Superluminal Signals Research Articles

Superluminal group velocity in a birefringent crystal

We examine the effect of superluminal signal propagation through a birefringent crystal, where the effect is not due to absorption or reflection, but to the filtration of a special polarization component. We first examine the effect by a stationary phase analysis, with results consistent with those of an earlier analysis of the system. We supplement this analysis by considering the transit of a gaussian wave and find bounds for the validity of the stationary phase result. The propagation of the gaussian wave is illustrated by figures.

Attractor scenarios and superluminal signals ink-essence cosmology

Cosmological scenarios with $k$-essence are invoked in order to explain the observed late-time acceleration of the Universe. These scenarios avoid the need for fine-tuned initial conditions (the ``coincidence problem'') because of the attractorlike dynamics of the $k$-essence field $\ensuremath{\phi}$. It was recently shown that all $k$-essence scenarios with Lagrangians $p=L(X){\ensuremath{\phi}}^{\ensuremath{-}2}$, where $X\ensuremath{\equiv}\frac{1}{2}{\ensuremath{\phi}}_{,\ensuremath{\mu}}{\ensuremath{\phi}}^{,\ensuremath{\mu}}$, necessarily involve an epoch where perturbations of $\ensuremath{\phi}$ propagate faster than light (the ``no-go theorem''). We carry out a comprehensive study of attractorlike cosmological solutions (``trackers'') involving a $k$-essence scalar field $\ensuremath{\phi}$ and another matter component. The result of this study is a complete classification of $k$-essence Lagrangians that admit asymptotically stable tracking solutions, among all Lagrangians of the form $p=K(\ensuremath{\phi})L(X)$. Using this classification, we select the class of models that describe the late-time acceleration and avoid the coincidence problem through the tracking mechanism. An analogous ``no-go theorem'' still holds for this class of models, indicating the existence of a superluminal epoch. In the context of $k$-essence cosmology, the superluminal epoch does not lead to causality violations. We discuss the implications of superluminal signal propagation for possible causality violations in Lorentz-invariant field theories.

Reply to ‘Comment on “Helmholtz Theorem and the V-Gauge in the Problem of Superluminal and Instantaneous Signals in Classical Electrodynamics” by A. Chubykalo et al.’ by J.A. Heras [Found. Phys. Lett. vol. 19(6) p. 579 (2006)

This is the reply to `COMMENT ON ``HELMHOLTZ THEOREM AND THE V-GAUGE IN THE PROBLEM OF SUPERLUMINAL AND INSTANTANEOUS SIGNALS IN CLASSICAL ELECTRODYNAMICS" BY A. CHUBYKALO ET AL' BY J. A. HERAS [FOUND. PHYS. LETT. vol. 19(6) p. 579 (2006)]

Self Replication and Signalling

It is known that if one could clone an arbitrary quantum state one could send signal faster than the speed of light. However it remains interesting to see that if one can perfectly self replicate an arbitrary quantum state, does it violate the no signaling principle? Here we see that perfect self replication would also lead to superluminal signaling.

Statistical Separabilityof the World and Consistency Between QuantumTheory, Relativity, and Causality

We show that the quantum world with non-local states and originalstatistics is statistically separable. According to relativisticdynamics, the super-luminal signal transmission is impossible. Thepresent quantum theory is therefore consistent with the relativity and the causality.

Developing the Deutsch–Hayden approach to quantum mechanics

The formalism of Deutsch and Hayden is a useful tool for describing quantum mechanics explicitly as local and unitary, and therefore quantum information theory as concerning a ‘flow’ of information between systems. In this paper we show that these physical descriptions of flow are unique, and develop the approach further to include the measurement interaction and mixed states. We then give an analysis of entanglement swapping in this approach, showing that it does not in fact contain either nonlocal effects or any form of superluminal signalling.

Causal field theory with an infinite speed of sound

We introduce a model of scalar field dark energy, Cuscuton, which can be realized as the incompressible (or infinite speed of sound) limit of a scalar field theory with a noncanonical kinetic term (or $k$-essence). Even though perturbations of Cuscuton propagate superluminally, we show that they have a locally degenerate phase space volume (or zero entropy), implying that they cannot carry any microscopic information, and thus the theory is causal. Even coupling to ordinary scalar fields cannot lead to superluminal signal propagation. Furthermore, we show that the family of constant field hypersurfaces is the family of constant mean curvature hypersurfaces, which are the analogs of soap films (or soap bubbles) in Euclidian space. This enables us to find the most general solution in $1+1$ dimensions, whose properties motivate conjectures for global degeneracy of the phase space in higher dimensions. Finally, we show that the Cuscuton action can model the continuum limit of the evolution of a field with discrete degrees of freedom and argue why it is protected against quantum corrections at low energies. While this paper mainly focuses on interesting features of Cuscuton in a Minkowski space-time, a companion paper examines cosmology with Cuscuton dark energy.

Nonlinear control of ‘fast’ light by ‘slow’ light

The phenomena of slow and super-luminal propagation of electromagnetic waves are considered in the context of a magnetized plasma with undulator induced transparency (UIT). Without the magnetic undulator, the plasma is opaque to the right-hand circularly polarized radiation at the electron cyclotron frequency. Addition of a helical undulator results in the dramatic slowing down of wave propagation. Super-luminal propagation occurs due to the strong coupling between the right- and left-hand circularly polarized waves. We demonstrate that, depending on the detected wave polarization, super-luminal and slow radiation can be observed at the same frequency. Moreover, the super-luminal signal can be controlled by the intensity of the incident signal.

Comment on “Helmholtz Theorem and the V-Gauge in the Problem of Superluminal and Instantaneous Signals in Classical Electrodynamics,” by A. Chubykalo et al.

Fundamental errors in a paper by Chubykalo et al. [2] are highlighted. Contrary to their claim that “… the irrotational component of the electric field has a physical meaning and can propagate exclusively instantaneously,” it is shown that this instantaneous component is physically irrelevant because it is always canceled by a term contained in the solenoidal component. This result follows directly from the solution of the wave equation that satisfies the solenoidal component. Therefore the subsequent inference of these authors that there are two mechanisms of transmission of energy and momentum in classical electrodynamics, one retarded and the other one instantaneous, has no basis. The example given by these authors in which the full electric field of an oscillating charge equals its instantaneous irrotational component on the axis of oscillations is proven to be false.

Variable-bias coin tossing

Alice is a charismatic quantum cryptographer who believes her parties are unmissable; Bob is a (relatively) glamorous string theorist who believes he is an indispensable guest. To prevent possibly traumatic collisions of self-perception and reality, their social code requires that decisions about invitation or acceptance be made via a cryptographically secure variable-bias coin toss (VBCT). This generates a shared random bit by the toss of a coin whose bias is secretly chosen, within a stipulated range, by one of the parties; the other party learns only the random bit. Thus one party can secretly influence the outcome, while both can save face by blaming any negative decisions on bad luck. We describe here some cryptographic VBCT protocols whose security is guaranteed by quantum theory and the impossibility of superluminal signaling, setting our results in the context of a general discussion of secure two-party computation. We also briefly discuss other cryptographic applications of VBCT.

Superluminal Signals and the Resolution of the Causal Paradox

The experimental evidence for electromagnetic signals propagating with superluminal group velocity is recalled. Transformations of space and time depending on a synchronization parameter, e1, indicate the existence of a privileged inertial system. The Lorentz transformations are obtained for a particular e1≠0. No standard experiment on relativity depends on e1, but if accelerations are considered only e1=0 remains possible. The causal paradox generated by superluminal signals (SLS) in the theory of relativity does not exist in the theory with e1=0. The irrelevance of SLS for the Einstein, Podolsky and Rosen paradox is pointed out.

Helmholtz Theorem and the V-Gauge in the Problem of Superluminal and Instantaneous Signals in Classical Electrodynamics

In this work we substantiate the applying of the Helmholtz vector decomposition theorem (H-theorem) to vector fields in classical electrodynamics. Using the H-theorem, within the framework of the two-parameter Lorentz-like gauge (so called v-gauge), we show that two kinds of magnetic vector potentials exist: one of them (solenoidal) can act exclusively with the velocity of light c and the other one (irrotational) with an arbitrary finite velocity $v$ (including a velocity more than c . We show also that the irrotational component of the electric field has a physical meaning and can propagate exclusively instantaneously.

General properties of nonsignaling theories

This article identifies a series of properties common to all theories that do not allow for superluminal signaling and predict the violation of Bell inequalities. Intrinsic randomness, uncertainty due to the incompatibility of two observables, monogamy of correlations, impossibility of perfect cloning, privacy of correlations, bounds in the shareability of some states; all these phenomena are solely a consequence of the no-signaling principle and nonlocality. In particular, it is shown that for any distribution, the properties of (i) nonlocal, (ii) no arbitrarily shareable, and (iii) positive secrecy content are equivalent.

Superluminal Signaling and Relativity

Special relativity is said to prohibit faster-than-light (superluminal) signaling, yet controversy regularly arises as to whether this or that physical phenomenon violates the prohibition. I argue that the controversy is a result of a lack of clarity as to what it means to ‘signal’, and I propose a criterion. I show that according to this criterion, superluminal signaling is not prohibited by special relativity.

Nonlinearity without superluminality

Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signaling. As Czachor, Gisin, and Polchinski pointed out, this is not generally true of general nonlinear modifications of the Schr\"odinger equation. Excluding superluminal signaling has thus been taken to rule out most nonlinear versions of quantum theory. The no-superluminal-signaling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by nonrelativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which display the values of localized pure states need not allow superluminal signaling, provided that the devices display the values of the states of entangled subsystems as defined in a nonstandard, although natural, way. It follows that any locally defined nonlinear evolution of pure states can be made consistent with Minkowski causality.

No Signaling and Quantum Key Distribution

Standard quantum key distribution protocols are provably secure against eavesdropping attacks, if quantum theory is correct. It is theoretically interesting to know if we need to assume the validity of quantum theory to prove the security of quantum key distribution, or whether its security can be based on other physical principles. The question would also be of practical interest if quantum mechanics were ever to fail in some regime, because a scientifically and technologically advanced eavesdropper could perhaps use postquantum physics to extract information from quantum communications without necessarily causing the quantum state disturbances on which existing security proofs rely. Here we describe a key distribution scheme provably secure against general attacks by a postquantum eavesdropper limited only by the impossibility of superluminal signaling. Its security stems from violation of a Bell inequality.

Superluminal hidden communication as the underlying mechanism for quantum correlations: constraining models

Since Bell's theorem, it is known that quantum correlations cannot be described by local variables (LV) alone: if one does not want to abandon classical mechanisms for correlations, a superluminal form of communication among the particles must be postulated. A natural question is whether such a postulate would imply the possibility of superluminal signaling. Here we show that the assumption of finite-speed superluminal communication indeed leads to signaling when no LV are present, and more generally when only LV derivable from quantum statistics are allowed. When the most general LV are allowed, we prove in a specific case that the model can be made again consistent with relativity, but the question remains open in general.

Nonlocal correlations as an information-theoretic resource

It is well known that measurements performed on spatially separated entangled quantum systems can give rise to correlations that are nonlocal, in the sense that a Bell inequality is violated. They cannot, however, be used for superluminal signaling. It is also known that it is possible to write down sets of ``superquantum'' correlations that are more nonlocal than is allowed by quantum mechanics, yet are still nonsignaling. Viewed as an information-theoretic resource, superquantum correlations are very powerful at reducing the amount of communication needed for distributed computational tasks. An intriguing question is why quantum mechanics does not allow these more powerful correlations. We aim to shed light on the range of quantum possibilities by placing them within a wider context. With this in mind, we investigate the set of correlations that are constrained only by the no-signaling principle. These correlations form a polytope, which contains the quantum correlations as a (proper) subset. We determine the vertices of the no-signaling polytope in the case that two observers each choose from two possible measurements with $d$ outcomes. We then consider how interconversions between different sorts of correlations may be achieved. Finally, we consider some multipartite examples.

Relativistic solitons and superluminal signals

Envelope solitons in the weakly nonlinear Klein–Gordon equation in 1 + 1 dimensions are investigated by the asymptotic perturbation (AP) method. Two different types of solitons are possible according to the properties of the dispersion relation. In the first case, solitons propagate with the group velocity (less than the light speed) of the carrier wave, on the contrary in the second case solitons always move with the group velocity of the carrier wave, but now this velocity is greater than the light speed. Superluminal signals are then possible in classical relativistic nonlinear field equations.

Superluminal Signal Velocity and Causality

A superluminal signal velocity (i.e. faster than light) is said to violate causality. However, superluminal signal velocities have been measured in tunneling experiments recently. The classical dipole interaction approach by Sommerfeld and Brillouin results in a complex refractive index with a finite real part. For the tunneling process with its purely imaginary refractive index this model obtaines a zero-time traversing of tunneling barriers in agreement with wave meechanics. The information of a signal is proportional to the product of its frequency band width and its time duration. The reasons that superluminal signal velocities do not violate causality are: (i) physical signals are frequency band limited and (ii) signals have a finite time duration.