2008-12-10 22:08:46 UTC
locally minimalize distance - it's trajectory is geodesic of some
metric (usually diagonal - isotropic) . It is the result of that
microscopic structure of the material can reduce wave propagation
Microscopic models of physics usually assume that we have some field
everywhere and it's fluctuations transfer interactions/energy/
So maybe these microscopic structure can reduce waves propagation
Reciprocals of these velocities creates (anisotropic) metric tensor
(g) and so for example particles travel through geodesics like in
general relativity theory.
Standard interpretation of general relativity says that particles goes
through geodesics because of space time internal curvature: theory,
experiments suggest some equations, which looks like being a result of
internal curvature of spacetime.
But if we live on some curved manifold, it intuitively should be
embedded somewhere(?) (and for example black holes are some spikes)
So why our energy/matter is imprisoned on something infinitely flat?
Why we doesn't interact with the rest of this something?
What happen if our manifold will intersect with itself? (optimists say
that it would allow for time travel/hyperspace jumps?...)
And less philosophical, but most fundamental (to connect GR and QM)
question is: how energy/momentum density can create curvature?
Maybe it's not the only possible interpretation.
Maybe we live in flat R^4 and GR is only the result of reducing the
speed of wave propagation by microscopic structure of some field,
which somehow is ruled by similar equations to Einstein-Hilbert.
This interpretation doesn't allow for instant time/space travel, but
it get rid of some inconvenient questions ... and creates a chance to
answer to the last one.
So how should look such connection of QM(QFT?) and GR?
What are particles? From spacetime point of view, they are some
localized in some three dimensions and relatively long in the last
one, solutions of let say some field to some equations. These
solutions want to be more or less straight in four dimensions
(constant velocities), but they turn accordingly to interactions
transferred by the field.
Many of them were created in big bang (boundary conditions), so their
long dimension is similarly directed - creating local time arrow (GR).
Bolzman distribution among such trajectories, can purely classically
create QM like statistical behavior ( http://www.scienceforums.net/forum/showthread.php?t=36034
Are there any arguments for spacetime internal curvature other than
that the equations looks like being be a result of it?
What do you think about these interpretations?
If the curvature is the only option, is spacetime embedded