dorsal/arxiv
View SchemaTwo Novel Special Relativistic Effects: Space Dilatation and Time Contraction
| Authors | J. H. Field |
|---|---|
| Categories | |
| ArXiv ID | physics/0004012 |
| URL | https://arxiv.org/abs/physics/0004012 |
| DOI | 10.1119/1.19439 |
| Journal | Am. J. Physics 68 (2000), 267-274 |
Abstract
The conventional discussion of the observed distortions of space and time in Special Relativity (the Lorentz-Fitzgerald Contraction and Time Dilatation) is extended by considering observations, from a stationary frame, of : (i) objects moving with constant velocity and uniformly illuminated during a short time $\tau_L$ (their `Luminous Proper Time') in their rest frame; these may be called `Transient Luminous Objects' and (ii) a moving, extended, array of synchronised `equivalent clocks' in a common inertial frame. Application of the Lorentz Transformation to (i) shows that such objects, observed from the stationary frame with coarse time resolution in a direction perpendicular to their direction of motion are seen to be at rest but {\it longer} in the direction of the relative velocity $\vec{v}$ by a factor $1/\sqrt{1-(v/c)^2}$ (Space Dilatation) and to (ii) that the moving equivalent clock at any fixed position in the rest frame of the stationary observer is seen to be running {\it faster} than a similar clock at rest by the factor $1/\sqrt{1-(v/c)^2}$ (Time Contraction). All four space-time `effects' of Special Relativity are simply classified in terms of the projective geometry of space-time, and the close analogy of these effects to linear spatial perspective is pointed out.
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"abstract": "The conventional discussion of the observed distortions of space and time in\nSpecial Relativity (the Lorentz-Fitzgerald Contraction and Time Dilatation) is\nextended by considering observations, from a stationary frame, of : (i) objects\nmoving with constant velocity and uniformly illuminated during a short time\n$\\tau_L$ (their `Luminous Proper Time\u0027) in their rest frame; these may be\ncalled `Transient Luminous Objects\u0027 and (ii) a moving, extended, array of\nsynchronised `equivalent clocks\u0027 in a common inertial frame. Application of the\nLorentz Transformation to (i) shows that such objects, observed from the\nstationary frame with coarse time resolution in a direction perpendicular to\ntheir direction of motion are seen to be at rest but {\\it longer} in the\ndirection of the relative velocity $\\vec{v}$ by a factor $1/\\sqrt{1-(v/c)^2}$\n(Space Dilatation) and to (ii) that the moving equivalent clock at any fixed\nposition in the rest frame of the stationary observer is seen to be running\n{\\it faster} than a similar clock at rest by the factor $1/\\sqrt{1-(v/c)^2}$\n(Time Contraction). All four space-time `effects\u0027 of Special Relativity are\nsimply classified in terms of the projective geometry of space-time, and the\nclose analogy of these effects to linear spatial perspective is pointed out.",
"arxiv_id": "physics/0004012",
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"doi": "10.1119/1.19439",
"journal_ref": "Am. J. Physics 68 (2000), 267-274",
"title": "Two Novel Special Relativistic Effects: Space Dilatation and Time Contraction",
"url": "https://arxiv.org/abs/physics/0004012"
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