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corrected punctuation, some typos and uppercasing the beginning of phrases.
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Frederic Thomas
Frederic Thomas
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soAs far as i understand, Poincaré invariance is invariance under spacetime rotations, translations and boost which is encoded in the group $ \operatorname{ISO}^+(n) $ which in 3+1D spacetime would be $ \operatorname{ISO}^+(1, 3) $ this$\operatorname{ISO}^+(1, 3)$. This is the most general extension of Lorentz invariance and the one we use in particle physics and special relativity. howeverHowever there's also the concept of general covariance which is the base idea from which we construct general relativity. itIt is the idea of invariance under coordinate transfromations and that physics doesn't depend on our choice of coordinates, which is encapsulated in the $ \operatorname{GL}(n) $ group which is the group of general coordinate transformations.

myMy question is ¿what: what are the differences and/or relations between these two concepts? isn'tIsn't it possible to reach all coordinate systems via Poincaré transfromationstransformations? becauseBecause if that were the case, they should be the same right?

so far as i understand, Poincaré invariance is invariance under spacetime rotations, translations and boost which is encoded in the group $ \operatorname{ISO}^+(n) $ which in 3+1D spacetime would be $ \operatorname{ISO}^+(1, 3) $ this is the most general extension of Lorentz invariance and the one we use in particle physics and special relativity. however there's also the concept of general covariance which is the base idea from which we construct general relativity. it is the idea of invariance under coordinate transfromations and that physics doesn't depend on our choice of coordinates, which is encapsulated in the $ \operatorname{GL}(n) $ group which is the group of general coordinate transformations.

my question is ¿what are the differences and/or relations between these two concepts? isn't it possible to reach all coordinate systems via Poincaré transfromations? because if that were the case, they should be the same right?

As far as i understand, Poincaré invariance is invariance under spacetime rotations, translations and boost which is encoded in the group $ \operatorname{ISO}^+(n) $ which in 3+1D spacetime would be $\operatorname{ISO}^+(1, 3)$. This is the most general extension of Lorentz invariance and the one we use in particle physics and special relativity. However there's also the concept of general covariance which is the base idea from which we construct general relativity. It is the idea of invariance under coordinate transfromations and that physics doesn't depend on our choice of coordinates, which is encapsulated in the $ \operatorname{GL}(n) $ group which is the group of general coordinate transformations.

My question is: what are the differences and/or relations between these two concepts? Isn't it possible to reach all coordinate systems via Poincaré transformations? Because if that were the case, they should be the same right?

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Qmechanic ♦
Qmechanic ♦
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difference Difference between general covariance and poincaréPoincaré invariance

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Tomás
Tomás
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difference between general covariance and poincaré invariance

so far as i understand, Poincaré invariance is invariance under spacetime rotations, translations and boost which is encoded in the group $ \operatorname{ISO}^+(n) $ which in 3+1D spacetime would be $ \operatorname{ISO}^+(1, 3) $ this is the most general extension of Lorentz invariance and the one we use in particle physics and special relativity. however there's also the concept of general covariance which is the base idea from which we construct general relativity. it is the idea of invariance under coordinate transfromations and that physics doesn't depend on our choice of coordinates, which is encapsulated in the $ \operatorname{GL}(n) $ group which is the group of general coordinate transformations.

my question is ¿what are the differences and/or relations between these two concepts? isn't it possible to reach all coordinate systems via Poincaré transfromations? because if that were the case, they should be the same right?