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of the physical laws under the group of admissible transformations although in most cases the equations are actually invariant. However, in the theory of
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emphasizes the formulation of physical laws using only those physical quantities the measurements of which the observers in different
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equation of motion of a charged particle in an electromagnetic field (a generalization of Newton's second law)
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the admissible frames of reference are all inertial frames. The transformations between frames are the
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between admissible frames of reference of the physical theory. This group is referred to as the
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78:. Time is then absolute and the transformations between admissible frames of references are
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which (together with the rotations, translations, and reflections) form the
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which (together with rotations, translations, and reflections) form the
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are the mass and charge of the particle (invariant 4-scalars);
550:) coordinate transformations. The covariant quantities are
542:. The transformations between frames are all arbitrary (
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and others). An example of a covariant equation is the
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Mathematically, the physical quantities must transform
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74:with relative velocities much smaller than the
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293:. The covariant quantities are four-scalars,
50:The principle of covariance does not require
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570:. Main example of covariant equation is the
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301:(and also more complicated objects like
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86:. The covariant physical quantities are
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70:the admissible frames of reference are
524:electromagnetic field strength tensor
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62:Covariance in Newtonian mechanics
530:Covariance in general relativity
277:Covariance in special relativity
224:of the body (vector), the force
24:could unambiguously correlate.
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31:, that is, under a certain
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246:{\displaystyle {\vec {F}}}
217:{\displaystyle {\vec {v}}}
41:coordinate transformations
572:Einstein field equations
80:Galilean transformations
584:Principle of relativity
287:Lorentz transformations
18:principle of covariance
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515:{\displaystyle F^{ab}}
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633:Theory of relativity
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450:{\displaystyle ds}
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562:etc., defined on
427:{\displaystyle q}
407:{\displaystyle m}
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266:{\displaystyle t}
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188:{\displaystyle m}
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56:weak interactions
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297:etc., of the
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526:(4-tensor).
461:(4-scalar);
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295:four-vectors
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174:
65:
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28:
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29:covariantly
612:E.J.Post,
600:References
544:invertible
490:4-velocity
52:invariance
564:spacetime
303:bispinors
238:→
209:→
154:→
128:→
90:scalars,
88:Euclidean
627:Category
578:See also
568:manifold
522:is the
488:is the
457:is the
96:tensors
92:vectors
35:of the
394:where
94:, and
37:group
546:and
414:and
534:In
281:In
66:In
39:of
629::
574:.
558:,
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273:.
102:,
47:.
508:b
505:a
501:F
474:a
470:u
445:s
442:d
422:q
402:m
379:,
374:b
370:u
364:b
361:a
357:F
353:q
350:=
344:s
341:d
334:a
330:u
326:d
320:m
261:t
235:F
206:v
183:m
160:,
151:F
145:=
139:t
136:d
125:v
119:d
113:m
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