Lorentz contraction, Bell's spaceships and rigid body motion in special relativity

Franklin, Jerrold

doi:10.1088/0143-0807/31/2/006

Cited by 30 publications

(47 citation statements)

References 17 publications

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“…The same formula was obtained by Franklin [11]. The above shows that each rest point of a uniformly accelerated system may itself be considered as the spatial origin of a uniformly accelerated system K y .…”

Section: The Acceleration Of Rest Points In a Uniformly Accelerated Fsupporting

confidence: 55%

Uniform acceleration in general relativity

Friedman

Scarr

2015

Gen Relativ Gravit

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We extend de la Fuente and Romero's [1] defining equation for uniform acceleration in a general curved spacetime from linear acceleration to the full Lorentz covariant uniform acceleration. In a flat spacetime background, we have explicit solutions. We use generalized Fermi-Walker transport to parallel transport the Frenet basis along the trajectory. In flat spacetime, we obtain velocity and acceleration transformations from a uniformly accelerated system to an inertial system. We obtain the time dilation between accelerated clocks. We apply our acceleration transformations to the motion of a charged particle in a constant electromagnetic field and recover the Lorentz-Abraham-Dirac equation.

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Section: The Acceleration Of Rest Points In a Uniformly Accelerated Fsupporting

confidence: 55%

Uniform acceleration in general relativity

Friedman

Scarr

2015

Gen Relativ Gravit

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“…This well-known, but admittedly counterintuitive fact is not a paradox in the true sense of the word and discussed extensively in the literature (see e.g., refs. [35][36][37][38][39][40]). …”

Section: Uniform Acceleration Of a Born-rigid Objectmentioning

confidence: 99%

Visualization of Thomas–Wigner Rotations

Beyerle

2017

Symmetry

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Abstract:It is well known that a sequence of two non-collinear Lorentz boosts (pure Lorentz transformations) does not correspond to a Lorentz boost, but involves a spatial rotation, the Wigner or Thomas-Wigner rotation. We visualize the interrelation between this rotation and the relativity of distant simultaneity by moving a Born-rigid object on a closed trajectory in several steps of uniform proper acceleration. Born-rigidity implies that the stern of the boosted object accelerates faster than its bow. It is shown that at least five boost steps are required to return the object's center to its starting position, if in each step the center is assumed to accelerate uniformly and for the same proper time duration. With these assumptions, the Thomas-Wigner rotation angle depends on a single parameter only. Furthermore, it is illustrated that accelerated motion implies the formation of a "frame boundary". The boundaries associated with the five boosts constitute a natural barrier and ensure the object's finite size.

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“…Given

d^{'}

, we can obtain the transformed FOV of the camera

α^{'}

α^{'} = 2 arctan (w / d^{'})

(for constant speed

g = 0,

it corresponds to Equation ). Note that in order to maintain a constant FOV

α^{'}

during acceleration, different accelerations would be needed in the pinhole and the sensor, as derived by Franklin [Fra10].…”

Section: Relativistic Renderingmentioning

confidence: 99%

Relativistic Effects for Time‐Resolved Light Transport

Jarabo

Masiá

Velten

et al. 2015

Computer Graphics Forum

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We present a real-time framework which allows interactive visualization of relativistic effects for time-resolved light transport. We leverage data from two different sources: real-world data acquired with an effective exposure time of less than 2 picoseconds, using an ultrafast imaging technique termed femto-photography, and a transient renderer based on ray-tracing. We explore the effects of time dilation, light aberration, frequency shift and radiance accumulation by modifying existing models of these relativistic effects to take into account the time-resolved nature of light propagation. Unlike previous works, we do not impose limiting constraints in the visualization, allowing the virtual camera to explore freely a reconstructed 3D scene depicting dynamic illumination. Moreover, we consider not only linear motion, but also acceleration and rotation of the camera. We further introduce, for the first time, a pinhole camera model into our relativistic rendering framework, and account for subsequent changes in focal length and field of view as the camera moves through the scene.

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Lorentz contraction, Bell's spaceships and rigid body motion in special relativity

Cited by 30 publications

References 17 publications

Uniform acceleration in general relativity

Uniform acceleration in general relativity

Visualization of Thomas–Wigner Rotations

Relativistic Effects for Time‐Resolved Light Transport

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