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Are you, with your perceptions, memories and observational data, a Boltzmann brain, namely a fleeting statistical fluctuation out of the thermal equilibrium of the universe? Arguments are given in the literature claiming that this bizarre hypothesis needs to be considered seriously, that all of our data about the past is actually a mirage. We point to a difficulty in these arguments. They are based on the dynamical laws and on statistical arguments, but they disregard the fact that we infer the dynamical laws presupposing the reliability of our data records about the past. Hence the reasoning in favor of the Boltzmann brain hypothesis contradicts itself, relying on the reliability of our data about the past to conclude that that data is wrong. More broadly, it is based on incomplete evidence. Incomplete evidence notoriously leads to false conclusions., Comment: 5 pages, no figures

This is a review of some recent developments on quantum gravity aspects of black hole physics. In particular, we focus on a scenario leading to the prediction of the existence of a Planck-mass quasi-stable object, that could form a component of dark matter., Comment: 24 pages, 18 figures

It is often stated that the second law of thermodynamics follows from the condition that at some given time in the past the entropy was lower than it is now. Formally, this condition is the statement that $E[S(t)|S(t_0)]$, the expected entropy of the universe at the current time $t$ conditioned on its value $S(t_0)$ at a time $t_0$ in the past, is an increasing function of $t $. We point out that in general this is incorrect. The epistemic axioms underlying probability theory say that we should condition expectations on all that we know, and on nothing that we do not know. Arguably, we know the value of the universe's entropy at the present time $t$ at least as well as its value at a time in the past, $t_0$. However, as we show here, conditioning expected entropy on its value at two times rather than one radically changes its dynamics, resulting in a unexpected, very rich structure. For example, the expectation value conditioned on two times can have a maximum at an intermediate time between $t_0$ and $t$, i.e., in our past. Moreover, it can have a negative rather than positive time derivative at the present. In such "Boltzmann bridge" situations, the second law would not hold at the present time. We illustrate and investigate these phenomena for a random walk model and an idealized gas model, and briefly discuss the role of Boltzmann bridges in our universe., Comment: 10 pages, 10 figures

These are lectures notes prepared for a series of seminars I am invited to give at Princeton Philosophy Department in November 2024. They cover the conceptual structure of quantum gravity, the relational interpretation of quantum mechanics, the structure of time, its orientation and the openness of the future, the physical underpinning of information and meaning, and some general considerations on the fact that concepts evolve, on perspectivalism and anti-foundationalism., Comment: 51 pages, 3 figures. Version 2 much cleaned. Sincere thanks to Richard Werthamer

An influential theorem by Satosi Watanabe convinced many that there can be no physical probabilistic theory with both non-trivial forward and backward transition probabilities. We show that this conclusion does not follow from the theorem. We point out the flaw in the argument, and we showcase examples of theories with well-defined backward and forward transition probabilities., Comment: 10 single column pages, no figures, version accepted for publication, improved thanks to peer review

Quantum gravitational tunneling effects are expected to give rise to a number of interesting observable phenomena, including, in particular, the evolution of black holes at the end of their existence or the emergence of the early universe from a quantum phase. Covariant Loop Quantum Gravity provides a framework to study these phenomena, yet a precise identification of tunneling processes is still not known. Motivated by this question, we consider a related, simpler case, that of Ponzano-Regge amplitudes: we find a surprising and detailed analogy of a class of simple transition amplitudes with tunneling processes in non-relativistic quantum mechanics., Comment: 6 pages, 5 figures. v2 matches the published version

In spite or the large astronomical evidence for its existence, the nature of dark matter remains enigmatic. Particles that interact only, or almost only, gravitationally, in particular with masses around the Planck mass -- the fundamental scale in quantum gravity, are intriguing candidates. Here we show that there is a theoretical possibility to directly detect such particles using highly sensitive gravity-mediated quantum phase shifts. In particular, we consider a protocol utilizing Josephson junctions., Comment: A refined protocol using Josephson junctions has been added

Choice can be defined in thermodynamical terms and be shown to have a thermodynamic cost: choosing between a binary alternative at temperature T dissipates an energy E > kT ln 2., Comment: 4 pages, 3 figures

A metric that describes a collapsing star and the surrounding black hole geometry accounting for quantum gravity effects has been derived independently by different research groups. There is consensus regarding this metric up until the star reaches its minimum radius, but there is disagreement about what happens past this event. The discrepancy stems from the appearance of a discontinuity in the Hamiltonian evolution of the metric components in Painlev\'e-Gullstrand coordinates. Here we show that the continuous geometry that describes this phenomenon is represented by a discontinuous metric when written in these coordinates. The discontinuity disappears by changing coordinates. The discontinuity found in the Hamiltonian approach can therefore be interpreted as a coordinate effect. The geometry continues regularly into an expanding white hole phase, without the occurrence of a shock wave caused by a physical discontinuity., Comment: 5 pages, 2 figures; v2: Corrected typos

We examine evaluations of the contributions of Matrix Mechanics and Max Born to the formulation of quantum mechanics from Heisenberg's Helgoland paper of 1925 to Born's Nobel Prize of 1954. We point out that the process of evaluation is continuing in the light of recent interpretations of the theory that deemphasize the importance of the wave function., Comment: 58 pages

Lawrence et al. have presented an argument purporting to show that "relative facts do not exist" and, consequently, "Relational Quantum Mechanics is incompatible with quantum mechanics". The argument is based on a GHZ-like contradiction between constraints satisfied by measurement outcomes in an extended Wigner's friend scenario. Here we present a strengthened version of the argument, and show why, contrary to the claim by Lawrence et al., these arguments do not contradict the consistency of a theory of relative facts. Rather, considering this argument helps clarify how one should not think about a theory of relative facts, like RQM., Comment: 4 pages

Locality is a central notion in modern physics, but different disciplines understand it in different ways. Quantum field theory focusses on relativistic locality, enforced by microcausality, while quantum information theory focuses on subsystem locality, which regulates how information and causal influences propagate in a system, with no direct reference to spacetime notions. Here we investigate how microcausality and subsystem locality are related. The question is relevant for understanding whether it is possible to formulate quantum field theory in quantum information language, and has bearing on the recent discussions on low-energy tests of quantum gravity. We present a first result in this direction: in the quantum dynamics of a massive scalar quantum field coupled to two localised systems, microcausality implies subsystem locality in a physically relevant approximation., Comment: 5 pages + 7 supplementary

We give a conceptual exposition of aspects of gravitational radiation, especially in relation to energy. Our motive for doing so is that the strong analogies with electromagnetic radiation seem not to be widely enough appreciated. In particular, we reply to some recent papers in the philosophy of physics literature that seem to deny that gravitational waves carry energy. Our argument is based on two points: (i) that for both electromagnetism and gravity, in the presence of material sources, radiation is an effective concept, unambiguously emerging only in certain regimes or solutions of the theory; and (ii) similarly, energy conservation is only unambiguous in certain regimes or solutions of general relativity. Crucially, the domain of (i), in which radiation is meaningful, has a significant overlap with the domain of (ii), in which energy conservation is meaningful. Conceptually, the overlap of regimes is no coincidence: the long-standing question about the existence of gravitational waves was settled precisely by finding a consistent way to articulate their energy and momentum., Comment: 16 pages, 6 page appendix

We write explicitly the complete Lorentzian metric of a singularity-free spacetime where a black hole transitions into a white hole located in its same asymptotic region. In particular, the metric interpolates between the black and white horizons. The metric satisfies the Einstein field equations up to the tunneling region. The matter giving rise to the black hole is described by the Oppenheimer-Snyder model, corrected with loop-quantum-cosmology techniques in the quantum region. The interior quantum geometry is fixed by a local Killing symmetry, broken at the horizon transition. At large scale, the geometry is determined by two parameters: the mass of the hole and the duration of the transition process. The latter is a global geometrical parameter. We give the full metric outside the star in a single coordinate patch., Comment: 16 pages, 12 figures

Understanding the quantum aspects of gravity is not only a matter of equations and experiments. Gravity is intimately connected with the structure of space and time, and understanding quantum gravity requires us to find a conceptual structure appropriate to make sense of the quantum aspects of space and time. In the course of the last decades, an extensive discussion on this problem has led to a clear conceptual picture, that provides a coherent conceptual foundation of today's Loop Quantum Gravity. We review this foundation, addressing issues such as the sense in which space and time are emergent, the notion of locality, the role of truncation that enables physical computations on finite graphs, the problem of time, and the characterization of the observable quantities in quantum gravity., Comment: This is a preprint of the chapter: "Philosophical Foundations of Loop Quantum Gravity", to appear in the "Handbook of Quantum Gravity", edited by Cosimo Bambi, Leonardo Modesto and Ilya Shapiro, 2023, Springer, reproduced with permission of Springer. 24 pages

The notions of cause and effect are widely employed in science. I discuss why and how they are rooted into thermodynamics. The entropy gradient (i) explains in which sense interventions affect the future rather than the past, and (ii) underpins the time orientation of the subject of knowledge as a physical system. Via these two distinct paths, it is this gradient, and only this gradient, the source of the time orientation of causation, namely the fact the cause comes before its effects., Comment: 8 pages

We provide a novel methodological approach to the estimate of the change of the Quantum Vacuum electromagnetic energy density in a High critical Temperature superconducting metal bulk sample, when it undergoes the transition in temperature, from the superconducting to the normal phase. The various contributions to the Casimir energy in the two phases are highlighted and compared. While the TM polarization of the vacuum mode allows for a macroscopic description of the superconducting transition, the changes in the TE vacuum mode induced by the superconductive correlations are introduced within a microscopic model, which does not explicitly take into account the anisotropic structure of the material., Comment: 20 pages, 13 figures, to be published in Phys.Rev. B

Field mediated entanglement experiments probe the quantum superposition of macroscopically distinct field configurations. We show that this phenomenon can be described by using a transparent quantum field theoretical formulation of electromagnetism and gravity in the field basis. The strength of such a description is that it explicitly displays the superposition of macroscopically distinct states of the field. In the case of (linearised) quantum general relativity, this formulation exhibits the quantum superposition of geometries giving rise to the effect., Comment: 27 pages, 1 figure; v.2: Added an appendix on the inner product of the states, improved discussion. To appear in Quantum

We point out that conservation of information implies that remnants produced at the end of black hole evaporation should radiate in the low-frequency spectrum. We model this emission and derive properties of the diffuse radiation emitted by an otherwise dark population of such objects. We show that for early universe black holes the frequency and energy density of this radiation, which are in principle measurable, suffice to estimate the remnant density., Comment: 8 pages, 4 figures

We discuss the physical interpretation of the gravity mediated entanglement effect. We show how to read it in terms of quantum reference systems. We pinpoint the single gravitational degree of freedom mediating the entanglement. We clarify why the distinction between longitudinal and transverse degrees of freedom is irrelevant for the interpretation of the results. We discuss the relation between the LOCC theorem and the interpretation of the effect, its different relevance for, respectively, the quantum gravity and quantum information communities, and the reason for the excitement raised by the prospect of detection., Comment: 8 pages

Detecting gravity mediated entanglement can provide evidence that the gravitational field obeys quantum mechanics. We report the result of a simulation of the phenomenon using a photonic platform. The simulation tests the idea of probing the quantum nature of a variable by using it to mediate entanglement, and yields theoretical and experimental insights. We employed three methods to test the presence of entanglement: Bell test, entanglement witness and quantum state tomography. We also simulate the alternative scenario predicted by gravitational collapse models or due to imperfections in the experimental setup and use quantum state tomography to certify the absence of entanglement. Two main lessons arise from the simulation: 1) which--path information must be first encoded and subsequently coherently erased from the gravitational field, 2) performing a Bell test leads to stronger conclusions, certifying the existence of gravity mediated nonlocality.

Relational quantum mechanics (RQM) is an interpretation of quantum mechanics based on the idea that quantum states describe not an absolute property of a system but rather a relationship between systems. In this article, we observe that there is a tension between RQM's naturalistic emphasis on the physicality of information and the inaccessibility of certain sorts of information in current formulations of RQM. Therefore we propose a new postulate for RQM which requires that all of the information possessed by a certain observer is stored in physical variables of that observer and thus accessible by measurement to other observers, so observers can reach intersubjective agreement about quantum events which have occurred in the past. Based on this postulate, we suggest an ontology for RQM which upholds the principle that quantum states are always relational, but which also postulates a set of quantum events which are not strictly relational. We show that the new postulate helps address some existing objections to RQM and finally we address the Frauchiger-Renner experiment in the context of RQM., Comment: Added a reference and some minor edits

The current interest in laboratory detection of entanglement mediated by gravity was sparked by an information--theoretic argument: entanglement mediated by a local field certifies that the field is not classical. Previous derivations of the effect modelled gravity as instantaneous; here we derive it from linearised quantum general relativity while keeping Lorentz invariance explicit, using the path integral formalism. In this framework, entanglement is clearly mediated by a quantum feature of the field. We also point out the possibility of observing retarded entanglement, which cannot be explained by an instantaneous interaction. This is a difficult experiment for gravity, but is plausible for the analogous electromagnetic case., Comment: 6 pages + 4 pages of supplementary, 1 figure. document updated to be the closest to the PRL version published in March 2023

I describe two phenomenological windows on quantum gravity that seem promising to me. I argue that we already have important empirical inputs that should orient research in quantum gravity., Comment: 3 Pages

We shed some light on the reason why the accidental flatness constraint appears in certain limits of the amplitudes of covariant loop quantum gravity. We show why this constraint is harmless, by displaying how analogous accidental constraints appear in transition amplitudes of simple systems, when certain limits are considered., Comment: 6 pages

In recent works, \v{C}aslav Brukner and Jacques Pienaar have raised interesting objections to the relational interpretation of quantum mechanics. We answer these objections in detail and show that, far from questioning the viability of the interpretation, they sharpen and clarify it., Comment: 11 pages, reply to arXiv:2107.00670 and arXiv:2107.03513

The relational interpretation (or RQM, for Relational Quantum Mechanics) solves the measurement problem by considering an ontology of sparse relative events, or "facts". Facts are realized in interactions between any two physical systems and are relative to these systems. RQM's technical core is the realisation that quantum transition amplitudes determine physical probabilities only when their arguments are facts relative to the same system. The relativity of facts can be neglected in the approximation where decoherence hides interference, thus making facts approximately stable., Comment: To appear in the "Oxford Handbook of the History of Interpretation of Quantum Physics". arXiv admin note: text overlap with arXiv:1712.02894

As a neuroscientist and a theoretical physicist, both working on time, we have decided to open a direct dialogue to examine if the apparent discrepancies regarding the nature of time can be composed., Comment: 11 pages

We present an exact solution of the Maxwell-Einstein equations, which describes the exterior of a charged spherical mass collapsing into its own trapping horizon and then bouncing back from an anti-trapping horizon at the same space location of the same asymptotic region. The solution is locally but not globally isometric to the maximally extended Reissner-Nordstr\"{o}m metric and depends on seven parameters. It is regular, and defined everywhere except for a small region, where quantum tunnelling is expected. This region lies outside the mass: the mass-bounce and its near exterior are governed by classical general relativity. We discuss the relevance of this result for the fate of realistic black holes. We comment on possible effects of the classical instabilities and the Hawking radiation., Comment: 12 pages, 13 figures

A recent paper by Mucino, Okon and Sudarsky attempts an assessment of the Relational Interpretation of quantum mechanics. The paper presupposes assumptions that are precisely those questioned in the Relational Interpretation, thus undermining the value of the assessment., Comment: 7 pages

We derive an explicit expression for the transition amplitude from black to white hole horizon at the end of Hawking evaporation using covariant loop quantum gravity., Comment: 10 pages, 12 figures. V2: added references, corrected typos

Confusion and disagreement around the notion of time is due to the fact that we often fail to recognize that we call 'time' a variety of distinct notions, only partially related to one another. Many apparently obvious properties of time are results of different kinds of approximations, idealizations, or special contexts. I illustrate a number of distinct notions of time, their differences and relations; they are all relevant for describing the real world. To understand time, we have to break it apart., Comment: 7 pages, Contribution to the volume 'Time and Science', R. Lestienne and P. Harris eds., World Scientific

According to Bohmian mechanics, we see the particle, not the pilot wave. But to make predictions we need to know the wave. How do we learn about the wave to make predictions, if we only see the particle? I show that the puzzle can be solved, but only thanks to decoherence., Comment: 3 pages

The operational formulations of quantum theory are drastically time oriented. However, to the best of our knowledge, microscopic physics is time-symmetric. We address this tension by showing that the asymmetry of the operational formulations does not reflect a fundamental time-orientation of physics. Instead, it stems from built-in assumptions about the $users$ of the theory. In particular, these formalisms are designed for predicting the future based on information about the past, and the main mathematical objects contain implicit assumption about the past, but not about the future. The main asymmetry in quantum theory is the difference between knowns and unknowns., Comment: 16 pages + references, a few diagrams. This version is to appear in Quantum. Title has changed, it used to be "Quantum information and the arrow of time''

Physical systems may couple to other systems through variables that are not gauge invariant. When we split a gauge system into two subsystems, the gauge-invariant variables of the two subsystems have less information than the gauge invariant variables of the original system; the missing information regards degrees of freedom that express relations between the subsystems. All this shows that gauge invariance is a formalization of the relational nature of physical degrees of freedom. The recent developments on boundary variables and boundary charges are clarified by this observation., Comment: 3 pages. To appear in the proceedings of the conference "One Hundred Years of Gauge Theory, Bad Honnef 2018", S. De Bianchi and C. Kiefer eds

At the end of Hawking evaporation, the horizon of a black hole enters a physical region where quantum gravity cannot be neglected. The physics of this region has not been much explored. We characterise its physics and introduce a technique to study it., Comment: 11 pages, 10 figures

I discuss three aspects of the notion of agency from the standpoint of physics: (i) what makes a physical system an agent; (ii) the reason for agency's time orientation; (iii) the source of the information generated in choosing an action. I observe that agency is the breaking of an approximation under which dynamics appears closed. I distinguish different notions of agency, and observe that the answer to the questions above differ in different cases. I notice a structural similarity between agency and memory, that allows us to model agency, trace its time asymmetry to thermodynamical irreversibility, and identify the source of the information generated by agency in the growth of entropy. Agency is therefore a physical mechanism that transforms low entropy into information. This may be the general mechanism at the source of the whole information on which biology builds., Comment: 7 pages

Facts happen at every interaction, but they are not absolute: they are relative to the systems involved in the interaction. Stable facts are those whose relativity can effectively be ignored. In this work, we describe how stable facts emerge in a world of relative facts and discuss their respective roles in connecting quantum theory and the world. The distinction between relative and stable facts resolves the difficulties pointed out by the no-go theorems of Frauchiger and Renner, Brukner, Bong et. al.. Basing the ontology of the theory on relative facts clarifies the role of decoherence in bringing about the classical world and solves the apparent incompatibility between the `linear evolution' and `projection' postulates., Comment: 6 pages; minor improvements, published version

Table-top tests of quantum gravity (QG) have long been thought to be practically impossible. However, remarkably, due to rapid progress in quantum information science (QIS), such tests may soon be achievable. Here, we uncover an exciting new theoretical link between QG and QIS that also leads to a radical new way of testing QG with QIS experiments. Specifically, we find that only a quantum, not classical, theory of gravity can create non-Gaussianity, a QIS resource that is necessary for universal quantum computation, in the quantum field state of matter. This allows for tests based on QIS in which non-Gaussianity in matter is used as a signature of QG. In comparison to previous studies of testing QG with QIS where entanglement is used to witness QG when all other quantum interactions are excluded, our non-Gaussianity witness cannot be created by direct classical gravity interactions, facilitating tests that are not constrained by the existence of such processes. Our new signature of QG also enables tests that are based on just a single rather than multi-partite quantum system, simplifying previously considered experimental setups. We describe a table-top test of QG that uses our non-Gaussianity signature and which is based on just a single quantum system, a Bose-Einstein condensate (BEC), in a single location. In contrast to proposals based on opto-mechanical setups, BECs have already been manipulated into massive non-classical states, aiding the prospect of testing QG in the near future., Comment: 34 pages

I study the physical nature of traces (or memories). Surprisingly, (i) systems separation with (ii) temperature differences and (iii) long thermalization times, are sufficient conditions to produce macroscopic traces. Traces of the past are ubiquitous because these conditions are largely satisfied in our universe. I quantify these thermodynamical conditions for memory and derive an expression for the maximum amount of information stored in such memories, as a function of the relevant thermodynamical parameters. This mechanism transforms low entropy into available information., Comment: 4 pages, 1 figure

The Einstein equations allow solutions containing closed timelike curves. These have generated much puzzlement and suspicion that they could imply paradoxes. I show that puzzlement and paradoxes disappears if we discuss carefully the physics of the irreversible phenomena in the context of these solutions., Comment: 3 pages, 1 figure

Is reality three-dimensional and becoming real (Presentism), or is reality four-dimensional and becoming illusory (Eternalism)? Both options raise difficulties. I argue that we do not need to be trapped by this dilemma. There is a third possibility: reality has a more complex temporal structure than either of these two naive options. Fundamental becoming is real, but local and unoriented. A notion of present is well defined, but only locally and in the context of approximations., Comment: 2 figures, 6 pages

We study the statistical underpinnings of life. We question some common assumptions about the thermodynamics of life and illustrate how, contrary to widespread belief, even in a closed system entropy growth can accompany an increase in macroscopic order. We consider viewing metabolism in living things as microscopic variables directly driven by the second law of thermodynamics, while viewing the macroscopic variables of structure, complexity and homeostasis as mechanisms that are entropically favored because they open channels for entropy to grow via metabolism. This perspective reverses the conventional relation between structure and metabolism, by emphasizing the role of structure for metabolism rather than the other way around. Structure extends in time, preserving information along generations, particularly in the genetic code, but also in human culture. We also consider why the increase in order/complexity over time is often stepwise and sometimes collapses catastrophically. We point out the relevance of the notions of metastable states and channels between these, which are discovered by random motion of the system and lead it into ever-larger regions of the phase space, driven by thermodynamics. We note that such changes in state can lead to either increase or decrease in order; and sometimes to complete collapse, as in biological extinction. Finally, we comment on the implications of these dynamics for the future of humanity., Comment: 21 pages, 3 figures

We construct and discuss the form of the (effective) spacetime geometry inside a black hole undergoing a quantum transition to a white hole, taking into account the back-reaction of the component of the Hawking radiation falling into the hole.

The kinematical phase space of classical gravitational field is flat (affine) and unbounded. Because of this, field variables may tend to infinity leading to appearance of singularities, which plague Einstein's theory of gravity. The purpose of this article is to study the idea of generalizing the theory of gravity by compactification of the phase space. We investigate the procedure of compactification of the phase space on a minisuperspace gravitational model with two dimensional phase space. In the affine limit, the model reduces to the flat de Sitter cosmology. The phase space is generalized to the spherical case, and the case of loop quantum cosmology is recovered in the cylindrical phase space limit. Analysis of the dynamics reveals that the compactness of the phase space leads to both UV and IR effects. In particular, the phase of re-collapse appears, preventing the universe from expanding to infinite volume. Furthermore, the quantum version of the model is investigated and the quantum constraint is solved. As an example, we analyze the case with the spin quantum number $s=2$, for which we determine transition amplitude between initial and final state of the classical trajectory. The probability of the transition is peaked at $\Lambda=0$., Comment: 13 pages, 5 figures

Inside a black hole, there is no local way to say which side of a sphere is the inside, and which is the outside. One can easily be gulled by this fact into mixing up the sign of the energy. We lead the reader astray with a na\"ive treatment of the energy of a null shell in black hole spacetimes. We then resolve the confusion, showing that global, rather than local, considerations offer good guidance., Comment: Essay written for the Gravity Research Foundation 2019 Awards for Essays on Gravitation