Re: [Phys-L] strange things in chem book

[John Denker <jsd@av8n.com>]

On 09/17/2012 06:40 AM, jbellina wrote:
> Indeed, you could make the point that models with known limits are
> more reliable than models whose limits are unknown. 

That's true.

>  In that sense,
> Newton's Laws are more reliable than GR.

I disagree, because:
 a) Relativity /contains/ Newtonian gravity as a corollary, and
 b) it tells us the limits of validity of the Newtonian approximation.

Meanwhile:
 c) Relativity does not tell us the limits of relativity, but
 d) by the same token, Newtonian theory does not tell us the limits 
  of Newtonian theory.

Therefore relativity is Pareto superior.  It is in some ways better and 
in no ways worse.  Most of what we know about the limits of the Newtonian 
theory comes from relativity -- not from the Newtonian theory itself --
so that should be considered a strength of relativity, not the other way 
around.

In other words, in limits where GR is telling you to trust the Newtonian 
theory, GR is just as good within those same limits.

In any practical application, the error you get by using GR is less than
or equal to the error you would get by using the Newtonian theory in the
same situation.