Re: [MLUG - DISCUSSION] In Math, Computers Don't Lie. Or Do They?

[Stephen Montgomery-Smith <EMAIL:PROTECTED>]

Stephen Montgomery-Smith wrote:

>> Hilbert was great.  Do you think Einstein really plagiarized him?
>>
>> http://home.comcast.net/~xtxinc/AEGRBook.htm
>> http://christianparty.net/einsteinplagiarist.htm
>>
>> This anti-Einstein stuff, though highly questionable, contains some
>> kernels of truth (e.g., regarding Lorentz).
>>
>>

As I said in an earlier message, I have read some of these original works.

At the turn of the century, it was becoming apparent that the 
consistency of the velocity of light was in violation with the then 
current views of space and time.  This was shown by the well known 
experiements of Michelson and Morley.  This was becoming intellectually 
very difficult to reconcile.  Attempts to figure this out included the 
work by Lorentz, who derived the so called Lorentz transformation, which 
showed that it could be accounted for if one allows certain distortions 
in space and time to be generated by changes in velocity.

However, Einstein's work is much deeper.  Einstein's greatness is not in 
his mathematics, but in his physics.  Whereas other scientists will work 
out the equations, and then try to understand how the equations affect 
reality, Einstein is a physicist, who through "thought experiments" 
comes to an intuitive understanding of what is really physically going 
on, and then develops his equations as a result.

Einstein's first work on special relativity does not see the Lorentz 
transformation as mere space-time distortions, but fundamentally 
rewrites the whole manner in which space and time is understood.  He 
realises that Maxwell's electromagnetic equations (the equations of 
light) are incompatible with the standard views (this is something which 
the physics community were understanding), and shows how in his new 
scheme that Maxwell's equations fit very nicely.  His work goes way 
beyond the work of Lorentz.

In a seperate paper, Einstein brilliantly shows that this new 
understanding of Maxwell's equations gives rise to the equivalence of 
energy and matter.  Furthermore, Einstein boldly asserts that maybe this 
equivalence could find practical application.  (When I first read and 
understood this paper, it just took my breath away.)

In later papers, Einstein struggled to understand how gravity effects 
space and time.  He understood the time distortions, but did not yet see 
the spacial distortions.  He predicted how light would be bent by the 
gravitational attraction of the sun, and obtained the same answer that 
Newton would have obtained.

But he must have realised that there was far more going on.  Einstein's 
new understanding of the relationship of space and time (which was 
developed by the mathematician Minkowski) must have showed him that 
space and time are somehow curved.  By coincidence, the equations of 
curved space had been recently figured out by Riemann, which built upon 
work of Gauss (whom some acknowledge as the greatest mathematician 
ever).  At its time, it was regarded as important mathematics, yet a 
curiousity from a practical point of view.  It is definitely hard stuff 
that typically takes people years or decades to understand.  Since 
Einstein was not an expert in this area (as indeed no physicist was) he 
did what anyone else would have done, and sought the help of an expert, 
Grossmann.

Einstein's realisation that space and time are curved is revolutionary. 
  He saw gravity not as a force, but rather as an artifact of the curved 
space.  As an example he computed how much the sun's gravity would bend 
light, and came up with a remarkable conclusion that it was in fact 
exactly double the effect that Newton would have obtained.  A few years 
later, this prediction was confirmed by observations of stars positions 
during an eclipse, and this startling find launched Einstein into fame.




-- 

Stephen Montgomery-Smith
EMAIL:PROTECTED
http://www.math.missouri.edu/~stephen
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