theory of relativity

tht

akstavrh
the general theory, i suppose

it's sometimes said that relativity, especially the general theory, was prohibitively difficult even for some eminent figures in contemporary theoretical physics to understand comprehensively, why was this? was it simply owing to its mathematical complexity or a 'conceptual' difficulty in comprehending a line of thought that would have seemed quite contrary? and is this still the case today?
 

tht

akstavrh
that's 'an introduction to', a condensed form?
surely the full theory of einstein that confounded so many people cannot be understood so easily?
 
As I understand it, it was Minkowski's idea to explain Einstein's theory in terms of a 4 dimensional spacetime. Before this, Einstein's own accounts were more opaque.
 

Mr. Tea

Let's Talk About Ceps
In answer to tht's question, I'd say it was a bit of both, at least initially. The theory makes use of some maths that was develped by Gauss and later Riemann (both German mathematicians) in the 19th century purely for the purposes of abstract mathematics, with no expectation that these concepts would ever be used to create a physical theory (specifically, they were interested in hypothetical geometries that contradicted laws laid down in ancient times by Euclid). Einstein realised (some sixty years later) that Riemann's geometry, in a suitably modified form, could be used to describe the curvature of space-time in the presence of mass, with the degree of curvature coresponding to the strength of gravitational fields. At the time of the theory's publication, very few people were familiar with the necessary mathematics, as it had not been thought relevant to physics and had largely been filed filed away as an interesting but practically unfruitful footnote.

The other big barrier, as you say, was the sheer weirdness of the theory: it's a huge departure even from the Minkowskian space-time of special relativity that had become a familiar part of theoretical physics just a decade earlier, replacing the absolute space and time of the Newtonian worldview. However, just as many physicists were quick to learn the requisite maths to understand GR (and I can tell you from personal experience, the most intimidating thing about it - to someone with at least some experience with vector calculus - is its forbidding notation), the ideas themselves were rapidly absorbed into the corpus of scientific thought, especially after Arthur Eddington's 1919 expedition to measure the deflection of starlight by the Sun's mass during a total eclipse (although it is now thought the results from that were somewhat 'fudged' to fit the prediction, but that's for another thread...).
At the time a journalist told Eddington he'd heard that "only three people in the world understood GR", and asked for his comments; Eddington is said to have replied "I'm tring to think who the third person is" (the implication being that the other two were himself and of course Einstein). But as borderpolice points out, the theory is now taught to undergraduates, so I wouldn't say any 'eminent theoretical physicists' can't understand the theory - a few may have rival theories of their own, but so far not one of these has come close to matching GR for mathematical elegance or predictive power.

Interestingly, the other great theory Einstein helped found (but later disavowed) - namely quantum mechanics - causes controversy to this day, mainly because of the extreme difficulty found in interpreting its 'meaning' for our picture of reality (a feature not shared with GR). Richard Feynman (arguably the greatest physicist since Einstein) once said (in reference to Eddington's comment), that while GR is understood by undergraduate students all over the world, no-one really understands quantum mechanics.
 
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tht

akstavrh
thanks!

i suppose when i left maths (17ish), hardcore physics seemed like a subset of maths, and i'd assumed the mathematic foundation of relativity would have been as new as the concept itself, that the 'difficulty' would be in the calculus
 
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Mr. Tea

Let's Talk About Ceps
Don't get me wrong, the maths in GR is far from trivial - I certainly wouldn't want to tackle it again without extensive revision, and given that I only studied it at an undergraduate level I obviously only met the introductory stuff. But the very fact that it can be taught at an undergraduate level (and to students of physics, rather than maths) indicates that the basics of the theory at least are not out there on this unattainable level of difficulty.

Interestingly, I've just been reading about this and it seems that when Einstein realised the direction his ideas were going in (while he was starting to develop GR off the back of the huge success he'd had with special relativity) he had to enlist a colleague to teach him this odd bit of maths from sixty years back. His genius was not in understanding the maths itself (which had after all been developed by someone else) but in applying it to physical systems to articulate the ideas he'd had, which no-one had had before.

Edit: also, Edwards is dead right - it was Minkowski, not Einstein, who came up with the idea of a four-dimensional space-time 'continuum', although this was after Einstein had formulated special relativity (and largely inspired by it, in fact). Whether or not Einstein could have formulated GR without Minkowski's earlier input I don't know.
 
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borderpolice

Well-known member
In answer to tht's question, I'd say it was a bit of both, at least initially. The theory makes use of some maths that was develped by Gauss and later Riemann (both German mathematicians) in the 19th century purely for the purposes of abstract mathematics, with no expectation that these concepts would ever be used to create a physical theory (specifically, they were interested in hypothetical geometries that contradicted laws laid down in ancient times by Euclid).

I think that's misleading. Riemann's interest in these weird geometry stems, at least in part, from his interest in the mystery of "action at a distance" that is at the heart of newton's axiomatisation of gravity.
 
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Mr. Tea

Let's Talk About Ceps
Is that so? I don't know much about him, only that he discovered the non-Euclidean geometry than Einstein later used, and also his zeta function, of course. I'd be interested to know what he thought about physics, got any links?
 

borderpolice

Well-known member
Is that so? I don't know much about him, only that he discovered the non-Euclidean geometry than Einstein later used, and also his zeta function, of course. I'd be interested to know what he thought about physics, got any links?

Sorry, nothing handy. I read about it in a history of mathematical physics book a while back in a library. can't remember the title/author. I'll post something if i can remember anything. A scientific biography of Riemann's would probably be a good place to look.
 
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