Tuesday, August 21, 2012

thought for the day/Mechanical Universe . . . Einstein's theories of Relativity


-I'd like to first comment about why there's no astronomy picture for the day.  I'm not sure what pictures I've got up.  I know I've got some repeats.  Unless there's some really new picture, I'm pretty much done right now, unfortunately.

The Mechanical Universe's account of Einstein's theories only covers his Special theory of Relavity.  In both cases, Special and General, mathematicians had a big role.  One could say that Einstein got the credit more because he derived the work of the mathematicians from axioms.  The Mechanical Universe episodes show most of this, except they don't note that it was a Minkowski who thought of spacetime unified.  Then, much later around 1910 to 1915, Einstein showed that mass bends spacetime. The videos explain the rest well enough.  In special relativity, speed is relative to the observer; in General Relativity, inertia and gravity are relative to the observer. 

For Physicists, the Michelson-Morley experiment was like dark energy today - a completely unexpected result.  Physicists thought that light being waves implied an aether.  The fact that they did follows my and Jacob Bronowski's points about defining a part of the universe generates 'infered units' as Jacob Bronowski calls them(see my third to first post about the nature and origin of mathematical knowledge).  Initially, one could argue that the Michelson-Morley experiments presents problems for Jacob Bronowski's theory of knowledge(and mine); but, the truth is that the Physicists failed to question assumptions.  And in mathematics, the reason why they do axiomatics and deductive proof of everything is  . . . at least one reason . . . is to question assumptions. 

For mathematicians, the relativity phenomenon destroyed their religion of group theory - at least for the most part.  Mathematicians, and perhaps Felix Klein specificaly, had started thinking group theory can unify all mathematics(geometry and algebra).  From late 1700s to early 1800s, mathematicians had come up with non-euclidean geometries.  Felix Klein had shown that group theory can describe and unify all these non-euclidean geometries. Riemanian geometry almost certainly took center stage by Einstein's time; well, that's not stricktly true.  Mathematicians had made connections between complex analyses, algebraic geometry, and Riemanian geometry long before.  But, that's another story.  Well, mathematicians had actualy thought of curved spacetime(both Riemann and I'm forgetting the name of another guy; i think he combined complex numbers with vectors . . . sorry, I can't remember his name). 

Getting back to the physicists, they were later to make the vacuum have properties kindof aether like with Paul Dirac's combining of special relativity and quantum mechanics - in his quantum electrodynamics. And of course, this leads to the effort to make a unified quantum theory of gravity.

No comments:

Post a Comment