On Apr 25, 11:50 am, Dan <dan.ms.ch...@gmail.com> wrote:
> > 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> > > http://sgovindarajan.wikidot.com/ricciflatmetrics
That also shows no such mathematical proof that when the Ricci tensor is not, the Riemann tensor does not necessarily vanish. So, perhaps, anther try to justify your claim. We believe this is going to be the third one. <shrug>
> > 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> > > I have no idea what you're talking about . And I'm pretty sure you > have no idea what you're talking about .
Well, you may be right on the first sentence above. However, you are dead wrong on the latter one. <shrug>
> "Spacetime tells matter how to move; matter tells spacetime how to > curve" -John Archibald Wheeler
Well, Koobee Wublee, then, would repeat. Hopefully Dan would understand it. <shrug>
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>
> > 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> > > Ether isn't needed in General relativity . It's a deterministic theory > where you have no arrow of time apart from the expansion of the > universe. Like a 3d holographic movie. It doesn't matter how you play > it or view it . An object moving at constant velocity can consider > itself at rest . Whether or not any notion of 'absolute space' of > 'absolute time' will be needed in a unified theory is beyond the scope > of this discussion .
Is Dan talking to himself? Please note. Koobee Wublee is talking about the negative mass density in vacuum which GR cleverly disguises as dark energy. <shrug>
> > 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> > > Here's the metric for a 3-sphere . Add an additional time dimension > (an extra row and column in the metric tensor with -1 in the corner > and zero in the other entries ) and you're ready to calculate > trajectories . > http://upload.wikimedia.org/math/5/d/3/5d3493e432ad0bdab4e10a3896368856.png
Hmmm... That is the geometry of an ordinary sphere in flat space. Does Dan recall what he said earlier?
?The only metric I can think of where the traveler in a straight line *must always* return to his starting point for every possible starting point is some sort of n-sphere, though it would have to have exceedingly small curvature to match experiments.?
Koobee Wublee is merely asking for what an amazing metric that is. A sphere in flat space does not constitute Dan?s claim, no? <shrug>
> > ?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 > > What methods count as 'scientific'?
The subject is deep. Perhaps, it is time for Dan to consult with his textbook. <shrug>
> Also ,you had to find the most reliable source to quote , right?
Yes, can?t Dan find the post in the newsgroup? Dan even quoted above. So, of course, the source is very reliable. <shrug>
> And you call me a 'self-styled physicists' .
Not really. It all depends on Dan. A self-styled physicist is not really a derogatory phrase. Amazingly, this phrase has the magical power of self-convicting a self-styled physicist. Wow! Only you (not necessarily Dan and not directly at Dan) would know if you are a self- styled physicist. <shrug>
> You're not deserving of the > title, however , you do qualify for hypocrite .
What hypocrite? Koobee Wublee is not contradicting Himself here. You can find hypocrites among self-styled physicists. They love to interpret the mathematics in different ways to suit their grossly biased observations or politically correct agendas. <shrug>
> > It is amazing that you certainly have spent a lot of energy engaging > > with the point you have claimed not to see. <shrug> > > It's always worthwhile to see if meaningful dialogue and understanding > can be achieved .
In another words, Dan is very curious. <shrug>
> Since, in the present case , it is impossible, rest > assured that I won't repeat the same mistake , and not waste any more > energy .
Sorry to disappoint Dan. Koobee Wublee did not become a trophy for his crackpot hunting safari trip. Better luck next time. Baad me milte hain. <shrug>
In the meantime, Dan has laid out the following two mathematical claims. Just like Fermat?s last theorem, they would appear not to have any chance of being proven. <shrug>
** When the Ricci tensor is null, the Riemann tensor does not necessarily vanish.
** There is a metric where a traveler traveling in a straight line will end up in his starting location.