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cianfa72
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- TL;DR
- On the definition of Born rigidity. Is the notion of proper distance well-defined not just locally ?
I'd ask for clarification on the definition of Born rigidity, see for instance Born Rigidity.
In the context of SR (flat spacetime) consider a ruler moving through spacetime. Its points define a timelike congruence in the (bounded) region of flat spacetime it occupies.
The general definition of Born rigidity involves the notion of proper distance (length) between neighboring congruence's worldlines. Basically, at any point/event along a timelike congruence's wordline, one takes the spacelike hyperplane orthogonal to the 4-velocity at that point. In general such an hyperplane won't be orthogonal to all the congruence's members (the congruence may not be irrotational, i.e. have not zero vorticity).
Therefore the notion of proper distance is well-defined only locally in an (open) neighborhood of the point along the chosen worldline. In other words the notion of proper distance (length) isn't well defined globally from a general point of view.
Does it makes sense ? Thanks.
In the context of SR (flat spacetime) consider a ruler moving through spacetime. Its points define a timelike congruence in the (bounded) region of flat spacetime it occupies.
The general definition of Born rigidity involves the notion of proper distance (length) between neighboring congruence's worldlines. Basically, at any point/event along a timelike congruence's wordline, one takes the spacelike hyperplane orthogonal to the 4-velocity at that point. In general such an hyperplane won't be orthogonal to all the congruence's members (the congruence may not be irrotational, i.e. have not zero vorticity).
Therefore the notion of proper distance is well-defined only locally in an (open) neighborhood of the point along the chosen worldline. In other words the notion of proper distance (length) isn't well defined globally from a general point of view.
Does it makes sense ? Thanks.
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