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PREFACE: QUANTUM RETROCAUSATION–THEORY AND EXPERIMENT

Daniel P. Sheehan and Michael Ibison

AIP Conf. Proc. 1408, pp. 1-3; doi:http://dx.doi.org/10.1063/1.3663713 (3 pages)

Online Publication Date: 18 November 2011

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03.67.Lx	Quantum computation architectures and implementations
02.50.Fz	Stochastic analysis
07.60.Ly	Interferometers
05.70.Ce	Thermodynamic functions and equations of state
03.65.Ca	Formalism

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The Broken Symmetry of Time

Ruth E. Kastner

AIP Conf. Proc. 1408, pp. 7-21; doi:http://dx.doi.org/10.1063/1.3663714 (15 pages)

Online Publication Date: 18 November 2011

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This paper seeks to clarify features of time asymmetry in terms of symmetry breaking. It is observed that, in general, a contingent situation or event requires the breaking of an underlying symmetry. The distinction between the universal anisotropy of temporal processes and the irreversibility of certain physical processes is clarified. It is also proposed that the Transactional Interpretation of quantum mechanics offers an effective way to explain general thermodynamic asymmetry in terms of the time asymmetry of radiation, where prior such efforts have fallen short.

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06.30.Ft	Time and frequency
05.70.Ce	Thermodynamic functions and equations of state
11.30.Qc	Spontaneous and radiative symmetry breaking
03.65.Ca	Formalism
03.70.+k	Theory of quantized fields

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Constructing Retrocausal Models: Decision Points and Pitfalls

Ken Wharton

AIP Conf. Proc. 1408, pp. 22-30; doi:http://dx.doi.org/10.1063/1.3663715 (9 pages)

Online Publication Date: 18 November 2011

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The scattered efforts to construct retrocausal models of quantum phenomena have utilized different conceptual and mathematical frameworks; in most cases a framework is assumed without explicit discussion or particular justification. Some of these frameworks are arguably internally inconsistent, and others incorporate standard quantum concepts that become problematic or unnecessary when used in a time‐symmetric manner.

With this in mind, I will examine the big‐picture choices facing a theorist who wishes to construct a coherent retrocausal model. These decisions include whether or not to couch the theory in a single “block universe”; the role (if any) of hidden variables; the implementation of boundary constraints; the use of conditional probability vs. joint probability; and the choice between Newtonian and Lagrangian approaches.

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03.65.Aa	Quantum systems with finite Hilbert space
04.20.Fy	Canonical formalism, Lagrangians, and variational principles
02.50.Cw	Probability theory
03.65.Ca	Formalism
03.65.Ud	Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)

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Retrocausal Effects As A Consequence of Orthodox Quantum Mechanics Refined To Accommodate The Principle Of Sufficient Reason

Henry P. Stapp

AIP Conf. Proc. 1408, pp. 31-44; doi:http://dx.doi.org/10.1063/1.3663716 (14 pages)

Online Publication Date: 18 November 2011

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The principle of sufficient reason asserts that anything that happens does so for a reason: no definite state of affairs can come into being unless there is a sufficient reason why that particular thing should happen. This principle is usually attributed to Leibniz, although the first recorded Western philosopher to use it was Anaximander of Miletus. The demand that nature be rational, in the sense that it be compatible with the principle of sufficient reason, conflicts with a basic feature of contemporary orthodox physical theory, namely the notion that nature's response to the probing action of an observer is determined by pure chance, and hence on the basis of absolutely no reason at all. This appeal to pure chance can be deemed to have no rational fundamental place in reason‐based Western science. It is argued here, on the basis of the other basic principles of quantum physics, that in a world that conforms to the principle of sufficient reason, the usual quantum statistical rules will naturally emerge at the pragmatic level, in cases where the reason behind nature's choice of response is unknown, but that the usual statistics can become biased in an empirically manifest way when the reason for the choice is empirically identifiable. It is shown here that if the statistical laws of quantum mechanics were to be biased in this way then the basically forward‐in‐time unfolding of empirical reality described by orthodox quantum mechanics would generate the appearances of backward‐time‐effects of the kind that have been reported in the scientific literature.

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05.30.Ch	Quantum ensemble theory
04.62.+v	Quantum fields in curved spacetime
02.50.Cw	Probability theory
02.10.Yn	Matrix theory
98.80.Bp	Origin and formation of the Universe

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Retroactive Event Determination and Its Relativistic Roots

Sky E. Nelson

AIP Conf. Proc. 1408, pp. 45-74; doi:http://dx.doi.org/10.1063/1.3663717 (30 pages)

Online Publication Date: 18 November 2011

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Quantum theory limits what we are allowed to say about the “true” state of a quantum system if that system is unobserved. But special relativity relies fundamentally on a universal assumption about what a light particle is doing at ALL times, regardless of being observed (namely, traveling at speed c relative to any inertial observer). This constitutes a fundamental conceptual gap between the theories. In resolving this impasse we show that the state of a light particle (and hence space and time) is not objective or continuous. Time dilation and length contraction become infinite for a photon, so light has no “experience” of event separation in space or time (Δt′ = 0, Δx′ = 0). The principle of simultaneity is applied between an inertial observer and a light particle, such that the relative speed of the two systems is c, and gamma = infinite/undefined. Although light experiences no separation between events, the Lorentz transform Δt′ = γ (Δt−ΔLv/c²) implies that the inertial observer experiences a separation between those same events of exactly Δt = ΔL/c, a light‐like separation. In other words, although light does not “register” time or space itself, light will always be measured by an inertial observer at a position and time exactly as if it had travelled at speed c continuously through the intervening medium. This fits nicely within the limitations set by quantum mechanics. This result is connected with previous work on retroactive event determination, suggesting the ubiquitous existence of “synchronicity”.

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04.62.+v	Quantum fields in curved spacetime
42.50.Ar	Photon statistics and coherence theory
03.67.Hk	Quantum communication
07.05.Kf	Data analysis: algorithms and implementation; data management
03.65.Pm	Relativistic wave equations

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An Exploration of Symmetries in the Friedmann Equation

Michael Ibison

AIP Conf. Proc. 1408, pp. 75-95; doi:http://dx.doi.org/10.1063/1.3663718 (21 pages)

Online Publication Date: 18 November 2011

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The Friedmann Equation for a conformal scale factor a(t) is observed to be invariant under a Mobius transformation. Using that freedom, a synthetic scale factor z(t) is defined that obeys a modified Friedman equation invariant under the replacement z(t)→±1/z(t). If this is taken this to be the more fundamental form then the traditional Friedmann equation can be shown to be missing a term due to a species with equation of state w = −2/3. We investigate in detail one particular cosmology in which it is possible to specify the contribution from this new species.

We suggest a means of avoiding a potentially redundant copy of the development of the universe the above implies through a novel cosmological spacetime manifold that is a Mobius band closed in time and non‐orientable in space. Though it is closed, a Dirac field in such a spacetime may still possess a global arrow of time by virtue of the twist of the Mobius band.

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03.65.Pm	Relativistic wave equations
98.80.Bp	Origin and formation of the Universe
04.40.Nr	Einstein-Maxwell spacetimes, spacetimes with fluids, radiation or classical fields
07.30.Dz	Vacuum gauges
02.40.Xx	Singularity theory

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Mechanism Of The Quantum Speed‐up

Giuseppe Castagnoli

AIP Conf. Proc. 1408, pp. 99-119; doi:http://dx.doi.org/10.1063/1.3663719 (21 pages)

Online Publication Date: 18 November 2011

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Bob chooses a function and gives to Alice the black box that computes it. Alice, without knowing Bob's choice, should find a character of the function (e. g. its period) by computing its value for different arguments. There is naturally correlation between Bob's choice and the solution found by Alice. We show that, in quantum algorithms, this correlation becomes quantum. This highlights an overlooked measurement problem: sharing between two completely or partly redundant measurements the determination of completely or partly correlated measurement outcomes. All is like Alice, by reading the solution at the end of the algorithm, contributed to the initial choice of Bob, with half of it in quantum superposition for all the possible ways of taking this half. This contribution, back evolved to before running the algorithm, where Bob's choice is located, becomes Alice knowing in advance half of the choice. The quantum algorithm is the quantum superposition of all the possible ways of taking half of Bob's choice and, given the advanced knowledge of it, classically computing the missing half. The quantum speed‐up comes from comparing two classical algorithms, with and without advanced knowledge of half of Bob's choice.

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03.67.Lx	Quantum computation architectures and implementations
07.05.Kf	Data analysis: algorithms and implementation; data management
05.70.Fh	Phase transitions: general studies
03.67.Hk	Quantum communication
02.30.Sa	Functional analysis

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The Retrocausal Nature of Quantum Measurement Revealed by Partial and Weak Measurements

Avshalom C. Elitzur and Eliahu Cohen

AIP Conf. Proc. 1408, pp. 120-131; doi:http://dx.doi.org/10.1063/1.3663720 (12 pages)

Online Publication Date: 18 November 2011

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Quantum measurement is sometimes more effective when its result is not definite. Partial measurement turns the initial superposition not into a certain state but to a greater probability for it, enabling probing the quantum state in cases where complete measurement makes the noncommuting variables inaccessible. It also enables full quantum erasure that, unlike prevailing method, can be carried out even on recorded results. Aharonov's weak measurement is another method of imprecisely measuring quantum variables, outsmarting the uncertainty principle in even subtler ways. Happily, the two methods complement and corroborate one another in several interesting ways. We gedankenly apply these measurements to the EPR case. A pair of entangled particles undergoes more than one pair of partial and weak measurements, which, unlike complete measurements, leave them partially correlated. Their erasure is then shown to be as nonlocal as measurement itself. Surprisingly, the temporal relations between such measurements in the EPR setting do not follow the temporal sequence perceived by an external observer. For each particle, the measurements performed on the other operate as if they occurred (with signs reversed) in its own past, and in reversed order. This fully accords with Cramer's transactional interpretation and Aharonov's two state‐vector formalism.

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03.65.Ca	Formalism
02.50.Cw	Probability theory
04.60.Pp	Loop quantum gravity, quantum geometry, spin foams
11.30.Er	Charge conjugation, parity, time reversal, and other discrete symmetries
05.70.Ce	Thermodynamic functions and equations of state

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Contextual values as a foundation for a unique Weak Value

J. Dressel and A. N. Jordan

AIP Conf. Proc. 1408, pp. 132-152; doi:http://dx.doi.org/10.1063/1.3663721 (21 pages)

Online Publication Date: 18 November 2011

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We expand on the contextual values formalism introduced in Dressel et al., Phys. Rev. Lett. 104, 240401 (2010) and describe in detail the sufficient conditions for uniquely defining the generalized weak value as the weak limit of a conditioned average. We also respond to Parrott's proposed counter‐example to the uniqueness of the generalization of the weak value [arXiv:1105.4188]. The counter‐example does not satisfy our prescription in the case of an underdetermined measurement context. We show that when the contextual values formalism is properly applied to this example, a natural interpretation of the measurement emerges and the uniqueness result in the weak limit holds. A proof of the uniqueness result is given in the general case. We discuss several applications of the formalism.

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03.65.Ca	Formalism
02.50.Ng	Distribution theory and Monte Carlo studies
42.25.Ja	Polarization
05.40.Ca	Noise
03.67.Hk	Quantum communication

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Delayed choice experiments, the arrow of time, and quantum measurement

L. S. Schulman

AIP Conf. Proc. 1408, pp. 153-167; doi:http://dx.doi.org/10.1063/1.3663722 (15 pages)

Online Publication Date: 18 November 2011

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By a radical modification of statistical mechanics the measurement process of quantum mechanics can be described in terms of pure, unitary time evolution, with no wave function collapse or many‐world ideas. The key notion is “special states,” rare microscopic states of a complex system. Recovering the standard probabilities requires of this theory the appearance of Cauchy‐distributed noise in some measurement processes. This article treats experimental situations where such noise might be detected and correlated with the need or absence of need for special states. Included in this possibility are “delayed choice” experiments, in which the correlation contravenes conventional ideas on causality. Background material on all topics is provided.

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06.30.Ft	Time and frequency
02.50.Ng	Distribution theory and Monte Carlo studies
05.40.Ca	Noise
02.50.Cw	Probability theory
04.20.Gz	Spacetime topology, causal structure, spinor structure

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Causality Is Inconsistent With Quantum Field Theory

Fred Alan Wolf

AIP Conf. Proc. 1408, pp. 168-188; doi:http://dx.doi.org/10.1063/1.3663723 (21 pages)

Online Publication Date: 18 November 2011

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Causality in quantum field theory means the vanishing of commutators for spacelike separated fields (VCSSF). I will show that VCSSF is not tenable. For VCSSF to be tenable, and therefore, to have both retarded and advanced propagators vanish in the elsewhere, a superposition of negative energy antiparticle and positive energy particle propagators, traveling forward in time, and a superposition of negative energy particle and positive energy antiparticle propagators, traveling backward in time, are required. Hence VCSSF predicts non‐vanishing probabilities for both negative energy particles in the forward‐through‐time direction and positive energy antiparticles in the backwards‐through‐time direction. Therefore, since VCSSF is unrealizable in a stable universe, tachyonic propagation must occur in denial of causality.

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03.70.+k	Theory of quantized fields
84.50.+d	Electric motors
02.50.Cw	Probability theory
03.65.Nk	Scattering theory
04.62.+v	Quantum fields in curved spacetime

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Experimental Evidence for Anomalous Retroactive Influences on Human Cognition and Affect

Daryl J. Bem

AIP Conf. Proc. 1408, pp. 191-203; doi:http://dx.doi.org/10.1063/1.3663724 (13 pages)

Online Publication Date: 18 November 2011

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Six experiments are described that take well‐established psychological effects on human cognition and affect and “time‐reverse” them so that the individual's responses are obtained before the putatively causal stimulus events occur. Two of the experiments tested for the retroactive facilitation of recall: It is well known that rehearsing or practicing a set of verbal materials enhances an individual's ability to recall them on a subsequent test. In our experiments, participants were first shown 48 common words one at a time and were then asked to recall as many of those words as they could. They were then given practice exercises on a randomly selected subset of those words. The results show that participants recalled more of the words they later practiced than the control words they did not practice. Two experiments on retroactive priming provide evidence for retroactive influence on an individual's response times when judging the pleasantness or unpleasantness of visual stimuli. Finally, two experiments provide evidence for the retroactive habituation to emotionally arousing visual stimuli. Each of the six experiments yielded statistically significant results, with a combined z = 3.66, p = .0001, and an effect size (d) of 0.25. The six experiments are a subset of nine retroactive influence experiments reported in Bem [1] that yielded a combined z = 6.66, p = 1.34×10⁻¹¹, and an effect size of 0.22.

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07.05.Bx	Computer systems: hardware, operating systems, computer languages, and utilities
07.05.Kf	Data analysis: algorithms and implementation; data management
03.67.Hk	Quantum communication
07.05.Pj	Image processing
11.30.Er	Charge conjugation, parity, time reversal, and other discrete symmetries

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Predicting the Unpredictable: 75 Years of Experimental Evidence

Dean I. Radin

AIP Conf. Proc. 1408, pp. 204-217; doi:http://dx.doi.org/10.1063/1.3663725 (14 pages)

Online Publication Date: 18 November 2011

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From time immemorial, people have reported foreknowledge of future events. To determine whether such experiences are best understood via conventional explanations, or whether a retrocausal phenomenon might be involved in some instances, researchers have conducted hundreds of controlled laboratory experiments over the past 75 years. These studies fall into four general classes, and each class has generated repeatable evidence consistent with retrocausation. The statistical results for a class of forced‐choice studies is associated with odds against chance of about 10²⁴; for a class of free‐response studies, odds about 10²⁰; for psychophysiological‐based studies, odds about 10¹⁷; and for implicit decision studies, odds about 10¹⁰. Effect sizes observed in the latter three classes are nearly identical, indicating replication of similar underlying effects. These effects are also in close agreement with the average effect size across 25,000 conventional social psychology experiments conducted over the last century, suggesting that retrocausal phenomena may not be especially unique, at least not in terms of the magnitude of effect. Bayesian analyses of the most recent classes of experiments confirm that the evidence is strongly in favor of a genuine effect, with Bayes Factors ranging from 13,669 to 1 for implicit decision experiments, to 2.9×10¹³ to 1 for psychophysiological designs. For the two most recent classes of studies examining retrocausal effects via unconscious physiological or behavioral measures, 85 of 101 studies (84%) reported by 25 different laboratories from the United States, Italy, Spain, Holland, Austria, Sweden, England, Scotland, Iran, Japan, and Australia, have produced results in the direction predicted by a retrocausal effect (odds against chance = 1.3×10¹², via a sign test). Assessment of the methodologies used in these studies has not identified plausible conventional alternatives for the observed outcomes, suggesting the existence of a genuine retrocausal phenomenon.

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07.05.Bx	Computer systems: hardware, operating systems, computer languages, and utilities
07.05.Kf	Data analysis: algorithms and implementation; data management
87.19.lc	Noise in the nervous system
05.30.Pr	Fractional statistics systems (anyons, etc.)
04.20.Gz	Spacetime topology, causal structure, spinor structure

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Laboratory Demonstration of Retroactive Influence in a Digital System

Garret Moddel, Zixu Zhu, and Adam M. Curry

AIP Conf. Proc. 1408, pp. 218-231; doi:http://dx.doi.org/10.1063/1.3663726 (14 pages)

Online Publication Date: 18 November 2011

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Retrocausation has been postulated in physical systems and observed in animate systems. The experiments described here extend methods used in human experiments to systems that are inanimate. One random‐event generator, the controller‐REG, was used to shut off a second REG, the subject‐REG, at a random time. The output of the subject‐REG was accumulated over several runs, each consisting of hundreds of trials, to look for a change in the randomness of its output bit stream in advance of the subject‐REGs shut off. For the first three runs large changes were observed during the last second before shut off, changes of approximately 1 bit in 40 that exceeded odds against chance of 1 million to 1. Variations and later an exact replication of the early results failed to show the changes observed in the first three runs. This failure to replicate is an indication that there is an additional uncontrolled variable that must be taken into account, quite possibly the intention and enthusiasm of the experimenters. That addition leads to the question as to whether the subject‐REG was subject to advance influence from its impending shut off, or instead whether its output was in a superposition of different states until the operator observed the results. The observation would then have caused a collapse of the superposition into a fixed state, like the collapse of quantum mechanical wavefunction. In either case, a retroactive influence was clearly in evidence.

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03.65.Ta	Foundations of quantum mechanics; measurement theory
05.30.Pr	Fractional statistics systems (anyons, etc.)
06.30.Ft	Time and frequency
04.20.Gz	Spacetime topology, causal structure, spinor structure
65.40.gd	Entropy

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Retrocausation, Consistency, and the Bilking Paradox

York H. Dobyns

AIP Conf. Proc. 1408, pp. 235-254; doi:http://dx.doi.org/10.1063/1.3663727 (20 pages)

Online Publication Date: 18 November 2011

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Retrocausation seems to admit of time paradoxes in which events prevent themselves from occurring and thereby create a physical instance of the liar's paradox, an event which occurs iff it does not occur. The specific version in which a retrocausal event is used to trigger an intervention which prevents its own future cause is called the bilking paradox (the event is bilked of its cause).

The analysis of Echeverria, Klinkhammer, and Thorne (EKT) suggests time paradoxes cannot arise even in the presence of retrocausation. Any self‐contradictory event sequence will be replaced in reality by a closely related but noncontradictory sequence. The EKT analysis implies that attempts to create bilking must instead produce logically consistent sequences wherein the bilked event arises from alternative causes.

Bilking a retrocausal information channel of limited reliability usually results only in failures of signaling. An exception applies when the bilking is conducted in response only to some of the signal values that can be carried on the channel. Theoretical analysis based on EKT predicts that, since some of the channel outcomes are not bilked, the channel is capable of transmitting data with its normal reliability, and the paradox‐avoidance effects will instead suppress the outcomes that would lead to forbidden (bilked) transmissions.

A recent parapsychological experiment by Bem displays a retrocausal information channel of sufficient reliability to test this theoretical model of physical reality's response to retrocausal effects. A modified version with partial bilking would provide a direct test of the generality of the EKT mechanism.

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04.62.+v	Quantum fields in curved spacetime
07.05.Kf	Data analysis: algorithms and implementation; data management
03.50.De	Classical electromagnetism, Maxwell equations
07.68.+m	Photography, photographic instruments; xerography
03.65.Ta	Foundations of quantum mechanics; measurement theory

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Understanding Retrocausality—Can a Message Be Sent to the Past?

Richard Shoup

AIP Conf. Proc. 1408, pp. 255-278; doi:http://dx.doi.org/10.1063/1.3663728 (24 pages)

Online Publication Date: 18 November 2011

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We examine why exactly it is that a message cannot be sent into the past and received there using quantum physics, yet certain anomalous correlations can make it appear just that way. To accomplish this, we must first explore more deeply the usual concepts of superposition, entanglement, measurement, locality, and causality. From these reinterpreted concepts, and through analyses of the usual forward EPR experimental arrangement and a time‐symmetrical backward version, we can better understand the fundamental inadequacy of the idea of “causality” (both forward and backward). We also discuss possible explanations for apparent retrocausal anomalies such as those of the recent experiments by psychologist Daryl Bem.

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04.20.Gz	Spacetime topology, causal structure, spinor structure
03.65.Aa	Quantum systems with finite Hilbert space
03.67.Hk	Quantum communication
41.85.Ct	Particle beam shaping, beam splitting
03.65.Ca	Formalism

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Using Psychokinesis to Explore the Nature of Quantum Randomness

Jean E. Burns

AIP Conf. Proc. 1408, pp. 279-290; doi:http://dx.doi.org/10.1063/1.3663729 (12 pages)

Online Publication Date: 18 November 2011

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In retrocausation different causal events can produce different successor events, yet a successor event reflecting a particular cause occurs before the causal event does. It is sometimes proposed that the successor event is determined by propagation of the causal effect backwards in time via the dynamical equations governing the events. However, because dynamical equations are time reversible, the evolution of the system is not subject to change. Therefore, the backward propagation hypothesis implies that what may have seemed to be an arbitrary selection of a causal factor was in reality predetermined.

Yet quantum randomness can be used to determine the causal factor, and a quantum random event is ordinarily thought of as being arbitrarily generated. So we must ask, when quantum random events occur, are they arbitrary (subject to their probabilistic constraints) or are they predetermined?

Because psychokinesis (PK) can act on quantum random events, it can be used as a probe to explore questions such as the above. It is found that if quantum random events are predetermined (aside from the action of PK), certain types of experimental design can show enhanced PK through the use of precognition. Actual experiments are examined and compared, and most of those for which the design is especially suitable for showing this effect had unusually low p values for the number of trials. It is concluded that either the experimenter produced a remarkably strong experimenter effect or quantum random events are predetermined, thereby enabling enhanced PK in suitable experimental designs.

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04.20.Gz	Spacetime topology, causal structure, spinor structure
11.30.Er	Charge conjugation, parity, time reversal, and other discrete symmetries
02.50.Cw	Probability theory
01.50.Pa	Laboratory experiments and apparatus
07.50.Hp	Electrical noise and shielding equipment

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Retro‐causation, Minimum Contradictions and Non‐locality

Menas Kafatos and Athanassios A. Nassikas

AIP Conf. Proc. 1408, pp. 291-296; doi:http://dx.doi.org/10.1063/1.3663730 (6 pages)

Online Publication Date: 18 November 2011

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Retro‐causation has been experimentally verified by Bem and proposed by Kafatos in the form of space‐time non‐locality in the quantum framework. Every theory includes, beyond its specific axioms, the principles of logical communication (logical language), through which it is defined. This communication obeys the Aristotelian logic (Classical Logic), the Leibniz Sufficient Reason Principle, and a hidden axiom, which basically states that there is anterior‐posterior relationship everywhere in communication. By means of a theorem discussed here, it can be proved that the communication mentioned implies contradictory statements, which can only be transcended through silence, i.e. the absence of any statements. Moreover, the breaking of silence is meaningful through the claim for minimum contradictions, which implies the existence of both a logical and an illogical dimension; contradictions refer to causality, implying its opposite, namely retro‐causation, and the anterior posterior axiom, implying space‐time non‐locality. The purpose of this paper is to outline a framework accounting for retro‐causation, through both purely theoretical and reality based points of view.

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03.65.Aa	Quantum systems with finite Hilbert space
03.65.Ta	Foundations of quantum mechanics; measurement theory
04.20.Gz	Spacetime topology, causal structure, spinor structure
03.67.Hk	Quantum communication
02.50.Fz	Stochastic analysis

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Toward a Classical Thermodynamic Model for Retro‐cognition

Edwin C. May

AIP Conf. Proc. 1408, pp. 297-307; doi:http://dx.doi.org/10.1063/1.3663731 (11 pages)

Online Publication Date: 18 November 2011

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Retro‐cognition—a human response before a randomly determined future stimulus—has always been part of our experience. Experiments over the last 80 years show a small but statistically significant effect. If this turns out to be true, then it suggests a form of macroscopic retro‐causation. The 2nd Law of Thermodynamics provides an explanation for the apparent single direction of time at the macroscopic level although time is reversible at the microscopic level. In a preliminary study, I examined seven anomalous cognition (a.k.a., ESP) studies in which the entropic gradients and the entropy of their associated target systems were calculated, and the quality of the response was estimated by a rating system called the figure of merit. The combined Spearman's correlation coefficient for these variables for the seven studies was 0.211 (p = 6.4×10⁻⁴) with a 95% confidence interval for the correlation of [0.084, 0.332]; whereas, the same data for a correlation with the entropy itself was 0.028 (p = 0.36; 95% confidence interval of [−0.120–0.175]). This suggests that anomalous cognition is mediated via some kind of a sensory system in that all the normal sensory sytems are more sensitive to changes than they are to inputs that are not changing. A standard relationship for the change of entropy of a binary sequence appears to provide an upper limit to anomalous cognition functioning for free response and for forced‐choice Zener card guessing. This entropic relation and an apparent limit set by the entropy may provide a clue for understanding macroscopic retro‐causation.

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65.40.gd	Entropy
05.70.Ce	Thermodynamic functions and equations of state
11.30.Er	Charge conjugation, parity, time reversal, and other discrete symmetries
07.05.Mh	Neural networks, fuzzy logic, artificial intelligence
07.68.+m	Photography, photographic instruments; xerography
07.05.Kf	Data analysis: algorithms and implementation; data management

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