Redshift z

[quantumtopology]

Hi, guys.

CC, how are you doing, I guess you got stuck, but don't be discouraged. You set yourself about a really hard task.

I think it's better to take little steps at a time.

 

For instance, to come back to the redshift topic:

We know that in the expansion model one of the current simple explanations of the observed redshift is that as space expands the wavelength is stretched, which seems logical if one accepts the premise that "space" is stretching itself so to speak. This explanation is now the prevalent one in mainstream cosmology, it has won over the infinitesimal Doppler redshifts sum over a certain distance, although for most maistream physicists both explanations are equivalent.

 

Now, in the setting of a universe with a space with the parameter K(gaussian curvature)=-1 that I use as a premise for my reasoning, but that I acknowledge to be only one possibility (admitted by mainstream, although right now the prevalent opinion is that K=0 for reasons we might discuss later, but that reduce basically to the data from the CMBR, and that it fits conveniently in the LCDM model-and I don't mean this as a critic, just trying to be neutral, Modest if you find fault with this just tell me), in this setting, I was saying, we find that redshift of EM waves can be explained by a parallel or similar mechanism to the one used by the expansion model, but in this case space stretches not in the longitudinal direction but in a tranversal direction to the light geodesic as the distance between geodesics gets larger as a function of distance from the source, according to Hyperbolic geometry ( Sommerville, The elements of Hyperbolic geometry, specially pages 56 to 94,J.W. Anderson, Hyperbolic Geometry (Springer-Verlag London, Ltd., London, 1999). R. Bonola, Non Euclidean Geometry, a Critical and Historical Study of Its Developments (Dover Publications, Inc., New York, 1955 ,H. Buseman and P. J. Kelly, Projective Geometry and Projective Metrics,).

So here we seem to have a perfectly valid, in principle, attending to geometrical relations, that aregenerally used in Physics, and certainly are used in the explanation of the stretching of space according to the expansion model.

 

 

 

This is a conformal representation of hyperbolic geometry called the Poincare disk, in it the lines departing from the point on the left of the circumference that represents a sphere are geodesics of hyperbolic space and distance between points along this geodesics are hyperbolic distances, the points where the geodesics cut the circuference are in Euclidean space(so the ball has radius Rin Euclidean space), as are the points belonging to the concentric smaller circunferences depicted, that are called in 3D Horospheres, horospheres are all parallel between them, and their surface space is also Euclidean, that's why this geometrical objects are called dual, they inhabit a Hyperbolic space but their surface geometry is Euclidean.

Horospheres are orthogonal to the geodesics, and have their center at infinite and are tangent to the Poincare circuference at infinity(in hyperbolic space).

These horospheres surface can be thought as wavefronts of EM waves, with constant phase.

Distance between geodesics can be seen as wavelengths that stretch in successive parallel horospheres.

 

 

The nature of the deformation. Poincare ball lies in the x+y=a plane. It is clearly shown that the hyperbolic distance δ>d, while the spherical distance s<d, where d is the Euclidean distance.

So it all comes down to a perspective problem, we would observe an stretched wavelength due to the fact we measure from our Euclidean POV but light travels in Hyperbolic space.

This would we some of the characteristics of EM waves in a Hyperbolic space, we don't know for certain if we live in a hyperbolic space, but if we did we would have to use Occam's razor, don't you think?

 

Source of the figures and geometrical explanations: von Brzeski (2008)

 

To be continued

 

Regards

QTop

[coldcreation]

Hi, guys.

CC, how are you doing, I guess you got stuck, but don't be discouraged. You set yourself about a really hard task.

I think it's better to take little steps at a time.

 

Hey Qtop, and modest, and others if you're following the discussion...

 

I'm not stuck or discouraged. I've just been occupied (side-tracked) with stuff like fossil hunting: one of my passions. The other passion is illustrating 2-, and 3-dimensional manifolds, and extrapolating to 4-dimensions. I've been doing that in the evenings. All the while preparing the text that accompanies those schematic diagrams.

 

Surely the task is hard but as I wrote earlier, I haven't yet found anything that disproves or falsifies the hypothesis. The lengthy part is preparing all the sections, organizing the diagrams, captions, and so on. The main brunt of the text is rather simple: redshift z due to global spacetime curvature (of the continuous Gaussian type), and global stability due to the same Gaussian curvature. The former is intuitive, since it's entirely based on general relativity. The latter is less intuitive, but evident once it's understood that the global field under review is homogenous (the same magnitude of curvature everywhere). The result is that light is redshifted since it travels geodesic paths, but objects do not partake geodesically.

 

The beauty resides in the simplicity. Both redshift and stability are due to the same thing: curvature.

 

The rest of the story will be posted soon.

 

 

CC (from the land of tennis, bulls and football :naughty:)

[modest]

I'm not stuck or discouraged. I've just been occupied (side-tracked) with stuff like fossil hunting: one of my passions.

 

No, no, no :naughty:

 

You should have blamed it on the world cup. Congrats to the land of the bull! Were there riots in the streets?

 

~modest

[quantumtopology]

No, no, no :naughty:

 

You should have blamed it on the world cup. Congrats to the land of the bull! Were there riots in the streets?

 

~modest

 

Si, Viva España!

 

Well, no riots, but really huge crowds here in Madrid to welcome the champions, they have been parading by the city mainstreets , showing that precious Cup.

It's a dream come true. Actually I must confess I never thought we'd made it. Not a great follower of soccer either, that might change now

 

Regards

QTop

[modest]

Congratulations!

 

Exciting game.

 

Si, Viva España!

 

de veras? CC tambien. No estoy seguro si el vive en madrid, pero en algun lugar de Espana.

 

Isn’t there a Spanish saying... all roads lead to Madrid?

 

~modest

 

EDIT: Sorry, I read "Viva Espana!" as "Vivo en Espana". I'm rusty with my spanish :naughty:

[quantumtopology]

Congratulations!

 

Exciting game.

 

 

 

de veras? CC tambien. No estoy seguro si el vive en madrid, pero en algun lugar de Espana.

 

Isn’t there a Spanish saying... all roads lead to Madrid?

 

~modest

 

Thanks!!

I think CC lives in Barcelona. Do you, CC?

Hey, How come you speak such good spanish? Or at least write it correctly?

The saying could be applied to Madrid since it's inthe center of Spain , but I always heard it regarding Rome.

I think there is a spanish forum in this site, whenever you want to have some conversation in spanish, you guys could tell me and we can just meet there. :naughty:

 

Regards

QTop

[modest]

Thanks!!

I think CC lives in Barcelona. Do you, CC?

Hey, How come you speak such good spanish? Or at least write it correctly?

The saying could be applied to Madrid since it's inthe center of Spain , but I always heard it regarding Rome.

I think there is a spanish forum in this site, whenever you want to have some conversation in spanish, you guys could tell me and we can just meet there. :naughty:

 

Regards

QTop

 

yep, yep, yep. I'm game:

 

http://hypography.com/forums/spanish-forum/23690-all-roads-lead-to-spain-%3B.html#post300402

 

~modest

[Qfwfq]

The saying could be applied to Madrid since it's inthe center of Spain :beer:, but I always heard it regarding Rome.

Indeed, in the days of the Empire the road network was much Rome-centric. The French roads and railways tended to be Paris-centric, though maybe not quite as much today.

[quantumtopology]

Hi,Qfwfq

BTW, I am curious about the pharase of your signature "Inutil insegnà al mus, si piart timp, in plui si infastidìs la bestie."

It is obviously a romance language but wich exactly? some italian dialect?

[quantumtopology]

Back to cosmology, and to post 596, I know it might be hard to understand since it demands some notions about hyperbolic geometry, that is not commonly taught, so any questions or comments?

 

Regards

QTop

[coldcreation]

The nature of the deformation. Poincare ball lies in the x+y=a plane. It is clearly shown that the hyperbolic distance δ>d, while the spherical distance s<d, where d is the Euclidean distance.

 

So it all comes down to a perspective problem, we would observe an stretched wavelength due to the fact we measure from our Euclidean POV but light travels in Hyperbolic space.

 

This would be some of the characteristics of EM waves in a Hyperbolic space, we don't know for certain if we live in a hyperbolic space, but if we did we would have to use Occam's razor, don't you think?

 

What do you mean by a "perspective problem"?

 

If the universe is nonexpanding, how would we not know we live in a hyperbolic space?

 

Also, what does Occam's razor have to do with it? Both the expansion redshift and hyperbolic space redshift are simple. How could you shave either one down to nothing, or eliminate one or the other on empirical grounds?

 

According to extrapolations of the equivalence principle (to cosmology) both interpretations are consistent with observations.

 

 

CC

[quantumtopology]

What do you mean by a "perspective problem"?

 

If the universe is nonexpanding, how would we not know we live in a hyperbolic space?

 

Also, what does Occam's razor have to do with it? Both the expansion redshift and hyperbolic space redshift are simple. How could you shave either one down to nothing, or eliminate one or the other on empirical grounds?

 

According to extrapolations of the equivalence principle (to cosmology) both interpretations are consistent with observations.

 

 

CC

Good questions CC.

The perspective problem comes from the fact that in case we lived in spatially hyperbolic universe we would perceive redshft due to the fact that what we detect is in Euclidean space, as I explained the space of horospheres is a surface with euclidean geometry, and can be seen as a constant phase wavefronts of EM waves, so when we detect the wave is like a conformal projection of hyperbolic space onto Euclidean space, the redshift would be the "deformation" that produces the projection, just like when you project the spheric geometry of the globe map onto a flat surface(Mercator) you get a deformation of distances towards the poles.

 

I don't understand your second question.

 

As for the Occam's razor, it is quite clear that the hyperbolic geometry explanation is much simpler in several ways, (although might bring further misteries), for one, it doesn't need Big Bang singularity no "new physics" , no need for Dark matter nor Dark energy, no global GR conservation energy trouble, no cosmological constand nor need to give it a value, no horizon problem, no fine tuning problem, no age problem.....

The thing is astronomical observations probably won't solve the problem since both models are very hard if not impossible to distinguish with the current and near future technology.

So the Occam's razor will decide, in case the geometrical view gets across which I doubt very much, but who knows?

 

Regards

QTop

[modest]

As for the Occam's razor, it is quite clear that the hyperbolic geometry explanation is much simpler in several ways

 

Occam's razor would prefer the theory that explains the most data with the fewest assumptions. Expansion explains redshift, CMB, the abundance of light elements, the lack of old stars, etc. Hyperbolic space explains (at best) redshift alone.

 

it doesn't need Big Bang singularity no "new physics"

 

To explain redshift with hyperbolic space you would need new physics. The current laws of physics do not predict a distance / redshift relationship due to hyperbolic space. The new physics would, for example, explain why space is hyperbolic (what causes it) and how curved it is.

 

The thing is astronomical observations probably won't solve the problem since both models are very hard if not impossible to distinguish with the current and near future technology.

 

Both models? I don't know of any cosmological model explaining redshift with hyperbolic space.

 

The way the scientific method works, a model would make predictions which could be compared to observation. For example, big bang cosmology predicts that 24% of baryonic matter should be helium. If there were no Big Bang then elements would exist in abundances predicted by Burbidge and Hoyle in the '60s. There would be almost no helium nor deuterium.

 

In this way, the scientific method corroborates explanations of redshift which include a big bang and rule out explanations which do not.

 

~modest

[coldcreation]

Occam's razor would prefer the theory that explains the most data with the fewest assumptions. Expansion explains redshift, CMB, the abundance of light elements, the lack of old stars, etc. Hyperbolic space explains (at best) redshift alone.

 

I have a few minutes to kill before my flight, so I'll take a stab at this. Curved spacetime explains redshift (whether it is curved hyperbolically or spherically). As long as light travels a geodesic you have redshift. However, if the universe were shaped like a cylinder, there would be no redshift. Nor is there a redshift in a Euclidean universe, unless it's expanding. The CMB is relatively easy to explain in the curved spacetime scenario. I'll come back to that at a later date. The age of stars is not proof of expansion, or that the universe itself is young (say 13.7 Gyr old). Not would it be proof to argue the age of the earth based on the age of trees. The presumed ages of stars has varied greatly over the years. Not long ago some of the oldest stars located in globular cluster were thought to be over 22 Gyr old (see Sandage). Ages are model-based to some extent: something may change again with further tests and increased knowledge, especially 'life' expectancy.

 

 

 

To explain redshift with hyperbolic space you would need new physics. The current laws of physics do not predict a distance / redshift relationship due to hyperbolic space. The new physics would, for example, explain why space is hyperbolic (what causes it) and how curved it is.

 

General relativity is all you need to explain redshift with hyperbolic space. Models will predict the redshift / distance relation not laws of physics. Curved spacetime is explained by the mass-energy content, which is nonzero and nonnegative. GR predicts that a universe with mass cannot be Euclidean.

 

 

 

Both models? I don't know of any cosmological model explaining redshift with hyperbolic space.

 

The de Sitter universe predicts redshift with hyperbolic space. There are others too.

 

 

The way the scientific method works, a model would make predictions which could be compared to observation. For example, big bang cosmology predicts that 24% of baryonic matter should be helium. If there were no Big Bang then elements would exist in abundances predicted by Burbidge and Hoyle in the '60s. There would be almost no helium nor deuterium.

 

Actually, the 1998 prediction by Hoyle and Burbidge (The Origin of Helium and the Other Light Elements) is consistent with observations. The only requirement is that stars have been burning hydrogen for 100 Gyrs. That is the timescale needed for stars to produce the abundance of helium observed according to Hoyle and Burbidge. The abundance of deuterium is nicely explained in the same work. As is too the CMB blackbody spectrum.

 

 

In this way, the scientific method corroborates explanations of redshift which include a big bang and rule out explanations which do not.

 

To date you may be correct. But fortunately the scientific method is not closed to alternative solutions, provided there is agreement with observations. The next step is to formulate a model that corroborates explanations of redshift as a curved spacetime phenomenon and excludes explanations which do not.

 

It would be a pity to rule out a potential scenario before it's fully developed.

 

 

 

CC

[modest]

Curved spacetime explains redshift (whether it is curved hyperbolically or spherically).

 

Right. Curved time gives a scale factor. We keep conflating space and spacetime.

 

The age of stars is not proof of expansion, or that the universe itself is young (say 13.7 Gyr old).

 

Low mass stars can be trillions of years old. The oldest dated stars and the oldest dated globular clusters are 1% of that age. It needs to be explained. If there was no big bang and the universe is not expanding then why aren't stars a hundred and more times older than they appear? Why isn't entropy at a maximum? Why isn't every celestial object at the same temperature? Why isn't iron the most abundant element?

 

These are real problems of an infinitely-aged universe that hyperbolic space doesn't solve. I'm not pointing them out to prove, or even support, expansion. I'm pointing them out because they are real problems for your proposed idea, and any non-dynamic solution.

 

Not would it be proof to argue the age of the earth based on the age of trees.

 

If we knew trees could acquire a trillion years of rings, but we found them no older than the earth (5 billion years) then anyone saying that the earth is at least a trillion years old would have a problem needing to be explained.

 

General relativity is all you need to explain redshift with hyperbolic space.

 

GR makes exact predictions.

 

Models will predict the redshift / distance relation not laws of physics.

 

Models follow laws of physics.

 

Curved spacetime is explained by the mass-energy content, which is nonzero and nonnegative. GR predicts that a universe with mass cannot be Euclidean.

 

Space can be euclidean in a GR universe that has mass.

 

The de Sitter universe predicts redshift with hyperbolic space. There are others too.

 

De Sitter's universe has a recession speed proportional to distance. A static metric with redshift means that distant galaxies are redshifted with recession due to Doppler shift. In other words, things move through static space. A dynamic metric with redshift means that distant galaxies are redshifted with expansion due to a scale factor. In other words, things stay where they are in space while space expands.

 

In both cases the physics interpretation is the same. Everything is getting further away from everything else. De Sitter used a static metric, but as Klein, Eddington, and others showed, the things in a de Sitter universe are not static. They scatter. They do exactly what an FLRW universe with de Sitter parameters says they should.

 

Actually, the 1998 prediction by Hoyle and Burbidge (The Origin of Helium and the Other Light Elements) is consistent with observations.

 

Hoyle makes clear in that paper that a physical mechanism must be "able to thermalize the radiation that is initially released through hydrogen burning as ultraviolet photons from hot stars in starburst situations in galaxies". That physical mechanism is expansion.

 

The things that you are proposing as solutions are inconsistent with a non-dynamic universe.

 

The only requirement is that stars have been burning hydrogen for 100 Gyrs. That is the timescale needed for stars to produce the abundance of helium observed according to Hoyle and Burbidge. The abundance of deuterium is nicely explained in the same work. As is too the CMB blackbody spectrum.

 

Again, the cause of CMBR in Hoyle's QSSU requires expansion. It is redshifted from ultraviolet to microwave via the expansion of space.

 

It would be a pity to rule out a potential scenario before it's fully developed.

 

That's fine, but in reality the problem is not that we are ruling out the unknown model which has made no predictions. The problem is that the model is unknown and has made no predictions.

 

~modest

Moderation Note: Replies to this topic have been moved to 23758 in favor of having their own topic of discussion in that thread.

[coldcreation]

Moved from here.

 

Due to the off-topic nature of the redshift-curvature relation, I've moved the response to Qfwfq to the appropriate thread: this one.

 

In other words, a universe where redshift is due to curvature solves the paradox [Olbers'], just as expansion.

 

Due to curvature without expansion, with what kind of metric? :(

 

In the generalized case the manifold would possess a metric with a pseudo-Riemannian signature, along with the associated curvature tensor, in a manner that varies smoothly from point to point.. :(

 

 

CC

[Qfwfq]

What I meant was: How would it give rise to a redshift?