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Actually Poincare did and assumed a four dimensional 'curved' spacetime, from which Euclid's three-dimensional space is a 'sub-chapter'.This is not true.
This euclidean space is kind of projection into the realm of the local observer, who 'cuts' spacetime into time and space, simply by being somewhere.This is not true.
This is a very different concept than the usual mainstream interpretation and actually different to the interpretation of Einstein in his 1905 paper, too.This is not true.
Poincare's idea was further developed by Hermann Minkowski.This is true.
So Poincare's relativity is different to Einstein's, which was mainly based on Hendrik Lorentz and his 'Lorentz transform'.This is not true.
But Poincare regarded this concept of Lorentz as wrongThis is not true.
(even if he invented the name 'Lorentz transform').This is true.
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