相关论文: Dispersion Relations and Relativistic Causality
In nonrelativistic quantum mechanics the wave-function of a free particle which initially is in a finite volume immediately spreads to infinity. In a nonrelativistic theory this is of no concern, but we show that the same instantaneous…
I derive a temporally propagated uni-directional optical pulse equation valid in the few cycle limit. Temporal propagation is advantageous because it naturally preserves causality, unlike the competing spatially propagated models. The exact…
We present a novel derivation of special relativity based on the information physics of events comprising a causal set. We postulate that events are fundamental, and that some events have the potential to receive information about other…
In this paper we present a pedestrian review of the theoretical fact that all relativistic wave equations possess solutions of arbitrary velocities $0 \leq v < \infty$. We discuss some experimental evidences of $v \geq c$ transmission of…
In this review, we take an extensive look at the role that the principles of causality and passivity have played in various areas of physics and engineering, including in the modern field of metamaterials. The aim is not to provide a…
A usual causal requirement on a viable theory of matter is that the speed of sound be at most the speed of light. In view of various recent papers querying this limit, the question is revisited here. We point to various issues confronting…
We re-examine the "Regge-Tolman paradox" with reference to some recent experimental results. It is straightforward to find a formula for the velocity v of the moving system required to produce causality violation. This formula typically…
Studies of new hyperbolic systems for the Einstein evolution equations show that the ``slicing density'' $\alpha(t,x)$ can be freely specified while the lapse $N = \alpha g^{1/2}$ cannot. Implementation of this small change in the…
One may believe that front velocities of waves in a given theory coincide with the UV limit of phase velocities for any dispersion relations. This implies that IR physics is irrelevant to the discussion of propagation speed of waves. We…
In this paper, we show that all non-trivial solutions of a broad class of nonlinear dispersive equations, whose linear evolution is governed by a dispersion relation under minimal regularity assumptions, cannot remain compactly supported…
All physical process are subject to some laws which determine with math accurately its time-space evolution. These laws are described, in the last analysis for the principle of causality. The physical space can be homogeneous or…
Two similar Minkowskian diffusions have been considered, on one hand by Barbachoux, Debbasch, Malik and Rivet ([BDR1], [BDR2], [BDR3], [DMR], [DR]), and on the other hand by Dunkel and H\"anggi ([DH1], [DH2]). We address here two questions,…
We study the long time behavior of positive solutions of the Cauchy problem for nonlinear reaction-diffusion equations in $\mathbb{R}^N$ with bistable, ignition or monostable nonlinearities that exhibit threshold behavior. For $L^2$ initial…
The group-velocity of evanescent waves (in undersized waveguides, for instance) was theoretically predicted, and has been experimentally verified, to be Superluminal (v_g > c). By contrast, it is known that the precursor speed in vacuum…
We develop a relativistic treatment of interference between light reflected from a falling cube retroreflector in the vertical arm of an interferometer, and light in a reference beam in the horizontal arm. Coordinates that are nearly…
The $\kappa$-Minkoswki space-time provides a quantum noncommutative-deformation of the usual Minkowski space-time. However, a notion of causality is difficult to be defined in such a space with noncommutative time. In this paper, we define…
The result from the SN1a projects suggest that the dark energy can be represented by a fluid with w<-1. However, it is commonly argued that a fluid with |w|>1 contradicts causality. Here, we will show that a fluid with |w|>1 does not…
We demonstrate the simultaneous propagation of slow- and fast-light optical pulses in a four-wave mixing scheme using warm potassium vapor. We show that when the system is tuned such that the input probe pulses exhibit slow-light group…
Dark energy candidates for which the equation-of-state parameter w is less than -1 violate the dominant energy condition, and are typically unstable. In scalar-tensor theories of gravity, however, the expansion of the universe can mimic the…
We consider reaction-diffusion equations of porous medium type, with different kind of reaction terms, and nonnegative bounded initial data. For all the reaction terms under consideration there are initial data for which the solution…