Time-symmetry in Quantum Mechanics
Sydney :: 23-26 July 2005
Locals and organisers
Huw Price, Guido Bacciagaluppi, David Miller, Rod Sutherland, Gerard Milburn, Stephen Bartlett, John Corbett, Michael Nielsen, Brad Weslake, Howard Wiseman, Jennifer Dodd, David Poulin, Thomas Durt, Frank Valkenborgh, Roy Hughes, David Pegg, Kenny Pregnell, Andrew Norton, Terry Rudolph, Paul Davies, Nick Smith, John Cusbert, Jason Grossman.
Tony Leggett, Richard Healey, Jos Uffink, John Cramer, Michael Cifone, Shelly Goldstein, Michael Silberstein, Roderich Tumulka, Ruth Kastner, Peter Lewis, Larry Schulman, Dipankar Home, Avshalom Elitzur, Howard Barnum, Jossi Berkovitz, Noboru Hokkyo, Wayne Myrvold, Jeff Tollaksen, Lev Vaidman, Mark Stuckey, Jason Semitecolos.
Click on titles for abstracts.
In the same framework of diffusion processes on configuration space as used by Nelson, but restricted to local theories, we show how imposing initial (or final) constraints on particle distributions can mimick nonlocal behaviour at the level of the probability distribution and probability current. The required constraints are distributions involving classical correlations. Specifically, we show that a non-linear Schroedinger equation for non-interacting (but generally entangled) particles can be derived from such a local theory with constraints.
Causal Loops in Retrocausal Interpretations of Quantum
Bellís theorem demonstrates that granted some natural premises about the physical realm, any model of the Einstein-Podolsky-Rosen/Bohm experiment must postulate some kind of nonlocal influences, which are difficult to reconcile with relativity theory. One of these premises is the assumption that the distribution of the states of particle pairs before the measurements is independent of the measured quantities. This assumption will be violated if measurement events influenced the state of particle pairs at the emission time. Cramerís transactional interpretation of quantum mechanics circumvents Bellís theorem by postulating such influences. In this paper, I argue that in Cramerís interpretation this type of retrocausation gives rise to closed causal loops. I then consider the peculiar nature of probabilities in such loops and the possible implications of this nature for the question of theory choice and empirical adequacy.
Meets Hilbert in a Relational Blockworld: A Geometric
Interpretation of Quantum Mechanics
Our goal is an interpretation of quantum mechanics that: (1) resolves the outstanding tensions between quantum mechanics (QM) and special relativity (SR) - what Albert has recently called the problem of "narratability" (2) respects the essence of Lorentz invariance and special covariance, and (3) provides a solution to the measurement problem and a resolution to such mysteries as quantum non-locality, non-separability, etc. Just as Einstein sought to reconcile or unify Newton and Maxwell via Minkowski spacetime, we ask what kind of spacetime is needed to accommodate QM and SR without having to give up on the essential features of either theory. The answer is the spacetime given by the restricted Poincaré group. More specifically, we adopt a result due to G. Kaiser whereby the relativity of simultaneity, stemming from the Poincaré algebra, is responsible for the familiar commutation relations of QM. We also adopt a result due to A. Bohr, B. Mottelson and O. Ulfbeck whereby the density matrix for a given experimental situation is obtained from its spacetime symmetry group.
We achieve our interpretive goals then with an account of QM that takes spacetime symmetries, not dynamical laws, as fundamental. The commonly accepted view that dynamical laws, such as the Schrödinger equation, generate or bring new events into being -- thereby giving rise to probabilities -- is incorrect on the relational blockworld (RBW) view. For RBW, dynamical laws are neither ontologically nor explanatorily fundamental; rather, the fundamental spacetime symmetries interpreted as irreducibly relational structures, plus initial and final boundary conditions, give rise to the Schrödinger equation (a dynamical law) and the QM probabilities. Thus, the determination of events is made not dynamically, but rather non-dynamically, by imposing a global determination relation (which is both non-local and non-separable) on a spacetime structure whose symmetries, and the geometry they support, are irreducibly relational. According to RBW, then, non-dynamical spatiotemporal relationalism is more fundamental than dynamism.
The measurement problem is simply deflated on this view since the linear Schrödinger dynamics, the Hilbert space representation of physical observables etc., constitute nothing more than calculational devices. Quantum non-locality and non-separability are not mysterious according to RBW since they are straightforward consequences of the geometry of spacetime as given by the restricted Poincaré group. We will illustrate our interpretation by applying it to the "quantum liar paradox" and, time-permitting, we will contrast RBW with other interpretations such as BCQM and other time-symmetric accounts.
Quantum Handshake: A Review of the Transactional
Interpretation of Quantum Mechanics
We summarize the transactional interpretation of quantum mechanics and review its applications to quantum paradoxes, wave function collapse, and quantum nonlocality. We consider a hierarchal pseudo-time structure for the emergence of a quantum event.
Histories: A New Family of Quantum Paradoxes and their
Bearing on the Nature of Spacetime
Much as the familiar quantum-mechanical paradoxes (double slit, EPR, etc) are odd from the classical viewpoint, the histories they entail are nevertheless self-consistent. We present here a new family of experiments that do not maintain self-consistency either. When a few particles perform mutual measurements on one another, prior to the measurementís completion by a macroscopic detector, self-contradictory histories seem to emerge.
We submit that such results call for a more radical version of Cramerís transactional interpretation, along lines proposed by Aharonov. According to this proposal, quantum transactions across different times, rather than being ìatemporal,î evolve in some real, higher time, within which the 4-dimensional spacetime is itself subject to dynamics. Inconsistent histories might thus indicate repeated ìreiterationsî of the same history.
We then outline a theory of becoming in which spacetime grows in the future direction, incessantly adding new events to the past. ìWave-function collapse,î which many interpretations of QM seek to avoid, and the ìmoving Now,î similarly dismissed by relativity theory, thereby constitute two aspects of the same objective feature of reality, namely, becoming, which turns future potentialities into present actualities.
The proposed model reverses the roles of quantum interactions and spacetime. Whereas the quantum interaction is usually believed to occur within spacetime, we propose that it gives rise to spacetime. First, at the pre-spacetime stage, the quantum interaction takes place beyond the ìNowî and hence outside spacetime. Then, the spacetime region associated with this interaction evolves, creating the spatiotemporal relations between the events.
This hypothesis offers a natural way of reconciling relativity and quantum theories, as spacetime geometry may be shaped by the interactions that precede it.
Bohmian mechanics is a theory about point particles moving in space according to a law of motion (an ordinary differential equation) involving a quantum mechanical wave function. It is a consequence of this law of motion that in a typical world governed by Bohmian mechanics, observers would observe for the results of their experiments exactly the frequencies predicted by quantum mechanics. Since the theory is time symmetric, arrows of time are grounded in the specialness of the initial wave function. A more complex situation arises in some recently studied relativistic variants of the law of motion: they imply backwards causation, though only in a very special and limited way that is free of causal paradoxes.
Early approaches to the integral (time-symmetric) formulation of physical processes, Fermat's stationary principle in geometrical optics (1661) to Feynman's path integral formulation in QM (1949), are revisited and shown to be useful in removing mystic (teleological) flavor surrounding the major quantum paradoxes : 1) acausal collapse of causal wave functions (quantum jump to final states), 2) nonlocal correlation of distant particles without nonlocal interactions (EPR correlation), 3) single electron double-slit self-interference (building up of visible pattern from a sequence of single electron processes) and 4) quantum coherence between macroscopically distinct states (Schroedinger's Cat paradox). An extension of double-slit experiment is proposed to test the time-symmetry by detecting the shadows of the retarded and advanced electron (photon) waves appearing on the rear side and in front of the double-slit, showing the advanced bifurcation and merging of the electron wave before and after passing through the slit followed by the convergence of the wave towards the detection point.
Transactional Interpretation and Causal Loop Problems
Tim Maudlin's argument for the inconsistency of Cramer's Transactional Interpretation (TI) of quantum theory has been considered in some detail by Joseph Berkovitz, who has provided a possible solution to this challenge at the cost of a significant empirical lacuna on the part of TI. The present paper proposes an alternative solution in which Maudlin's charge of inconsistency is evaded but at no cost of empirical content on the part of TI. However, Maudlin's argument is taken as ruling out Cramer's heuristic "pseudotime" explanation of the realization of one transaction out of many.
mechanics as a consistency condition on initial and final
us assume that events in our world depend on initial and
final boundary conditions. Since our current physical
theories are based on initial boundary conditions only, we
would expect to encounter inexplicable events (namely all
those that depend on the final boundary conditions). That is
exactly what occurs in quantum mechanics which contains many
inexplicable phenomena. For example, von Neumann's process
one is inexplicable even on quantum mechanics' own terms and
nonlocality has led many to contend that physics should be
satisfied with 'saving the appearances'. I will argue that
one should regard this predicament as evidence for the
existence of final boundary conditions. If quantum mechanics
is reformulated in terms of initial and final boundary
conditions, one sees that quantum mechanics is not a theory
about physical systems but is instead a consistency
condition between the initial and final
Partial Primer on Time & Causality
This talk is a brief and opinionated introduction to some general issues about time, time-asymmetry and causation. I'll try to provide a framework which will be helpful in focussing on more specific issues concerning time, causation and QM, in the rest of the workshop.
paths to local hidden variables?
The Feynman path integral approach is usually interpreted as merely a calculation device for quantum probabilities, rather than the basis for a realistic model of the origins of quantum phenomena. The main obstacle to realism is that the probabilities derived from the amplitudes associated with individual trajectories do not obey the classical sum rule -- i.e., the phenomenon of quantum interference.
However, some writers (Sinha & Sorkin 1991, Stachel, 1997) have argued that the path integral approach provides a way of reducing the puzzle of the EPR/Bell correlations to that of quantum interference -- and this seems to require an element of realism. Sinha & Sorkin are explicit about this, and favour real trajectories governed by non-classical probabilities. Stachel's view seems to amount to a weaker realism about bundles of trajectories. Either way, the 'reality' between measurements seems influenced symmetrically by past and future settings, so that both versions involve an element of retrocausality (although neither is presented in these terms).
Stachel's version of the view has the disadvantage that it requires a sharp distinction between (i) the 'definite' or 'determinate' conditions that comprise the initial and final events between which the path integral is evaluated, and (ii) the indeterminate events in the region in which the particle's trajectory is indeterminate. However, the need for this distinction introduces the measurement problem in a stark form. Hence it is a big advantage of Sinha & Sorkin's version seems to be that it has the potential to avoid this consequence. On this version, reality is determinate at all levels, and there is no need to ground a sharp macro/micro distinction (whether by allowing measurement to play a fundamental role or otherwise).
On the face of it, however, explicit recognition of the possibility of retrocausality seems to provide a simple answer to the standard objection to realism about Feynman trajectories. If the underlying reality can be a function of the future measurement, the 'one-slit' and 'two-slit' cases involve different reference classes, and the respective probabilities should not be expected to obey the classical sum rule. In other words, the fact that the formalism yields a probability for the case in which a which-way measurement is made is no longer inconsistent with the existence of a different (and thoroughly classical) probability for the trajectory in question, in the case in which a which-way measurement is not made.
This observation raises the interesting possibility that the Feynman formalism might provide a ready-made basis for a retrocausal hidden-variable model. I conclude with some thoughts about the development of this approach, in the light of the measurement problem.
is an effect, quantum determinism and other consequences of
the two-time boundary condition perspective.
I stress the importance of using a time-symmetric framework for studying the thermodynamic arrow. Such a framework can be established through the use of two-time boundary conditions. As one example, I examine macroscopic causality. At the quantum level, with this perspective, the avoidance of grotesque states through the use of "special states" (and the consequent quantum determinism) gains enhanced plausibility. Another topic (probably for discussion only) is the subjectivity of the work/heat distinction, fundamental to the Second Law. Using recent results on non-equilibrium statistical mechanics I discuss a relatively (but not completely) objective scheme for defining "coarse grains."
A time-symmetric version of David Bohmís well-known model will be summarized as an explicit example of a theory involving backwards-in-time effects. The rationale is that such effects can be examined more easily in the context of a specific model. Furthermore, the fairly classical ontology employed in Bohm-type models helps to highlight more clearly the consequences of imposing time-symmetry. In particular, it is seen that we are able to (i) avoid a preferred reference frame, (ii) explain EPR nonlocality and (iii) work with separate 3D wavefunctions in the correlated multiparticle case. Of course, there are trade-offs and the pros and cons of the time-symmetric versus the usual Bohm model will be compared.
Two-State Vector Formalism Of Quantum Mechanics
The basic concepts of the two-state vector formalism of quantum mechanics will be reviewed: the two-state vector, the Aharonov-Bergmann-Lebowitz formula, the time-symmetric counterfactuals, the elements of reality of the pre- and post-selected system, the failure of the product rule, the weak values (the outcomes of weak measurements) and the weak-measurement elements of reality. Few examples, such as three-box paradox, will demonstrate usefulness of the formalism for discovering peculiar quantum effects.
Last updated: 13 September 2005