"John" wrote in message
...
I know this has probably been discussed many times but I still haven't
found and answer I can understand. Basic question is why does an apple
fall when I let go of it ?

From GR's perspective, it "falls" since your hand is no longer preventing it
from moving the shortest path in it's immediate (local) 4-dimensional
spacetime which is distorted or curved predominately by the presence of the
earth. Once released, the apple is in freefall motion which is its natural,
unaffected state. If the apple were hollow, a scientifically minded bug on
the inside could not tell the difference between freefall and being "at
rest" or in uniform (unaccelerated) motion in some distant part of the
universe free from gravitational influence. Freefall and uniform motion are
straight line (geodesic) trajectories through spacetime - even if that
spacetime geometry is not Euclidean or flat. Geodesics are the shortest and
most efficient courses that can be traversed through a given geometry (i.e.
the shortest "distance" between two points in that particular geometry -
straight). Before releasing the apple your hand was constantly exerting a
force on it which prevented its natural geodesic motion. You experienced
this forceful interaction between hand and apple as the apple's weight. Your
hand was causing a deviation in the apple's straight line natural motion in
the locally curved spacetime just as the earth is doing the same with your
own body.

Regards

On Thu, 21 Aug 2003 11:07:10 -0400, "Perion"
wrote:


"John" wrote in message
.. .
I know this has probably been discussed many times but I still haven't
found and answer I can understand. Basic question is why does an apple
fall when I let go of it ?

From GR's perspective, it "falls" since your hand is no longer preventing it
from moving the shortest path in it's immediate (local) 4-dimensional
spacetime which is distorted or curved predominately by the presence of the
earth. Once released, the apple is in freefall motion which is its natural,
unaffected state. If the apple were hollow, a scientifically minded bug on
the inside could not tell the difference between freefall and being "at
rest" or in uniform (unaccelerated) motion in some distant part of the
universe free from gravitational influence. Freefall and uniform motion are
straight line (geodesic) trajectories through spacetime - even if that
spacetime geometry is not Euclidean or flat. Geodesics are the shortest and
most efficient courses that can be traversed through a given geometry (i.e.
the shortest "distance" between two points in that particular geometry -
straight). Before releasing the apple your hand was constantly exerting a
force on it which prevented its natural geodesic motion. You experienced
this forceful interaction between hand and apple as the apple's weight.


Your hand was causing a deviation in the apple's straight line natural motion in
the locally curved spacetime just as the earth is doing the same with your
own body.

What natural motion and where did it come from ?

John wrote:
:[snip]
: What natural motion and where did it come from ?

Inertial motion, which all objects do if
not accelerated.

To get a good feel for General Relativity,
forget a lot of the Newtonian terminology and concepts
and think of the Divergent Matter model of gravitation
where the Earth is expanding with an acceleration of
all points on the surface away from it's center of
mass.
Don't worry about the math or consequences
of the model, just think of what the apple would do
if you are accelerating upward and you let go of it.

It continues with the same velocity upward
that it attained before you let go of it, and you
continue to be accelerated upward by the ground.

Don't consider taking the model any further,
it requires a completely different physics, where
size changes and time slows, and motion is not the
same as in Newtonian physics and Euclidean space.

Einstein got an idea like this in 1907,
and wrote more about it in 1911, and continued
the idea in 1915 with more emphasis on inertial
motion rather than on accelerated motion and
the cause of the proper acceleration of the
Earth's surface upward.

He could not have presented any concept
like the Earth expanding, they would have put
him in an institution.
But you can appreciate the concept of
General Relativity by just thinking of the
ground accelerating upward.

Joe Fischer

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