
#19
Jun206, 11:37 PM

P: 58

So, is it flat or is it curved?




#20
Jun306, 02:13 AM

Sci Advisor
PF Gold
P: 3,273

The curvature of spacetime is revealed by working out all the components of the Riemannian tensor with the RobertsonWalker metric in which k = 0, they are not all zero. It is this 4D spacetime curvature that describes the gravitational field. The peculiar thing about the GR cosmological solution is when all the Riemannian components are zero, in the empty universe case, then the 3D space hypersurface is not flat but hyperbolic and expanding linearly. My caveat on that consensus opinion is, as the WMAP data is angular in nature and conformal transformations preserve angles, it is also consistent with a spatially conformally flat universe. Garth 



#21
Jun306, 11:40 PM

P: 58

Thanks garth,
Sorry for the delay, been stargazing  the alignment of the planets is brill at present! So, what you are saying is that it has taken nearly one hundred years and several COBE type satellite results to show that in X,Y,Z coordinates space is flat  which is what they thought it looked like at the beginning? Out of interest, what evidence is there that space is curved in 4D space time? Thanks. 



#22
Jun406, 12:57 AM

Sci Advisor
PF Gold
P: 3,273

It particular, the finer details of the orbits of planets such as Mercury and the trajectories of light rays passing close to the Sun follow the geodesics ('straight lines') through a curved 4D spacetime as predicted by GR. Garth 



#23
Jun406, 05:00 AM

P: 58

Well no, These are local perturbations and I am sure we are all happy with that. In this thread we are looking at the universe in total. When we look at the Universe as a whole, in 3d it is flat and in 4d it is supposedly curved? I was just wondering which way it curves in 4D space (do we know?) and what evidence do we have?
Ta 



#24
Jun406, 07:40 AM

Sci Advisor
PF Gold
P: 3,273

Astrophysics, and scientific cosmology, is the application of the physics 'down here' in the laboratory to observations of the universe 'out there'. The 'down here' bit in GR are the solar system experiments that verify the predictions of the theory. These verify the understanding that "space is curved in 4D space time". Once GR is accepted as an accurate description of gravitational fields the GR field equation is solved for the cosmological case, with a maximally symmetric space, which is homogeneous and isotropic. This yielded the Friedmann models that are then verified by: 1. Hubble red shift. 2. BB nucleosynthesis predicting a 3/4 H and 1/4 He composition by mass of the primordial gas exiting the BB. This is concordant with the present day element relative abundance mix taking 10 Gyrs. worth of stellar nucleosynthesis into account. 3. The CMB. 4. The relative abundance of some rare isotopes that were produced in the BB, although these are often model dependent and do not constitute a hard prediction. The standard model also requires, Inflation, nonbaryonic DM and DE which have been able to be combined into a self consistent model. Although I have an issue with this as they have not been discovered in laboratory physics. However, the veracity of the first three predictions are grounds for confidence in the basic GR understanding that ""space is curved in 4D space time". Garth 



#25
Jun406, 09:16 AM

Sci Advisor
PF Gold
P: 3,273

Also there is large scale gravitational lensing of distant quasars by nearer galaxies. Although this is not quite on the cosmological scale.
The expression "spacetime curvature" is a mathematical one that may be confusing. It may have a spacial component as well as a temporal one. The temporal 'curvature' though manifests itself as a time dilation  you cannot 'bend' time in the normal sense (Salvador Dali not withstanding!) Garth 



#26
Jun406, 02:28 PM

Emeritus
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PF Gold
P: 2,977





#27
Jun406, 02:31 PM

P: 58

Thanks Garth,
You see my interest in 'curvature' is entwined with the queston of "where does the energy go" in the BB theory. Photons of light have a longer wavelength on arrival than when these same photons set off. Ergo, their frequency and hence energy is therefore less. So in BB, where did this energy go and how did they lose it? Now the standard BB answer is that it went into "curving space". BUT we know from this thread that space in the x,y,z coords is flat  so it must have gone into curving space time? But if space time is a mathematical concept then how do photons curve it in becomng redshifted? 



#28
Jun406, 02:36 PM

P: 58





#29
Jun406, 02:58 PM

Sci Advisor
PF Gold
P: 3,273

This question vexed Einstein, Hilbert and Klein and others until it was resolved by Emmy Noether (great name for a relativist! ) who coined the phrase "improper energy theorem". You can read more about Noether's work in Nina Byers paper E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws. If you are interested in an alternative published theory that tries a different approach you might be interested in Self creation cosmology. (You can find links to the published articles from that Wikipedia page) Garth 



#31
Jun406, 03:15 PM

P: 58

Nah,
energy is conserved. if a photon has enough energy to expose a photographic plate on galaxy x, then surely it cannot expose it on galaxy y? It must have lost energy on the way. Are you saying that whilst a photon exposes a photo of their hols on their plates it also exposes a photo on our photographicplates even though it 'lost energy' on the way? No way! 



#32
Jun406, 03:20 PM

P: 58





#33
Jun406, 03:30 PM

Emeritus
Sci Advisor
PF Gold
P: 2,977

http://physicsforums.com/showpost.ph...6&postcount=10 Evidence for an expanding universe is also evidence for a curved spacetime. 



#34
Jun406, 03:32 PM

Emeritus
Sci Advisor
PF Gold
P: 2,977





#35
Jun406, 03:42 PM

P: 58





#36
Jun406, 03:55 PM

P: 58

So, would the photographic plate be exposed on both galaxies or only one?
This is what energy conservation is about (and forums for that matter too!) 


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