The Potential of a Thick Present through Undefined Causality and Non-Locality

Abstract

This paper elaborates on the interpretation of time and entanglement, offering insights into the possible ontological nature of information in the emergence of spacetime, towards a quantum description of gravity. We first investigate different perspectives on time and identify in the idea of a "thick present" the only element of reality needed to describe evolution, differences, and relations. The thick present is connected to a spacetime information "sampling rate", and it is intended as a time symmetric potential bounded between a causal past of irreversible events and a still open future. From this potential, spacetime emerges in each instant as a space-like foliation (in a description based on imaginary paths). In the second part, we analyze undefined causal orders to understand how their potential could persist along the thick present instants. Thanks to a C-NOT logic and the concept of an imaginary time, we derive a description of entanglement as the potential of a logically consistent open choice among imaginary paths. We then conceptually map the imaginary paths identified in the entanglement of the undefined orders to Closed Time-like Curves (CTC) in the thick present. Considering a universe described through information, CTC are interpreted as "memory loops", elementary structures encoding the information potential related to the entanglement in both time and space, manifested as undefined causality and non-locality in the emerging foliation. We conclude by suggesting a possible extension of the introduced concepts in a holographic perspective.

Keywords: CTC; causality; entanglement; free will; information; logic; non-locality; presentism; time.

Figure 1

Identification of the thick present as the current thick space-like foliation and corresponding kth elaboration cycle of the quantum information T_k, from which spacetime is considered to be emerging.

Figure 2

Controlled quantum SWITCH reproducing an UCO described as a XOR function, implemented as a C-NOT quantum gate. The entanglement of the Controller qubit C with the Target S at the point ⊕ allows the superposition of paths in which “A(B) is met first and B(A) is not”, and consequently the UCO. The entanglement in the C-NOT gate can be seen as the information potential of a choice instantiated in the instant of the interaction and of which the answer is undetermined.

Figure 3

Superposition of the imaginary paths of the particle $\left(iv{\tau }_{|1⟩}\oplus iv{\tau }_{|0⟩}\right)$ in a space-like foliation at a given instant after the time of traversal Δτ. The result can be described as the superposition of a forward- and backward-evolving wave in the imaginary time of motion $\left(iv{\tau }_{|C⟩}\right)$ and a CTC closed between C and any two points A and B on the circuit.

Figure 4

The imaginary space emerges from the information potential in the thick present, and it is described through an imaginary time. CTCs in the thickness are an expression of non-local potential.

Figure 5

Successive snapshots of the imaginary space foliation, from the EPR pair generation to the spin measurement at Alice’s location. The information potential persists along the successive instants through the entanglement/CTC as long as it is undetermined. When A defines a contextual outcome in her measurement (blue arrow), the state of the particle directed towards B is coherently defined so that the information keeps a global logical consistency within the thick present.

Figure 6

Graphics illustrating the space foliation at 2kT in the thick present as the boundary between two symmetric bulk regions extending from (2k − 1)T to 2kT and from (2k + 1)T to 2kT. The bulks encode the information T_k (intended in a holographic perspective as an entanglement among quanta of space) from which spacetime emerges. CTCs in the thickness of the present represent the non-local potential; CTC developing in the imaginary time are equivalent to undefined orders of traversed points.