PREPRINT FOR PEER REVIEW - DOI: 10.31219/osf.io/52xyd (download the latest version) Contribution shared under a CC-BY Attribution license (creativecommons.org/licenses/by/4.0/) The potential of a thick present through undefined causality and non-locality Alessandro Capurso# May 29, 2021 - Rome, Italy Abstract: In the context of a spacetime described through information, we identify in a thick present the only quantum potential needed to describe evolution, differences and relations. The analysis of undefined causal orders through a Controlled-NOT quantum logic and the concept of superposed imaginary times (developing in a thick space-like foliation), allowed us to consider entanglement as the information related to the persistence of an open choice (in the time order or the spatial position). The superposed imaginary paths identified are then mapped to Closed Time-like Curves (CTC), which develop in the imaginary space-foliation and represent undefined causality and non-locality within each present instant. The proposal suggests the interpretation of CTC as memory-loops, considered the elementary structures for the persistence (in the thick present and along consecutive instants) of the information potential related to both the entanglement and the wave function. Keywords: time; causality; free will; thick present; entanglement; CTC; quantum potential; logic; information; quantum gravity; Introduction The nature of Time is often at the root of the debate in physics and possibly sits at the core of General Relativity (GR) and Quantum Mechanics (QM) incompatibility. In recent years, the search for a theory of Quantum Gravity (QG), able to include both the success of GR and QM, revived the study of time as a key ingredient for the understanding of a quantum description of spacetime. Beside time, the concept of entanglement has puzzled the physics community for decades, stimulating the discussion around causality and locality in physical laws. This paper investigates the possibility of a thick present as the only element of reality, intended as a quantum potential from which spacetime could emerge in a sequence of space-like foliations. In the context of an evolution occurring in discrete present instants, we investigate how undefined causal orders could be considered. Thanks to a parallel with a CNOT quantum gateway, the information of the undefined order is described through imaginary paths, developing as superposed imaginary times within each space-like foliation. We then describe the potential of the superposition of imaginary times through CTC withing the thick present. Following a Quantum Information Science (QIS) perspective, CTC are interpreted as logically consistent “memory-loops”, in which the still undefined potential of a possible “open choice” (temporal order or spatial position) could persist along the successions of present instants. The derived description promotes the connection of entanglement with non-locality, investigated in the final part of the contribution. Existence in a thick present The interpretation of the nature of time in physics has seen two opposite descriptions. The first, called Eternalism, is often related to the theory of Relativity and consider an ever-existing time, real in both the past and the future, and of which we perceive only limited cones of information. The opposite perspective, known as Presentism, is connected to the idea of evolution itself and pictures time as everchanging: a vanishing present compressed between past and future instants. The focus is on the difference between the past, already happened and irreversible, and the future, still undefined and open. The axis of time seems to become real only in the current instant and in the causal consequences of the past ones. Between these extremes, all the other meanings humans associate to time. # [email protected] - orcid.org/0000-0003-3277-3588 A. Capurso - The potential of a thick present through undefined causality and non-locality 2 of 9 Beside physics, the common experience sees a forward and causal progression of time, usually associated to thermodynamics and defined on average or macroscopically, as phenomena naturally tend to higher entropy states. In the context of the Free Will theorem (introduced by Conway in [1]), we should assume that the future is open and undetermined and pose a serious threat on the idea of a classical and ever-existing time in a “block-universe”. Moreover, from a QIS perspective, recent “gargantuan simulations” (reported in [2]) showed that time seems irreversible at the most fundamental level, beyond thermodynamic reasons. It has been shown that even a simple 3-bodies system “would require an accuracy of smaller than the Planck length in order to produce a time-reversible solution”: what had been already can causally influence the present but cannot be changed and, beyond fundamental physical limits, cannot even be known with certainty. The irreversibility of events might seem in contradiction with a symmetric description of time, even if physical laws in a classical framework are time symmetric and there are several QM symmetric approaches too. The idea of an emerging causal reality connected to the superposition of both a forward and a backward propagating wave was proposed in the Two-State-Vector Formalism (TSVF) (introduced in [3]), and further elaborated recently in a more extensive description including elements of Energetic Causal Sets (in [4] and [5]). Even in a context of the irreversibility of events, we could still consider a QM time symmetric approach within a thick present, as a description of the spacelike foliation coming from a superposition of perspectives from a near past and a near future. If the future is open and yet to come, and the past is fixed and irreversible but might not be known beyond the causal consequences, we could consider a thick present as the elementary quanta in the passage of time and the only element of reality along an emerging thermodynamic arrow of time (idea also elaborated in [6], following an intuitionist mathematical language, and [7] from an QM ontological perspective). A thick present could be described as a thick space-like foliation of the universe, bounded between -T and +T. Within a thick present we could consider both a quantum information potential (connected to a QM probabilistic description and an open future in the coming cycles) as well as the information of the irreversible events (as causal fixed points from which the present emerges, and the future opens), efficiently discarding the information of the far past states that is not needed to reconstruct the current spacetime. A thick present could be intended as well as the realization of the idea of a “discreteness of time”. The possibility of a minimum interval in the passage of time has been recently investigated in [8], where an experimental proof of a discrete time is proposed though the relation with the Planck mass and a minimum corresponding phase difference. A thick present has also been recently considered in the description of human perception of time and it is often related in QIS to a discrete elaboration cycle of the information. There are several theories that consider evolution in discrete cycles. To mention a few, Finite State Classical Mechanics (proposed in [9]) is based on Lattice Dynamics, where the information is described through discrete positions and the evolution rules are often referred as “cellular automata” models. Signal-State Quantum Mechanics, further developed in a theory of Quantized Detector Networks (presented in [10]), describes particles as storing entangled phase information and focus on observers and their apparatus, as a realization of the Heisenberg’s “instrumentalist approach” to quantum physics. To describe a thick present in a cyclic evolution, we could consider a minimum time interval T like a π rotation, as to see things from a different perspective and as if 2T (equivalent to 2π) were needed for a full cycle. We could consider these discrete 2T steps, from -T to +T, as the elaboration cycle of the quantum information potential from which spacetime could emerge. As Freeman Dyson wrote (in [11]), the only role of a local observer seems becoming the distinction between a classical past and a still open and probabilistic future. The relation between the observation of a variable at a given instant (identifying an event) and the derived difference between past and future has also been elaborated in [12] as a “dynamics of difference”. A. Capurso - The potential of a thick present through undefined causality and non-locality 3 of 9 Observers, events or potential ones, all exist in a thick present able to account for a superposition of perspectives from a near past and a near future, resulting time symmetric within its thickness, and assuring consistency between “what it was” (causally happened) and “what it could be” in the current cycle. Information could persist as a potential in case no events occurred in the present elaboration cycle, while events of collapse or “measurements” should be interpreted as irreversible, also in line with the QIS and computational perspective. From the irreversibility of events (in the succession of the thick present instants), a thermodynamic oriented arrow of time could also be considered as emerging in the memory of the observers, from lower to higher entropy states at different scales of observation. It is worth to clarify that the “present” is not intended as a global “perceived now”. The passage of time for local observers within spacetime follows relativity and time intervals measured by local quantum clocks are lengthen according to the equations of GR. The thick present represents the potential of the current space of events and possibilities. In a QIS description, its duration could be related to a “spacetime sampling rate”. It could represent a global reference for a minimum time interval, allowing relative confrontation of local quantum clocks with respect to one another in a discrete passage of time.