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I study several aspects of the path(st) integral we formulated in previous papers on energetic causal sets with Cortes and others. The focus here is on quantum field theories, including the standard model of particle physics. I show that the the theory can be extended to a quantum field theory, cut off in momentum space. Fields of spin 0, 1/2 and 1 may be naturally included, which allows us to formulate the standard model in this framework. The theory is at first formulated in momentum space. Under certain conditions, spacetime can emerge in a semiclassical limit. The theory comes with a $uv$ cutoff in momentum space, $\mu$, hence that is also a scale for lorentz invariance to break down. Traditionally, m is taken to be. a Planck energy, but we explore as a possibility making m smaller., Comment: 13 pages, 4 Figures

The Universe contains everything that exists, including life. And all that exists, including life, obeys universal physical laws. Do those laws then give adequate foundations for a complete explanation of biological phenomena? We discuss whether and how cosmology and physics must be modified to be able to address certain questions which arise at their intersection with biology. We show that a universe that contains life, in the form it has on Earth, is in a certain sense radically non-ergodic, in that the vast majority of possible organisms will never be realized. We argue from this that complete explanations in cosmology require a mixture of reductionist and functional explanations., Comment: 28 pages. See also companion paper arXiv:2204.09378

This paper describes a continuation of the program of causal views, in which the world consists of nothing but a vast number of partial views of its past. Each view is associated to an event, and is a representation of the immediate causal past of that event. These consists mainly of processes that transfer energy, momentum and other charges to it from its past events. There is fundamentally no space or spacetime, just a large number of events, which are the causes of events to come. This is a development of energetic causal set theories, developed with Marina Cortes. Momentum and energy are fundamental, and are conserved under their transformation from present events to future events. As a result Minkowski spacetime emerges, in a way that preserves causal relations. The locality of events as constructed in the emergent spacetime is a consequence of the conservation of energy-momentum fundamentally. In this paper we propose that the views of events can be represented in terms of degrees of freedom on punctured two surfaces-each puncture corresponding to an immediate past event. This opens up to the use of mathematical tools from twistor theory and the nascent area of celestial spheres. We show that This makes possible versions of the theory that are relativistically invariant., Comment: 27 pages, no figures

We present an approach to cosmology in which the Universe learns its own physical laws. It does so by exploring a landscape of possible laws, which we express as a certain class of matrix models. We discover maps that put each of these matrix models in correspondence with both a gauge/gravity theory and a mathematical model of a learning machine, such as a deep recurrent, cyclic neural network. This establishes a correspondence between each solution of the physical theory and a run of a neural network. This correspondence is not an equivalence, partly because gauge theories emerge from $N \rightarrow \infty $ limits of the matrix models, whereas the same limits of the neural networks used here are not well-defined. We discuss in detail what it means to say that learning takes place in autodidactic systems, where there is no supervision. We propose that if the neural network model can be said to learn without supervision, the same can be said for the corresponding physical theory. We consider other protocols for autodidactic physical systems, such as optimization of graph variety, subset-replication using self-attention and look-ahead, geometrogenesis guided by reinforcement learning, structural learning using renormalization group techniques, and extensions. These protocols together provide a number of directions in which to explore the origin of physical laws based on putting machine learning architectures in correspondence with physical theories., Comment: 79 pages, 11 figures

We provide a new extension of general relativity (GR) which has the remarkable property of being more constrained than GR plus a cosmological constant, having one less free parameter. This is implemented by allowing the cosmological constant to have a consistent space-time variation, through coding its dynamics in the torsion tensor. We demonstrate this mechanism by adding a `quasi-topological' term to the Einstein action, which naturally realizes a dynamical torsion with an automatic satisfaction of the Bianchi identities. Moreover, variation of the action with respect to this dynamical $\Lambda$ fixes it in terms of other variables, thus providing a scenario with less freedom than general relativity with a cosmological constant. Once matter is introduced, at least in the homogeneous and isotropic reduction, $\Lambda$ is uniquely determined by the field content of the model. We make an explicit construction using the Palatini formulation of GR and describe the striking properties of this new theory. We also highlight some possible extensions to the theory. A companion paper [1] explores the Friedmann--Robertson--Walker reduction for cosmology, and future work will study Solar System tests of the theory., Comment: Companion paper to arXiv:1905.10382. Minor updates to match published version

Inserting a varying Lambda in Einstein's field equations can be made consistent with the Bianchi identities by allowing for torsion, without the need to add scalar field degrees of freedom. In the minimal such theory, Lambda is totally free and undetermined by the field equations in the absence of matter. Inclusion of matter ties Lambda algebraically to it, at least when homogeneity and isotropy are assumed, i.e. when there is no Weyl curvature. We show that Lambda is proportional to the matter density, with a proportionality constant depending on the equation of state. Unfortunately, the proportionality constant becomes infinite for pure radiation, ruling out the minimal theory prima facie despite of its novel internal consistency. It is possible to generalize the theory still without the addition of kinetic terms, leading to a new algebraically-enforced proportionality between Lambda and the matter density. Lambda and radiation may now coexist in a form consistent with Big Bang Nucleosynthesis, though this places strict constraints on the single free parameter of the theory, $\theta$. In the matter epoch Lambda behaves just like a dark matter component. Its density is proportional to the baryonic and/or dark matter, and its presence and gravitational effects would need to be included in accounting for the necessary dark matter in our Universe. This is a companion paper to Ref. [1] where the underlying gravitational theory is developed in detail., Comment: Companion paper to arXiv:1905.10380. Minor updates to match published version

We describe a new form of retrocausality, which is found in the behaviour of a class of causal set theories, called energetic causal sets (ECS). These are discrete sets of events, connected by causal relations. They have three orders: (1) a birth order, which is the order in which events are generated; this is a total order which is the true causal order, (2) a dynamical partial order, which prescribes the flows of energy and momentum amongst events, (3) an emergent causal order, which is defined by the geometry of an emergent Minkowski spacetime, in which the events of the causal sets are embedded. However, the embedding of the events in the emergent Minkowski spacetime may preserve neither the true causal order in (1), nor correspond completely with the microscopic partial order in (2). We call this disordered causality, and we here demonstrate its occurrence in specific ECS models. This is the second in a series of papers centered around the question: Should we accept violations of causality as a lesser price to pay in order to keep realist formulations of quantum theory? We begin to address this in the first paper [1] and continue here by giving an explicit example of an ECS model in the classical regime, in which causality is disordered., Comment: Accepted to Physical Review D

Of all basic principles of classical physics, realism should arguably be the last to be given up when seeking a better interpretation of quantum mechanics. We examine the de Broglie-Bohm pilot wave theory as a well developed example of a realistic theory. We present three challenges to a naive reading of pilot-wave theory, each based on a system of several entangled particles. With the help of a coarse graining of pilot wave theory into a discrete system, we show how these challenges can be answered. However this comes with a cost. In the description of individual systems, particles appear to scatter off empty branches of the wave function as if they were particles, and conversely travel through particles as if they were waves. More generally, the "particles" of pilot wave theory are led by the guidance equation to move in ways no classical particle would, involving apparent violations of the principles of inertia and momentum conservation.We next argue that the aforementioned cost can be avoided within a retrocausal model. In the proposed version of the pilot wave theory, the particle is guided by a combination of advanced and retarded waves. The resulting account for quantum physics seems to have greater heuristic power, it demands less damage to intuition, and moreover provides some general hints regarding spacetime and causality. This is the first of two papers. In the second [1] we show that, in the context of an explicit model, retrocausality, with respect to an effective, emergent spacetime metric, can coexist with a strict irreversibility of causal processes., Comment: Minorly revised version. Accepted to Phys. Rev. D

In this paper we propose that cosmological time is a quantum observable that does not commute with other quantum operators essential for the definition of cosmological states, notably the cosmological constant. This is inspired by properties of a measure of time---the Chern-Simons time---and the fact that in some theories it appears as a conjugate to the cosmological constant, with the two promoted to non-commuting quantum operators. Thus, the Universe may be "delocalised" in time: it does not {\it know} the time, a property which opens up new cosmological scenarios, as well as invalidating several paradoxes, such as the timelike tower of turtles associated with an omnipresent time line. Alternatively, a Universe with a sharply defined clock time must have an indeterminate cosmological constant. The challenge then is to explain how islands of localized time may emerge, and give rise to localized histories. In some scenarios this is achieved by backward transitions in quantum time, cycling the Universe in something akin to a time machine cycle, with classical flow and quantum ebbing. The emergence on matter in a sea of Lambda probably provides the ballast behind classical behaviour.

We present an extension of general relativity in which the cosmological constant becomes dynamical and turns out to be conjugate to the Chern-Simons invariant of the Ashtekar connection on a spatial slicing. The latter has been proposed in \cite{Chopin-Lee} as a time variable for quantum gravity: the Chern-Simons time. In the quantum theory the inverse cosmological constant and Chern-Simons time will then become conjugate operators. The "Kodama state" gets a new interpretation as a family of transition functions. These results imply an uncertainty relation between $\Lambda$ and Chern-Simons time; the consequences of which will be discussed elsewhere., Comment: 15 pages. no figures, minor improvments

Because of the non-locality of quantum entanglement, realist approaches to completing quantum mechanics have implications for our conception of space. Quantum gravity also is expected to predict phenomena in which the locality of classical spacetime is modified or disordered. It is then possible that the right quantum theory of gravity will also be a completion of quantum mechanics in which the foundational puzzles in both are addressed together. I review here the results of a program, developed with Roberto Mangabeira Unger, Marina Cortes and other collaborators, which aims to do just that. The results so far include energetic causal set models, time asymmetric extensions of general relativity and relational hidden variables theories, including real ensemble approaches to quantum mechanics. These models share two assumptions: that physics is relational and that time and causality are fundamental., Comment: Invited contribution to a collection of essays on {\it Beyond spacetime}, edited by Nick Huggett, Keizo Matsubara and Christian Wuthrich. Latex 34 pages

We explain flat rotation curves and the baryonic Tully-Fisher relation by a combination of three hypotheses. The first is a formulation of the equivalence principle for gravitationally bound quantum $N$ body systems, while the second is a second order phase transition hypothesized to arise from a competition between the effects of Unruh and deSitter radiation experienced by a static observer in a galaxy. The third is a light dark matter particle, coupled to a dark photon. The phase transition is triggered in a ring where the Unruh temperature of a static observer falls below the deSitter temperature, thus explaining the apparent coincidence that Milgrom's $a_0 \approx a_\Lambda = c^2 \sqrt{\frac{\Lambda}{3}}$ This phase transition drives the dark matter particles to a regime characterized by a broken $U(1)$ invariance and an approximate scale invariance. In this regime, the dark matter condenses to a super-current characterized by a differentially rotating ring with a flat rotation curve, coupled to a dark magnetic field. The baryonic Tully Fisher relation is a direct consequence of the approximate scale invariance., Comment: 10 pages LaTeX

A proposal is made for a fundamental theory, in which the history of the universe is constituted of diverse views of itself. Views are attributes of events, and the theory's only be-ables; they comprise information about energy and momentum transferred to an event from its causal past. A dynamics is proposed for a universe constituted of views of events, which combines the energetic causal set dynamics with a potential energy based on a measure of the distinctiveness of the views, called the variety. As in the real ensemble formulation of quantum mechanics, quantum pure states are associated to ensembles of similar events; the quantum potential of Bohm then arises from the variety., Comment: Latex 15 pages, no figues, small improvements

Some reflections are presented on the state of the search for a quantum theory of gravity. I discuss diverse regimes of possible quantum gravitational phenomenon, some well explored, some novel., Comment: Latex, 21 pages. For Foundations of Mathematics and Physics : an IJGMMP special issue

We propose that there is a regime of quantum gravity phenomena, for the case that the cosmological constant is small and positive, which concerns phenomena at temperatures below the deSitter temperature, or length scales larger than the horizon. We observe that the standard form of the equivalence principle does not apply in this regime; we consider instead that a weakened form of the equivalence principle might hold in which the ratio of gravitational to inertial mass is a function of environmental and global parameters. We consider possible principles to determine that function. These lead to behaviour that, in the limit of hbar to zero and the speed of light is taken to infinity, reproduces the modifications of Newtonian dynamics first proposed by Milgrom. Thus MOND is elucidated as coding the physics of a novel regime of quantum gravity phenomena. We propose also an effective description of this regime in terms of a bi-metric theory, valid in the approximation where the metric is static. This predicts a new effect, which modifies gravity for radial motions., Comment: LaTex 22 pages, one figure. Thee revision contains many small improvements

In 1979 Penrose hypothesized that the arrows of time are explained by the hypothesis that the fundamental laws are time irreversible. That is, our reversible laws, such as the standard model and general relativity are effective, and emerge from an underlying fundamental theory which is time irreversible. In Cort\^{e}s and Smolin (2014a, 2014b, 2016) we put forward a research program aiming at realizing just this. The aim is to find a fundamental description of physics above the planck scale, based on irreversible laws, from which will emerge the apparently reversible dynamics we observe on intermediate scales. Here we continue that program and note that a class of discrete dynamical systems are known to exhibit this very property: they have an underlying discrete irreversible evolution, but in the long term exhibit the properties of a time reversible system, in the form of limit cycles. We connect this to our original model proposal in Cort\^{e}s and Smolin (2014a), and show that the behaviours obtained there can be explained in terms of the same phenomenon: the attraction of the system to a basin of limit cycles, where the dynamics appears to be time reversible. Further than that, we show that our original models exhibit the very same feature: the emergence of quasi-particle excitations obtained in the earlier work in the space-time description is an expression of the system's convergence to limit cycles when seen in the causal set description., Comment: 22 pages, 8 figures

Four principles are proposed to underlie the quantum theory of gravity. We show that these suffice to recover the Einstein equations. We also suggest that MOND results from a modification of the classical equivalence principle, due to quantum gravity effects., Comment: 26 pages, one figure and caption taken from McGaugh, Lelli, Schombert, arXiv:1609.05917v1

It is shown that a relation between entropy and minimal area holds in loop quantum gravity, reminiscent of the Ryu-Takayanagi relation., Comment: 21 pages, many figures

We develop the model proposed by Cort\^es, Gomes & Smolin, to predict cosmological signatures of time-asymmetric extensions of general relativity they proposed recently. Within this class of models the equation of motion of chiral fermions is modified by a torsion term. This term leads to a dispersion law for neutrinos that associates a new time-varying energy with each particle. We find a new neutrino contribution to the Friedmann equation resulting from the torsion term in the Ashtekar connection. In this note we explore the phenomenology of this term and observational consequences for cosmological evolution. We show that constraints on the critical energy density will ordinarily render this term unobservably small, a maximum of order $10^{-25}$ of the neutrino energy density today. However, if the time-asymmetric dark energy is tuned to cancel the cosmological constant, the torsion effect may be a dark matter candidate., Comment: v2 added explanations and definitions; 11 pages

There is a myth that Einstein's discovery of general relativity was due to his following beautiful mathematics to discover new insights about nature. I argue that this is an incorrect reading of the history and that what Einstein did was to follow physical insights which arose from asking that the story we tell of how nature works be coherent., Comment: This is an expanded version of a text that was originally prepared for, and its Polish translation appeared in, the September 2015 issue of Niezbednik inteligenta. An extract also appears in the Fall/Winter 2015/2016 edition of Inside the Perimeter. Latex 14 pages

We show that the simplicity constraints, which define the dynamics of spin foam models, imply, and are implied by, the first law of thermodynamics, when the latter is applied to causal diamonds in the quantum spacetime. This result reveals an intimate connection between the holographic nature of gravity, as reflected by the Bekenstein entropy, and the fact that general relativity and other gravitational theories can be understood as constrained topological field theories. To state and derive this correspondence we describe causal diamonds in the causal structure of spin foam histories and generalize arguments given for the near horizon region of black holes by Frodden, Gosh and Perez and Bianchi. This allows us to apply a recent argument of Jacobson to show that if a spin foam history has a semiclassical limit described in terms of a smooth metric geometry, that geometry satisfies the Einstein equations. These results suggest also a proposal for a quantum equivalence principle., Comment: Latex 39 pages, 6 figures

In this paper, we show that the Hamiltonian approach to loop quantum gravity has a fermion doubling problem. To obtain this result, we couple loop quantum gravity to a free massless scalar and a chiral fermion field, gauge fixing the many fingered time gauge invariance by interpreting the scalar field as a physical clock. We expand around a quantum gravity state based on a regular lattice and consider the limit where the bare cosmological constant is large but the fermonic excitations have energies low in Planck units. We then make the case for identifying the energy spectrum in this approximation with that of a model of lattice fermion theory which is known to double.

A modification of general relativity is presented in which Newton's constant and the cosmological constant become a conjugate pair of dynamical variables., Comment: 18 pages, For a related talk see http://pirsa.org/15060033/

Of course not, but if one believes that information cannot be destroyed in a theory of quantum gravity, then we run into apparent contradictions with quantum theory when we consider evaporating black holes. Namely that the no-cloning theorem or the principle of entanglement monogamy is violated. Here, we show that neither violation need hold, since, in arguing that black holes lead to cloning or non-monogamy, one needs to assume a tensor product structure between two points in space-time that could instead be viewed as causally connected. In the latter case, one is violating the semi-classical causal structure of space, which is a strictly weaker implication than cloning or non-monogamy. We show that the lack of monogamy that can emerge in evaporating space times is one that is allowed in quantum mechanics, and is very naturally related to a lack of monogamy of correlations of outputs of measurements performed at subsequent instances of time of a single system. A particular example of this is the Horowitz-Maldacena proposal, and we argue that it needn't lead to cloning or violations of entanglement monogamy. For measurements on systems which appear to be leaving a black hole, we introduce the notion of the temporal product, and argue that it is just as natural a choice for measurements as the tensor product. For black holes, the tensor and temporal products have the same measurement statistics, but result in different type of non-monogamy of correlations, with the former being forbidden in quantum theory while the latter is allowed. In the case of the AMPS firewall experiment we find that the entanglement structure is modified, and one must have entanglement between the infalling Hawking partners and early time outgoing Hawking radiation which surprisingly tame violation of entanglement monogamy., Comment: 20 pages, comments welcome, grants added to acknowledgements

Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem. The quantum state of a microscopic system is defined to correspond to an ensemble of subsystems of the universe with identical constituents and similar preparations and environments. A new kind of interaction is posited amongst such similar subsystems which acts to increase their distinctiveness, by extremizing the variety. In the limit of large numbers of similar subsystems this interaction is shown to give rise to Bohm's quantum potential. As a result the probability distribution for the ensemble is governed by the Schroedinger equation. The measurement problem is naturally and simply solved. Microscopic systems appear statistical because they are members of large ensembles of similar systems which interact non-locally. Macroscopic systems are unique, and are not members of any ensembles of similar systems. Consequently their collective coordinates may evolve deterministically. This proposal could be tested by constructing quantum devices from entangled states of a modest number of quits which, by its combinatorial complexity, can be expected to have no natural copies., Comment: latex, no figures, 24 pages. For a talk based on this paper, see http://pirsa.org/15050087/

We describe a class of modified gravity theories that deform general relativity in a way that breaks time reversal invariance and, very mildly, locality. The algebra of constraints, local physical degrees of freedom, and their linearized equations of motion, are unchanged, yet observable effects may be present on cosmological scales, which have implications for the early history of the universe. This is achieved in the Hamiltonian framework, in a way that requires the constant mean curvature gauge conditions and is, hence, inspired by shape dynamics., Comment: 19 pages, LaTex, no figures

Dualities are often supposed to be foundational, but they may come into conflict with background independence, because a hidden fixed structures is needed to define the duality transformation. This conflict can be eliminated by extending a duality to a triality. This renders that fixed structure dynamical, while unifying it with the dual variables. To illustrate this, we study matrix models with a cubic action, and show how breaking its natural triality symmetry by imposing different compactifications yields particle mechanics, string theory and Chern-Simons theory. These result from compactifying, respectively, one, two and three dimensions. This may explain the origin of Born's duality between position and momenta operators in quantum theory, as well as some of the the dualities of string theory., Comment: Latex, 12 pages

Shape dynamics is a reformulation of general relativity, locally equivalent to Einstein's theory, in which the refoliation invariance of the older theory is traded for local scale invariance. Shape dynamics is here derived in a formulation related to the Ashtekar variables by beginning with a modification of the Plebanski action. The constraints of shape dynamics and their algebra are reproduced in terms of these new variables., Comment: 12 pages, no figures, mistake fixed, other small changes

Energetic causal sets are causal sets endowed by a flow of energy-momentum between causally related events. These incorporate a novel mechanism for the emergence of space-time from causal relations. Here we construct a spin foam model which is also an energetic causal set model. This model is closely related to the model introduced in parallel by Wolfgang Wieland in arXiv:1407.0025, and this construction makes use of results used there. What makes a spin foam model also an energetic causal set is Wieland's identification of new momenta, conserved at events (or four-simplices), whose norms are not mass, but the volume of tetrahedra. This realizes the torsion constraints, which are missing in previous spin foam models, and are needed to relate the connection dynamics to those of the metric, as in general relativity. This identification makes it possible to apply the new mechanism for the emergence of space-time to a spin foam model., Comment: 16 pages, 4 figures. v2 typo corrected, references added

This paper addresses the question of whether Witten's proof of positive ADM energy for classical general relativity can be extended to give a proof of positive energy for a non-perturbative quantization of general relativity. To address this question, a set of conditions is shown to be sufficient for showing the positivity of a Hamiltonian operator corresponding to the ADM energy. One of these conditions is a particular factor ordering for the constraints of general relativity, in a representation where the states are functionals of the Ashtekar connection, and the auxiliary, Witten spinor. These developments are partly based on results derived with Artem Starodubtsev (unpublished notes, 2004)., Comment: 14 pages, no figures

We propose an approach to quantum theory based on the energetic causal sets, introduced in Cort\^{e}s and Smolin (2013). Fundamental processes are causal sets whose events carry momentum and energy, which are transmitted along causal links and conserved at each event. Energetic causal set models differ from other spacetime-free causal set approaches, e.g. Ref. [2] proposed causal sets based on quantum information processing systems, and Ref. [3] proposed causal sets constructed out of standard model particles. Fundamentally there are amplitudes for causal processes in energetic causal sets, but no space-time. An embedding of the causal processes in an emergent space-time arises only at the semiclassical level. Hence, fundamentally there are no commutation relations, no uncertainty principle and, indeed, no $\hbar$. All that remains of quantum theory is the relationship between the absolute value squared of complex amplitudes and probabilities. Consequently, we find that neither locality, nor non locality, are primary concepts, only causality exists at the fundamental level., Comment: 9 pages, no figures. Article companion to arXiv:1307.6167

We describe a new class of models of quantum space-time based on energetic causal sets and show that under natural conditions space-time emerges from them. These are causal sets whose causal links are labelled by energy and momentum and conservation laws are applied at events. The models are motivated by principles we propose govern microscopic physics which posit a fundamental irreversibility of time. One consequence is that each event in the history of the universe has a distinct causal relationship to the rest; this requires a novel form of dynamics which an be applied to uniquely distinctive events. We hence introduce a new kind of deterministic dynamics for a causal set in which new events are generated from pairs of progenitor events by a rule which is based on extremizing the distinctions between causal past sets of events. This dynamics is asymmetric in time, but we find evidence from numerical simulations of a 1+1 dimensional model, that an effective dynamics emerges which restores approximate time reversal symmetry. Energetic causal set models differ from other spacetime-free causal set approaches, e.g. Ref. [1] proposed causal sets based on quantum information processing systems, and Ref. [2] proposed causal sets constructed out of standard model particles. Finally we also present a natural twistorial representation of energetic causal sets., Comment: 26 pages, 5 figures

We provide a bottom-up argument to derive some known results from holographic renormalization using the classical bulk-bulk equivalence of General Relativity and Shape Dynamics, a theory with spatial conformal (Weyl) invariance. The purpose of this paper is twofold: 1) to advertise the simple classical mechanism: trading of gauge symmetries, that underlies the bulk-bulk equivalence of General Relativity and Shape Dynamics to readers interested in dualities of the type of AdS/CFT; and 2) to highlight that this mechanism can be used to explain certain results of holographic renormalization, providing an alternative to the AdS/CFT conjecture for these cases. To make contact with usual the semiclassical AdS/CFT correspondence, we provide, in addition, a heuristic argument that makes it plausible why the classical equivalence between General Relativity and Shape Dynamics turns into a duality between radial evolution in gravity and the renormalization group flow of a conformal field theory. We believe that Shape Dynamics provides a new perspective on gravity by giving conformal structure a primary role within the theory. It is hoped that this work provides the first steps towards understanding what this new perspective may be able to teach us about holographic dualities., Comment: 27 pages, no figures. Version to appear in EPJC. Title changed. Minor corrections to text

We present a new unification of the electro-weak and gravitational interactions based on the joining the weak SU(2) gauge fields with the left handed part of the space-time connection, into a single gauge field valued in the complexification of the local Lorentz group. Hence, the weak interactions emerge as the right handed chiral half of the space-time connection, which explains the chirality of the weak interaction. This is possible, because, as shown by Plebanski, Ashtekar, and others, the other chiral half of the space-time connection is enough to code the dynamics of the gravitational degrees of freedom. This unification is achieved within an extension of the Plebanski action previously proposed by one of us. The theory has two phases. A parity symmetric phase yields, as shown by Speziale, a bi-metric theory with eight degrees of freedom: the massless graviton, a massive spin two field and a scalar ghost. Because of the latter this phase is unstable. Parity is broken in a stable phase where the eight degrees of freedom arrange themselves as the massless graviton coupled to an SU(2) triplet of chirally coupled Yang-Mills fields. It is also shown that under this breaking a Dirac fermion expresses itself as a chiral neutrino paired with a scalar field with the quantum numbers of the Higgs., Comment: 21 pages

Physical theories are developed to describe phenomena in particular regimes, and generally are valid only within a limited range of scales. For example, general relativity provides an effective description of the Universe at large length scales, and has been tested from the cosmic scale down to distances as small as 10 meters. In contrast, quantum theory provides an effective description of physics at small length scales. Direct tests of quantum theory have been performed at the smallest probeable scales at the Large Hadron Collider, ${\sim} 10^{-20}$ meters, up to that of hundreds of kilometers. Yet, such tests fall short of the scales required to investigate potentially significant physics that arises at the intersection of quantum and relativistic regimes. We propose to push direct tests of quantum theory to larger and larger length scales, approaching that of the radius of curvature of spacetime, where we begin to probe the interaction between gravity and quantum phenomena. In particular, we review a wide variety of potential tests of fundamental physics that are conceivable with artificial satellites in Earth orbit and elsewhere in the solar system, and attempt to sketch the magnitudes of potentially observable effects. The tests have the potential to determine the applicability of quantum theory at larger length scales, eliminate various alternative physical theories, and place bounds on phenomenological models motivated by ideas about spacetime microstructure from quantum gravity. From a more pragmatic perspective, as quantum communication technologies such as quantum key distribution advance into Space towards large distances, some of the fundamental physical effects discussed here may need to be taken into account to make such schemes viable., Comment: 34 pages, 9 figures. Journal version, modified to respond to numerous suggestions

Building on recent significant results of Frodden, Ghosh and Perez (FGP) and Bianchi, I present a quantum version of Jacobson's argument that the Einstein equations emerge as the equation of state of a quantum gravitational system. I give three criteria a quantum theory of gravity must satisfy if it is to allow Jacobson's argument to be run. I then show that the results of FGP and Bianchi provide evidence that loop quantum gravity satisfies two of these criteria and argue that the third should also be satisfied in loop quantum gravity. I also show that the energy defined by FGP is the canonical energy associated with the boundary term of the Holst action., Comment: 9 pages, Latex, 3 figures

A new interpretation of quantum mechanics is proposed according to which precedence, freedom and novelty play central roles. This is based on a modification of the postulates for quantum theory given by Masanes and Muller. We argue that quantum mechanics is uniquely characterized as the probabilistic theory in which individual systems have maximal freedom in their responses to experiment, given reasonable axioms for the behavior of probabilities in a physical theory. Thus, to the extent that quantum systems are free, in the sense of Conway and Kochen, there is a sense in which they are maximally free. We also propose that laws of quantum evolution arise from a principle of precedence, according to which the outcome of a measurement on a quantum system is selected randomly from the ensemble of outcomes of previous instances of the same measurement on the same quantum system. This implies that dynamical laws for quantum systems can evolve as the universe evolves, because new precedents are generated by the formation of new entangled states., Comment: 12 pages, latex, no figures

I discuss the historical roots of the landscape problem and propose criteria for its successful resolution. This provides a perspective to evaluate the possibility to solve it in several of the speculative cosmological scenarios under study including eternal inflation, cosmological natural selection and cyclic cosmologies., Comment: Invited contribution for a special issue of Foundations of Physics titled: Forty Years Of String Theory: Reflecting On the Foundations. 31 pages, no figures

We argue that the recently proposed principle of relative locality offers a new way to resolve the black hole information puzzle., Comment: 11 pages, one figure

A new ensemble interpretation of quantum mechanics is proposed according to which the ensemble associated to a quantum state really exists: it is the ensemble of all the systems in the same quantum state in the universe. Individual systems within the ensemble have microscopic states, described by beables. The probabilities of quantum theory turn out to be just ordinary relative frequencies probabilities in these ensembles. Laws for the evolution of the beables of individual systems are given such that their ensemble relative frequencies evolve in a way that reproduces the predictions of quantum mechanics. These laws are highly non-local and involve a new kind of interaction between the members of an ensemble that define a quantum state. These include a stochastic process by which individual systems copy the beables of other systems in the ensembles of which they are a member. The probabilities for these copy processes do not depend on where the systems are in space, but do depend on the distribution of beables in the ensemble. Macroscopic systems then are distinguished by being large and complex enough that they have no copies in the universe. They then cannot evolve by the copy law, and hence do not evolve stochastically according to quantum dynamics. This implies novel departures from quantum mechanics for systems in quantum states that can be expected to have few copies in the universe. At the same time, we are able to argue that the centre of masses of large macroscopic systems do satisfy Newton's laws., Comment: 14 pages, no figures

We study the application of the recently proposed framework of relative locality to the problem of energy dependent delays of arrival times of photons that are produced simultaneously in distant events such as gamma ray bursts. Within this framework, possible modifications of special relativity are coded in the geometry of momentum space. The metric of momentum space codes modifications in the energy momentum relation, while the connection on momentum space describes possible non-linear modifications in the laws of conservation of energy and momentum. In this paper, we study effects of first order in the inverse Planck scale, which are coded in the torsion and non-metricity of momentum space. We find that time delays of order Distance * Energies/m_p are coded in the non-metricity of momentum space. Current experimental bounds on such time delays hence bound the components of this tensor of order 1/m_p. We also find a new effect, whereby photons from distant sources can appear to arrive from angles slightly off the direction to the sources, which we call gravitational lensing. This is found to be coded into the torsion of momentum space., Comment: 21 pages, 13 figures

We propose a deepening of the relativity principle according to which the invariant arena for non-quantum physics is a phase space rather than spacetime. Descriptions of particles propagating and interacting in spacetimes are constructed by observers, but different observers, separated from each other by translations, construct different spacetime projections from the invariant phase space. Nonetheless, all observers agree that interactions are local in the spacetime coordinates constructed by observers local to them. This framework, in which absolute locality is replaced by relative locality, results from deforming momentum space, just as the passage from absolute to relative simultaneity results from deforming the linear addition of velocities. Different aspects of momentum space geometry, such as its curvature, torsion and non-metricity, are reflected in different kinds of deformations of the energy-momentum conservation laws. These are in principle all measurable by appropriate experiments. We also discuss a natural set of physical hypotheses which singles out the cases of momentum space with a metric compatible connection and constant curvature., Comment: 12 pages, 3 figures; in version 2 one reference added and some minor modifications in sects. II and III made

We study the interplay of non-locality and Lorentz invariance in a version of deformed or doubly special relativity (DSR) based on kappa-Minkowski spacetime. We find that Einstein's procedure for an inertial observer to assign coordinates to distant events becomes ambiguous for sufficiently distant events. The accuracy to which two clocks can be synchronized turns out to depend on the distance between them. These are consequences of the non-commutativity of space and time coordinates or a dependence of the speed of light on energy in relativistic theories. These ambiguities grow with distance and only become relevant for real observations for the description of cosmologically distant events. They do not afflict the interpretation of the detection of gamma rays in stationary or moving frames near the detector. Consequently there is no disagreement between the principles of DSR and the observation that interactions in nature are local down to currently observable scales., Comment: 21 pages, Latex, no figures, Section 4 argument improved strengthening limit on synchronization; recent critique addressed

We consider a diffeomorphism invariant theory of a gauge field valued in a Lie algebra that breaks spontaneously to the direct sum of the spacetime Lorentz algebra, a Yang-Mills algebra, and their complement. Beginning with a fully gauge invariant action -- an extension of the Plebanski action for general relativity -- we recover the action for gravity, Yang-Mills, and Higgs fields. The low-energy coupling constants, obtained after symmetry breaking, are all functions of the single parameter present in the initial action and the vacuum expectation value of the Higgs., Comment: 12 pages, no figures. v2 minor corrections

In deformed or doubly special relativity (DSR) the action of the lorentz group on momentum eigenstates is deformed to preserve a maximal momenta or minimal length, supposed equal to the Planck length. The classical and quantum dynamics of a particle propagating in kappa-Minkowski spacetime is discussed in order to examine an apparent paradox of locality which arises in the classical dynamics. This is due to the fact that the Lorentz transformations of spacetime positions of particles depend on their energies, so whether or not a local event, defined by the coincidence of two or more particles, takes place appears to depend on the frame of reference of the observer. Here it is proposed that the paradox arises only in the classical picture, and may be resolved when the quantum dynamics is taken into account. If so, the apparent paradoxes arise because it is inconsistent to study physics in which Planck's constant is zero but the Planck length is non-vanishing. This may be relevant for phenomenology such as observations by FERMI, because at leading order there is both a direct and a stochastic dependence of arrival time on energy, due to an additional spreading of wavepackets., Comment: LaTeX, 28 pages, no figures, substantially revised

We apply a recent argument of Verlinde to loop quantum gravity, to conclude that Newton's law of gravity emerges in an appropriate limit and setting. This is possible because the relationship between area and entropy is realized in loop quantum gravity when boundaries are imposed on a quantum spacetime., Comment: 16 pages, small improvements to introduction and conclusion

If the history of science has taught us anything, it's that persistence and creativity makes the once impossible possible. It has long been thought experimental tests of quantum gravity are impossible. But during the last decade, several different approaches have been proposed that allow us to test, if not the fundamental theory of quantum gravity itself, so at least characteristic features this theory can have. For the first time we can probe experimentally domains in which quantum physics and gravity cohabit, in spite of our failure so far to make a convincing marriage of them on a theoretical level., Comment: space limited to 3 pages. To appear in Physics in Canada

We study the field equations of the Plebanski action for general relativity when both the cosmological constant and an Immirzi parameter are present. We show that the Lagrange multiplier, which usually gets identified with the Weyl curvature, now acquires a trace part. Some consequences of this for a class of modified gravity theories recently proposed in the literature are briefly discussed., Comment: 14 pages. v2: factor 2 corrected, updated references

We study the power of closed timelike curves (CTCs) and other nonlinear extensions of quantum mechanics for distinguishing nonorthogonal states and speeding up hard computations. If a CTC-assisted computer is presented with a labeled mixture of states to be distinguished--the most natural formulation--we show that the CTC is of no use. The apparent contradiction with recent claims that CTC-assisted computers can perfectly distinguish nonorthogonal states is resolved by noting that CTC-assisted evolution is nonlinear, so the output of such a computer on a mixture of inputs is not a convex combination of its output on the mixture's pure components. Similarly, it is not clear that CTC assistance or nonlinear evolution help solve hard problems if computation is defined as we recommend, as correctly evaluating a function on a labeled mixture of orthogonal inputs., Comment: 4 pages, 3 figures. Final version. Added several references, updated discussion and introduction. Figure 1(b) very much enhanced

We discuss the prospects for bounding and perhaps even measuring quantum gravity effects on the dispersion of light using the highest energy photons produced in gamma ray bursts measured by the Fermi telescope. These prospects are brigher than might have been expected as in the first 10 months of operation Fermi has reported so far eight events with photons over 100 MeV seen by its Large Area Telescope (LAT). We review features of these events which may bear on Planck scale phenomenology and we discuss the possible implications for the alternative scenarios for in-vacua dispersion coming from breaking or deforming of Poincare invariance. Among these are semi-conservative bounds, which rely on some relatively weak assumptions about the sources, on subluminal and superluminal in-vacuo dispersion. We also propose that it may be possible to look for the arrival of still higher energy photons and neutrinos from GRB's with energies in the range 10^14 - 10^17 eV. In some cases the quantum gravity dispersion effect would predict these arrivals to be delayed or advanced by days to months from the GRB, giving a clean separation of astrophysical source and spacetime propagation effects., Comment: revised version: correction of typos