Dear vanesh,

I have decided to move the anti-gravitation discussion into a new thread. At least in this regard josh is right, it's gotten a bit off-topic in the old one.

For those who want to follow, discussion is about the paper

http://arxiv.org/abs/gr-qc/0508013" [Broken]

see also garrett's smart comments on http://backreaction.blogspot.com/2006/04/anti-gravitation.html" [Broken]

The manifold has one metric. The different set of connection coefficients corresponds to the different properties of the quantity to be transported, not to any different properties of the manifold. If it's too implausible to think about anti-gravitation, think about transporting a spinor. It has a well defined transport-behaviour. The connection you use for this however, is not that of a vector. It's different, because it transforms under another representation than the vector.

Same with the anti-gravitating particle. It has a different transformation behaviour under general diffeomorphism than a usual particle. Therefore, the covariant derivative (and the connection coefficients appearing in it) are different. They can be derived directly from the metric and the transformation law of the particle, but they are not identical to the usual Christoffelsymbols.

Best,

B.

I have decided to move the anti-gravitation discussion into a new thread. At least in this regard josh is right, it's gotten a bit off-topic in the old one.

For those who want to follow, discussion is about the paper

http://arxiv.org/abs/gr-qc/0508013" [Broken]

see also garrett's smart comments on http://backreaction.blogspot.com/2006/04/anti-gravitation.html" [Broken]

No, it has not. (Actually, that offends me because that is what I criticize most about the works by Frederic Henry-Couannier etal. They do have two metrics, which is imo completely unphysical. They should at least try to interpret this).vanesch said:Exactly. That's my whole point, because LOCALLY there is no difference between this patch of manifold and a patch of manifold in deep space, concerning its metrical structure. BOTH are essentially flat, you see. So there is NO WAY in which to derive this OTHER curve, if the only thing that is given, is the metric.

The metric is THE SAME in the two cases, but the curves are DIFFERENT.

[...] a DIFFERENT set of connection coefficients corresponds to a DIFFERENT metric. So we now have TWO different metrics on our manifold. Is this what you are after ? But, it is a strange manifold who has two different metrics !

The manifold has one metric. The different set of connection coefficients corresponds to the different properties of the quantity to be transported, not to any different properties of the manifold. If it's too implausible to think about anti-gravitation, think about transporting a spinor. It has a well defined transport-behaviour. The connection you use for this however, is not that of a vector. It's different, because it transforms under another representation than the vector.

Same with the anti-gravitating particle. It has a different transformation behaviour under general diffeomorphism than a usual particle. Therefore, the covariant derivative (and the connection coefficients appearing in it) are different. They can be derived directly from the metric and the transformation law of the particle, but they are not identical to the usual Christoffelsymbols.

Best,

B.

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