Minkowski and Einstein

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Nugatory

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Thank you, that is very interesting and I can understand much of it. :smile:

But can someone tell me if it was the application of hyperbolic geometry that was Minkowski's breakthrough in depicting Einstein's theory?
Hyperbolic geometry was discovered and studied during the 19th century. Minkowski’s contribution was making the connection between Einstein’s work and what had previously been an interesting abstract mathematical concept with no known practical application.
 
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I thought that might have been the case - but how did Einstein respond to his old teachers discovery with regard to his theory?
 

Nugatory

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I thought that might have been the case - but how did Einstein respond to his old teachers discovery with regard to his theory?
Enthusiastically, once he recognized the power of Minkowski’s approach (although he was initially skeptical). And of course it was an essential step on the way to General Relativity.
 
Enthusiastically, once he recognized the power of Minkowski’s approach (although he was initially skeptical). And of course it was an essential step on the way to General Relativity.
In fact Minkowski was working on special relativity, indpendently, when Einstein beat him to publication. Minkowski was shocked when Einstein's papers hit the world, especially since he'd regarded Einstein as a "lazy dog" - but it did mean he was ready with his own reworking of SR with the development of "spacetime" as a unified entity. (Not anything to do with hyperbolic geometry, BTW. Minkowski spacetime is strictly flat.)
 

epenguin

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I thought that might have been the case - but how did Einstein respond to his old teachers discovery with regard to his theory?
Was it about that that he said "I no longer recognise my own theory! " or was it something else?
 

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