Markus Schwarz wrote:neufer wrote:
Space-time curves convergently into local gravitation bodies and all free falling space coordinates (whether arbitrarily fixed to baseballs, the Earth or Voyager 1) are FORCED to be attracted to local gravitation bodies (i.e., they are constantly being sucked into such bodies).
What exactly do you mean by "space-time curves"? Do you mean the paths taken by particles or the coordinate lines?
What I mean by "space-time curves" are the coordinate line curves that are due to
Ricci and
Riemann curvature.
Markus Schwarz wrote:
Since you emphasized the coordinates, keep in mind that these are precisely the quantities that have no physical meaning. What is physically meaningful are the paths taken by particles, all of which are affected by gravitation.
Time & space have a physical meaning that we can keep track of
with arbitrary: clocks, measuring sticks and coordinate systems.
Markus Schwarz wrote:
Free falling coordinates are adopted for calculations of free falling particles. In these coordinates the metric components depend on time, since the infalling observer notices an increase in the gravitational pull.
A infalling observer could only notice an increase in gravitational
tidal forces (i.e.,
Ricci curvature).
Markus Schwarz wrote:
I go back to my question: how do you propose to build a "space-flow-o-meter",
which would measure the "flow of space"? All you can measure is the flow of particles.
Precisely!
A "space-flow-o-meter" would make use of the flow of particles
the same way that one might measure the "flow of a stream" by dropping
(biodegradable) floating bodies into the flow and keeping track of their motion.
Or one could observe the motion of natural floating bodies such as
Sir Arthur Eddington did with the starlight photons "floating" past the sun
(although the use of photons is often a somewhat trickier proposition as Michelson & Morley found out).