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Lorentz uniqueness

For concreteness, let us suppose that the universe has a temporal depth of two to accommodate a Fi edkin-type reversibility i.e. the present and immediate past are used to determine the future, and from which the past can be recovered uniquely. The RUGA itself is deterministic, is applied synchronously at each site in the lattice, and is characterized by three basic dimensional units (1) digit transition, D, which represents the minimal informational change at a given site (2) the length, L, which is the shortest distance between neighboring sites and (3) an integer time, T, which, while locally similar to the time in physics, is not Lorentz invariant and is not to be confused with a macroscopic (or observed) time t. While there are no a priori constraints on any of these units - for example, they may be real or complex - because of the basic assumption of finite nature, they must all have finite representations. All other units of physics in DM are derived from D, L and T. [Pg.666]

The most simple, but general, model to describe the interaction of optical radiation with solids is a classical model, due to Lorentz, in which it is assumed that the valence electrons are bound to specific atoms in the solid by harmonic forces. These harmonic forces are the Coulomb forces that tend to restore the valence electrons into specific orbits around the atomic nuclei. Therefore, the solid is considered as a collection of atomic oscillators, each one with its characteristic natural frequency. We presume that if we excite one of these atomic oscillators with its natural frequency (the resonance frequency), a resonant process will be produced. From the quantum viewpoint, these frequencies correspond to those needed to produce valence band to conduction band transitions. In the first approach we consider only a unique resonant frequency, >o in other words, the solid consists of a collection of equivalent atomic oscillators. In this approach, coq would correspond to the gap frequency. [Pg.117]

In this second technical appendix, it is shown that the Maxwell-Heaviside equations can be written in terms of a field 4-vector = (0, cB + iE) rather than as a tensor. Under Lorentz transformation, GM transforms as a 4-vector. This shows that the field in electromagnetic theory is not uniquely defined as a... [Pg.259]

We observe that the gauge transform is unique and cannot allow us to eliminate the vector potential outside the solenoid. In addition, the vector potential A derives from a multiform scalar potential F. This result contradicts the solenoidal characteristic of the A = — VA r In (r)Bo/2] vector potential. Henceforth, the gauge transform given above represents nonobservable stationary waves in vacuum since the Lorentz gauge ... [Pg.602]

Exercise. The property that the sum of two independent Gaussian variables is again Gaussian is not unique. Prove that the Lorentz and the Poisson distribution have a similar property. [Compare the Remark in 7.]... [Pg.23]

The molar refractions of the amino acids were determined by measurements on their aqueous solutions and the expanded Lorenz-Lorentz equation. The refractive indices of a number of proteins were calculated from their amino acid compositions and the values for the refraction of the amino acid residues. These calculated results are in good agreement with those experimentally determined, demonstrating that refractive index is a unique characteristic of a protein. A comparison of the refractive index of heat denatured /3-lactoglobulin with the native protein demonstrated that changes in structure produced a small change in refractive index, not associated with a change in volume. [Pg.77]

Lorentz and polarization effects [14,15], No correction for crystal decomposition was necessary. Inspection of the azimuthal scan data [16] showed a variation which was not symmetric around 180° in phi, probably due to a mis-centering of the crystal. For this reason an empirical correction was made to the data based on the combined differences of Fobs and Fcic following refinement of all atoms with isotropic thermal parameters (Tmax = 1.16, Tmin = 0.87, no theta dependence) [17]. Inspection of the systematic absences indicated uniquely space group Ia3. Removal of systematically absent data and averaging of redundant data yielded the unique data in the final sets, which were 149 for 20°C and 241 for -127°C For the former, R(I) = 5.1% for observed data and 5.4% for all data, and for the latter R(I) = 3.9% for the observed data and 4.3% for all data. [Pg.38]

Among the few determinations of of molecular crystals, the CPHF/ INDO smdy of Yamada et al. [25] is unique because, on the one hand, it concerns an open-shell molecule, the p-nitrophenyl-nitronyl-nitroxide radical (p-NPNN) and, on the other hand, it combines in a hybrid way the oriented gas model and the supermolecule approach. Another smdy is due to Luo et al. [26], who calculated the third-order nonlinear susceptibility of amorphous thinmultilayered films of fullerenes by combining the self-consistent reaction field (SCRF) theory with cavity field factors. The amorphous namre of the system justifies the choice of the SCRF method, the removal of the sums in Eq. (3), and the use of the average second hyperpolarizability. They emphasized the differences between the Lorentz Lorenz local field factors and the more general Onsager Bbttcher ones. For Ceo the results differ by 25% but are in similar... [Pg.49]

V=4629.5(7) A, Z=2, Dc=4.108 g cm , [x=237.58 cm The structure was solved by direct methods (MULTAN 88) and refined using a full-matrix least-squares refinement procedure 19552 unique reflections (Rint=0.077), 10246 observed reflections with />3a(/), J =0.067, R ,=0.078, 680 refined parameters, and 20max=55°. Lorentz polarization and absorption correction (ABSCQR) were applied to the intensity data. The transmission... [Pg.170]

Here x = (xo,x) = (ct,x) is a point in four-dimensional space-time, and a describes a translation in space-time. A is the 4 x 4-matrix of a Lorentz transformation. M is a 4 X 4-matrix that can be computed (uniquely up to a sign) from the given Lorentz transformation A. [Pg.54]

We finally note that more general Lorentz transformations are now obtained easily because any proper Lorentz transformation can be written in a unique way as the product of a boost and a rotation. [Pg.60]

Intensity data were collected on the diffractometer by using the w —26 scanning mode and a scan rate of 4° /min. Stationary background counts of 5 s were taken at both limits of each scan. Four reference reflections were monitored periodically and showed no significant intensity deterioration. Corrections were made for Lorentz and polarization factors, but not for absorption effects. A total of 2024 unique reflections, of which 24 had no net intensities, were measured to the limit 20=130°. ... [Pg.577]

Although kij apparently retains its usefulness up to very high carbon numbers, the description of the properties of liquid mixtures of Ci0+ hydrocarbons is not completely satisfactory when only ki is used. An additional parameter is required, most likely as a correction for the deviation of an from the arithmetic mean (or from the Lorentz or cube-root mean). Such a correction has been used even for cryogenic mixtures (9), but it should be more meaningful—and important—for mixtures of heavy hydrocarbons. If the value of kn has been fixed already by fitting By or some other property of the vapor mixture, then the analysis of VLE data will permit the unique determination of the second parameter. [Pg.162]

Further, we will analyze the situation from Figure A. 5.1, for which the 3D vector of velocity has the components v = (v, 0,0). Although non-unique in general, there is convenient to choose the sub-matrix A , a,P = 1,2,3, in such way that together with the above (time-time and space-time) components to generate Lorentz transformations as phenomenologically deduced this form can be... [Pg.591]

We note again that any tensor of second rank can always be expressed as a matrix, but that not every matrix is a tensor. Any tensor is uniquely defined within one given inertial system IS, and its components may be transformed to another coordinate system IS. This transition to another coordinate system is described by Lorentz transformation matrices A, which are therefore not tensors at all but mediate the change of coordinates. The matrices A are not defined with respect to one specific IS, but relate two inertial systems IS and IS. Nevertheless, due to Eq. (3.26) the indices of components A of Lorentz transformation matrices may be raised or lowered as if they were tensors. [Pg.65]

The deeper reason for calling E and p the relativistic energy and momentum, respectively, is that they are conserved quantities in the following sense. If an observer in one specific inertial frame of reference IS sees that E and/or p are conserved throughout a reaction or process, so does any other observer in another frame of reference IS related to IS via a Lorentz transformation. This unique feature of energy and momentum directly follows from the 4-vector property of p since the change Ap in energy or momentum in IS is related to those in IS by... [Pg.80]


See other pages where Lorentz uniqueness is mentioned: [Pg.678]    [Pg.132]    [Pg.706]    [Pg.60]    [Pg.563]    [Pg.684]    [Pg.527]    [Pg.43]    [Pg.490]    [Pg.356]    [Pg.201]    [Pg.63]    [Pg.170]    [Pg.78]    [Pg.171]    [Pg.387]    [Pg.106]    [Pg.24]    [Pg.91]    [Pg.470]    [Pg.100]    [Pg.22]    [Pg.59]    [Pg.320]    [Pg.644]    [Pg.645]    [Pg.646]    [Pg.43]    [Pg.217]    [Pg.165]   
See also in sourсe #XX -- [ Pg.644 ]




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