On Apr 25, 4:34 am, Dan <dan.ms.ch...@gmail.com> wrote: > Koobee Wublee wrote:
> > Let?s look at spacetime. According to GR, it is the curvature of > > spacetime that causes gravity. So, spacetime is curved around a > > gravitating mass. In free space, the Einstein tensor vanishes which > > means the Ricci tensor also vanishes which mean the Riemann tensor > > also vanishes. So, you have vanished Riemann tensor in curved > > spacetime. That means the curvature tensors really do not address the > > curvature thing. The field equations are merely differential > > equations that allow you solve the local geometry and nothing more. > > <shrug> > > http://en.wikipedia.org/wiki/Ricci-flat_manifold > The Ricci tensor vanishing does not imply the Riemann tensor does .
There is still no mathematical proof showing that null Ricci tensor with non-vanishing Riemann tensor. Even if you are right, Riemann tensor does not play a role in the final interpretation of differential geometry. The Riemann tensor represents only one of the steps from the Christoffel symbols to the field equations. <shrug>
> Also ,don't confuse space with space-time .
Consider that already done. <shrug>
> Even factoring out the > gravitational effects (which predominantly affect the time-time > component of the metric tensor, not it's space components ) ,we still > have to consider the expansion of the universe .
So, the flatness of cosmology is not the same flatness when discussing gravitation. Now, Koobee Wublee is with you. <shrug>
So, the flatness of cosmology is determined through how much of negative mass density is in vacuum. If there is more negative mass in vacuum, the universe will expand its acceleration just like antigravity of the Newtonian system. Koobee Wublee find that very amazing that the self-styled physicists would choose to embrace negative mass density in vacuum while vehemently denying the Aether. <shrug>
> Space can be predominantly flat (provided it's free from strong > gravitational effects) , while still being embedded in a curved space- > time .
Koobee Wublee is also very amazed that the solutions to the FLRW metric would be interpreted as expansion of space while the Schwarzschild metric would be interpreted as the geometry that determines how an object is going to behave --- same mechanism in mathematics but interpreted in two drastically different ways. If there is not enough or no negative mass density in vacuum, Koobee Wublee supposes space would collapse back onto itself dragging all objects in space along with it, no? So much for the scientific axiom that the laws of physics are the same everywhere and whenever. <shrug>
> > Write down the metric for n-sphere please. <shrug> > > If the earth were perfectly round , you would return to your point of > origin when going around it . Generalize . Or better yet, use Google > to figure out the metric .
No, Koobee Wublee cannot generalize an ordinary 3-dimensional object with the profoundness of curved space where space is able to curve back onto itself. Please present the metric. <shrug>
> > At least, you admit your own version of cosmology is purely > > speculation. The so-called experts believe in their speculated > > ?reality? more whole heartedly. > > First, don't underestimate the value of rational speculation .
You also need to distinguish rational speculations from the irrational ones. <shrug>
> I speculate that the sun will rise tomorrow .
You actually have a very good chance of being right, and it is supported by history. <shrug>
> All science has origin in rational speculation.
?All science came out of a sea of irrational speculations plus a tiny trace of rational one, but scientific methods when properly applied allow science to find just that rational one. <shrug>? --- Koobee Wublee, 2013