arXiv subjects

Eduardo O. Dias

Publications and source records attributed to Eduardo O. Dias.

13 recordsLinked to original sources

arXiv2026

Einstein's equation as a geometric encoding of correlations with quantum reference frames

In general relativity, the metric field describes spacetime intervals between events relative to any ideal material reference frame as if the frame were not present; in this sense, the metric encodes these intervals. In quantum mechanics, by contrast, such events are naturally accompanied by correlations with that frame. Motivated by this complementarity, we propose a geometry-information equivalence hypothesis (GIEH), according to which the metric field geometrically encodes the relational information otherwise carried by correlations with a local reference frame (LRF). In a small geodesic ball, the GIEH yields the full nonlinear Einstein equation when ideal-LRF conditions are imposed, without assuming an AdS background or an underlying CFT. The framework further allows background correlations to provide an informational origin for the cosmological constant, with their local mutual-information density equal to the Gibbons-Hawking entropy per unit thermodynamic volume, and permits the reference spacetime to remain Minkowski even for a nonzero cosmological constant.

gr-qc↗

arXiv2025

Space-time-symmetric non-relativistic quantum mechanics: Time and position of arrival and an extension of a Wheeler-DeWitt-type equation

We generalize a space-time-symmetric (STS) extension of non-relativistic quantum mechanics (QM) to describe a particle moving in three spatial dimensions. In addition to the conventional time-conditional (Schrödinger) wave function $ψ(x, y, z | t)$, we introduce space-conditional wave functions such as $ϕ(t, y, z | x)$, where $x$ plays the role of the evolution parameter. The function $ϕ(t, y, z | x)$ represents the probability amplitude for the particle to arrive on the plane $x = \text{constant}$ at time $t$ and transverse position $(y, z)$. Within this framework, the coordinate $x^μ\in \{t, x, y, z\}$ can be conveniently chosen as the evolution parameter, depending on the experimental context under consideration. This leads to a unified formalism governed by a generalized Schrödinger-type equation, $\hat{P}^μ |ϕ^μ(x^μ)\rangle = -i\hbar \, η^{μν} \frac{d}{dx^ν} |ϕ^μ(x^μ)\rangle$. It reproduces standard QM when $x^μ= t$, with $|ϕ^0(x^0)\rangle = |ψ(t)\rangle$, and recovers the STS extension when $x^μ= x^i \in \{x, y, z\}$. For a free particle, we show that $ϕ(t, y, z | x) = \langle t, y, z | ϕ(x) \rangle$ naturally reproduces the same dependence on the momentum wave function as the axiomatic Kijowski distribution. Possible experimental tests of these predictions are discussed. Finally, we demonstrate that the different states $|ϕ^μ(x^μ)\rangle$ can emerge by conditioning (i.e., projecting) a timeless and spaceless physical state onto the eigenstate $|x^μ\rangle$, leading to constraint equations of the form $\hat{\mathbb{P}}^μ|Φ^μ\rangle = 0$. This formulation generalizes the spirit of the Wheeler-DeWitt-type equation: instead of privileging time as the sole evolution parameter, it treats all coordinates on equal footing.

quant-ph↗

arXiv2024

Space-time-symmetric extension of quantum mechanics: Interpretation and arrival-time predictions

An alternative quantization rule, in which time becomes a self-adjoint operator and position is a parameter, was proposed by Dias and Parisio [Phys. Rev. A {\bf 95}, 032133 (2017)]. In this approach, the authors derive a space-time-symmetric (STS) extension of quantum mechanics (QM) where a new quantum state (intrinsic to the particle), $|ϕ(x)\rangle$, is defined at each point in space. $|ϕ(x)\rangle$ obeys a space-conditional (SC) Schrödinger equation and its projection on $|t\rangle$, $\langle t|ϕ(x)\rangle$, represents the probability amplitude of the particle's arrival time at $x$. In this work, first we provide an interpretation of the SC Schrödinger equation and the eigenstates of observables in the STS extension. Analogous to the usual QM, we propose that by knowing the "initial" state $|ϕ(x_0)\rangle$ -- which predicts any measurement on the particle performed by a detector localized at $x_0$ -- the SC Schrödinger equation provides $|ϕ(x)\rangle={\hat U}(x,x_0)|ϕ(x_0)\rangle$, enabling us to predict measurements when the detector is at $x \lessgtr x_0$. We also verify that for space-dependent potentials, momentum eigenstates in the STS extension, $|P_b(x)\rangle$, depend on position just as energy eigenstates in the usual QM depend on time for time-dependent potentials. In this context, whereas a particle in the momentum eigenstate in the standard QM, $|ψ(t)\rangle=|P\rangle|_t$, at time $t$, has momentum $P$ (and indefinite position), the same particle in the state $|ϕ(x)\rangle=|P_b(x)\rangle$ arrives at position $x$ with momentum $P_b(x)$ (and indefinite arrival time). By investigating the fact that $|ψ(t)\rangle$ and $|ϕ(x)\rangle$ describe experimental data of the same observables collected at $t$ and $x$, respectively, we conclude that they provide complementary information about the same particle...

quant-ph↗

arXiv2022

Controlling fluid adhesion force with electric fields

Developing adhesives whose bond strength can be externally manipulated is a topic of considerable interest for practical and scientific purposes. In this work, we propose a method of controlling the adhesion force of a regular fluid, such as water and/or glycerol, confined between two parallel plates by applying an external electric field. Our results show the possibility of enhancing or diminishing the bond strength of the liquid sample by appropriately tuning the intensity and direction of the electric current generated by the applied electric field. Furthermore, we verify that, for a given direction of the electric current, the adhesion force can be reduced enough for the fluid to lose its adhesive properties and begin exerting a force to move apart the confining plates. In these circumstances, we obtain an analytical expression for the minimum electric current required to detach the plates without requiring the action of an external force.

physics.flu-dyn↗

arXiv2022

Signatures of causality and determinism in a quantum theory of events

By representing an event as the joint state of a detector-timer couple that interact with a system, we recover the familiar tensor product structure, used to describe spatially separated systems, in the context of timelike events. Furthermore, with this approach, we extend the superposition principle to the moment of occurrence of events. We then outline quantum signatures of causality that manifest through coherence in the detector state and correlation functions of time operators. Finally, we expand the scope of quantum information theoretic measures of state discrimination and information content, commonly used to characterize spatially separated systems, to events in spacetime. For causally connected events, we illustrate a deterministic relationship between events (akin to spatially entangled physical systems) where observing a previous event (one subsystem), enables us to delineate a later event (the other subsystem).

quant-ph↗

arXiv2021

Indefinite Causal Orders from Superpositions in Time

Treating the time of an event as a quantum variable, we derive a scheme in which superpositions in time are used to perform operations in an indefinite causal order. We use some aspects of a recently developed space-time-symmetric formalism of events. We propose a specific implementation of the scheme and recover the Quantum SWITCH, where quantum operations are performed in an order which is entangled with the state of a control qubit. Our scheme does not rely on any exotic quantum gravitational effect, but instead on phenomena which are naturally fuzzy in time, such as the decay of an excited atom.

quant-ph↗

arXiv2020

A quantum formalism for events and how time can emerge from its foundations

Although time is one of our most intuitive physical concepts, its understanding at the fundamental level is still an open question in physics. For instance, time in quantum mechanics and general relativity are two distinct and incompatible entities. While relativity deals with events (points in spacetime), with time being observer-dependent and dynamical, quantum mechanics describes physical systems by treating time as an independent parameter. To resolve this conflict, in this work, we extend the classical concept of an event to the quantum domain by defining an event as a transfer of information between physical systems. Then, by describing the universe from the perspective of a certain observer, we introduce quantum states of events with space-time-symmetric wave functions that predict the joint probability distribution of a measurement (observation) at $ (t, {\vec x}) $. Under these circumstances, we propose that a well-defined instant of time, like any other observable, arises from a single event, thus being an observer-dependent property. As a result, a counterfactual asymmetry along a particular sequence of events within a stationary quantum state gives rise to the flow of time as being successive "snapshots" from the observer's perspective. In this proposal, it is the many distinguishable states in which the observer stores information that makes the existence of time possible.

quant-ph↗

arXiv2018

Comparing experiments on quantum traversal time with the predictions of a space-time-symmetric formalism

The question of how long a particle takes to pass through a potential barrier is still a controversial topic in quantum mechanics. Arguably, the main theoretical problem in obtaining estimates for measurable times is the fact that previously defined time operators, that remained within the borders of standard quantum mechanics, present some kind of pathology. Recently, a time operator acting on an additional Hilbert space has been shown to support both Hermiticity and canonical relation with an energy observable. The theory is built in a framework which treats space and time as symmetrically as possible, in the nonrelativistic regime. In this work, we use this formalism to derive a closed analytic expression for the traversal time of a quantum particle impinging on a constant-potential barrier. We test our theory in the specific experimental scenario of a realization by Rafagni et al [Appl. Phys. Lett. {\bf 58}, 774 (1991)]. The proposed approach displays a much better performance in comparison with the Büttiker-Landauer and the phase-time approximations.

quant-ph↗

arXiv2017

Physical and mathematical properties of the space-time-symmetric formalism

It is well known that nonrelativistic quantum mechanics presents a clear asymmetry between space and time. Much of this asymmetry is attributed to the lack of Lorentz invariance of the theory. Nonetheless, a recent work [Phys. Rev. A \textbf{95}, 032133 (2017)] showed that even though this is partially true, there is a broader physical scenario in which space and time can be handled in nonrelativistic quantum theory in a more symmetric way. In this space-time-symmetric formalism, an additional Hilbert space is defined so that time is raised to the status of operator and position becomes a parameter. As a consequence, the Hilbert space now requires a space-conditional quantum state governed by a new quantum dynamics. In this manuscript, we reveal some physical and mathematical properties of the space-time-symmetric formalism such as: symmetries between the Hamilton-Jacobi and the space-conditional equation; the general solution for a time-independent potential; and a new Lagrangian for a spinless particle in one dimensional. Finally, we present the space-conditional equation for a particle under the effect of an electromagnetic field, and the gauge invariance of this equation is proved.

quant-ph↗

arXiv2017

Space-time symmetric extension of non-relativistic quantum mechanics

In quantum theory we refer to the probability of finding a particle between positions $x$ and $x+dx$ at the instant $t$, although we have no capacity of predicting exactly when the detection occurs. In this work, first we present an extended non-relativistic quantum formalism where space and time play equivalent roles. It leads to the probability of finding a particle between $x$ and $x+dx$ during [$t$,$t+dt$]. Then, we find a Schrödinger-like equation for a "mirror" wave function $ϕ(t,x)$ associated with the probability of measuring the system between $t$ and $t+dt$, given that detection occurs at $x$. In this framework, it is shown that energy measurements of a stationary state display a non-zero dispersion, and that energy-time uncertainty arises from first principles. We show that a central result on arrival time, obtained through approaches that resort to {\it ad hoc} assumptions, is a natural, built-in part of the formalism presented here.

quant-ph↗

arXiv2016

Hamiltonian formulation towards minimization of viscous fluid fingering

A variational approach has been recently employed to determine the ideal time-dependent injection rate Q(t) that minimizes fingering formation when a fluid is injected in a Hele-Shaw cell filled with another fluid of much greater viscosity. However, such a calculation is approximate in nature, since it has been performed by assuming a high capillary number regime. In this work, we go one step further, and utilize a Hamiltonian formulation to obtain an analytical exact solution for Q(t), now valid for arbitrary values of the capillary number. Moreover, this Hamiltonian scheme is applied to calculate the corresponding injection rate that minimizes fingering formation in a uniform three-dimensional porous media. An analysis of the improvement offered by these exact injection rate expressions in comparison with previous approximate results is also provided.

physics.flu-dyn↗

arXiv2015

Elements of a new approach to time in Quantum Mechanics

In this work we present a re-evaluation of the concept of time in non-relativistic quantum theory. We suggest a formalism in which time is changed into the status of an operator, and where expectation values of observables and the state of a quantum system are reworked. This approach leads us to an additional concept, given by a temporal probability distribution associated with the actual measurement of an observable.

quant-ph↗

arXiv2010

Suppression of viscous fluid fingering: a piecewise constant-injection process

The injection of a fluid into another of larger viscosity in a Hele-Shaw cell usually results in the formation of highly branched patterns. Despite the richness of these structures, in many practical situations such convoluted shapes are quite undesirable. In this letter we propose an efficient and easily reproducible way to restrain these instabilities based on a simple piecewise constant pumping protocol. It results in a reduction in the size of the viscous fingers by one order of magnitude.

cond-mat.soft↗