Re: is free, open source software ethical?

On Wed, 05 Mar 2008 21:17:52 -0800, Ron Garret <rNOSPAMon@[EMAIL PROTECTED]
>
wrote:

>If all frames of reference are equivalent, how does one distinguish 
>between an inertial frame and a non-inertial one?

In general, you don't "distinguish" between them per se. Inertial frames
are the idealized, limiting case. Much as Newtonian mechanics is an
idealized approximation of "real" physics, appropriate under some set of
conditions, inertial frames are an approximation of "real" frames.

>That's correct.  But just because general relativity extended the theory 
>to non-inertial frames that does *not* mean that all frames (inertial 
>and non-inertial) are equivalent.

Well, I suppose you could come up with a definition of "equivalent"
where that is true, but that's just semantics. From the physicist's
point of view, they are equivalent (i.e., there exists a mathematical
formulation of physics that works equally well in either case).

>1.  The earth is not a perfect sphere.  It bulges at the equator.  If 
>the sun revolves around the earth and not vice versa, how do you account 
>for this bulge?

It's funny that you mention that, because I had started to write
something about that in my earlier message, and then decided that it was
unnecessary detail.

The motion of the sun (and the rest of the universe) around the
stationary earth sets up a time-varying curvature of the space-time in
which the earth is embedded. This curvature induces an apparent outward
force that leads to the equatorial bulge. It's in the math.

>2.  Notwithstanding this bulge, the earth is a very close approximation 
>to a sphere.  And yet the motion of the sun around the earth is not 
>spherically symmetric.  The sun not only revolves around the earth every 
>24 hours, but it also oscillates vertically (that is, along the sun's 
>axis of rotation around the earth) with a period of approximately 365.25 
>days.  How do you account for this?

Same as (1).

The central tenet of general relativity is that there is no "priveleged"
viewpoint in the universe, that the physics is the same no matter where
you stand. Newtonian mechanics (Gallilean, actually, in this case) is
the first step towards this view: The physics for an object in uniform
motion is the same as it would be if we considered the object to be at
rest and everything else to be in uniform motion. But Newtonian
relativity breaks down in the face of acceleration, and this is where
general relativity takes over.

You're probably familiar with the 2D and 3D coordinate transformation
matrices that are used in computer graphics. If we extend that concept
with a fourth (time) coordinate, we can formalize Newtonian relativity
as a coordinate transformation.

What general relativity does (albeit with much, much more complicated
mathematics) is extend that same idea even further to the cases where
Newtonian relativity no longer applies. The transformation from
geocentric to heliocentric views then becomes, in effect, a coordinate
transformation (that's a bit of a simplification, but you get the idea).

Regarding Occam's Razor: As Einstein himself said, things should be as
simple as possible, but not simpler. General relativity is the response
to the failures of Newtonian mechanics. Newtonian mechanics can't
explain the precession of the perhelion of Mercury. Newtonian mechanics
can't explain why the clocks in GPS satellites run more slowly than the
same clocks at the earth's surface. And so on.

Newtonian mechanics is an approximation, one that is appropriate to a
very wide variety of circumstances. But it doesn't hold in all cases.
For all we know, general relativity is also an approximation, but it's a
"better" one, in the sense that it is appropriate in an even wider
variety of circumstances. Is general relativity "simpler" than Newtonian
mechanics? If we consider the mathematics at face value, clearly
not--the mathematics of relativity are horrendous. But in another sense,
relativity _is_ simpler than Newtonian mechanics, because the _same_
mathematics are applicable in all reference frames, something that you
can't say in the Newtonian view.

Steve Schafer
Fenestra Technologies Corp.
http://www.fenestra.com/