like to explore the different scales in which time is able to operate, while also looking into how time is differently applied to perturbative and non-perturbative descriptions of the quantum field theories. Is it possible for time to be rendered unobservable when separated from the other physical properties, and time, embedded within interactions of physical qualities with finite and infinite energy fields, could contain predictive powers of new physics, and even provide explanations as to how data can be grounded.

Therefore, I would like to produce a critique of time against Whitehead’s philosophy of organism, particularly of his categoreal scheme and theory of extension found in Process and Reality because they provide useful framework for thinking about time within mathematical and physical bounds. Moreover, Whitehead was perhaps thinking of the embodiment of time in the then ‘new’ physics of quantum mechanics in the quantum ‘jumps’ he discusses in Science and the Modern World, which was his way of making sense of the temporal space of microphysical events that were gradually being worked out in the parallel developments of relativity and quantum physics. I would like to demonstrate how Whitehead was onto the problems of the developing ontology of quantum theory, especially where time stands, and how his arguments resonate with the thinking of time from ordinary quantum mechanics to quantum field theory.