Heisenberg’s uncertainty relation may be violated in a single measurement

The well-known Heisenberg’s uncertainty relation is an inequality between uncertainties of canonically conjugate observables in a given state. In this interpretation, the Heisenberg’s uncertainty relation is a rigorous mathematical theorem and is, therefore, always valid. However, the same inequality is often applied in the situation of measurement, where it is illustrated in a quite different way. The uncertainty relation is then an inequality connecting the precision (resolution) of the measurement of one observable and the uncertainty of the conjugate observable in the state arising after the measurement. It turns out that in such an interpretation the Heisenberg’s inequality may be violated for some measurement readouts that emerge with small but finite probabilities. Making use of the uncertainties averaged in a special way over all possible measurement readouts, one may formulate an inequality of the type of Heisenberg’s inequality but valid for any measurement. Paper submitted by the author in English on 28 April 2006.     

Development of a two-color interferometer for observing wide range electron density profiles with a femtosecond time resolution

A two-color interferometer for preformed plasma characterization is developed. We observe the electron density distribution of preformed plasmas on a 5 μm-thick copper target irradiated with a high-intensity Ti:sapphire laser. The two-color interferometer extended the observable electron density region using a fundamental (800 nm) probe beam to cover the lower density region and a second harmonic (400 nm) probe beam to cover the higher density region, simultaneously. This characterization of the electron density distribution of preformed plasmas with femtosecond time resolution significantly contributes to the understanding of high-intensity laser–thin-foil interactions during high-energy electron, ion, and X-ray generation. PACS 52.38.-r; 52.50.Jm; 52.70.-m     

Spatio-temporal correlation of the maximum observable frequency on midlatitude radio lines

We present the results of studying the spatial and temporal correlation of the maximum observable frequency on two midlatitude paths, Inskip (England)–Rostov-on-Don and Cyprus–Rostov-on-Don. Dynamics of variation in the maximum observable frequency on these paths as a function of the time of the day and geophysical conditions is explored. The presence of a high spatial correlation (up to 93.5%) between the studied maximum observable frequencies allowed the values of the maximum observable frequency on the Cyprus–Rostov-on-Don path to be retrieved from the data on the Inskip–Rostov-on-Don path by the method of artificial neural networks with a training efficiency of up to 97%. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 52, No. 1, pp. 28–35, January 2009.     

Teleportation of a continuous variable

Measurements used in quantum teleportation are examined from the standpoint of the general theory of quantum-mechanical measurements. It is shown that in order to find a teleported state, it is sufficient to know only the resolution of the identity operator (positive operator-valued measure) generated by the respective instrument (the quantum operation determining the change in the state of the system as a result of the measurement) in the state space of the system, rather than the instrument itself. A protocol for quantum teleportation of the state of a system with a nondegenerate continuous spectrum based on a measurement which corresponds to a certain nonorthogonal resolution of the identity operator is proposed. Zh. éksp. Teor. Fiz. 116, 777–792 (September 1999)     

Simplerealizations of generalized measurements in quantum mechanics

This paper discusses the approach to the analysis of measurements in quantum mechanics which is based on a set of "detection operators" forming a resolution of identity. The expectation value of each of these operators furnishes the counting rate at a detector for any object state that is prepared. "Predictable measurements" are those for which there is a representation in which only one element of each diagonal matrix representing each operator is not zero. A set of commuting detection operators defines the class of "spectral measurements", which may be either predictable or not. An even more general definition of measurement may be given by abandoning the requirement of commutativity of the detection operators. In this case one cannot define an observable which corresponds to a single self-adjoint operator, which violates the standard theory of quantum mechanical measurement. Simple experimental realizations of each of these classes of measurement are suggested.     

High-resolution Brillouin spectroscopy of water

An experimental set-up is described for measuring, with high resolution, the hypersound-phase velocity and damping by means of Brillouin spectroscopy in the Giga-Hertz range. Measurements on water at 20°C between 3 and 6 GHz are presented showing no observable onset of dispersion in this region. Due to the high-power single-frequency HeNe-laser used and due to an effective collection of Brillouin-scattered light our experimental error is far smaller and the data are more reliable than in earlier investigations. Supported by the “Deutsche Forschungsgemeinschaft”.     

Algebraic structure of Nambu mechanics

Abstracting from Nambu’s work [1] on the generalization of Hamiltonian mechanics, we obtain the concept of a classical Nambu algebra of type I (CNA-I). Consistency requirement of time evolution of the trilinear Nambu bracket leads to a new five point identity (FPI). Incorporating the FPI into CNA-I, we obtain a classical Nambu algebra of type II (CNA-II). Nambu’s algorithm for generalized classical mechanics turns out to be compatible with CNA-II. Tensor product composition of two CNA-I’s results in another CNA-I whereas that of two CNA-II’s does not. This implies that interacting systems cannot be consistently treated in Nambu’s framework. It is shown that the recent generalization of Nambu mechanics based on an arbitrary Lie group (instead of the particular case of the rotation group as in the case of Nambu’s original algorithm) suggested by Biyalinicki-Birula and Morrison [2], is compatible with CNA-I but not with CNA-II. Relaxation of the commutative and associative observable product by making it nonassociative so as to arrive at the quantum counterpart meets with serious difficulties from the view point of tensor product composition property. Thus neither CNA-I nor CNA-II have quantum counterparts. Implications of our results are discussed with special reference to existing work on Nambu mechanics in the literature.     

The deformable universe

The concept of smooth deformations of Riemannian manifolds, recently evidenced by the solution of the Poincaré conjecture, is applied to Einstein’s gravitational theory and in particular to the standard FLRW cosmology. We present a brief review of the deformation of Riemannian geometry, showing how such deformations can be derived from the Einstein-Hilbert dynamical principle. We show that such deformations of space-times of general relativity produce observable effects that can be measured by four-dimensional observers. In the case of the FLRW cosmology, one such observable effect is shown to be consistent with the accelerated expansion of the universe.     

Vacuum Polarisation Effects in the Lorentz Violating Electrodynamics

In this work we reconsider the one loop calculation for the vacuum polarisation tensor in the Lorentz violating quantum electrodynamics. The electron propagator is “dressed” by a Lorentz breaking extra term in the fermion Lagrangian density. We check gauge invariance and use the Schwinger–Dyson equation to discuss the full photon propagator. After a discussion on a possible photon mass shift, we show how a finite quantum correction can be chosen in a unique way in order to ensure—in the spirit of spontaneously broken theories—the standard normalisation conditions for the vacuum polarisation tensor. Then we comment on possible observable physical consequences on the Lamb-shift.     

A simplified basis for Bell–Kochen–Specker theorems

We show that a reduced form of the structural requirements for deterministic hidden variables used in Bell–Kochen–Specker theorems is already sufficient for the no-go results. Those requirements are captured by the following principle: an observable takes a spectral value x if and only if the spectral projector associated with x takes the value 1. We show that the “only if” part of this condition suffices. The proof identifies an important structural feature behind the no-go results; namely, if at least one projector is assigned the value 1 in any resolution of the identity, then at most one is.     

Cryptohermitian Hamiltonians on Graphs. II.?Hermitizations

In the second step of our systematic study of non-Hermitian quantum graphs simplified via their discretization and possessing real (i.e., in principle, observable) spectra we show how the related Hamiltonian H may be assigned either a pseudometric P\mathcal{P} and/or metric Θ. Our two alternative constructions convert the Hamiltonian in question into the operator which becomes Hermitian either in a formal, ad hoc Krein/Pontryagin space and/or in one of available standard quantum-mechanical Hilbert spaces, respectively.     

Transverse polarization in <Emphasis Type="Italic">γZ,H Z</Emphasis> production

With the use of transverse polarization (TP), a CP-odd and T-odd observable can be constructed when the final-state particles are self-conjugate. In the case of HZ production, this observable can be used to probe a certain effective four-point e ⁺ e ⁻ ZH CP-violating coupling, not accessible without TP. Effective CP-violating ZZH coupling does not contribute to this observable. A similar observable in γZ production can be used to probe e ⁺ e ⁻ γZ four-point couplings.      

Observing high energy neutrons of solar origin using the TEMP muon hodoscope

A new method of searching for high-energy solar neutrons using the ground-based TEMP muon hodoscope with a high angular resolution of ∼1°–2° is considered. An excess in the muon flux (about four standard deviations) was observed during solar flare GLE 60 (April 15, 2001). A small excess in the permanent muon flux from the Sun (2.2σ) was also detected in the daytime over a period of 230 days upon daily 4-hour exposure.     

Interpretations of Quantum Mechanics in Terms of Beable Algebras

In terms of beable algebras Halvorson and Clifton [International Journal of Theoretical Physics 38 (1999) 2441–2484] generalized the uniqueness theorem (Studies in History and Philosophy of Modern Physics 27 (1996) 181–219] which characterizes interpretations of quantum mechanics by preferred observables. We examine whether dispersion-free states on beable algebras in the generalized uniqueness theorem can be regarded as truth-value assignments in the case where a preferred observable is the set of all spectral projections of a density operator, and in the case where a preferred observable is the set of all spectral projections of the position operator as well.     

Effects related to spacetime foam in particle physics

It is found that the existence of spacetime foam leads to a situation in which the number of fundamental quantum bosonic fields is a variable quantity. The general aspects of an exact theory that allows for a variable number of fields are discussed, and the simplest observable effects generated by the foam are estimated. It is shown that in the absence of processes related to variations in the topology of space, the concept of an effective field can be reintroduced and standard field theory can be restored. However, in the complete theory the ground state is characterized by a nonvanishing particle number density. From the effective-field standpoint, such particles are “dark.” It is assumed that they comprise dark matter of the universe. The properties of this dark matter are discussed, and so is the possibility of measuring the quantum fluctuation in the field potentials. Zh. éksp. Teor. Fiz. 115, 1921–1934 (June 1999)     

Observation of nanometer-scale optical property discrimination by use of a near-field scanning apertureless microscope

We examine fundamental issues related to discriminating structural and optical features in near-field scanning apertureless microscopy. We report a series of controlled experiments with nanosphere-sized standard spheres in which we observed significant differences in resolution and structure between an atomic-force microscope image and a simultaneously acquired near-field optical (NFO) image. Further, in experiments that employed a mix of dyed and undyed nanospheres we found that we can observe differences in the same NFO image for adjacent nanospheres. Therefore we conclude that near-field scanning apertureless microscopy not only meets the criteria for a NFO image but also is capable of measuring optical properties below the diffraction limit. The two-point resolution was at least 200 nm when we were detecting optical phase and 50 nm when we were detecting optical intensity. The edge response was typically 15 nm, and the minimum observable features were of the order of 3 nm.     

Hierarchy of local minimum solutions of Heisenberg's uncertainty principle

We derive a new hierarchy of local minimum Heisenberg-uncertainty states by introducing a superposition of "small waves" onto some initial state. Our objective is to increase the resolution in one observable, with the least decrease in the resolution in the conjugate observable. This leads to a constrained minimization which in a well-defined sense yields the best possible way of achieving this goal. The results are relevant to many topics (e.g., quantum optics and control, Bose-Einstein condensation, path integration, etc.).     

Probing R-parity violating interactions from top-quark polarization at LHC

In the minimal supersymmetric standard model the R-parity violating interactions can induce anomalous top pair productions at the LHC through the t-channel process d_Rd̄_R→t_Lt̄_L by exchanging a slepton or by the u-channel process d_Rd̄_R→t_Rt̄_R exchanging a squark. Such top pair productions with a certain chirality cause top-quark polarization in the top pair events. We found that at the LHC, due to the large statistics, the statistical significance of the polarization observable, and thus the probing ability for the corresponding R-parity violating couplings, is much higher than at the Tevatron upgrade. PACS 14.65.Ha; 14.80.Ly     

Natural line shape

The observable line shape of the spontaneous emission depends on the procedure of atom’s excitation. The spectrum of radiation emitted by a two-level atom excited from the ground state by a π pulse of the resonant pump field is calculated for the case when the Rabi frequency is much larger than the relaxation rate. It is shown that the central part of the spectral distribution has a standard Lorentzian form, whereas for detunings from the resonance that are larger than the Rabi frequency the spectral density falls off faster. The shape of the wings of the spectral line is sensitive to the form of the π pulse. The implications for the quantum Zeno effect theory and for the estimates of the duration of quantum jumps are discussed. The article is published in the original.     

Bell’s theory with no locality assumption

We prove versions of the Bell and the GHZ theorems that do not assume locality but only the effect after cause principle (EACP) according to which for any Lorentz observer the value of an observable cannot change because of an event that happens after the observable is measured. We show that the EACP is strictly weaker than locality. As a consequence of our results, locality cannot be considered as the common cause of the contradictions obtained in all versions of Bell’s theory. All versions of Bell’s theorem assume weak realism according to which the value of an observable is well defined whenever the measurement could be made and some measurement is made. As a consequence of our results, weak realism becomes the only hypothesis common to the contradictions obtained in all versions of Bell’s theory. Usually, one avoids these contradictions by assuming non-locality; this would not help in our case since we do not assume locality. This work indicates that it is weak realism, not locality, that needs to be negated to avoid contradictions in microscopic physics, at least if one refuses as false the de Broglie-Bohm hidden variable theory because of its essential violation of Lorentz invariance.