arXiv subjects
Publications and source records attributed to H. Nikolic.
It is shown that the apparent incompatibility of Bohmian mechanics with standard quantum mechanics, found by Akhavan and Golshani quant-ph/0305020, is an artefact of the fact that the initial wavefunction they use, being proportional to a $δ$-function, is not a regular wavefunction.
Since any fermionic operator ψcan be written as ψ=q+ip, where q and p are hermitian operators, we use the eigenvalues of q and p to construct a functional formalism for calculating matrix elements that involve fermionic fields. The formalism is similar to that for bosonic fields and does not involve Grassmann numbers. This makes possible to perform numerical fermionic lattice computations that are much faster than not only other algorithms for fermions, but also algorithms for bosons.
A new approach to the concept of particles and their production in quantum field theory is developed. A local operator describing the current of particle density is constructed for scalar and spinor fields in arbitrary gravitational and electromagnetic backgrounds. This enables one to describe particles in a local, general-covariant and gauge-invariant way. However, the current depends on the choice of a 2-point function. There is a choice that leads to the local non-conservation of the current in a gravitational or an electromagnetic background, which describes local particle production consistent with the usual global description based on the Bogoliubov transformation. The most natural choice based on the Green function calculated using the Schwinger-DeWitt method leads to the local conservation of the current, provided that interactions with quantum fields are absent. Interactions with quantum fields lead to the local non-conservation of the current which describes local particle production consistent with the usual global description based on the interaction picture.
A local current of particle density for scalar fields in curved background is constructed. The current depends on the choice of a two-point function. There is a choice that leads to local non-conservation of the current in a time-dependent gravitational background, which describes local particle production consistent with the usual global description based on the Bogoliubov transformation. Another choice, which might be the most natural one, leads to the local conservation of the current.
In a recent paper [Phys. Rev. A 61, 022117 (2000)], quant-ph/9906034, A. Peres argued that quantum mechanics is consistent with special relativity by proposing that the operators that describe time evolution do not need to transform covariantly, although the measurable quantities need to transform covariantly. We discuss the weaknesses of this proposal.
The possibility of electron-positron pair creation by an electric field is studied by using only those methods in field theory the predictions of which are confirmed experimentally. These methods include the perturbative method of quantum electrodynamics and the bases of classical electrodynamics. Such an approach includes the back reaction. It is found that the vacuum is always stable, in the sense that pair creation, if occurs, cannot be interpreted as a decay of the vacuum, but rather as a decay of the source of the electric field or as a process similar to bremsstrahlung. It is also found that there is no pair creation in a static electric field, because it is inconsistent with energy conservation. The non-perturbative aspects arising from the Borel summation of a divergent perturbative expansion are discussed. It is argued that the conventional methods that predict pair creation in a classical background electric field cannot serve even as approximations. The analogy with the possibility of particle creation by a gravitational field is qualitatively discussed.
The theory of quantum fields in classical backgrounds is re-examined for the cases in which the Lagrangian is quadratic in quantum fields. Various methods that describe particle production are discussed. It is found that all methods suffer from certain ambiguities, related to the choice of coordinates, gauge, or counter-terms. They also seem to be inconsistent with the conservation of energy. This suggests that such classical backgrounds may not cause particle production.
It is argued that the Rindler quantization is not a correct approach to study the effects of acceleration on quantum fields. First, the "particle"-detector approach based on the Minkowski quantization is not equivalent to the approach based on the Rindler quantization. Second, the event horizon, which plays the essential role in the Rindler quantization, cannot play any physical role for a local noninertial observer.
If particle creation is described by a Bogoliubov transformation, then, in the Heisenberg picture, the raising and lowering operators are time dependent. On the other hand, this time dependence is not consistent with field equations and the conservation of the stress-energy tensor. Possible physical interpretations and resolutions of this inconsistency are discussed.
We study the role of acceleration in the twin paradox. From the coordinate transformation that relates an accelerated and an inertial observer we find that, from the point of view of the accelerated observer, the rate of the differential lapses of time depends not only on the relative velocity, but also on the product of the acceleration and the distance between the observers. However, this result does not have a direct operational interpretation because an observer at a certain position can measure only physical quantities that are defined at the same position. For local measurements, the asymmetry between the two observers can be attributed to the fact that noninertial coordinate systems, contrary to inertial coordinate systems, can be correctly interpreted only locally.
Fermi co-ordinates are proper co-ordinates of a local observer determined by his trajectory in space-time. Two observers at different positions belong to different Fermi frames even if there is no relative motion between them. Use of Fermi co-ordinates leads to several physical conclusions related to relativistic effects seen by observers in arbitrary motion. In flat space-time, the relativistic length seen by an observer depends only on his instantaneous velocity, not on his acceleration or rotation. In arbitrary space-time, for any observer the velocity of light is isotropic and equal to $c$, provided that it is measured by propagating a light beam in a small neighbourhood of the observer. The value of a covariant field measured at the position of the observer depends only on his instantaneous position and velocity, not on his acceleration. The notion of radiation is observer independent. A "freely" falling charge in curved space-time does not move along a geodesic and therefore radiates.
The Unruh effect can be correctly treated only by using the Minkowski quantization and a model of a "particle" detector, not by using the Rindler quantization. The energy produced by a detector accelerated only for a short time can be much larger than the energy needed to change the velocity of the detector. Although the measuring process lasts an infinite time, the production of the energy can be qualitatively explained by a time-energy uncertainty relation.
Although there is no relative motion among different points on a rotating disc, each point belongs to a different noninertial frame. This fact, not recognized in previous approaches to the Ehrenfest paradox and related problems, is exploited to give a correct treatment of a rotating ring and a rotating disc. Tensile stresses are recovered, but, contrary to the prediction of the standard approach, it is found that an observer on the rim of the disc will see equal lengths of other differently moving objects as an inertial observer whose instantaneous position and velocity are equal to that of the observer on the rim. The rate of clocks at various positions, as seen by various observers, is also discussed. Some results are generalized for observers arbitrarily moving in a flat or a curved spacetime. The generally accepted formula for the space line element in a non-time-orthogonal frame is found inappropriate in some cases. Use of Fermi coordinates leads to the result that for any observer the velocity of light is isotropic and is equal to $c$, providing that it is measured by propagating a light beam in a small neighborhood of the observer.
A local observer can measure only the values of fields at the point of his own position. By exploring the coordinate transformation between two Fermi frames, it is shown that two observers, having the same instantaneous position and velocity, will observe the same values of covariant fields at their common instantaneous position, even if they have different instantaneous accelerations. In particular, this implies that in classical physics the notion of radiation is observer independent, contrary to the conclusion of some existing papers. A "freely" falling charge in curved spacetime does not move along a geodesic and therefore radiates. The essential feature of the Unruh effect is the fact that it is based on a noninstantaneous measurement, which may also be viewed as a source of effective noncovariance of measured quantities. The particle concept in Minkowski spacetime is clarified. It is argued that the particle concept in general spacetime does not depend on the observer and that there exists a preferred coordinate frame with respect to which the particle number should be defined.
The relativistic motion of an arbitrary point of an accelerated rigid rod is discussed for the case when velocity and acceleration are directed along the rod's length. The discussion includes the case of a time-dependent force applied to a single point, as well as a time-independent force arbitrary distributed along the rod. The time dependence of the rod's relativistic length depends on the application point of the force, but after the termination of acceleration the final velocity and length do not depend on it. An observer on a uniformly accelerated rod feels an inertial force which decreases in the direction of acceleration. The influence of non-rigidity of realistic rods on our results is qualitatively discussed.
In a nongeometrical interpretation of gravity, the metric $g_{μν}(x)=η_{μν}+Φ_{μν}(x)$ is interpreted as an {\em effective} metric, whereas $Φ_{μν}(x)$ is interpreted as a fundamental gravitational field, propagated in spacetime which is actually flat. Some advantages and disadvantages of such an interpretation are discussed. The main advantage is a natural resolution of the flatness problem.
The standard definition of the Poisson brackets is generalized to the non-equal-time Poisson brackets. Their relationship to the equal-time Poisson brackets, as well as to the equal- and non-equal-time commutators, is discussed.
A clear explanation is given on how the causal, psychological, and electrodynamic time arrows emerge from the thermodynamic time arrow.