Can Spacetime be a Condensate?

We explore further the proposal [Hu, B. L. (1996). General relativity as geometro-hydrodynamics. (Invited talk at the Second Sakharov Conference, Moscow, May 1996); gr-qc/9607070.] that general relativity is the hydrodynamic limit of some fundamental theories of the microscopic structure of spacetime and matter, i.e., spacetime described by a differentiable manifold is an emergent entity and the metric or connection forms are collective variables valid only at the low-energy, long-wavelength limit of such micro-theories. In this view it is more relevant to find ways to deduce the microscopic ingredients of spacetime and matter from their macroscopic attributes than to find ways to quantize general relativity because it would only give us the equivalent of phonon physics, not the equivalents of atoms or quantum electrodynamics.It may turn out that spacetime is merely a representation of certain collective state of matter in some limiting regime of interactions, which is the view expressed by Sakharov [Sakharov, A. D. (1968). Soviet Physics-Doklady 12, 1040–1041; Sakharov, A. D. (1967). Vacuum quantum fluctuations in curved space and the theory of gravitation. Doklady Akad. Nauk S.S.R. 177, 70; Adler, S. L. (1982). Reviews of Modern Physics 54, 729]. In this talk, working within the conceptual framework of geometro-hydrodynamics, we suggest a new way to look at the nature of spacetime inspired by Bose–Einstein condensate (BEC) physics. We ask the question whether spacetime could be a condensate, even without the knowledge of what the‘atom of spacetime’ is. We begin with a summary of the main themes for this new interpretation of cosmology and spacetime physics, and the ‘bottom-up’ approach to quantum gravity. We then describe the ‘Bosenova’ experiment of controlled collapse of a BEC and our cosmology-inspired interpretation of its results. We discuss the meaning of a condensate in different context. We explore how far this idea can sustain, its advantages and pitfalls, and its implications on the basic tenets of physics and existing programs of quantum gravity.     

Topological Entanglement Entropy from the Holographic Partition Function

We study the entropy of chiral 2+01-dimensional topological phases, where there are both gapped bulk excitations and gapless edge modes. We show how the entanglement entropy of both types of excitations can be encoded in a single partition function. This partition function is holographic because it can be expressed entirely in terms of the conformal field theory describing the edge modes. We give a general expression for the holographic partition function, and discuss several examples in depth, including abelian and non-abelian fractional quantum Hall states, and $p+ip$ superconductors. We extend these results to include a point contact allowing tunneling between two points on the edge, which causes thermodynamic entropy associated with the point contact to be lost with decreasing temperature. Such a perturbation effectively breaks the system in two, and we can identify the thermodynamic entropy loss with the loss of the edge entanglement entropy. From these results, we obtain a simple interpretation of the non-integer ‘ground state degeneracy’ which is obtained in 1+1-dimensional quantum impurity problems: its logarithm is a 2+1-dimensional topological entanglement entropy.     

Causal stochastic interpretation of quantum statistics

The differences between Einstein and Bohr on the interpretation of quantum mechanics revolved around the question of completeness of the Copenhagen Interpretation. This fundamental problem is examined here in the light of recent neutron interference experiments which allow for novel experimental situations. Exploiting the possibility of neutron spin flip in these experiments, the inadequacy of the Copenhagen interpretation to fully understand the experimental results is brought out. Instead a causal interpretation of quantum mechanics is advocated, in which the neutron, as a particle, does always have a definite space time trajectory but also involves a wave which creates a potential affecting the particle neutron. The reestablishment of definite particle trajectories in the microscopic domain obliges us to reexamine the statistical treatment of ‘identical’ particles, as well as the problem of negative energies and probabilities in relativistic quantum mechanics.     

Paradox in Wave-Particle Duality

We report on the simultaneous determination of complementary wave and particle aspects of light in a double-slit type “welcher-weg” experiment beyond the limitations set by Bohr’s Principle of Complementarity. Applying classical logic, we verify the presence of sharp interference in the single photon regime, while reliably maintaining the information about the particular pinhole through which each individual photon had passed. This experiment poses interesting questions on the validity of Complementarity in cases where measurements techniques that avoid Heisenberg’s uncertainty principle and quantum entanglement are employed. We further argue that the application of classical concepts of waves and particles as embodied in Complementarity leads to a logical inconsistency in the interpretation of this experiment. A Preliminary version of this paper was presented by S.S.A. at a Seminar titled “Waving Copenhagen Good-bye: Were the Founders of Quantum Mechanics Wrong?,” Department of Physics, Harvard University, Cambridge, MA 02138, 23 March, 2004.     

An Introduction to Many Worlds in Quantum Computation

The interpretation of quantum mechanics is an area of increasing interest to many working physicists. In particular, interest has come from those involved in quantum computing and information theory, as there has always been a strong foundational element in this field. This paper introduces one interpretation of quantum mechanics, a modern ‘many-worlds’ theory, from the perspective of quantum computation. Reasons for seeking to interpret quantum mechanics are discussed, then the specific ‘neo-Everettian’ theory is introduced and its claim as the best available interpretation defended. The main objections to the interpretation, including the so-called “problem of probability” are shown to fail. The local nature of the interpretation is demonstrated, and the implications of this both for the interpretation and for quantum mechanics more generally are discussed. Finally, the consequences of the theory for quantum computation are investigated, and common objections to using many worlds to describe quantum computing are answered. We find that using this particular many-worlds theory as a physical foundation for quantum computation gives several distinct advantages over other interpretations, and over not interpreting quantum theory at all.     

Three Slit Experiments and the Structure of Quantum Theory

In spite of the interference manifested in the double-slit experiment, quantum theory predicts that a measure of interference defined by Sorkin and involving various outcome probabilities from an experiment with three slits, is identically zero. We adapt Sorkin’s measure into a general operational probabilistic framework for physical theories, and then study its relationship to the structure of quantum theory. In particular, we characterize the class of probabilistic theories for which the interference measure is zero as ones in which it is possible to fully determine the state of a system via specific sets of ‘two-slit’ experiments.     

The Theory of (Exclusively) Local Beables

It is shown how, starting with the de Broglie–Bohm pilot-wave theory, one can construct a new theory of the sort envisioned by several of QM’s founders: a Theory of Exclusively Local Beables (TELB). In particular, the usual quantum mechanical wave function (a function on a high-dimensional configuration space) is not among the beables posited by the new theory. Instead, each particle has an associated “pilot-wave” field (living in physical space). A number of additional fields (also fields on physical space) maintain what is described, in ordinary quantum theory, as “entanglement.” The theory allows some interesting new perspective on the kind of causation involved in pilot-wave theories in general. And it provides also a concrete example of an empirically viable quantum theory in whose formulation the wave function (on configuration space) does not appear—i.e., it is a theory according to which nothing corresponding to the configuration space wave function need actually exist. That is the theory’s raison d’etre and perhaps its only virtue. Its vices include the fact that it only reproduces the empirical predictions of the ordinary pilot-wave theory (equivalent, of course, to the predictions of ordinary quantum theory) for spinless non-relativistic particles, and only then for wave functions that are everywhere analytic. The goal is thus not to recommend the TELB proposed here as a replacement for ordinary pilot-wave theory (or ordinary quantum theory), but is rather to illustrate (with a crude first stab) that it might be possible to construct a plausible, empirically viable TELB, and to recommend this as an interesting and perhaps-fruitful program for future research.     

Reconciling Spacetime and the Quantum: Relational Blockworld and the Quantum Liar Paradox

The Relational Blockworld (RBW) interpretation of non-relativistic quantum mechanics (NRQM) is introduced. Accordingly, the spacetime of NRQM is a relational, non-separable blockworld whereby spatial distance is only defined between interacting trans-temporal objects. RBW is shown to provide a novel statistical interpretation of the wavefunction that deflates the measurement problem, as well as a geometric account of quantum entanglement and non-separability that satisfies locality per special relativity and is free of interpretative mystery. We present RBW’s acausal and adynamical resolution of the so-called “quantum liar paradox,” an experimental set-up alleged to be problematic for a spacetime conception of reality, and conclude by speculating on RBW’s implications for quantum gravity.     

Division Algebras and Quantum Theory

Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of axiomatic approaches. However, there are internal problems with real or quaternionic quantum theory. Here we argue that these problems can be resolved if we treat real, complex and quaternionic quantum theory as part of a unified structure. Dyson called this structure the ‘three-fold way’. It is perhaps easiest to see it in the study of irreducible unitary representations of groups on complex Hilbert spaces. These representations come in three kinds: those that are not isomorphic to their own dual (the truly ‘complex’ representations), those that are self-dual thanks to a symmetric bilinear pairing (which are ‘real’, in that they are the complexifications of representations on real Hilbert spaces), and those that are self-dual thanks to an antisymmetric bilinear pairing (which are ‘quaternionic’, in that they are the underlying complex representations of representations on quaternionic Hilbert spaces). This three-fold classification sheds light on the physics of time reversal symmetry, and it already plays an important role in particle physics. More generally, Hilbert spaces of any one of the three kinds—real, complex and quaternionic—can be seen as Hilbert spaces of the other kinds, equipped with extra structure.     

Reply to “quantum tunneling times: A crucial test for the causal program?”

Because Bohm’s Interpretation models particles with continuous trajectories, a natural property to attribute to a Bohmian particle is atunneling time, the time it takes for a particle to pass through a barrier. We also attribute a property-a different property-named ‘tunneling time’ to Copenhagen systems, systems that do not have particles with continuous trajectories. Cushing presents a discussion of the possibility of measuring Bohmian particle tunneling time; however, as becomes clear when considering the differences between properties named ‘tunneling time,’ he incorrectly argues that if such a measurement were possible, the measurement might constitute an empirical test between the Copenhagen interpretation and Bohm’s interpretation.     

The universe formation by space reduction cascades with random initial parameters

In this paper we discuss the creation of our universe using the idea of extra dimensions. The initial, multidimensional Lagrangian contains only metric tensor. We have found many sets of the numerical values of the Lagrangian parameters corresponding to the observed low-energy physics of our Universe. Different initial parameters can lead to the same values of fundamental constants by the appropriate choice of a dimensional reduction cascade. This result diminishes the significance of the search for the ‘unique’ initial Lagrangian. We also have obtained a large number of low-energy vacua, which is known as ‘landscape’ in the string theory.     

Interpreting Quantum Interference Using a Berry’s Phase-like Quantity

We show that quantum interference can be interpreted in terms of a phase invariant quantity, not unlike the Berry’s phase. Under this interpretation, closed loops in time become fundamental quantum entities, and all quantum states become periodic. Decoherence is then seen to occur naturally as a consequence. This formalism, although counterintuitive, provides another useful way of assigning meaning to quantum probabilities and quasi-probabilities.     

Interference due to coherence swapping

We propose a method called ‘coherence swapping’ which enables us to create superposition of a particle in two distinct paths, which is fed with initially incoherent, independent radiation. This phenomenon is also present for the charged particles, and can be used to swap the effect of flux line due to the Aharonov-Bohm effect. We propose an optical version of experimental set-up to test the coherence swapping. The phenomenon, which is simpler than entanglement swapping or teleportation, raises some fundamental questions about the true nature of wave-particle duality, and also opens up the possibility of studying the quantum erasure from a new angle.     

Macro-scale observation of curl-free vector potential: A manifestation of quantum modulation of the de Broglie wave

Experimental results are presented here reporting the detection of a curl-free vector potential on the macro-scale as contrasted with the detection on the micro-scale à la Aharonov-Bohm. Such a detection is attributed to the ‘quantum modulation’ of the plane wave state of the guiding centre motion of a charged particle in a magnetic field, which is generated concomitantly with the excitation of its Landau levels in a scattering episode, through the mechanism of quantum entanglement between the parallel and perpendicular degrees of freedom of the particle. Such a ‘quantum modulation’ is also a matter wave, but on the macro-scale, and leads to the ‘sensing’ of the curl-free vector potential on the macro-scale. Thus while the Aharonov-Bohm effect is attributed to the sensing of the curl-free vector potential by the de Broglie wave, its sensing on the macro-scale is attributed to the modulation of the de Broglie wave.     

Coherence vs. decoherence in (some) problems of condensed matter physics

We present an ‘overview’ of coherence-to-decoherence transition in certain selected problems of condensed matter physics. Our treatment is based on a subsystem-plus-environment approach. All the examples chosen in this paper have one thing in common — the environmental degrees of freedom are taken to be bosonic and their spectral density of excitations is assumed to be ‘ohmic’. The examples are drawn from a variety of phenomena in condensed matter physics involving, for instance, quantum diffusion of hydrogen in metals, Landau diamagnetism and c-axis transport in high T _c superconductors.     

Schrödinger’s Cat Meets Einstein’s Twins: A Superposition of Different Clock Times

The phenomenon of quantum superposition, which allows a physical system to exist in different states ‘simultaneously’, is one of the most bizarre notions in physics. Here we illustrate an even more bizarre example of it: a superposed state of a physical system consisting of both an ‘older’ version and a ‘younger’ version of that system. This can be accomplished by exploiting the special relativistic effect of time dilation featuring in Einstein’s famous twin paradox.     

What price the spin-statistics theorem?

We examine a number of recent proofs of the spin-statistics theorem. All, of course, get the target result of Bose-Einstein statistics for identical integral spin particles and Fermi-Dirac statistics for identical half-integral spin particles. It is pointed out that these proofs, distinguished by their purported simple and intuitive kinematic character, require assumptions that are outside the realm of standard quantum mechanics. We construct a counterexample to these non-dynamical kinematic ‘proofs’ to emphasize the necessity of a dynamical proof as distinct from a kinematic proof. Sudarshan’s simple non-relativistic dynamical proof is briefly described. Finally, we make clear the price paid for any kinematic ‘proof’.     

Observability of the effects of curl-free magnetic vector potential on the macroscale and the nature of the ‘transition amplitude wave’

We discuss here the prediction, based on a formalism by the author, on the observable effects of a curl-free magnetic vector potential on the macroscale as against the microscale of the Aharonov-Bohm effect. A new quantum concept — the ‘transition amplitude wave’ — postulated in the formalism has already been shown to exhibit matter wave manifestations in the form of one-dimensional interference effects on the macroscale. It was predicted by the formalism that the same entity would lead to the detection of a curl-free magnetic vector potential on the macroscale. We describe here the manner of generation of this quantum entity in an inelastic scattering episode and work out an algorithm to observe this radically new phenomenon, the detection of a curl-free magnetic vector potential on the macroscale. We determine the various characteristic features of such an observation which can then be looked for experimentally so as to verify the predicted effect, establishing thereby the physical reality of the new quantum entity, and to fully validate the formalism predicting it. It is also shown that this ‘transition amplitude wave’ can be regarded as a novel kind of ‘quasiparticle’ excited in the charged particle trajectory as a consequence of the scattering episode.     

The physics of 2≠1+1

One of the most surprising consequences of quantum mechanics is the entanglement of two or more distant particles. In an entangled EPR two-particle system, the value of the momentum (position) for neither single subsystem is determined. However, if one of the subsystems is measured to have a certain momentum (position), the other subsystem is determined to have a unique corresponding value, despite the distance between them. This peculiar behavior of an entangled quantum system has surprisingly been observed experimentally in two-photon temporal and spatial correlation measurements, such as “ghost” interference and “ghost” imaging. This article addresses the fundamental concerns behind these experimental observations and to explore the nonclassical nature of two-photon superposition by emphasizing the physics of 2 ≠ 1 + 1.      

Glafka–2004 ‘Iconoclasm’: The Soul and Spirit of the Meeting

The following is a brief talk that opened and attempted to set the atmosphere for the first ‘Glafka–2004: Iconoclastic Approaches to Quantum Gravity’ international theoretical physics conference. It aimed to capture the general spirit of the meeting, as well as to inspire and unite its participants under the following envisioned ‘cause’: to bring together and scrutinize certain important current quantum gravity research approaches in a fresh, unconventional, almost unorthodox, way.Introductory remarks to the 1st Glafka–2004: Iconoclastic Approaches to Quantum Gravity international theoretical physics conference, held in Athens, Greece (summer 2004).