Chronology | Current Month | Current Thread | Current Date |
[Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |
First, I apologize to A. R. Marlow and the list for my last few posts. They
have been too cynical...
curvature of space and time.
First, I'll assume that whatever Newtonian mechanics tells me concerning the
motion of a mass, GR will tell me the same thing at least within the scope
where Newtonian mechanics gives good results.
If I drop a ball, then I see it is accelerating with respect to my frame of
reference. To analyze this using Newtonian mechanics, I would say there is a
force acting down on the mass and describe this force as the weight. I'd
write (I'll assign up as my positive direction):
Fnet = ma
-W = ma
-mg = ma
a = -g
I would therefore conclude that the weight being the only force, the
acceleration would be g downward.
Now, Marlow states that W is a fictitious force, so I don't want to include it
on the Fnet side of the equation (where the real forces belong). Therefore, I
move it to the right side (as a frame of reference acceleration) and write:
Fnet = m(a+g)
0 = m(a+g)
a = -g
This says that when no force is acting on the mass, then it will have an
acceleration of g with respect to my frame of reference, the same result as
Newtonian mechanics.
Now, I stand on the floor and feel a force acting up on me. In Newtonian
mechanics I write:
N - W = ma
N - W = 0
N = W
N = mg
In GR I write:
N = m(a+g)
a = 0
N = mg
Now, I stand in an elevator that is accelerating. In Newtonian mechanics I
write:
N - W = ma
N = m(a+g)
In GR, N is the only real force and write:
N = m(a+g) directly.
How am I doing so far? Got to go to class.
Bob Carlson