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Results for “LORENTZ TRANSFORMS”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Explicit Form for the Most General Lorentz Transformation Revisited

Explicit formulae for the 4×4 Lorentz transformation matrices corresponding to a pure boost and a pure three-dimensional rotation are very well known. Significantly less well known is the explicit formula for a general Lorentz transformation with arbitrary non-zero boost and rotation parameters. We revisit this more general formula by presenting two different derivations. The first derivation (which is somewhat simpler than previous ones appearing in the literature) evaluates the exponential of a 4×4 real matrix A, where A is a product of the diagonal matrix diag(+1,−1,−1,−1) and an arbitrary 4×4 real antisymmetric matrix. The formula for expA depends only on the eigenvalues of A and makes use of the Lagrange interpolating polynomial. The second derivation exploits the observation that the spinor product η†σ¯μχ transforms as a Lorentz four-vector, where χ and η are two-component spinors. The advantage of the latter derivation is that the corresponding formula for a general Lorentz transformation Λ reduces to the computation of the trace of a product of 2×2 matrices. Both computations are shown to yield equivalent expressions for Λ.

Science & Technology - Other Topics↗
DOE OSTI2019

Lorentz transformations of the thermodynamic quantities

In modern physics there exist several formulations of relativistic thermodynamics of a moving body. The Planck and Ott formalisms are the main ones. However, it is not clear which one is correct. In the present paper, we have solved this problem. We have required the equivalence of the dynamical Hamiltonian of a system to the fundamental thermodynamic potential in addition to the principle of entropy invariance and derived the first law of thermodynamics from this fundamental potential. We have found that in the case of momentum being an independent variable in the Hamiltonian, the Lorentz transformations of the thermodynamic quantities belong to the Planck formalism. However, if we suppose that the velocity is an independent variable in the Hamiltonian (though it is not correct from the point of view of the relativistic dynamics), the Lorentz transformations of the thermodynamic quantities belong to the Ott formalism. It demonstrates that the Ott formalism cannot be appropriate. Moreover, we have proved that in the Planck description the first law of thermodynamics is covariant and the Legendre transform of the Lagrangian is preserved. However, in the Ott description the first law of thermodynamics is not covariant and the Legendre transform is violated. Thus we have demonstrated that only the Planck formulation of relativistic thermodynamics of a moving body is properly defined and the Ott formalism should be discarded.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1976

Extending the Lorentz transformation by characteristic coordinates

The problem considered is that of rectilinear motion with variable velocity. The paper gives, by an elementary construction, a system of coordinates which is conformal in a restricted region near the axis of the motion. In such coordinates the velocity of light remains invariant even for observers moving with variable velocity. By a particular choice of the scale relation the restricted conformal transformations can be made to reduce to the Lorentz transformation everywhere in the case of constant velocity and locally in the case of variable velocity.

Jones, R. T.↗
NASA NTRS1959

Extending the Lorentz Transformation to Motion with Variable Velocity

The problem considered is that of rectilinear motion with variable velocity. The paper gives, by an elementary construction, a system of coordinates which is conformal in the vicinity of the axis of motion. By a particular choice of the scale relation, such restricted conformal transformations can be made to reduce to the Lorentz transformation everywhere in the case of uniform velocity and locally in the case of variable velocity.

Jones, Robert T.↗
NASA NTRS1988

Dual properties of spacetime under an alternative Lorentz transformation

A coordinate time, t(A), with absolute synchronization is defined as an alternative fourth spatial coordinate for model universes with flat space-time, and the theoretical implications of t(A) are explored in detail. Particular attention is given to a t(A)-based reformulation of the Lorentz transformation, the generalized Galilean transformation, which is found to offer significant advantages in understanding special-relativistic phenomena such as length contraction, time dilation, and the interaction of objects with the physical vacuum. With respect to astrophysical observations of superluminal motion, it is shown that the problem of causality violation can be avoided; the theory also predicts that weak anisotropic effects may be detectable in the earth reference frame.

Chang, T.↗
DOE OSTI2020

Effect of Thomas Rotation on the Lorentz Transformation of Electromagnetic fields

A relativistic particle undergoing successive boosts which are non collinear will experience a rotation of its coordinate axes with respect to the boosted frame. This rotation of coordinate axes is caused by a relativistic phenomenon called Thomas Rotation. We assess the importance of Thomas rotation in the calculation of physical quantities like electromagnetic fields in the relativistic regime. We calculate the electromagnetic field tensor for general three dimensional successive boosts in the particle’s rest frame as well as the laboratory frame. We then compare the electromagnetic field tensors obtained by a direct boost β δβ → + → and successive boosts β → and Δβ → and check their consistency with Thomas rotation. This framework might be important to situations such as the calculation of frequency shifts for relativistic spin1/2 particles undergoing Larmor precession in electromagnetic fields with small field non-uniformities.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1996

Two Different Squeeze Transformations

Lorentz boosts are squeeze transformations. While these transformations are similar to those in squeezed states of light, they are fundamentally different from both physical and mathematical points of view. The difference is illustrated in terms of two coupled harmonic oscillators, and in terms of the covariant harmonic oscillator formalism.

Han, D.↗
DOE OSTI2023

Dressed vs. pairwise states, and the geometric phase of monopoles and charges

We construct the Faddeev-Kulish dressed multiparticle states of electrically and magnetically charged particles, incorporating the effects of real and virtual soft photons. We calculate the properties of such dressed states under Lorentz transformations, and find that they can be identified with the pairwise multi-particle states that transform under the pairwise little group. The shifts in the dressing factors under Lorentz transformations are finite and have a simple geometric interpretation. Using the transformation properties of the dressed states we also present a novel, fully quantum field theoretic derivation of the geometric (Berry) phase obtained by an adiabatic rotation of the Dirac string, and also of the Dirac quantization condition. For half integer pairwise helicity, we show that these multiparticle states have flipped spin-statistics, reproducing the surprising fact that fermions can be made out of bosons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1991

Unified aeroacoustics analysis for high speed turboprop aerodynamics and noise. Volume 2: Development of theory for wing shielding

A unified theory for aerodynamics and noise of advanced turboprops is presented. The theory and a computer code developed for evaluation at the shielding benefits that might be expected by an aircraft wing in a wing-mounted propeller installation are presented. Several computed directivity patterns are presented to demonstrate the theory. Recently with the advent of the concept of using the wing of an aircraft for noise shielding, the case of diffraction by a surface in a flow has been given attention. The present analysis is based on the case of diffraction of no flow. By combining a Galilean and a Lorentz transform, the wave equation with a mean flow can be reduced to the ordinary equation. Allowance is also made in the analysis for the case of a swept wing. The same combination of Galilean and Lorentz transforms lead to a problem with no flow but a different sweep. The solution procedures for the cases of leading and trailing edges are basically the same. Two normalizations of the solution are given by the computer program. FORTRAN computer programs are presented with detailed documentation. The output from these programs compares favorably with the results of other investigators.

Amiet, R. K.↗
NASA NTRS1966

Lectures on Relativity Theory

Relativity theory lectures involving Lorentz transformations, Minkowski space, and tensor analysis

RELATIVITY THEORY↗
DOE OSTI2018

Lorentzian geometry for detecting qubit entanglement

We describe a new approach based on Lorentzian geometry to detect qubit entanglement. The treatment is based physically, on the causal structure of Minkowski spacetime, and mathematically, on a Lorentzian Singular Value Decomposition. A surprising feature is the natural emergence of “Energy conditions” used in Relativity. All states satisfy a “Dominant Energy Condition” (DEC) and separable states satisfy the Strong Energy Condition(SEC), while entangled states violate the SEC. We thus propose a test for two qubit entanglement which is an alternative to the positive partial transpose (PPT) test. This test is based on the partial Lorentz transformation (PLT) on individual qubits. Apart from testing for entanglement, our approach also enables us to construct a separable form for the density matrix in those cases where it exists. Our approach leads to a simple graphical three dimensional representation of the state space which shows the entangled states within the set of all states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Probing the Holomorphic Anomaly of the D = 2, N = 2, Wess–Zumino Model on the Lattice

We study a generalization of the Langevin equation, that describes fluctuations, of commuting degrees of freedom, for scalar field theories with worldvolumes of arbitrary dimension, following Parisi and Sourlas and correspondingly generalizes the Nicolai map. Supersymmetry appears inevitably, as defining the consistent closure of system + fluctuations and it can be probed by the identities satisfied by the correlation functions of the noise fields, sampled by the action of the commuting fields. This can be done effectively, through numerical simulations. We focus on the case where the target space is invariant under global rotations, in Euclidian signature, corresponding to global Lorentz transformations, in Lorentzian signature. This can describe target space supersymmetry. In this case a cross-term, that is a total derivative for abelian isometries, or when the fields are holomorphic functions of their arguments, can lead to obstructions. We study its effects and find that, in two dimensions, it cannot lead to the appearance of the holomorphic anomaly, in any event, when fluctuations are taken into account, because continuous symmetries can’t be broken in two dimensions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1976

Conformal coordinates associated with space-like motions

Conformal transformations in two dimensions provide a simple extension of the Lorentz transformation. The velocity of light appears in such transformations as a singular velocity rather than as an upper limit for the velocity. A well ordered branch of the theory exists for velocities in excess of the velocity of light. If the velocity of a point exceeds the singular velocity in an inertial system, then the conformal representation of the motion is no longer uniform, but contains a folded region. However, the branching of the transformation may be determined so that the elapsed time along the path of such a motion remains positive. Kinematic relations on the other side of the singular velocity seem to complement the usual results of relativity theory in an interesting way. Thus it is known that motion at the speed of light occurs along a null geodesic, and hence corresponds in a certain sense to motion at infinite velocity. The complementary relation is that a motion of infinite velocity corresponds in the same sense to motion at the speed of light.

Jones, R. T.↗
DOE OSTI2021

Quantum space, quantum time, and relativistic quantum mechanics

We treat space and time as bona fide quantum degrees of freedom on an equal footing in Hilbert space. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, first-order Hamiltonian and momentum constraints that lead to emergent features of temporal and spatial translations. Unlike the conventional treatment, we show that Klein-Gordon and Dirac equations in relativistic quantum mechanics can be unified in our paradigm by applying relativistic dispersion relations to eigenvalues rather than treating them as operator-valued equations. With time and space being treated on an equal footing in Hilbert space, we show symmetry transformations to be implemented by unitary basis changes in Hilbert space, giving them a stronger quantum mechanical footing. Global symmetries, such as Lorentz transformations, modify the decomposition of Hilbert space; and local symmetries, such as U(1) gauge symmetry are diagonal in coordinate basis and do not alter the decomposition of Hilbert space. Here, we briefly discuss extensions of this paradigm to quantum field theory and quantum gravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2024

DDFRG3: Double-Differential FRaGmentation model for Neutron production

A Double-Differential FRaGmentation (DDFRG) model for neutron production from nucleus - nucleus collisions is developed for space radiation applications. DDFRG1 was a previous model developed for production of protons and light ions, and DDFRG2 was a model developed for pion production. A new model (DDFRG3) for neutron production is developed in the present work, and is based upon thermal production of neutrons from the projectile, the target and central fireball sources. The Lorentz-invariant double-differential cross sections are calculated in the various source frames, and are Lorentz transformed to the laboratory frame, resulting in a closed-form analytic formula involving no numerical integration, and which can be run very efficiently in radiation transport codes. The Lorentz-invariant double-differential cross section is then integrated over angle to give the single-differential energy spectral distribution. The DDFRG3 neutron model compares very well to an extensive experimental data set.

neutrons↗