sci.physics.electromag

maxwell says...
>
>On Mar 16, 4:51=A0pm, nade wrote:
>> ...
>> Hi, uhm... if special relativity is wrong. It means General Relativity
>> is wrong too? If you believe they are both wrong. What do you
>> think is the cause of gravity?
>>
>There is almost no connection between Einstein's Special Theory of
>Relativity (SRT) and his General Theory of Relativity (GRT) apart from
>the (marketing) fact that they both include the exciting word
>'relativity'.

That's not at all correct. There is an intimate relationship between
Special Relativity and General Relativity, which is that Special
Relativity is the small-region limit of General Relativity.

Here's an analogy with Euclidean geometry. We all know how to
do Euclidean geometry on a plane: (1) A straight line is the
shortest distance between two points. (2) The measure (in degrees)
of the interior angles of a triangle add up to 180. (3) A right
triangle has sides with lengths related by A^2 + B^2 = C^2.

Now, instead of a flat plane, consider geometry on the surface
of the Earth (which is approximately a sphere).
The shortest distance between two points isn't a straight
line, it is what's called a "great circle" (on the Earth,
the lines of longitude are great circles). If you want to
know the quickest way to get from point X to point Y, you
find the circle whose center is the center of the Earth
that goes through X and Y. Along that circle is the shortest
path between X and Y.

In some ways, great circles are like "straight lines" of
planar geometry, but in other ways they are different.
If you take three points X, Y and Z on the surface of the
Earth, and make a "triangle" by taking the great circle
route from X to Y, then the great circle route from Y to
Z, then the great circle route from Z back to X, the
resulting triangle will have interior angles that add up
to greater than 180 degrees. If it is a right triangle
with small sides A and B, and large side C, then
A^2 + B^2 adds up to more than C^2. So the geometry of
great circles is not much like the geometry of straight
lines.

However, if you are not concerned with a big region of
the Earth, but only with a tiny region (maybe your back
yard), then the difference between a great circle and
a straight line becomes negligible. If in your back
yard, you make a triangle out of great circles, its
angles will add up to 180 degrees to the limits of
your ability to measure. If you make a right triangle
in your back yard, it's sides will satisfy the Pythagorean
theorem, to within the limits of your ability to measure
distances.

The conclusion is this: The small-region limit of
spherical geometry is planar geometry. An alternative
way to see the same conclusion is this: Instead of
having a *real* sphere, take many, many tiny planar
triangles and connect them together in 3D to form a
spherical "geodesic dome". If the dome is big enough
compared to the size of the triangles, then spherical
geometry can be used (approximately) to describe
the large-scale shape of the dome. But for small
scales, in a tiny region that only involves one or
two triangles, the dome will look like a section of
a flat plane.

The relationship between General Relativity and Special
Relativity is analogous. In a very large region of
spacetime, a region large enough to include planets and
stars, General Relativity looks very different from
Special Relativity. However, if you focus in on a small
region of spacetime (say, a few seconds in the inside of
an elevator that is in free-fall) General Relativity
becomes indistinguishable from Special Relativity.
Special Relativity is the small-region limit of General
Relativity. If your measurement devices (for measuring
times and distances) have limited precision, then in a
small enough region of spacetime, the predictions of
Special Relativity will be true (to the limits of your
ability to measure).

--
Daryl McCullough
Ithaca, NY