Related Scientific Papers

Scientific papers related to Einstein’s Unfinished Revolution

Several reviewers and readers have asked about where to go to find the details of the recent work on a realist approach to quantum foundations I describe in the last three chapters of Einstein’s Unfinished Revolution.  

The details are fully described in the following papers, which can be found on the arXiv.org; all, but the most recent are also published.

The causal theory of views is described in detail here:

Lee Smolin, The dynamics of difference  arXiv:1712.04799,

10.1007/s10701-018-0141-8 

Abstract: 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.

The causal theory of views brings together results from two lines of development:  energetic causal sets, developed  with Marina Cortes, and the real ensemble formulation of quantum mechanics.

Energetic causal sets were described in a series of five papers:

Marina Cortês, Lee Smolin, The Universe as a Process of Unique Events, arXiv:1307.6167,      10.1103/PhysRevD.90.084007 ,

Journal ref: Phys. Rev. D 90, 084007 (2014)

Abstract: 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.

Marina Cortês, Lee Smolin, Energetic Causal Sets, 

 Journal ref: Phys. Rev. D 90, 044035 (2014)

Abstract: We propose an approach to quantum theory based on the energetic causal sets, introduced in Cortês 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 ℏ. 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.

Marina Cortês, Lee Smolin,, Spin foam models as energetic causal sets, arXiv:1407.0032, 10.1103/PhysRevD.93.084039 , Phys. Rev. D 93, 084039 (2016)

Abstract: 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. △ Less

Marina Cortês, Lee Smolin,  Reversing the irreversible: from limit cycles to emergent time symmetry,  arXiv:1703.09696  10.1103/PhysRevD.97.026004 ,  Phys. Rev. D 97, 026004 (2018)

Abstract: 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 Cortês 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 Cortês 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.

Eliahu Cohen, Marina Cortês, Avshalom C. Elitzur, Lee Smolin,  Realism and Causality II: Retrocausality in Energetic Causal Sets,  arXiv:1902.05082

Abstract: 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 a classical model in which causality is disordered.

The real ensemble formulation of quantum theory was presented in three papers:

Lee Smolin, A real ensemble interpretation of quantum mechanics,

arXiv:1104.2822, 10.1007/s10701-012-9666-4 

Abstract: 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.

Lee Smolin, Precedence and freedom in quantum physics, arXiv:1205.3707

Abstract: 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.

Lee Smolin, Quantum mechanics and the principle of maximal variety,  arXiv:1506.02938, 10.1007/s10701-016-9994-x 

Abstract: 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.

Some other recent, related papers are:

arXiv:1902.05108  Realism and causality I: Pilot wave and retrocausal models as possible facilitators

Eliahu Cohen, Marina Cortês, Avshalom C. Elitzur, Lee Smolin

Abstract: 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 systems of several entangled particles. With the help of a coarse graining of pilot wave theory into a discrete system, we show how these challenges are answered. However this comes with a cost. In the description of individual systems, particles appear to scatter off empty branches of the wave function, 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. Once this cost is paid, the de Broglie-Bohm pilot wave theory does consistently describe the thought experiments that appeared originally to challenge it. We then suggest that a retrocausal version of the pilot wave theory, in which the particle is guided by a combination of advanced and retarded waves, might account for quantum physics with less damage to intuition. This is the first of two papers. In the second we show that, in the context of an explicit model, retrocausality, with respect to an effective, emergent spacetime metric, can co-exist with a strict irreversibility of causal processes.

Lee Smolin, Temporal relationalism, arXiv:1805.12468.

Invited contribution to a collection of essays on {\it Beyond spacetime}, edited by Nick Huggett, Keizo Matsubara and Christian Wuthrich.

Abstract: 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.

Some talks related to this work are http://pirsa.org/15050087/.