D. T. Pegg, Times' arrows, quantum measurement and superluminal behavior (eds. D. Mugnai, A. Ranfagni and L. S. Schulman) (Consiglio Nazionale Delle Richerche, Roma, 2001) p. 113
The closed causal chains arising from backward time travel do not lead to paradoxes if they are self consistent. This raises the question as to how physics ensures that only self-consistent loops are possible. We show that, for one particular case at least, the condition of self consistency is ensured by the interference of quantum mechanical amplitudes associated with the loop. If this can be applied to all loops then we have a mechanism by which inconsistent loops eliminate themselves.
It is claimed in the above paper that, if time travel were possible, quantum propagation would prevent classic time travel paradoxes by establishing consistent loops; an example circuit is used to demonstrate such a loop. It is argued here that established loops are not the framework in which the classic paradoxes arise; rather they arise via the establishment of a concrete initial history in which no disturbing time travel is allowed and then disturbing that history via the launch of the time traveller. It is shown that, operated in this two-pass fashion, if the first forward evolution of the…
Errors and paradoxes in quantum mechanics, entry in the Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy, ed. F. Weinert, K. Hentschel, D. Greenberger and B. Falkenburg (Springer), to appear
We discuss the Einstein, Podolsky, and Rosen paradox as it was formulated by Asher Peres in 1992 [4]. On this basis we realize an algebraic quantum like elaboration showing that in this formulation the paradox may be still interpreted and solved.
As it is well-known one of the most fascinating examples in remarkable discussion between Einstein and Bohr on the conceptual foundation of the quantum mechanics (Heisenberg energy-time uncertainty relation especially) was an experimental device representing a box hanged on an elastic spring. The pair of similar devices is used in this work for formulation of a classical and (implicitly) quantum mechanical analog of the famous two capacitors paradox. It admits a simple solution of the paradox since energy difference or seeming paradoxical "loss" can be explained by work of the elastic force fo…
The prediction of the N-box paradox, that whichever box is opened will contain the record of the particle having passed through it, is traced to a failure to specify whether the other boxes are distinguishable or indistinguishable. These correspond to different ways of lifting the degeneracy of a certain measurement, and have incompatible consequences.
A formulation of quantum mechanics based on an operational definition of state is presented. This formulation, which includes explicitly the macroscopic systems, assumes the probabilistic interpretation and is nevertheless objective. The classical paradoxes of quantum mechanics are analyzed and their origin is found to be the fictitious properties that are usually attributed to quantum-mechanical states. The hypothesis that any mixed state can always be considered as an incoherent superposition of pure states is found to contradict quantum mechanics. A solution of EPR paradox is proposed. It i…
I argue that Deutsch's model for the behavior of systems traveling around closed timelike curves (CTCs) relies implicitly on a substantive metaphysical assumption. Deutsch is employing a version of quantum theory with a significantly supplemented ontology of parallel existent worlds, which differ in kind from the many worlds of the Everett interpretation. Standard Everett does not support the existence of multiple identical copies of the world, which the D-CTC model requires. This has been obscured because he often refers to the branching structure of Everett as a "multiverse", and describes q…
In the standard physical interpretation of quantum theory, prediction and retrodiction are not symmetric. The opposite assertion by some authors results from their use of non-standard interpretations of the theory.
The orthodox quantum mechanics has been commonly regarded as being supported decisively by the polarization EPR experiments, in which Bell's inequalities have been violated. The given conclusion has been based, however, on several mistakes that have not been yet commonly known and sufficiently analyzed. The whole problem will be newly discussed and a corresponding solution will be proposed.
In this paper we concentrate on the nature of the liar paradox as a cognitive entity; a consistently testable configuration of properties. We elaborate further on a quantum mechanical model [Aerts, Broekaert, Smets 1999] that has been proposed to analyze the dynamics involved, and we focus on the interpretation and concomitant philosophical picture. Some conclusions we draw from our model favor an effective realistic interpretation of cognitive reality.
The many-worlds interpretation (MWI) of quantum mechanics is studied from an unprecedented ontological perspective based on the reality of (semi-) deterministic parallel worlds in the interpretation. It is demonstrated that with thanks to the uncertainty principle there would be no consistent way to specify the correct ontology of the Universe, hence the MWI is subject to an inherent contradiction which claims that the world where we live in is unreal.
We introduce a quantum mechanical model of time travel which includes two figurative beam splitters in order to induce feedback to earlier times. This leads to a unique solution to the paradox where one could kill one's grandfather in that once the future has unfolded, it cannot change the past, and so the past becomes deterministic. On the other hand, looking forwards towards the future is completely probabilistic. This resolves the classical paradox in a philosophically satisfying manner.
Many seemingly paradoxical effects are known in the predictions for outcomes of intermediate measurements made on pre- and post-selected quantum systems. Despite appearances, these effects do not demonstrate the impossibility of a noncontextual hidden variable theory, since an explanation in terms of measurement-disturbance is possible. Nonetheless, we show that for every paradoxical effect wherein all the pre- and post- selected probabilities are 0 or 1 and the pre- and post-selected states are nonorthogonal, there is an associated proof of contextuality. This proof is obtained by considering…
The Einstein's Boxes paradox was developed by Einstein, de Broglie, Heisenberg, and others to demonstrate the incompleteness of the Copenhagen Formulation of quantum mechanics. I explain the paradox using the Copenhagen Formulation.~I then show how a time-symmetric formulation of quantum mechanics resolves the paradox in the way envisioned by Einstein and de Broglie. Finally, I describe an experiment that can distinguish between these two formulations.
We consider the non-overlapping wave function paradox of Aharanov \textit{et al.}, wherein the relative phase between two wave functions cannot be measured by the moments of position or momentum. We show that there is an unlimited number of other expectation values that depend on the phase. We further show that the Wigner distribution is M-indeterminate, that is, a distribution whose moments do not uniquely determine the distribution. We generalize to more than two non-overlapping functions. We consider arbitrary representations and show there is an unlimited number of M-indeterminate distribu…
Based on the general thought that mechanics cannot be absolutely exact, supported by pulsed nuclear magnetic resonance (NMR) experiments on the reversal of time in spin systems, we postulate existence of a probability which do not follow from the Schroudinger equation, or X-probability. It is shown that the X-probability allows explain irreversibility of evolution of macrosystems, and also creates a basis for using probabilistic methods in statistical mechanics and for deliverance from the mechanical determinism.
We present an analysis of quantum mechanics and its problems and paradoxes taking into account the results that have been obtained during the last two decades by investigations in the field of `quantum structures research'. We concentrate mostly on the results of our group FUND at Brussels Free University. By means of a spin 1/2 model where the quantum probability is generated by the presence of fluctuations on the interactions between measuring apparatus and physical system, we show that the quantum structure can find its origin in the presence of these fluctuations. This appraoch, that we ha…
The Gibbs paradox has frequently been interpreted as a sign that particles of the same kind are fundamentally indistinguishable; and that quantum mechanics, with its identical fermions and bosons, is indispensable for making sense of this. In this article we shall argue, on the contrary, that analysis of the paradox supports the idea that classical particles are always distinguishable. Perhaps surprisingly, this analysis extends to quantum mechanics: even according to quantum mechanics there can be distinguishable particles of the same kind. Our most important general conclusion will according…
Backward causation in which future events affect the past is formalized in a way consistent with Special Relativity and shown to restore locality to nonrelativistic quantum mechanics. It can explain the correlations of the EPR paradox without using hidden variables. It also restores time-symmetry to microphysics. Quantum Mechanics has the right properties to allow for backward causation. The new model is probably untestable experimentally but it has profound philosophical implications concerning reality.
This article concerns a phenomenon of elementary quantum mechanics that is quite counter-intuitive, very non-classical, and apparently not widely known: a quantum particle can get reflected at a downward potential step. In contrast, classical particles get reflected only at upward steps. The conditions for this effect are that the wave length is much greater than the width of the potential step and the kinetic energy of the particle is much smaller than the depth of the potential step. This phenomenon is suggested by non-normalizable solutions to the time-independent Schroedinger equation, and…
A ring resonator involves a scattering process where a part of the output is fed again into the input. The same formal structure is encountered in the problem of time travel in a neighborhood of a closed timelike curve (CTC). We know how to describe quantum optics of ring resonators, and the resulting description agrees with experiment. We can apply the same formal strategy to any looped quantum evolution, in particular to the time travel. The argument is in its essence a topological one and thus does not refer to any concrete geometry. It is shown that the resulting paradigm automatically rem…
The Dirac equation has been applied to fermions scattering from the downward potential step. The results show some particles do not fall off the edge of the step and reflect. Also, based on de Broglie-Bohm interpretation of quantum mechanics (Bohmian mechanics) and Bohmian trajectories we have resolved the problem. Lastly, a phenomenological study of the Bohmian trajectory of the Klein paradox has been discussed.
A so called 'weak value' of an observable in quantum mechanics (QM) may be obtained in a weak measurement + post-selection procedure on the QM system under study. Applied to number operators, it has been invoked in revisiting some QM paradoxes (e.g., the so called Three Box paradox and Hardy s paradox). This requires the weak value to be interpreted as a bona fide property of the system considered, a par with entities like operator mean values and eigenvalues. I question such an interpretation; it has no support in the basic axioms of quantum mechanics and it leads to unreasonable results in c…
A concept of Kinetic Energy in Quantum Mechanics is analyzed. Kinetic Energy is not zero in many cases where there are no motion and flux. This paradox can be understood, using expansion of the wave function in Fourier integral, that is on the basis of virtual plane waves.
In the normal presentation of the EPR problem a comparison is made between the (weak) Copenhagen interpretation of quantum mechanics which seems to suggest that at times action at a distance may take place, and the hidden parameter interpretation which must satisfy Bell's inequality, in contradiction to the predictions of quantum mechanics. In this paper, we consider a relativistic approach to the paradox. However, the frame of reference under consideration is not the usual Lorenz frame but rather the spin frame of reference which is invariant with respect to the SU(2) group.
The quantum teleportation protocol can be used to probabilistically simulate a quantum circuit with backward-in-time connections. This allows us to analyze some conceptual problems of time travel in the context of physically realizable situations, to realize encrypted measurements of future states for which the decryption key becomes available only after the state is created, and to probabilistically realize a multistage quantum state processing within the time needed to complete only one stage. The probabilistic nature of the process resolves any paradox.
A seldom recognized fundamental difficulty undermines the concept of individual ``state'' in the present formulations of quantum statistical mechanics (and in its quantum information theory interpretation as well). The difficulty is an unavoidable consequence of an almost forgotten corollary proved by E. Schroedinger in 1936 and perused by J.L. Park, Am. J. Phys., Vol. 36, 211 (1968). To resolve it, we must either reject as unsound the concept of state, or else undertake a serious reformulation of quantum theory and the role of statistics. We restate the difficulty and discuss a possible resol…
We analyse in detail the reshaping mechanism leading to apparently "superluminal" advancement of a wave packet traversing a classically forbidden region. In the coordinate representation, a barrier is shown to act as an effective beamsplitter, recombining envelopes of the freely propagating pulse with various spacial shifts. Causality ensures that none of the constituent envelopes are advanced with respect to free propagation, yet the resulting pulse is advanced due to a peculiar interference effect, similar to the one responsible for "anomalous" values which occur in Aharonov's "weak measurem…
Recently we proposed the linguistic interpretation of quantum mechanics (called quantum and classical measurement theory), which was characterized as a kind of metaphysical and linguistic turn of the Copenhagen interpretation. This turn from physics to language does not only extend quantum theory to classical systems but also yield the quantum mechanical world view (i.e., quantum philosophy or quantum language). The purpose of this paper is to formulate the double-slit experiment, the quantum eraser experiment, Wheeler's delayed choice experiment, Hardy's paradox and the three boxes paradox (t…
Entangled states are in conflict with a general physical principle which expresses that a composite entity exists if and only if its components also exist, and the hypothesis that pure states represent the actuality of a physical entity, i.e., its 'existence'. A possible way to solve this paradox consists in completing the standard formulation of quantum mechanics, by adding more pure states. We show that this can be done, in a consistent way, by using the extended Bloch representation of quantum mechanics, recently introduced to provide a possible solution to the measurement problem. Hence, w…
A new interpretation of quantum mechanics, similar to the Copenhagen interpretation, is developed from time-symmetry arguments and commonly held principles concerning time and causality. These principles, which are grounded in ideas outside of quantum mechanics, suggest that the strange features and paradoxes of quantum mechanics come from backward causation, in which future events can change the past. Using these principles this paper gives a better understanding of (and reasons for) stationary states, tunneling, wave-particle duality, the measurement problem with the collapse of the state ve…
A new interpretation offers a consistent conceptual basis for nonrelativistic quantum mechanics. The Einstein-Podolsky-Rosen (EPR) paradox is solved and the violation of Bell's inequality is explained by maintaining realism, inductive inference and Einstein separability.
The main distinction between classical mechanics and quantum mechanics is the lack in the latter of a full mechanical determinism: different final states can arise from the same physical state, after the measurement. No hidden variable is supposed to exist, nothing can discriminate two apparently identical states even if they give a different result. In this paper we try to put the basis for a more fundamental theory that (approximately) coincides with quantum mechanics when comparing statistics, but it is more fundamental, since it mathematically describes measurement processes giving an expl…
The EPR paradox dates back to 1935 when Einstein et al., through the use of non commuting operators, proposed that quantum mechanics was not complete in that it suggested a `spooky action at a distance.' Later in 1964 John Bell was able to express the dilemma in a simple inequality involving spin-singlet states. If the inequality were satisfied then Einstein was correct and if it were violated then it favored the quantum mechanics point of view. In what follows, we present two approaches to Bell's inequality, and then offer an interpretation from the viewpoint of quantum mechanics based on the…
We describe how to generate an Einstein-Podolsky-Rosen (EPR) paradox between a mesoscopic mechanical oscillator and an optical pulse. We find two types of paradox, defined by whether it is the oscillator or the pulse that shows the effect Schrodinger called "steering". Only the oscillator paradox addresses the question of mesoscopic local reality for a massive system. In that case, EPR's "elements of reality" are defined for the oscillator, and it is these elements of reality that are falsified (if quantum mechanics is complete). For this sort of paradox, we show that a thermal barrier exists,…
Contrary to the opinion of J. Polchinski [Phys.Rev.Lett. {\bf 66}, 397-400 (1991)], the phenomenon of superluminal messages in nonlinear versions of quantum mechanics is not a specific difficulty in a class of theories formulated by S. Weinberg [Ann.Phys. (N.Y.), {\bf 194}, 336-386 (1989)]. It appears in all schemes which try to enlarge the orthodox class of observables, while conserving the traditional structure of the pure and mixed states.
The formalism of abstracted quantum mechanics is applied in a model of the generalized Liar Paradox. Here, the Liar Paradox, a consistently testable configuration of logical truth properties, is considered a dynamic conceptual entity in the cognitive sphere. Basically, the intrinsic contextuality of the truth-value of the Liar Paradox is appropriately covered by the abstracted quantum mechanical approach. The formal details of the model are explicited here for the generalized case. We prove the possibility of constructing a quantum model of the m-sentence generalizations of the Liar Paradox. T…
We consider quantum circuits with time travel designed for distinguishing specific nonorthogonal quantum states in two most popular models: Deutschs and postselected. We modify them by a presence of weakly coupled thermal environment. Using the Davies approximation we study how the thermal noise affects an ability of the circuits to distinguish nonorthogonal quantum states. We show that for purely dephasing environment a paradoxial power of such circuits remains preserved. We also present a physics based argument for conditions of validity of the maximum entropy rule introduced by David Deutsc…
Hardy's paradox was originally presented as a demonstration, without inequalities, of the incompatibility between quantum mechanics and the hypothesis of local causality. Equipped with newly developed tools that allow for a quantitative assessment of realism, here we revisit Hardy's paradox and argue that non-local causality is not mandatory for its solution; quantum irrealism suffices.
The Einstein-Podolski-Rosen paradox highlights several strange properties of quantum mechanics including the super position of states, the non locality and its limitation to determine an experiment only statistically. Here, this well known paradox is revisited theoretically for a pair of spin 1/2 systems in a singlet state under the assumption that in classical physics time evolves in discrete time steps Deltat while in quantum mechanics the individual spin system(s) evolve(s) between the eigenstates harmonically with a period of 4 Deltat. It is further assumed that time is a single variable, …
Most physicists agree that the Einstein-Podolsky-Rosen-Bell paradox exemplifies much of the strange behavior of quantum mechanics, but argument persists about what assumptions underlie the paradox. To clarify what the debate is about, we employ a simple and well-known thought experiment involving two correlated photons to help us focus on the logical assumptions needed to construct the EPR and Bell arguments. The view presented in this paper is that the minimal assumptions behind Bell's inequality are locality and counterfactual definiteness, but not scientific realism, determinism, or hidden …
Hardy's paradox is analysed within Feynman's formulation of quantum mechanics. A transition amplitude is represented as a sum over virtual paths which different intermediate measurements convert into different sets of real pathways. Contradictory statements emerge when applying to the same statistical ensemble. The "strange" weak values result is also investigated in this context.
This paper discusses the quantum mechanics of closed timelike curves (CTC) and of other potential methods for time travel. We analyze a specific proposal for such quantum time travel, the quantum description of CTCs based on post-selected teleportation (P-CTCs). We compare the theory of P-CTCs to previously proposed quantum theories of time travel: the theory is physically inequivalent to Deutsch's theory of CTCs, but it is consistent with path-integral approaches (which are the best suited for analyzing quantum field theory in curved spacetime). We derive the dynamical equations that a chrono…
The suggestion that particles of the same kind may be indistinguishable in a fundamental sense, even so that challenges to traditional notions of individuality and identity may arise, has first come up in the context of classical statistical mechanics. In particular, the Gibbs paradox has sometimes been interpreted as a sign of the untenability of the classical concept of a particle and as a premonition that quantum theory is needed. This idea of a quantum connection stubbornly persists in the literature, even though it has also been criticized frequently. Here we shall argue that although thi…
Statistical classical mechanics and quantum mechanics are developed and well-known theories that represent a basis for modern physics. The two described theories are well known and have been well studied. As these theories contain numerous paradoxes, many scientists doubt their internal consistencies. However, these paradoxes can be resolved within the framework of the existing physics without the introduction of new laws. To clarify the paper for the inexperienced reader, we include certain necessary basic concepts of statistical physics and quantum mechanics in this paper without the use of …
In this paper, we demonstrate how the interpretation of quantum mechanics due to Landé resolves the Schrödinger cat paradox and disposes of the problem of wave function collapse.
We formulate a paradox in relation to the description of a joint entity consisting of two subentities by standard quantum mechanics. We put forward a proposal for a possible solution, entailing the interpretation of density states as pure states. We explain where the inspiration for this proposal comes from and how its validity can be tested experimentally. We discuss the consequences on quantum axiomatics of the proposal.
We present a unified approach, based on the use of quantum uncertainty relations, for arriving at criteria for the demonstration of the EPR paradox and macroscopic superpositions. We suggest to view each criterion as a means to demonstrate an EPR-type paradox, where there is an inconsistency between the assumptions of a form of realism, either macroscopic realism (MR) or local realism (LR), and the completeness of quantum mechanics.
A new interpretation of nonrelativistic quantum mechanics is presented. It explains the violation of Bell's inequality by maintaining realism and the principle of locality. Schrodinger's cat paradox and the Einstein-Podolsky-Rosen paradox are solved, too. The new approach assumes the universal validity of the Schrodinger equation, while von Neumann's postulates about the measurement process are replaced with a new, consistent set of postulates. The underlying idea is that quantum states depend on quantum reference systems in a fundamental way. Quantum reference systems (a new concept, first in…
This is a short text covering some topics on the Foundations of Quantum Theory and it includes some comments on the recent Nature article by D. Frauchiger and R. Renner. The so-called "paradox" is simply due to a misunderstanding on the appropriate way to apply the quantum mechanical rules. The text is meant to be accessible to non physicists and the math is kept to a minimum (just some Linear Algebra and extremely elementary Probability Theory).
Quantum experiments detect particles, but they reveal information about wave properties. No matter how quanta are detected, they always express the local net state of the corresponding wave-function. The mechanism behind this process is still a mystery. However, quantum wave-functions evolve like classical waves. If they determine all the observations, why do they entail "weird" phenomena? In particular, why do they produce conceptual problems, such as the EPR paradox? It turns out that all the major interpretations in quantum mechanics are particle-based ontologies. Variables of fundamental i…
In this paper we re-investigate the core of Schroedinger's 'cat paradox'. We argue that one has to distinguish clearly between superpositions of macroscopic cat states and superpositions of entangled states which comprise both the state of the cat. It is shown, that in the first instance recurrence to decoherence or other mechanisms is not necessary in this special case in order to explain the absence of macroscopic superpositions. Additionally, we present modified versions of two quantum optical experiments as experimenta crucis. Applied rigorously, quantum mechanical formalism reduces the pr…
Quantum mechanics represents one of the greatest triumphs of human intellect and, undoubtedly, is the most successful physical theory we have to date. However, since its foundation about a century ago, it has been uninterruptedly the center of harsh debates ignited by the counterintuitive character of some of its predictions. The subject of one of these heated discussions is the so-called "retrodiction paradox", namely a deceptive inconsistency of quantum mechanics which is often associated with the "measurement paradox" and the "collapse of the wave function"; it comes from the apparent time-…
