Andrey Akhmeteli, Intelligent Optical Systems
Electromagnetic Field as the Guiding Field in the Bohmian Mechanics
It is shown (http://www.arxiv.org/abs/quant-ph/0509044) that the Klein-Gordon-Maxwell electrodynamics in the unitary gauge, where the wave function is real, allows natural elimination of the particle wave function and describes independent evolution of the electromagnetic field in the following sense: if the components of the electromagnetic potential vector and their first derivatives with respect to time are known in the entire space at some point in time, their second derivatives with respect to time can be calculated from the equations of motion, so integration yields these components for any point in time. The particle current vector has the same direction as the electromagnetic potential vector, so the latter fully determines the Bohmian trajectories and may be regarded as the guiding field in the Bohmian mechanics. An extension of these results to the Dirac-Maxwell electrodynamics is less general, but can be regarded at least as an interesting toy model of quantum theory. This extension was significantly reworked in comparison with the preprint.

Nathan Argaman, N.R.C.N.
Retro-causal, stochastic microscopic variables
How has unitary evolution come to be perceived as fundamental?  After all, it requires us to believe that several mutually-exclusive alternatives coexist, in the face of direct evidence registering which alternative has, in fact, occurred.  In this talk, it will be argued that the present situation has arisen, at least in part, due to a misapplication of the causal arrow of time to all degrees of freedom, including microscopic ones, which should be expected to obey time-reversal symmetric rules.[begin new paragraph]A class of mathematical models involving stochastic microscopic variables associated with space-time positions -- stochastic beables -- will be discussed.  The probability distributions of these variables may depend on conditions (described by other beables) in their future, as well as on conditions in their past.  A possible representative of this class involves the stochastic quantization (SQ) approach to quantum field theory (Parisi and Wu, 1981).  This approach allows one to evaluate quantum expectation values using strictly positive probabilities, i.e., without probability amplitudes, at the price of introducing imaginary components to ostensibly real fields.  A second representative is a simple model involving a single microscopic variable, which reproduces the quantum correlations considered in Bell's theorem without directly violating locality (it is retro-causal rather than non-local).  The fact that such models are hardly discussed in the literature constitutes the misapplication of the arrow of time alluded to above.[new para]Further exploration of this class of models is called for.  In particular, one may envision a description of a quantum system (e.g., the fields of SQ) coupled to measurement devices (detectors), where the stochastic beables follow time-reversal symmetric rules, but the symmetry is broken by applying initial (rather than final) conditions.  The detectors are coupled to macroscopically many degrees of freedom (a bath) and thus may click irreversibly.  One may then consider a less microscopic level of description, which ignores the fluctuating stochastic beables, and follows only the detector clicks.  Following the information concerning the clicks, sequentially in time from the initial conditions into the future, would necessarily involve conservation of information between the clicks, punctuated by a jump at the time of each click.  This could correspond to unitary evolution, interrupted by wavefunction-collapse at the times of measurement.[new para]If, within this class, a model which reproduces all the quantitative predictions of quantum mechanics can be constructed, then a resolution of the measurement problem would have been found.  In particular, unitary evolution between measurements would come to be viewed as a result of our having access only to irreversibly-registered information, not to the truly microscopic degrees of freedom.

Andor Frenkel, Research Institute for Particle and Nuclear Physics
Comments on the derivations of a foamy space-time formula
Similarities and differences in the derivations of the foamy space-time formula of Y. J. Ng and H. van Dam and of F. Karolyhazy are exposed and commented. Attention is called to the importance of designing a reading mechanism for their quantum clocks, eg. a similar one to that of the Salecker-Wigner clock.

Sean Gryb, Perimeter Institute
Finding Time in Temporally Relational Quantum Mechanics
We "gauge" the time translational invariance of Newtonian Mechanics (NM) using a procedure inspired by Barbour's best-matching. We can move back and forth between absolute and relational time by changing the way in which the auxiliary (gauge) fields are varied. When quantizing using both Dirac and path integral quantizations, we find that there is a constraint which removes the background time. This constraint we call the "Machian" constraint and is responsible for making the theory relational. Because general relativity is formally similar to this model, we expect that analogous things should hold for gravity. This may shed new light on the problem of time in quantum gravity and the emergence of time on quantum subsystems of the universe.

Isabel Guerra, Universidad Complutense de Madrid
On Quantum Conditionalization

Noriyuki Hatakenaka, Hiroshima University
Proposal for a temporal Greenberger-Horne-Zeilinger test
We describe a Greenberger-Horne-Zeilinger (GHZ) scheme for testing macrorealism using quantum correlations in time. A seminal work on macrorealism in the connection with applicability of quantum mechanics in macroscopic scales was done by Leggett and Garg (LG) on the basis of Bell inequality in time domain. However, this involves similar difficulties in original (spatial) Bell inequality experiments, i.e., the scheme using the Bell inequality requires a statistical treatment. On the other hand, Greenberger, Horne and Zeilinger developed a proof of the Bell theorem without inequalities. Entanglement of more than two particles leads to a strong conflict with local realism for nonstatistical predictions of quantum mechanics. Here we propose a new scheme for testing macrorealism without statistical treatments by combining LG and GHZ ideas, i.e., temporal GHZ test.

Carsten Held, Universität Erfurt
The Quantum Completeness Problem - Can Consistent Histories Help?
Quantum mechanics (QM) cannot be supplemented by noncontextual hidden variables. In this sense the theory is complete. The generally accepted interpretation of this fact is that a QM system in a pure non-eigen state of some observable does not possess a value of this observable but takes on a value during a measurement interaction. But this interpretation cannot be harmonized with QM (in a standard axiomatization) because that would require two independent time parameters. Thus completeness cannot be expressed in the standard way. This is the completeness problem. It is indirectly addressed in  the consistent histories interpretation. One of the leading proponents, Rober Griffiths, proposes a solution in his 2002 book. I argue that the proposal fails and the problem remains as pressing as ever.

Lucian Ionescu, Illinonois State University
From Feynman Amplitudes to Qubit Flows
The Feynman Path Integral model (FPI) leading to the computation of the amplitude of probability of a quantum process, is based on an underlying ambient continuum space-time. This is the cause of major difficulties in QFT and renormalization, while opening the door for semi-classical interpretations of quantum mechanics, e.g. the Bohmian mechanics, which demise the new possibilities of the quantum world. We present the Qubit Model of quantum computing, adapted to QFT and an invitation to develop Quantum Information Dynamics and Quantum Infotronics, as a natural solution of the above mentioned difficulties. It is an ``upgrade'' of the FPI where qubits, instead of complex amplitudes, are associated with the elementary transitions of a causal network structure, which is part of a graded resolution of finite type replacing the concept of ambient space-time.The immediate consequence is a conceptual shift regarding the meaning of space and time, as mere dual computational resources, serial and parallel. In particular, the arrow of time has both a natural interpretation, as well as a precise mathematical formulation in the framework of tensor categories with duality: Feynman categories and their representations, the Feynman Processes.An immediate consequence is the CPT-Theorem.

Nima Khosravi, Shahid Beheshti University
Probabilistic Evolutionary Process:a possible solution to the problem of time in quantum cosmology and creation from nothing
We present a method, which we shall call the probabilistic evolutionary process, based onthe probabilistic nature of quantum theory to offer a possible solution to the problem of time inquantum cosmology. It is shown that the interpretation of wave functions in this method resultsin the same predictions as those obtained in the deformed phase space of quantum cosmologywithin the context of the models studied here. It offers an alternative for perceiving an arrow oftime which is compatible with the thermodynamical arrow of time and makes a new interpretationof the FRW universe in vacua which is consistent with creation of a de-Sitter space-time fromnothing. This is a completely quantum result with no correspondence in classical cosmology.

Maria Kon, University of Leeds
Method for a Structuralist Analysis of the Role of Time in Scientific Theories 

Louis Marchildon, Universite du QuebecCausal Loops and Collapse in the Transactional Interpretation of Quantum Mechanics
Cramer's transactional interpretation of quantum mechanics is briefly reviewed, as well as Maudlin's challenge to its consistency.  The challenge exploits the fact that the configuration of relevant absorbers, crucial in Cramer's theory, may depend on the result of a quantum measurement (or transaction) that the absorbers themselves help bring about.  This raises a number of issues related to advanced interactions, time reversal invariance and state vector collapse, which are carefully analyzed.  Where some have suggested that Cramer's predictions may not be correct or definite, I argue that they are, but I point out that the classical-quantum distinction problem in the Copenhagen interpretation has its parallel in the transactional interpretation.  I also add reasons why advanced causation in Cramer's theory does not lead to pathological causal loops.

Toru Ohira, Sony Computer Science Laboratories
Stochasticity and Non-locality on the Time Axis
The main theme of this paper is to consider concepts of stochasticity and non-locality in the domain of time rather than space. They are normally considered as a space-like concepts. For example, time is normally viewed as not having stochastic characteristics. This is so in quantum dynamics as well. In quantum mechanics, the concept of fluctuation is considered in the time-energy uncertainty principle.
However, time is not a dynamical quantum observable and clearer understanding is required. Similar argument goes with non-locality.
We will present a simple classical dynamical model to address the issue of temporal non-locality and stochasticity. We observe rather peculiar behaviors with these models. We hope to discuss issues of extending these models to quantum domain.

References:
T. Ohira, "Stochasticity and Non-locality of Time,''
Physica A Vol. 379, pp. 483-490, 2007.

Jay Olson, University of Queensland
Self-referential physics and the quantum-mechanical arrow of time.
I point out a basic principle, and a contradiction -- that all measurement outcomes are fundamentally statements about the experience of an observer, yet the traditional formulation of quantum mechanics (QM) treats the observer as an external, classical agent.  I recall and demonstrate that by explicitly including the observer as a quantum mechanical agent, the unitarity of time evolution in the context of measurements can be restored, while the usual probabilistic features of QM are recoverable via quantum information theory.  I show that the quantum mechanical arrow of time can then be identified as an explicit, information theoretic statement about the observer from within a closed, unitary framework.  I note that this concept of the arrow of time may be general enough to extend to fundamentally timeless physics (such as quantum cosmology), provided that an observer can be identified from within the formalism.

Garnet Ord, Ryerson University
What is a Wavefunction?
Conventional quantum mechanics can only answer this question by specifying the required mathematical properties of wavefunctions and invoking the Born postulate. The ontological question remains unanswered. There is one exception to this. A variation of the Feynman chessboard model allows us to see how a classical stochastic process assembles a wavefunction, based solely on the geometry of spacetime paths. A direct comparison of how a related process assembles a Probability Density Function reveals both how and why PDFs and wavefunctions differ, including the ubiquitous implication of complex numbers for the latter.

If the fine-scale motion of a particle through spacetime is continuous and position is a single valued function of time, then we are able to describe ensembles of paths directly by PDFs. However, should paths have time reversed portions so that position is not a single-valued function of time, a simple Bernoulli counting of paths fails, breaking the link to PDF's! Correcting the path-counting to accommodate time-reversed sections results in wavefunctions not PDFs.

The result is that a single `switch' simultaneously turns on both special relativity and quantum propagation. Physically, fine-scale random motion in space alone yields a diffusive process with PDFs governed by the Telegraph equations. If the fine-scale motion includes both directions in time, the result is a wavefunction satisfying the Dirac equation that also provides a detailed answer to the title question.

Allen D. Parks & John E. Gray, Quantum Processing Group Electromagnetic and Sensor Systems Department Naval Surface Warfare Center Dahlgren Division Dahlgren, Virginia USA
Weak Energy and Quantum Evolution
The weak value of a quantum mechanical observable was introduced by Aharonov et al over two decades ago. This quantity is the statistical result of a standard measurement procedure performed upon a pre-selected and post-selected (PPS) ensemble of quantum systems when the interaction between the measurement apparatus and each system is sufficiently weak. Unlike the standard strong measurement of a quantum mechanical observable which significantly disturbs the measured system, a weak measurement of an observable for a PPS system does not appreciably disturb the quantum system and yields the weak value as the measured value of the observable. Weak values reflect the nature of a virtually undisturbed quantum reality that exists between the boundaries defined by the PPS states. The equation of motion for a time dependent weak value of a quantum mechanical observable contains a complex valued energy factor - the weak energy of evolution (WEE) - that is defined by the dynamics of the PPS states which specify the observable's weak value. The WEE occurs during the weak measurement process and is contemporaneous with the observable's measurement time t. It is created at t by the forward and backward unitary time evolutions to t of the associated Hamiltonian actions upon the PPS states. The time accumulation of these evolutions is physically manifested at t as dynamical phases and complex valued pure geometric phases which determine and influence the weak value of the observable at t.  Pointed weak energy (PWE) is the complex valued energy associated with the unitary evolution of any quantum state relative to its fixed initial state. Its time integral is the sum of a dynamical phase and a purely geometric complex phase. The real part of this geometric phase is the Mukunda-Simon geometric phase for arbitrary evolutions and - consequently - is also the Aharonov-Anandan phase for cyclic evolutions. The imaginary part governs the survival probability of the initial state. Both the WEE and PWE can be expressed in terms of the associated Pancharatnam phase and Fubini-Study metric distance as generalized coordinates. When represented in these coordinates, the WEE and PWE satisfy the Euler-Lagrange equations of motion and - therefore - define conjugate momenta and provide conservation laws and stationary action principles for quantum state evolution. These weak energies also define the non-unitary evolution of correlation amplitudes and generalize the temporal persistence of state normalization.

Andrew Randono, Penn State University
Canonical Lagrangian Dynamics and General Relativity
The standard Hamiltonian treatment of General Relativity breaks spacetime into space and time. This splitting has ramifications. Most notably in the standard treatment the local Lorentz group is broken to the rotation subgroup, and spatial and temporal diffeomorphisms are treated on different footing. In this talk we address both problems. Building towards a more covariant approach to canonical classical and quantum gravity we outline an approach to constrained dynamics that de-emphasizesthe role of the Hamiltonian phase space and highlights the role of the Lagrangianphase space. Using geometric quantization techniques, we discuss implications of the formalism for the quantum theory and the problem of time. In particular, we find a new representation of the pre-quantum operators where the total Hamiltonian constraint is a kinematic operator. This open the door for a kinematic quantum spacetime geometry analogous to the kinematic quantum spatial geometry of LQG.

Metod Saniga, Astronomical Institute, Slovak Academy of Sciences
Space versus Time: Unimodular versus Non-Unimodular Projective Ring Geometries?
Finite projective (lattice) geometries defined over rings instead of fields have recently been recognized to be of great importance for quantum information theory (see, e.g., [1,2]). We believe that there is much potential hidden in these geometries to be unleashed for physics. There exist specific rings over which the projective spaces feature two principally distinct kinds of basic constituents (points and linear subspaces), intricately interwoven with each other  unimodular and non-unimodular [3]. We conjecture that these two projective degrees of freedom can rudimentary be associated with spatial and temporal dimensions of physics, respectively. Our hypothesis will briefly be illustrated on projective spaces over the smallest ring of ternions [4-6]. We shall demonstrate both the fundamental difference and intricate connection between time and space, outlining even the ring geometrical seed of the observed macroscopic dimensionality (3+1) of space-time. Some other conceptual implications of this speculative model (like a hierarchical structure of physical systems, circular times, etc.) will also be mentioned.References1. Havlicek, H., and Saniga, M.: 2008, Projective Ring Line of an Arbitrary Single Qudit, Journal of Physics A: Mathematical and Theoretical, Vol. 41, No. 1, 015302, 12pp (arXiv:0710.0941).2. Planat, M., and Baboin, A.-C.: 2007, Qudits of Composite Dimension, Mutually Unbiased Bases and Projective Ring Geometry, Journal of Physics A: Mathematical and Theoretical, Vol. 40, No. 46, pp. F1005-F1012 (arXiv:0709.2623).3. Brehm, U., Greferath, and Schmidt, S. E.: 1995, Projective Geometry on Modular Lattices, in Handbook of Incidence Geometry, F. Buekenhout (ed.), Elsevier, Amsterdam, pp. 1115-1142.4. Saniga, M., Havlicek, H., Planat, M., and Pracna, P.: 2008, Twin Fano-Snowflakes over the Smallest Ring of Ternions, Symmetry, Integrability and Geometry: Methods and Applications, Vol. 4, Paper 050, 7 pages (arXiv:0803.4436).5. Havlicek, H., and Saniga, M.: 2008, Vectors, Cyclic Submodules and Projective Spaces Linked with Ternions, Journal of Geometry, submitted (arXiv:0806.3153).6. Saniga, M., and Pracna, P.: 2008, A Jacobson Radical Decomposition of the Fano-Snowflake Configuration, Symmetry, Integrability and Geometry: Methods and Applications, to be submitted (arXiv:0807.1790). Joint work with Petr Pracna,J. Heyrovsky Institute of Physical Chemistry, v.v.i., Academy of Sciences of the Czech Republic, Dolejskova 3, CZ - 182 23 Prague, Czech Republic.

Mark Shumelda, University of Toronto
The Ontology of 'Timeless' Observables 
Several approaches to constructing a quantum theory of gravity are faced with the so-called 'problem of time'.  In particular, the problem appears in methods which attempt to quantize the canonical formulation of general relativity (loop quantum gravity is a well-known example).  In such approaches, the Hamiltonian, which expresses the dynamical content of the theory, vanishes; witness the Wheeler-DeWitt equation in quantum geometrodynamics.  One can conclude from this that the physical states described by the theory do not evolve over a background 'time'.Closely related to the problem of time is the question of how to interpret the observables postulated by such theories.  Both problems can be seen as consequences of the gauge freedom of canonical general relativity.  Since the Hamiltonian acts as a first-class constraint, it is a generator of gauge transformations.  Hence dynamical evolution seems to be a gauge evolution; but again this means that no 'physical' state changes over time.  In particular, since the observables of a theory should be gauge-independent quantities, they must be 'timeless' constants of the evolution of any physical system.Both physicists and philosophers have made progress in identifying what such timeless observables could be.  Carlo Rovelli and John Earman are among those who favour a correlational account of observables.  An observable 'event' is defined as a relation between two gauge dependent quantities; the resulting correlation satisfies the gauge-independence requirement.  Thus while the elements of the correlation are not observable, the correlation itself is.My paper will explore some of the implications of correlational observables for our fundamental ontology of space and time.  While Rovelli and other practitioners of loop quantum gravity have argued explicitly that correlational observables express a relationalist view of space and time, some philosophers insist that such observables can only be given a structuralist reading.  The disagreement stems over the ontological status that one should assign the relations versus the relata.  I will argue that neither the structuralist nor relationalist views are fully satisfactory.  How best to understand the nature of space and time in the light of 'timeless' correlational observables is still an open question.

Mark Stuckey, Elizabethtown College
A New Self-Consistency View of Time in Quantum Gravity
When it comes to the status of time in quantum gravity (QG) Smolin (2008) provides the following taxonomy: time as an illusion such as the Barbour theory, Wheeler-DeWitt, etc., time as emergent as in many versions of string theory and time as fundamental as in Smolins more recent Heraclitean solution wherein change and becoming are fundamental such that fundamental dynamical laws, the values of constants that figure in those laws and configuration space itself evolve in time. Smolin and others have begun to suspect that the problems of time in QG, current roadblocks to unification such as various fine-tuning problems, etc., might be a function of the relatively Parmenidean nature of most QG theories, not to mention the blockworld implication of special relativity per the relativity of simultaneity. We propose another view of time in QG that falls outside of Smolin's taxonomy. In our view, time, space and matter are understood as a mutually self-consistent whole. To codify this demand for self-consistency, we propose a self-consistency criterion (SCC) in the context of discrete graph theory that underlies the discrete action. The manner by which our SCC eliminates matter/geometry dualism inextricably mingles time, space and things (trans-temporal objects) such that time is not autonomously fundamental, i.e., even at the fundamental level of so-called quantum gravity time is not a standalone concept that can be discussed without explicit reference to things and space, rather all three are co-fundamental. This view of time negates many standard dichotomies, e.g., classical blockworld versus presentism (given our relationalism there is no Gods eye view outside of spacetime as suggested by the Archimedean imagery of blockworld, yet the actual histories of every system are equally real), timelessness versus change, etc. Consequently, there is no ultimate tension between the treatment of time in general relativity and relativistic quantum field theory, for example, given our fully relational view of time the very idea of the wavefunction of the universe as given by the radically timeless Wheeler-DeWitt equation is a non-sequitur. Time is not an illusion as in the Barbour view because dynamical becoming is germane to its formalism. Furthermore, our graph theoretical basis for quantum and classical physics constitutes a unification of physics as opposed to a mere discrete approximation thereto, since we are proposing a basis for the action, which is otherwise fundamental. Therefore, our view champions neither absolute timelessness nor absolute becoming, but it harbors qualities of both views in that it possesses the full explanatory power of blockworld (at base it employees acausal and adynamical formal tools) and it encodes perspectivally invariant dynamism (SCC --> symmetry amplitude --> dynamism per stationary phase limit). Thus our view resolves some of the well-known problems of time.

Zachary Walton, Yale University
Time Flow and Hardy's Axioms
We propose a new theory of time flow which suggests an explanation for why classical probability theory must be a special case of a more robust inference theory.  In our theory of time flow, a pure state of an N-dimensional system is represented by a pair of probability distrubtions over N outcomes.  Two properties are intrinsic to our theory: size of the state space (2N-2 for normalized pure states) and continuously accessible pure states.  These two properties are closely related to the crucial axioms that distinguish quantum theory from classical probability theory in Hardy's derivation of quantum theory.  Thus, we adapt Hardy's argument to show that quantum mechanics can be viewed as a natural consequence of a theory of time flow.  This work follows a direction suggested by Wootters (Is Time Asymmetry Logically Prior to Quantum Mechanics? in Physical Origins of Time Asymmetry, Halliwell ed.) and is inspired by the program outlined by Wheeler (Information, Physics, Quantum: The Search for Links in Complexity, Entropy and the Physics of Information, Zurek, ed.).

Ken Wharton, San Jose State University
Quantum Mechanics in a Block Universe
In the four-dimensional block universe of general relativity, it is difficult to make much sense of quantum mechanics (QM).   When using this timeless perspective (where dynamics is encoded by structure), certain conceptual problems arise: the meaning of outcome probability, wave-function reduction, and a missing external clock.  These problems can in turn motivate alternative formulations of QM, incorporating time in a manner that makes sense in a block-universe framework.  I will outline such an approach based on classical fields constrained by closed-hypersurface boundary conditions (arXiv:0706.4075), and sketch what this version of QM might look like from such a timeless perspective.  While many details of this approach have yet to be satisfactorily resolved, the conceptual framework demonstrates that QM can probably be made compatible with a block universe.