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I read somewhere that projective geometry was an inspiration to Einstein to build the theory of relativity. However, the keyword "projective geometry" isn't mentioned in history of general relativity and only passingly in history of special relativity that Clifford had contributions to the field.

Though the connection has been showed later by Penrose (1984), did it really inspire Einstein? If yes, how? If no, then what really intuitively inspired him?

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  • $\begingroup$ The answer would be "no, most certainly he was not inspired by projective geometry", so perhaps it would be better to change the title and to rewrite the text. Actually Einstein was baffled by Minkowski's view and it took him a few years to accept it, even if later history tends to credit him for this innovative step. $\endgroup$ – sand1 Mar 24 '18 at 9:06
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    $\begingroup$ Might you be misremembering something about Dirac instead? See e.g. Chap. XI in Darrigol, From c-Numbers to q-Numbers, or this interview: “I’ve found [projective geometry] useful since then in understanding the relations which you have in Minkowski space. You can picture all the directions in Minkowski space as the points in a three-dimensional projective space (...) I always used these geometrical ideas for getting clear notions about relationships in relativity”. $\endgroup$ – Francois Ziegler Mar 25 '18 at 18:13
  • $\begingroup$ @FrancoisZiegler I only knew that Dirac use geometry for his intuition, not projective geometry in specific. But if he had said so, why did it take so long until Penrose "rediscovered" the relation? $\endgroup$ – Ooker Mar 26 '18 at 4:09
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    $\begingroup$ Well, there is that Dirac concluded the quote above with “although I didn’t refer to them in my published works”. Also, while I’m not sure exactly what your “Penrose (1984)” refers to (?), I doubt it was claiming originality. E.g. Synge (1956, eq. 158) has a projective picture in a section (§IV.10) that Penrose already quoted in (1959). Finally, your “somewhere” doesn’t mention Einstein at all, does it? $\endgroup$ – Francois Ziegler Mar 26 '18 at 6:04
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It is hard to prove that the answer is negative, but have this in mind: a friend who helped Einstein a lot (and who co-wrote two articles with him) while Einstein was trying to formulate the General Theory of Relativity was Marcel Grossmann, who was a geometer (his PhD thesis was about Non-Euclidean Geometry and he wrote two textbooks on Descriptive Geometry). However, the Geometry that he used to help Einstein was the tensor calculus which was developed by Gregorio Ricci-Curbastro and Tullio Levi-Civita, not Projective Geometry.

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