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Abstract: In the debate about the direction of time in physics, the concept of time reversal has been central. Tradition has it that time-reversal invariant laws are sufficient to state that the direction of time is non-fundamental or emergent. In this paper, we review some of the debates that have gravitated around the concept of time reversal and its relation to the direction of time. We also clarify some of the central concepts involved, showing that the very concept of time reversal is more complex than frequently thought. [ABSTRACT FROM AUTHOR]

Abstract: In the debate about the direction of time in physics, the concept of time reversal has been central. Tradition has it that time-reversal invariant laws are sufficient to state that the direction of time is non-fundamental or emergent. In this paper, we review some of the debates that have gravitated around the concept of time reversal and its relation to the direction of time. We also clarify some of the central concepts involved, showing that the very concept of time reversal is more complex than frequently thought.

Armor composite structures have attracted interest in structural health monitoring (SHM) for their applications in damage localization. The signal propagation and the frequency dispersion features of the Lamb wave signal on thick armor composite structures are more complicated than their counterparts on other composite plates. In this research, a time-reversal localization and imaging method for impact localization of armor composite structures is proposed. First, composite sandwich structures were designed that are typically composed of ballistic-resistant ceramic materials as the face panel and a composite material as the core layer, sandwiched between metal materials serving as the backplate. The results show that the proposed method can validate the position of impact efficiently, and radial error is within 4.12 mm and 5.39 mm in single-damage and multi-damage imaging localization, respectively.

In Newtonian physics, the equation of motion is invariant when the direction of time (t→−t) is flipped. However, in quantum physics, flipping the direction of time changes the sign of the Schrödinger equation. An anti-unitary operator is needed to restore time reversal in quantum physics, but this is at the cost of not having a consistent definition of time reversal applicable to all fundamental theories. On the other hand, a quantum system composed of a pair of entangled particles behaves in such a manner that when the state of one particle is measured, the second particle ‘simultaneously’ acquires a determinate state. A notion of absolute simultaneity seems to be inferred by quantum mechanics, even though it is forbidden by the postulates of relativity. We aim to point out that the above two problems can be overcome if the wavefunction is defined with respect to proper time, which in fact is the real physical time instead of ordinary time.

This paper claims that, to the extent that temporal direction figures in physics at all, it is found there as part of the extra-scientific language science employs. The asymmetry between "before" and "after" is not captured by the mathematics of any theory, nor can it be derived from the laws of any theory. This, I argue, is true even of theories whose laws are not time reversal invariant. Recognizing that physics does not yield temporal direction but receives it from the background in which physics develops and operates does not, however, expose any hitherto unknown limitations or deficiencies of physics. The claim is not about physics, but about metaphysical stances regarding physics, specifically, physicalism, which requires from physics to deliver more than it does, or should. Once the place of temporal direction in physics is understood, infamous difficulties can be addressed in a novel way. Issues emerging from the 2nd law of thermodynamics, such as the minimum problem, and the worry that the law generates outlandish predictions, are removed. A side benefit is the recognition that the past hypothesis is superfluous. A final conclusion of the paper is that the relationship between physics and everyday language, far from being a source of difficulties, is healthy and beneficial to both. [ABSTRACT FROM AUTHOR]

Measurements of angular correlations in nuclear beta decay are important tests of the Standard Model (SM). Among those, the so-called D correlation parameter occupies a particular place because it is odd under time reversal, and because the experimental sensitivity is at the 10 - 4 level, with plans of further improvement in the near future. Using effective field theory (EFT) techniques, we reassess its potential to discover or constrain new physics beyond the SM. We provide a comprehensive classification of CP-violating EFT scenarios which generate a shift of the D parameter away from the SM prediction. We show that, in each scenario, a shift larger than 10 - 5 is in serious tension with the existing experimental data, where bounds coming from electric dipole moments and LHC observables play a decisive role. The tension can only be avoided by fine tuning of the parameters in the UV completion of the EFT. We illustrate this using examples of leptoquark UV completions. Finally, we comment on the possibility to probe CP-conserving new physics via the D parameter. [ABSTRACT FROM AUTHOR]

Photoacoustic tomography (PAT) provides high resolution optical images of tissue at depths of up to several centimetres. This modality has been of interest to researchers for at least 30 years and is still the subject of intensive research. However, PAT researchers lack access to a comprehensive open-source graphical simulation and reconstruction software package. In this article, we introduce PATLAB, an open-source MATLAB-based graphical software package that can perform both PAT simulation and image reconstruction. PATLAB is simple to use yet is capable of complex PAT data processing tasks and offers advanced users a framework to build and test new methods.

In this work we study the concept of instantaneous time mirrors that were recently introduced in the physics literature in [V. Bacot et al., Nature Phys., 12 (2016), pp. 972-977). They offer a new method for time reversal with a simplified experimental setup compared to classical techniques. At the mathematical level, these time mirrors are modeled by singularities in the time variable in the coefficients of a wave equation, and a prototype of such singularity is a Dirac delta. Our main goal in this work is to obtain refocusing estimates for the wavefield that quantify the quality of time reversal. This amounts to analyzing the wave equation with Dirac-type singularities and developing a proper regularity theory as well as deriving uniform estimates. [ABSTRACT FROM AUTHOR]

The inference of causal relations between observable phenomena is paramount across scientific disciplines; however, the means for such enterprise without experimental manipulation are limited. A commonly applied principle is that of the cause preceding and predicting the effect, taking into account other circumstances. Intuitively, when the temporal order of events is reverted, one would expect the cause and effect to apparently switch roles. This was previously demonstrated in bivariate linear systems and used in design of improved causal inference scores, while such behaviour in linear systems has been put in contrast with nonlinear chaotic systems where the inferred causal direction appears unchanged under time reversal. The presented work explores the conditions under which the causal reversal happens—either perfectly, approximately, or not at all—using theoretical analysis, low-dimensional examples, and network simulations, focusing on the simplified yet illustrative linear vector autoregressive process of order one. We start with a theoretical analysis that demonstrates that a perfect coupling reversal under time reversal occurs only under very specific conditions, followed up by constructing low-dimensional examples where indeed the dominant causal direction is even conserved rather than reversed. Finally, simulations of random as well as realistically motivated network coupling patterns from brain and climate show that level of coupling reversal and conservation can be well predicted by asymmetry and anormality indices introduced based on the theoretical analysis of the problem. The consequences for causal inference are discussed.

An information-theoretic approach for detecting causality and information transfer is used to identify interactions of solar activity and interplanetary medium conditions with the Earth’s magnetosphere–ionosphere systems. A causal information transfer from the solar wind parameters to geomagnetic indices is detected. The vertical component of the interplanetary magnetic field (Bz) influences the auroral electrojet (AE) index with an information transfer delay of 10 min and the geomagnetic disturbances at mid-latitudes measured by the symmetric field in the H component (SYM-H) index with a delay of about 30 min. Using a properly conditioned causality measure, no causal link between AE and SYM-H, or between magnetospheric substorms and magnetic storms can be detected. The observed causal relations can be described as linear time-delayed information transfer.

In this study, the information flow time arrow is investigated for stochastic data defined by vector autoregressive models. The time series are analyzed forward and backward by different Granger causality detection methods. Besides the normal distribution, which is usually required for the validity of Granger causality analysis, several other distributions of predictive errors are considered. A clear effect of a change in the order of cause and effect on the time-reversed series of unidirectionally connected variables was detected with standard Granger causality test (GC), when the product of the connection strength and the ratio of the predictive errors of the driver and the recipient was below a certain level, otherwise bidirectional causal connection was detected. On the other hand, opposite causal link was detected unconditionally by the methods based on the time reversal testing, but they were not able to detect correct bidirectional connection. The usefulness of the backward analysis is manifested in cases where falsely detected unidirectional connections can be rejected by applying the result obtained after the time reversal, and in cases of uncorrelated causally independent variables, where the absence of a causal link detected by GC on the original series should be confirmed on the time-reversed series.

Time reversal (TR) can achieve temporal and spatial focusing by exploiting spatial diversity in complex underwater environments with significant multipath. This property makes TR useful for underwater acoustic (UWA) communications. Conventional TR is realized by performing equal gain combining (EGC) on the single element TR output signals of each element of the vertical receive array (VRA). However, in the actual environment, the signal-to-noise ratio (SNR) and the received noise power of each element are different, which leads to the reduction of the focusing gain. This paper proposes a time reversal maximum ratio combining (TR-MRC) method to process the received signals of the VRA, so that a higher output SNR can be obtained. The theoretical derivation of the TR-MRC weight coefficients indicates that the weight coefficients are only related to the input noise power of each element, and are not affected by the multipath structure. The correctness of the derivation is demonstrated with the experimental data of the long-range UWA communications conducted in the South China Sea. In addition, the experimental results illustrate that compared to the conventional TR, TR-MRC can provide better performance in terms of output SNR and bit error rate (BER) in UWA communications.

Chemical kinetics govern the dynamics of chemical systems leading towards chemical equilibrium. There are several general properties of the dynamics of chemical reactions such as the existence of disparate time scales and the fact that most time scales are dissipative. This causes a transient relaxation to lower dimensional attracting manifolds in composition space. In this work, we discuss this behavior and investigate how a time reversal effects this behavior. For this, both macroscopic chemical systems as well as microscopic chemical systems (elementary reactions) are considered.

Due to the light scattering effect, it is difficult to directly achieve optical focusing and imaging in turbid media, such as milk and biological tissue. The turbidity suppression of a scattering medium and control of light through the scattering medium are important for imaging on biological tissue or biophotonics. Optical phase conjugation is a novel technology on turbidity suppression by directly creating phase conjugation light waves to form time-reversed light. In this work, we report a digital optical phase conjugation system based on off-axis holography. Compared with traditional digital optical phase conjugation methods, the off-axis holography acquires the conjugation phase using only one interference image, obviously saving photo acquisition time. Furthermore, we tested the optical phase conjugate reduction performance of this system and also achieved optical focusing through the diffuser. We also proved that the reversing of random scattering in turbid media is achievable by phase conjugation.

Photo-Acoustic Tomography (PAT) is an emerging non-invasive hybrid modality driven by a constant yearning for superior imaging performance. The image quality, however, hinges on the acoustic reflection, which may compromise the diagnostic performance. To address this challenge, we propose to incorporate a deep neural network into conventional iterative algorithms to accelerate and improve the correction of reflection artifacts. Based on the simulated PAT dataset from computed tomography (CT) scans, this network-accelerated reconstruction approach is shown to outperform two state-of-the-art iterative algorithms in terms of the peak signal-to-noise ratio (PSNR) and the structural similarity (SSIM) in the presence of noise. The proposed network also demonstrates considerably higher computational efficiency than conventional iterative algorithms, which are time-consuming and cumbersome.

Time reversal (TR) concept is widely used for Lamb wave-based damage detection. However, the time reversal process (TRP) faces the challenge that it requires two actuating-sensing steps and requires the extraction of re-emitted and reconstructed waveforms. In this study, the effects of the two extracted components on the performance of TRP are studied experimentally. The results show that the two time intervals, in which the waveforms are extracted, have great influence on the accuracy of damage detection of the time reversal method (TRM). What is more, it requires a large number of experiments to determine these two time intervals. Therefore, this paper proposed an efficient time reversal method (ETRM). Firstly, a broadband excitation is applied to obtain response at a wide range of frequencies, and ridge reconstruction based on inverse short-time Fourier transform is applied to extract desired mode components from the broadband response. Subsequently, deconvolution is used to extract narrow-band reconstructed signal. In this method, the reconstructed signal can be easily obtained without determining the two time intervals. Besides, the reconstructed signals related to a series of different excitations could be obtained through only one actuating-sensing step. Finally, the effectiveness of the ETRM for damage detection in composite laminates is verified through experiments.

From basic principles, we review some fundamentals of entropy calculations, some of which are implicit in the literature. We mainly deal with microcanonical ensembles to effectively compare the counting of states in continuous and discrete settings. When dealing with non-interacting elements, this effectively reduces the calculation of the microcanonical entropy to counting the number of certain partitions, or compositions of a number. This is true in the literal sense, when quantization is assumed, even in the classical limit. Thus, we build on a moderately dated, ingenuous mathematical work of Haselgrove and Temperley on counting the partitions of an arbitrarily large positive integer into a fixed (but still large) number of summands, and show that it allows us to exactly calculate the low energy/temperature entropy of a one-dimensional Bose–Einstein gas in a box. Next, aided by the asymptotic analysis of the number of compositions of an integer as the sum of three squares, we estimate the entropy of the three-dimensional problem. For each selection of the total energy, there is a very sharp optimal number of particles to realize that energy. Therefore, the entropy is ‘large’ and almost independent of the particles, when the particles exceed that number. This number scales as the energy to the power of ( 2 / 3 ) -rds in one dimension, and ( 3 / 5 ) -ths in three dimensions. In the one-dimensional case, the threshold approaches zero temperature in the thermodynamic limit, but it is finite for mesoscopic systems. Below that value, we studied the intermediate stage, before the number of particles becomes a strong limiting factor for entropy optimization. We apply the results of moments of partitions of Coons and Kirsten to calculate the relative fluctuations of the ground state and excited states occupation numbers. At much lower temperatures than threshold, they vanish in all dimensions. We briefly review some of the same results in the grand canonical ensemble to show to what extents they differ.

Single-photon wave packets can carry quantum information between nodes of a quantum network. An important general operation in photon-based quantum information systems is ‘blind’ reversal of a photon’s temporal wave packet envelope, that is, the ability to reverse an envelope without knowing the temporal state of the photon. We present an all-optical means for doing so, using nonlinear-optical frequency conversion driven by a short pump pulse. The process used may be sum-frequency generation or four-wave Bragg scattering. This scheme allows for quantum operations such as a temporal-mode parity sorter. We also verify that the scheme works for arbitrary states (not only single-photon ones) of an unknown wave packet.

In this paper, a scheme based on the time reversal technique is proposed to improve the detection performance for detecting a cylindrical object bottoming at the seafloor in shallow water. When the time reversal technique is applied to the response of the clutter with the strong time-varying characteristic of shallow water, it is difficult to obtain a high peak response. However, in the case where a cylindrical object is placed on the seafloor because the time-invariant property of the target response is stronger than the time-varying property of the reverberation by the clutters, the time reversal technique can be applied to enhance the target signal. In this paper, it is demonstrated that the peak due to the target that is contacted at the seabed becomes higher when applying the time reversal technique. The performance is investigated by using numerical computation of the probability of detection for various probabilities of false alarm and computer simulation.

Barely visible indentation damage after quasi-static indentation in sandwich CF/EP composites was assessed using ultrasonic guided wave signals. Finite element analyses were conducted to investigate the interaction between guided waves and damage, further to assist in the selection process of the Lamb wave sensitive modes for debonding identification. Composite sandwich beams and panels structures were investigated. Using the beam structure, a damage index was defined based on the change in the peak magnitude of the captured wave signals before and after the indentation, and the damage index was correlated with the residual deformation (defined as the depth of the dent), that was further correlated with the amount of crushing within the core. Both A 0 and S 0 Lamb wave modes showed high sensitivity to the presence of barely visible indentation damage with residual deformation of 0.2 mm. Furthermore, barely visible indentation damage was assessed in composite sandwich panels after indenting to 3 and 5 mm, and the damage index was defined, based on (a) the peak magnitude of the wave signals before and after indentation or (b) the mismatch between the original and reconstructed wave signals based on a time-reversal algorithm, and was subsequently applied to locate the position of indentation. [ABSTRACT FROM AUTHOR]

We consider stochastic interacting particle systems with more than one conservation law in a regime far from equilibrium. Using time reversal we derive symmetry relations for the stationary currents of the conserved quantities that are reminiscent of Onsager's reciprocity relations. These relations are valid for a very large class of particles with only some mild assumption on the decay of stationary relations and imply that the coarse-grained macroscopic dynamics is governed by a system of hyperbolic conservation laws. An explicit expression for the conserved Lax entropy is obtained. [ABSTRACT FROM AUTHOR]

Following a Gallavotti's conjecture, stationary states of Navier-Stokes fluids are proposed to be described equivalently by alternative equations besides the Navier-Stokes equation itself. We discuss a model system symmetric under time reversal based on the Navier-Stokes equations constrained to keep the enstrophy constant. It is demonstrated through highly resolved numerical experiments that the reversible model evolves to a stationary state which reproduces quite accurately all statistical observables relevant for the physics of turbulence extracted by direct numerical simulations (DNS) at different Reynolds numbers. The possibility of using reversible models to mimic turbulence dynamics is of practical importance for the coarse-grained version of Navier-Stokes equations, as used in large-eddy simulations. Furthermore, the reversible model appears mathematically simpler, since enstrophy is bounded to be constant for every Reynolds number. Finally, the theoretical interest in the context of statistical mechanics is briefly discussed. [ABSTRACT FROM AUTHOR]

Abstract: We obtain an exact expression of the negativity for SU(2)-invariant bipartite spin- states via the partial time reversal method. Studies of thermal states show that the threshold temperature of entanglement may be arbitrary high when is sufficient large, indicating that the entanglement is very robust against temperature. Negativities in bilinear-biquadratic system are also considered. [Copyright &y& Elsevier]

It is shown that some basic physical concepts when carried over from Newtonian physics into relativistic physics have inherent or intrinsic difficulties that are very hard to surmount or overcome. Further, some of the misconceptions or misunderstandings in physics are also pointed out. These include: The Newtonian concept of action-at-a-distance forces (such as the Coulomb's law, restoring force of a simple harmonic oscillator or a vibrating string, Newton's law of gravity, rigid-body constraints, orbital and spin angular momentum and the associated rigid-body spatial rotations, etc.); and some basic misconceptions or misunderstandings in physics such as assuming that Dirac's relativistic Hamiltonian for the electron is Lorentz covariant even though it is the total energy which is the fourth component of the energy-momentum four vector, Dirac's claim that g =2 for the electron and Feynman's claim that the (g-2) for the electron are a direct consequence of the theory of relativity ignoring the facts that g=2 follows directly from the nonrelativistic Pauli Hamiltonian and (g-2) calculation is very much analogous to the Bethe's nonrelativistic calculation of the Lamb shift, taking for granted that the experimentally measured fundamental unit of magnetic flux is a direct verification of the "electron pairs" of the Bardeen-ooper-Schrieffer theory of low-temperature superconductivity whereas it need not imply "electron pairing," the general feeling that the canonical orbital angular momentum can only take integral values and can not take half-odd-integral values whereas it is not true in general, etc. All these exemplify some of the wrong developments and claims in the existing physics literature. [ABSTRACT FROM AUTHOR]

An exact solution to the classical Liouville equation is derived. It is found that it can have a partial solution with a broken symmetry with respect to time. Thus, in the general case, it does not follow from the invariance of the fundamental Liouville law concerning time reversal that the past and future play similar roles. [ABSTRACT FROM AUTHOR]

A time-symmetric formulation of nonrelativistic quantum mechanics is developed by applying two consecutive boundary conditions onto solutions of a time- symmetrized wave equation. From known probabilities in ordinary quantum mechanics, a time-symmetric parameter P0 is then derived that properly weights the likelihood of any complete sequence of measurement outcomes on a quantum system. The results appear to match standard quantum mechanics, but do so without requiring a time-asymmetric collapse of the wavefunction upon measurement, thereby realigning quantum mechanics with an important fundamental symmetry. [ABSTRACT FROM AUTHOR]

We tell the tale of the first writing of a partial transpose, without guaranteeing historical authenticity. [ABSTRACT FROM AUTHOR]

On pure states of n quantum bits, the concurrence entanglement monotone returns the norm of the inner product of a pure state with its spin-flip. The monotone vanishes for n odd, but for n even there is an explicit formula for its value on mixed states, i.e., a closed-form expression computes the minimum over all ensemble decompositions of a given density. For n even a matrix decomposition ν=k1ak2 of the unitary group is explicitly computable and allows for study of the monotone’s dynamics. The side factors k1 and k2 of this concurrence canonical decomposition (CCD) are concurrence symmetries, so the dynamics reduce to consideration of the a factor. This unitary a phases a basis of entangled states, and the concurrence dynamics of u are determined by these relative phases. In this work, we provide an explicit numerical algorithm computing ν=k1ak2 for n odd. Further, in the odd case we lift the monotone to a two-argument function. The concurrence capacity of ν according to the double argument lift may be nontrivial for n odd and reduces to the usual concurrence capacity in the literature for n even. The generalization may also be studied using the CCD, leading again to maximal capacity for most unitaries. The capacity of νxI2 is at least that of ν, so odd-qubit capacities have implications for even-qubit entanglement. The generalizations require considering the spin-flip as a time reversal symmetry operator in Wigner’s axiomatization, and the original Lie algebra homomorphism defining the CCD may be restated entirely in terms of this time reversal. The polar decomposition related to the CCD then writes any unitary evolution as the product of a time-symmetric and time-antisymmetric evolution with respect to the spin-flip. En route we observe a Kramers’ nondegeneracy: the existence of a nondegenerate eigenstate of any time reversal symmetric n-qubit Hamiltonian demands (i) n even and (ii) maximal concurrence of said eigenstate. We provide examples of how to apply this work to study the kinematics and dynamics of entanglement in spin chain Hamiltonians. [ABSTRACT FROM AUTHOR]

In the present paper we show that in a certain sense the violation of Bell’s inequality does not entail a real non-locality. We definematerialityas the capacity to be modified; and it results that in the case of the singlet state the non-locality previewed by quantum mechanics and experimentally confirmed is not material. [ABSTRACT FROM AUTHOR]

A concept of time-reversed entropy per unit time is introduced in analogy with the entropy per unit time by Shannon, Kolmogorov, and Sinai. This time-reversed entropy per unit time characterizes the dynamical randomness of a stochastic process backward in time, while the standard entropy per unit time characterizes the dynamical randomness forward in time. The difference between the time-reversed and standard entropies per unit time is shown to give the entropy production of Markovian processes in nonequilibrium steady states. [ABSTRACT FROM AUTHOR]