A Review of the Concept of Time Reversal and the Direction of Time.

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.

Does Quantum Mechanics Require "Conspiracy"?

Quantum states containing records of incompatible outcomes of quantum measurements are valid states in the tensor-product Hilbert space. Since they contain false records, they conflict with the Born rule and with our observations. I show that excluding them requires a fine-tuning to an extremely restricted subspace of the Hilbert space that seems "conspiratorial", in the sense that (1) it seems to depend on future events that involve records (including measurement settings) and on the dynamical law (normally thought to be independent of the initial conditions), and (2) it violates Statistical Independence, even when it is valid in the context of Bell's theorem. To solve the puzzle, I build a model in which, by changing the dynamical law, the same initial conditions can lead to different histories in which the validity of records is relative to the new dynamical law. This relative validity of the records may restore causality, but the initial conditions still must depend, at least partially, on the dynamical law. While violations of Statistical Independence are often seen as non-scientific, they turn out to be needed to ensure the validity of records and our own memories and, by this, of science itself. A Past Hypothesis is needed to ensure the existence of records and turns out to require violations of Statistical Independence. It is not excluded that its explanation, still unknown, ensures such violations in the way needed by local interpretations of quantum mechanics. I suggest that an as-yet unknown law or superselection rule may restrict the full tensor-product Hilbert space to the very special subspace required by the validity of records and the Past Hypothesis.

Small and Simple Systems That Favor the Arrow of Time.

The 2nd law of thermodynamics yields an irreversible increase in entropy until thermal equilibrium is achieved. This irreversible increase is often assumed to require large and complex systems to emerge from the reversible microscopic laws of physics. We test this assumption using simulations and theory of a 1D ring of N Ising spins coupled to an explicit heat bath of N Einstein oscillators. The simplicity of this system allows the exact entropy to be calculated for the spins and the heat bath for any N, with dynamics that is readily altered from reversible to irreversible. We find thermal-equilibrium behavior in the thermodynamic limit, and in systems as small as N=2, but both results require microscopic dynamics that is intrinsically irreversible.

Memory Systems, the Epistemic Arrow of Time, and the Second Law.

The epistemic arrow of time is the fact that our knowledge of the past seems to be both of a different kind and more detailed than our knowledge of the future. Just like with the other arrows of time, it has often been speculated that the epistemic arrow arises due to the second law of thermodynamics. In this paper, we investigate the epistemic arrow of time using a fully formal framework. We begin by defining a memory system as any physical system whose present state can provide information about the state of the external world at some time other than the present. We then identify two types of memory systems in our universe, along with an important special case of the first type, which we distinguish as a third type of memory system. We show that two of these types of memory systems are time-symmetric, able to provide knowledge about both the past and the future. However, the third type of memory systems exploits the second law of thermodynamics, at least in all of its instances in our universe that we are aware of. The result is that in our universe, this type of memory system only ever provides information about the past. We also argue that human memory is of this third type, completing the argument. We end by scrutinizing the basis of the second law itself. This uncovers a previously unappreciated formal problem for common arguments that try to derive the second law from the "Past Hypothesis", i.e., from the claim that the very early universe was in a state of extremely low entropy. Our analysis is indebted to prior work by one of us but expands and improves upon this work in several respects.

Comparing the cost of violating causal assumptions in Bell experiments: locality, free choice and arrow-of-time.

The causal modelling of Bell experiments relies on three fundamental assumptions: locality, freedom of choice and arrow-of-time. It turns out that nature violates Bell inequalities, which implies the failure of at least one of those assumptions. Since rejecting any of them, even partially, is sufficient to explain the observed correlations, it is natural to inquire about the cost in each case. This paper builds upon the findings in Blasiak et al. 2021 Proc. Natl Acad. Sci. USA 118, e2020569118 (doi:10.1073/pnas.2020569118) showing the equivalence between the locality and free choice assumptions. Here, we include retrocausal models to complete the picture of causal explanations of the observed correlations. Furthermore, we refine the discussion by considering more challenging causal scenarios which allow only single-arrow type violations of a given assumption. The figure of merit chosen for the comparison of the causal cost is defined as the minimal frequency of violation of the respective assumption required for a simulation of the observed experimental statistics. This article is part of the theme issue 'Quantum contextuality, causality and freedom of choice'.

Nonlocality, Superposition, and Time in the 4+1 Formalism.

The field of quantum gravity struggles with several problems related to time, quantum measurement, nonlocality, and realism. To address these issues, this study develops a 4+1 formalism featuring a flat 4D spacetime evolving with a second form of time, τ, worldlines that locally conserve momentum, and a hypersurface representing the present. As a function of τ, worldlines can spatially readjust and influences can travel backward or forward in the time dimension along these worldlines, offering a physical mechanism for retrocausality. Three theoretical models are presented, elucidating how nonlocality in an EPR experiment, the arrival time problem, and superposition in a Mach-Zehnder interferometer can be understood within this 4+1 framework. These results demonstrate that essential quantum phenomena can be reproduced in the 4+1 formalism while upholding the principles of realism, locality, and determinism at a fundamental level. Additionally, there is no measurement or collapse problem, and a natural explanation for the quantum-to-classical transition is obtained. Furthermore, observations of a 4D block universe and of the flow of time can be simultaneously understood. With these properties, the presented 4+1 formalism lays an interesting foundation for a quantum gravity theory based on intuitive principles and compatible with our observation of time.

The arrow-of-time in neuroimaging time series identifies causal triggers of brain function.

Moving from association to causal analysis of neuroimaging data is crucial to advance our understanding of brain function. The arrow-of-time (AoT), that is, the known asymmetric nature of the passage of time, is the bedrock of causal structures shaping physical phenomena. However, almost all current time series metrics do not exploit this asymmetry, probably due to the difficulty to account for it in modeling frameworks. Here, we introduce an AoT-sensitive metric that captures the intensity of causal effects in multivariate time series, and apply it to high-resolution functional neuroimaging data. We find that causal effects underlying brain function are more distinctively localized in space and time than functional activity or connectivity, thereby allowing us to trace neural pathways recruited in different conditions. Overall, we provide a mapping of the causal brain that challenges the association paradigm of brain function.

Relating a System's Hamiltonian to Its Entropy Production Using a Complex Time Approach.

We exploit the properties of complex time to obtain an analytical relationship based on considerations of causality between the two Noether-conserved quantities of a system: its Hamiltonian and its entropy production. In natural units, when complexified, the one is simply the Wick-rotated complex conjugate of the other. A Hilbert transform relation is constructed in the formalism of quantitative geometrical thermodynamics, which enables system irreversibility to be handled analytically within a framework that unifies both the microscopic and macroscopic scales, and which also unifies the treatment of both reversibility and irreversibility as complementary parts of a single physical description. In particular, the thermodynamics of two unitary entities are considered: the alpha particle, which is absolutely stable (that is, trivially reversible with zero entropy production), and a black hole whose unconditional irreversibility is characterized by a non-zero entropy production, for which we show an alternate derivation, confirming our previous one. The thermodynamics of a canonical decaying harmonic oscillator are also considered. In this treatment, the complexification of time also enables a meaningful physical interpretation of both "imaginary time" and "imaginary energy".

The lack of temporal brain dynamics asymmetry as a signature of impaired consciousness states.

Life is a constant battle against equilibrium. From the cellular level to the macroscopic scale, living organisms as dissipative systems require the violation of their detailed balance, i.e. metabolic enzymatic reactions, in order to survive. We present a framework based on temporal asymmetry as a measure of non-equilibrium. By means of statistical physics, it was discovered that temporal asymmetries establish an arrow of time useful for assessing the reversibility in human brain time series. Previous studies in human and non-human primates have shown that decreased consciousness states such as sleep and anaesthesia result in brain dynamics closer to the equilibrium. Furthermore, there is growing interest in the analysis of brain symmetry based on neuroimaging recordings and since it is a non-invasive technique, it can be extended to different brain imaging modalities and applied at different temporo-spatial scales. In the present study, we provide a detailed description of our methodological approach, paying special attention to the theories that motivated this work. We test, for the first time, the reversibility analysis in human functional magnetic resonance imaging data in patients suffering from disorder of consciousness. We verify that the tendency of a decrease in the asymmetry of the brain signal together with the decrease in non-stationarity are key characteristics of impaired consciousness states. We expect that this work will open the way for assessing biomarkers for patients' improvement and classification, as well as motivating further research on the mechanistic understanding underlying states of impaired consciousness.

Supernovae and the Arrow of Time.

Supernovae are explosions of stars and are a central problem in astrophysics. Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities develop during the star's explosion and lead to intense interfacial RT/RM mixing of the star materials. We handle the mathematical challenges of the RT/RM problem based on the group theory approach. We directly link the conservation laws governing RT/RM dynamics to the symmetry-based momentum model, derive the model parameters, and find the analytical solutions and characteristics of RT/RM dynamics with variable accelerations in the linear, nonlinear and mixing regimes. The theory outcomes explain the astrophysical observations and yield the design of laboratory experiments. They suggest that supernova evolution is a non-equilibrium process directed by the arrow of time.

Quantum Gravity If Non-Locality Is Fundamental.

I take non-locality to be the Michelson-Morley experiment of the early 21st century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but must somehow be emergent from entangled coherent quantum variables and their behaviors. There are, then, two immediate consequences: (i). if we start with non-locality, we need not explain non-locality. We must instead explain an emergence of locality and spacetime. (ii). There can be no emergence of spacetime without matter. These propositions flatly contradict General Relativity, which is foundationally local, can be formulated without matter, and in which there is no "emergence" of spacetime. If these be true, then quantum gravity cannot be a minor alteration of General Relativity but must demand its deep reformulation. This will almost inevitably lead to: matter not only curves spacetime, but "creates" spacetime. We will see independent grounds for the assertion that matter both curves and creates spacetime that may invite a new union of quantum gravity and General Relativity. This quantum creation of spacetime consists of: (i) fully non-local entangled coherent quantum variables. (ii) The onset of locality via decoherence. (iii) A metric in Hilbert space among entangled quantum variables by the sub-additive von Neumann entropy between pairs of variables. (iv) Mapping from metric distances in Hilbert space to metric distances in classical spacetime by episodic actualization events. (v) Discrete spacetime is the relations among these discrete actualization events. (vi) "Now" is the shared moment of actualization of one among the entangled variables when the amplitudes of the remaining entangled variables change instantaneously. (vii) The discrete, successive, episodic, irreversible actualization events constitute a quantum arrow of time. (viii) The arrow of time history of these events is recorded in the very structure of the spacetime constructed. (ix) Actual Time is a succession of two or more actual events. The theory inevitably yields a UV cutoff of a new type. The cutoff is a phase transition between continuous spacetime before the transition and discontinuous spacetime beyond the phase transition. This quantum creation of spacetime modifies General Relativity and may account for Dark Energy, Dark Matter, and the possible elimination of the singularities of General Relativity. Relations to Causal Set Theory, faithful Lorentzian manifolds, and past and future light cones joined at "Actual Now" are discussed. Possible observational and experimental tests based on: (i). the existence of Sub- Planckian photons, (ii). knee and ankle discontinuities in the high-energy gamma ray spectrum, and (iii). possible experiments to detect a creation of spacetime in the Casimir system are discussed. A quantum actualization enhancement of repulsive Casimir effect would be anti-gravitational and of possible practical use. The ideas and concepts discussed here are not yet a theory, but at most the start of a framework that may be useful.

Introduction of a Power Law Time-Temperature Equivalent Formulation for the Description of Thermorheologically Simple and Complex Behavior.

In this work, a conceptual framework is suggested for analyzing thermorheologically simple and complex behavior by using just one approach. Therefore, the linear relation between master time and real time which is required in terms of the time-temperature superposition principle was enhanced to a nonlinear equivalent relation. Furthermore, we evaluate whether there is any relation among well-known existing time-temperature equivalent formulations which makes it possible to generalize different existing formulations. For this purpose, as an example, the power law formulation was used for the definition of the master time. The method introduced here also contributes a further framework for a unification of established time-temperature equivalent formulations, for example the time-temperature superposition principle and time-temperature parameter models. Results show, with additional normalization conditions, most of the developed time-temperature parameter models can be treated as special cases of the new formulation. In the aspect of the arrow of time, the new defined master time is a bended arrow of time, which can help to understand the corresponding physical meaning of the suggested method.

Assessment of Arrow-of-Time Metrics for the Characterization of Underwater Explosions.

Anthropogenic impulsive sound sources with high intensity are a threat to marine life and it is crucial to keep them under control to preserve the biodiversity of marine ecosystems. Underwater explosions are one of the representatives of these impulsive sound sources, and existing detection techniques are generally based on monitoring the pressure level as well as some frequency-related features. In this paper, we propose a complementary approach to the underwater explosion detection problem through assessing the arrow of time. The arrow of time of the pressure waves coming from underwater explosions conveys information about the complex characteristics of the nonlinear physical processes taking place as a consequence of the explosion to some extent. We present a thorough review of the characterization of arrows of time in time-series, and then provide specific details regarding their applications in passive acoustic monitoring. Visibility graph-based metrics, specifically the direct horizontal visibility graph of the instantaneous phase, have the best performance when assessing the arrow of time in real explosions compared to similar acoustic events of different kinds. The proposed technique has been validated in both simulations and real underwater explosions.

The Matter of Time.

About a century ago, in the spirit of ancient atomism, the quantum of light was renamed the photon to suggest that it is the fundamental element of everything. Since the photon carries energy in its period of time, a flux of photons inexorably embodies a flow of time. Thus, time comprises periods as a trek comprises legs. The flows of quanta naturally select optimal paths (i.e., geodesics) to level out energy differences in the least amount of time. The corresponding flow equations can be written, but they cannot be solved. Since the flows affect their driving forces, affecting the flows, and so on, the forces (i.e., causes) and changes in motions (i.e., consequences) are inseparable. Thus, the future remains unpredictable. However, it is not all arbitrary but rather bounded by free energy. Eventually, when the system has attained a stationary state where forces tally, there are no causes and no consequences. Since there are no energy differences between the system and its surroundings, the quanta only orbit on and on. Thus, time does not move forward either but circulates.

Causality Is an Effect, II.

Causality follows the thermodynamic arrow of time, where the latter is defined by the direction of entropy increase. After a brief review of an earlier version of this article, rooted in classical mechanics, we give a quantum generalization of the results. The quantum proofs are limited to a gas of Gaussian wave packets.

The five problems of irreversibility.

Thermodynamics has a clear arrow of time, characterized by the irreversible approach to equilibrium. This stands in contrast to the laws of microscopic theories, which are invariant under time-reversal. Foundational discussions of this "problem of irreversibility" often focus on historical considerations, and do therefore not take results of modern physical research on this topic into account. In this article, I will close this gap by studying the implications of dynamical density functional theory (DDFT), a central method of modern nonequilibrium statistical mechanics not previously considered in philosophy of physics, for this debate. For this purpose, the philosophical discussion of irreversibility is structured into five problems, concerned with the source of irreversibility in thermodynamics, the definition of equilibrium and entropy, the justification of coarse-graining, the approach to equilibrium and the arrow of time. For each of these problems, it is shown that DDFT provides novel insights that are of importance for both physicists and philosophers of physics.

Maxwell's Demon in Quantum Mechanics.

Maxwell's Demon is a thought experiment devised by J. C. Maxwell in 1867 in order to show that the Second Law of thermodynamics is not universal, since it has a counter-example. Since the Second Law is taken by many to provide an arrow of time, the threat to its universality threatens the account of temporal directionality as well. Various attempts to "exorcise" the Demon, by proving that it is impossible for one reason or another, have been made throughout the years, but none of them were successful. We have shown (in a number of publications) by a general state-space argument that Maxwell's Demon is compatible with classical mechanics, and that the most recent solutions, based on Landauer's thesis, are not general. In this paper we demonstrate that Maxwell's Demon is also compatible with quantum mechanics. We do so by analyzing a particular (but highly idealized) experimental setup and proving that it violates the Second Law. Our discussion is in the framework of standard quantum mechanics; we give two separate arguments in the framework of quantum mechanics with and without the projection postulate. We address in our analysis the connection between measurement and erasure interactions and we show how these notions are applicable in the microscopic quantum mechanical structure. We discuss what might be the quantum mechanical counterpart of the classical notion of "macrostates", thus explaining why our Quantum Demon setup works not only at the micro level but also at the macro level, properly understood. One implication of our analysis is that the Second Law cannot provide a universal lawlike basis for an account of the arrow of time; this account has to be sought elsewhere.

Entropy and Time.

The idea that entropy is associated with the "arrow of time" has its roots in Clausius's statement on the Second Law: "Entropy of the Universe always increases." However, the explicit association of the entropy with time's arrow arises from Eddington. In this article, we start with a brief review of the idea that the "increase in entropy" is somehow associated with the direction in which time increases. Then, we examine three different, but equivalent definitions of entropy. We find that none of these definitions indicate any hint of a relationship between entropy and time. We can, therefore, conclude that entropy is a timeless quantity. We also discuss the reasons as to why some scientists went astray in associating entropy with time's arrow. Finally, we shall discuss Boltzmann's H-Theorem, which is viewed by many as a proof of the Second Law of Thermodynamics.

Quantum Computation and Arrows of Time.

Quantum physics is surprising in many ways. One surprise is the threat to locality implied by Bell's Theorem. Another surprise is the capacity of quantum computation, which poses a threat to the complexity-theoretic Church-Turing thesis. In both cases, the surprise may be due to taking for granted a strict arrow-of-time assumption whose applicability may be limited to the classical domain. This possibility has been noted repeatedly in the context of Bell's Theorem. The argument concerning quantum computation is described here. Further development of models which violate this strong arrow-of-time assumption, replacing it by a weaker arrow which is yet to be identified, is called for.

Time-Reversal Symmetry and Arrow of Time in Quantum Mechanics of Open Systems.

It is one of the most important and long-standing issues of physics to derive the irreversibility out of a time-reversal symmetric equation of motion. The present paper considers the breaking of the time-reversal symmetry in open quantum systems and the emergence of an arrow of time. We claim that the time-reversal symmetric Schrödinger equation can have eigenstates that break the time-reversal symmetry if the system is open in the sense that it has at least a countably infinite number of states. Such eigenstates, namely the resonant and anti-resonant states, have complex eigenvalues. We show that, although these states are often called "unphysical", they observe the probability conservation in a particular way. We also comment that the seemingly Hermitian Hamiltonian is non-Hermitian in the functional space of the resonant and anti-resonant states, and hence there is no contradiction in the fact that it has complex eigenvalues. We finally show how the existence of the states that break the time-reversal symmetry affects the quantum dynamics. The dynamics that starts from a time-reversal symmetric initial state is dominated by the resonant states for t > 0 ; this explains the phenomenon of the arrow of time, in which the decay excels the growth. The time-reversal symmetry holds in that the dynamic ending at a time-reversal symmetric final state is dominated by the anti-resonant states for t < 0 .