Re: Gravitational Confusion
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Posted by ronron on December 20, 19100 at 17:51:31:
In Reply to: Re: Gravitational Confusion posted by Brian on December 20, 19100 at 08:48:12:
the marble example might not have been the best, but it
came to mind. let's make it a bedspread pulled tight
and then imagine placing a bowling ball on top of it. at first, the bedspread is nice and flat and if you
roll a marble in a straight line it will continue in a
straight line on the bedspread. this is maybe a
reasonable 3-d analogy for spacetime in special
relativity - a flat 4-d spacetime (with a metric, a
"function" to measure differences between events) now if you place a bowling ball on the bedspread, you
make the spread curve in towards the ball in the area
near the ball. so suppose you roll a marble towards
the bowling ball from about a meter away. at first,
the marble will roll in a straight line, since the
"spacetime" far away from the bowling ball is still
flat. but as it approaches the bowling ball, the
marble will curve towards the ball. it will follow
the curvature in the bedspread that the bowling ball
has caused. this is analogous (in spirit at least)
to what happens in general relativity. instead of
saying that the "bowling ball attracted the marble
and made it move towards it", GTR says that "the marble
followed its geodesic, followed the straightest path
available to it." two ways to explain the same thing:
the gravitational attraction between the marble and the
ball made them move closer together, OR the massive
object changed the local geometry near it and other
objects moving in that area must travel according to
the new local geometry. if you want to understand *how* two objects attract, i
don't think anybody ever knew that. Newtonian gravitation
just gives us a force law to compute the attractive force
between material bodies. it notes that the force is proportional
to the masses and inversely proportional to the separation
of the objects, but what exactly CAUSES the attraction ?
who knows ? in GTR they sort of still beg the question
because there (if i understand GTR, and that's a big if :-)
they explain gravitational effects by using curvature of
spacetime. but the curvature of the spacetime depends on
the masses present, and they don't really explain the
magic of how masses cause spacetime to curve, they only
use math that lets you compute curvature. and if you
know the curvature, you can compute trajectories. it's
really the ability to predict rather than to explain the
why. recall too that this all came about as a result of the
incompatibility of action-at-a-distance gravitation with
special relativity. Einstein needed something that
did not require masses to "know" about each other
instantaneously, which was the case with Newtonian
gravitation. the result was this curvature of spacetime
caused by mass business. so the short answer might be that in Newtonian gravitation,
the objects actively determine their path by the
attraction between them, and space and time are
backdrops against which all this happens. that is,
space and time are not variables in your gravitational
problems. the objects determine their paths based on
mass and separation. in general relativity, an object
moving on a worldline is more passive and just follows
the local geometry. and as opposed to the Newtonian
theory, in GTR when you solve the Einstein equations
you are solving for the spacetime(s) itself. the
spacetime in question is a dynamical variable. G = 8pi T seems simple enough, but when you expand
this, the Einstein equation, you get a set of
non-linear, partial, coupled differential equations.
not many exact solutions are known, but in that
equation (supposedly) are contained all physically
significant spacetimes. you get to choose which
ones you are interested in. i hope this helps, and i apologize in
advance for any inaccuracies. i'm new to it myself
and invite other replies. ronron
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