Speed of Light: Length Contraction & 20AU Paths

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traveling at the ~speed of light leads to length contraction.
based on that wouldn't a 20AU path be shorter if traveled at speeds near the speed of light ?
 
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EbolaHost said:
traveling at the ~speed of light leads to length contraction.
based on that wouldn't a 20AU path be shorter if traveled at speeds near the speed of light ?

Yes. However that doesn't change the speed of light. Because of time dilation both the traveler (who sees the distance contracted) and an observer at rest relative to the endpoints of the traveler's journey will find that a flash of light travels between the two points at the speed of light - divide the contracted length by the dilated time and you'll get ##c##.
 
Thread 'Can this experiment break Lorentz symmetry?'

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Thread '1-Way Speed of Light'

Does the speed of light change in a gravitational field depending on whether the direction of travel is parallel to the field, or perpendicular to the field? And is it the same in both directions at each orientation? This question could be answered experimentally to some degree of accuracy. Experiment design: Place two identical clocks A and B on the circumference of a wheel at opposite ends of the diameter of length L. The wheel is positioned upright, i.e., perpendicular to the ground...
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Thread 'A sufficient condition for integrability of equation ##\nabla g=0##'

In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this: $$ \partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}. $$ The integrability conditions for the existence of a global solution ##F_{lj}## is: $$ R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0 $$ Then from the equation: $$\nabla_b e_a= \Gamma^c_{ab} e_c$$ Using cartesian basis ## e_I...
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