Einstein Causality Research Articles

On causality proofs of superluminal barrier traversal of frequency band limited wave packets

Recently several approaches have been presented to prove causality for the measured superluminal photonic tunneling velocity. It is shown here that these proofs are not relevant for the frequency band limited microwave experiments in question (FM and AM signals) and that such experiments cannot be used to test Einstein causality.

Atomic coherence effects which produce superluminal (but causal) propagation of wavepackets

Analytic, limited-bandwidth signals, e.g. Gaussian wavepackets, whose frequencies lie in a transparent spectral window far below the resonance of an amplifying atomic medium, can propagate with phase, group, energy and 'signal' velocities (as defined by Sommerfeld and Brillouin) all exceeding the vacuum speed of light c. This 'superluminal' propagation may occur without significant distortion or gain. The front velocity, however, is not superluminal, and therefore Einstein causality is not violated. Applications will be discussed, including the possibility of using superluminal atomic coherence in condensed matter (e.g. macroscopic mass currents in superfluid helium which arise from vortex motions) for efficient gravitational antennae.

There are no causality problems for Fermi's two-atom system.

A repeatedly discussed gedanken experiment, proposed by Fermi to check Einstein causality, is reconsidered. It is shown that, contrary to a recent statement made by Hegerfeldt, there appears no causality paradoxon in a proper theoretical description of the experiment.

Causality problems for Fermi's two-atom system.

Let [ital A] and [ital B] be two atoms or, more generally, a source'' and a detector'' separated by some distance [ital R]. At [ital t]=0[ital A] is in an excited state, [ital B] in its ground state, and no photons are present. A theorem is proved that in contrast to Einstein causality and finite signal velocity the excitation probability of [ital B] is nonzero immediately after [ital t]=0. Implications are discussed.

Causality of superluminal barrier traversal

Recent microwave experiments have exhibited an apparently superluminal transport of evanescent mode packets in an undersized waveguide. Here it is shown that this effect is compatible with electrodynamics and respects Einstein causality in that no faster-than-light signals can be transmitted.

Measurement of the single-photon tunneling time.

Using a two-photon interferometer, we have measured the time delay for a photon to tunnel across a barrier consisting of a 1.1-\ensuremath{\mu}m-thick 1D photonic band-gap material. The peak of the photon wave packet appears on the far side of the barrier 1.47\ifmmode\pm\else\textpm\fi{}0.21 fs earlier than it would if it were to travel at the vacuum speed of light c. Although the apparent tunneling velocity (1.7\ifmmode\pm\else\textpm\fi{}0.2)c is superluminal, this is not a genuine signal velocity, and Einstein causality is not violated. The measured tunneling time is consistent with the group delay (``phase time''), but not with the semiclassical time.

Causality in the Schrödinger picture: Diagrammatical approach.

The Schroedinger picture of Einstein causality is discussed in the framework of relativistic local field theory. The essential tool is the diagrammatic expansion of the time-evolution kernel which elucidates the propagation of the disturbance at each step of the interaction. At the level of the wave function, the causal character of the theory is rather complicated. However if the spacelike density matrix {rho}{sub {ital s}} is defined by integrating over the timelike field variables, it receives no influence of the signal. Any local disturbance is shown to propagate inside the forward light cone. It is also shown that causality is most clearly seen in the Wigner representation of the density matrix. The result automatically includes a proof of nonrelativistic causality.

Einstein causality and Artin braids

Within the restricted context of conformal QFTh 2 we present a systematic analysis of the exchange algebras of light-cone fields which result from the previously studied global decomposition theory of Einstein-causal fields. Although certain aspects of the representation theory of exchange algebras with their Artin braid structure-constants appear in our illustrative examples (minimal and WZW models), our main interest are algebraic aspects. We view the present work as a new non-lagrangian (non-hamiltonian) approach to non-perturbative QFTh.

Einstein-Podolsky-Rosen constraints on quantum action at a distance: The Sutherland paradox

Assuming that future experiments confirm Aspect's discovery of nonlocal interactions between quantum pairs of correlated particles, we analyze the constraints imposed by the EPR reasoning on the said interactions. It is then shown that the nonlocal relativistic quantum potential approach plainly satisfies the Einstein causality criteria as well as the energy-momentum conservation in individual microprocesses. Furthermore, this approach bypasses a new causal paradox for timelike separated EPR measurements deduced by Sutherland in the frame of an approach by means of space-time zigzags with advanced potentials. It is finally demonstrated that this inherent quantum causal direct interaction establishes permanent EPR correlations which are always restricted to spacelike separations and are instantaneous only in the center-of-mass rest frame of the two-particle system.

Violation of Einstein causality in a model quantum system.

A series of theorems have been proved showing that localization in quantum mechanics is inconsistent with Einstein causality. In this paper a simple model of a localized source and a localized detector is studied. This model does not satisfy the assumptions of the rigorous theorems; nonetheless, it is found that the model violates Einstein causality. The effect is very small and resides in the nonresonant part of the transition probability.

Violation of causality in relativistic quantum theory?

We show that states of systems which, in a very general sense, are approximately localized at time $t=0$ in a finite region, with exponentially bounded tails outside, violate Einstein causality at later times. Implications are discussed.

Stochastic microcausality in relativistic quantum mechanics

A recently formulated concept of stochastic localizability is shown to be consistent with a concept of stochastic microcausality, which avoids the conclusions of Hegerfeldt's no-go theorem as to the inconsistency of sharp localizability of quantum particles and Einstein causality. The proposed localizability on quantum space-time is shown to lead to strict asymptotic causality. For finite time evolutions, upper bounds on propagation to the exterior of stochastic light cones are derived which show that the resulting probabilities are too small to be actually observable in a realistic context.

Analysis of the Einstein-Podolsky-Rosen experiment by relativistic quantum logic

The EPR experiment is investigated within the abstract language of relativistic quantum physics (relativistic quantum logic). First we show that the principles of reality (R) and locality (L) contradict the validity principle (Q) of quantum physics. A reformulation of this argument is then given in terms of relativistic quantum logic which is based on the principlesR andQ. It is shown that the principleL must be replaced by a convenient relaxation ¯L, by which the contradiction can be eliminated. On the other hand this weak locality principle ¯L does not contradict Einstein causality and is thus in accordance with special relativity.

Constraints, positivity, 'obscure' representations and the spin-3/2 problem

The authors trace the failure of Einstein causality in interacting high-spin field theories to the presence of secondary constraints in the Cauchy initial value problem. They bring in and extend a theorem of Gel'Fand and Yaglom (1948), and use it to show that non-negativity of the field anticommutators for half-integral spin, and non-negativity of the field energy for integral spin, necessarily imply the existence of such constraints, except for the privileged spin values 0, 1/2 and 1. This is proven under very lax assumptions as to the nature of the mass spectrum. A systematic search is carried out for alternative spin-3/2 constraint schemes, taking a Lagrangian which contains thirteen adjustable parameters, many of which couple in the hitherto 'obscure' unmixed-spinor representations (3/2,0) and (0,3/2) of the Lorentz group. The search reveals two unfamiliar spin-3/2 equations, one of which is entirely new. The new equations are analysed and each contains a Rarita-Schwinger constraint subchain. This means that the new equations will also show causality failures. In five or more space-time dimensions additional field equations appear, which are very much simpler and give a much more fundamental role to the 'obscure' representation.

On conformal invariance in quantum field theory

We study the transformation law of interacting fields under the universal convering group of the conformal group. It is defined with respect to the representations of the discrete series. These representations are field representations in the sense that they act on finite component fields defined over Minkowski space. The conflict with Einstein causality is avoided as in the case of free fields with canonical dimension. Furthermore, we determine the conformal invariant two-point function of arbitrary spin. Our result coincides with that obtained by Rühl. In particular, we investigate the two-point function of symmetric and traceless tensor fields and give the explicit form of the trace terms.

Conformal transformations for quantized fields

Finite conformal transformations for quantized fields are obtained. The apparent conflict with Einstein's causality principle is resolved. It is shown that in quantum field theory one is in general dealing with representations of the universal covering group of the conformal group.

On the Energy Transport in Linear Chains

Equations of motion are solved for linear chains with an arbitrary number and arrangement of embedded heavy particles. Explicit results are given for the case of 2 heavy particles. In this case a continuum limit is studied whereby the light particles are represented by the motion of a field. The transmission of energy between the heavy particles will then clearly display the Einstein causality, i.e. there is a maximum signal velocity inherent in the mechanical model.

Acausality and Renormalizability

A few years ago, Velo and Zwanziger1l made an interesting observation: The covariant wave equation of an interacting higher-spin particle generally violates the Einstein causality. The covariant wave equation of a free higher-spin particle consists of equations of motion and constraints. When interaction is switched on, the constraints also are modified nontrivially. After eliminating them, therefore, the propagation character of the wave equation, which IS det.ermined by its highest-derivative terms, will be different from that in the free case. Then the action can generally propagate faster than light velocity, that is, ~e encounter acausality. No such phenomenon takes place for the spin-0 and spin-1/2 cases. The spin-1 case is marginal; the acausality depends on the form of interaction. The Proca equation for a vector field u# having a self-interaction .£int=g(U~'U) 2 was shown to be acausal for g<O. If the interaction of the higher-spin particle is due to an external field, the above acausality is not very troublesome because the existence of the external field already violates the Lorentz invariance of the theory. If, however, we consider a manifestly covariant quantum field theory, though the V elo-Zwanziger argument does not rigorously apply to it, the acausality trouble is very serious. Because of Lorentz invariance, super-light-velocity propagation implies propagation to the past in some other Lorentz frames. If quantum field theory is acausal, Heisenberg operators will not commute (or anticommute) at spacelike separations, so that T-products cannot be defined covariantly. On the other hand, we know that perturbation theory satisfies local commutativity in every order. The above· two aspects are compatible only if the order of the singularity on the light cone increases indefinitely for higher-order perturbation terms. Since the order of the light-cone singularity is bounded in. a renormalizable theory, it is natural to conjecture that a renormalizable field theory cannot be acausal in the sense of V elo and Zwanziger. [Of course, the converse is not true because the ¢5 theory is causal but unrenormalizable.] In the following, we present an instructive example to support the above conjecture.

Is the Maxwell Field Local?

Is the classical Maxwell field truly local? This question is raised by several observations, among them the Aharonov-Bohm effect; but the question cannot be answered without a systematic definition and characterization of local subalgebras of observables. This paper reformulates classical field theory in analogy to axiomatic quantum field theory and introduces a precise statement for local independence. (Synonyms for local independence are Einstein causality and principle of maximum signal velocity.) The formal answer of the analysis is: The free Maxwell field does not have local independence. This conclusion is critically discussed.

The energy momentum spectrum of quantum fields

It is proved, assuming Einstein causality, that the energy-momentum spectrum of a quantum field cannot be bounded. More is known under special assumptions [1, 4]. Our main concern is the method and general applicability of the result.