Redshift z

[quantumtopology]

Whenever mathematics deals with infinity problems arise.

That is right in some way but still have to be addressed in any physically plausible model

 

 

We live in a submanifold of a manifold.

That's what I'm saying, extrinsic curvatures would only be perceived from an n+1 manifold, not from an n-1 manifold. Or that is how I understand it.

 

 

It is because it affects the photon that it is apparent. Said differently, it is an apparent affect on the photon from the observers frame. It is thus an apparent and physically real affect.

These affects are apparent and they are real

This is a bit hard as I believed the terms apparent and real to be mutually contradictory when applied to one concept simultaneosly.

 

 

Let's say we measure something, e.g., the distance to a galaxy far removed, and we deduce curvature. We can conclude something happens, either at the source, during travel time, or hear in the vicinity of our planet that distorts the image of the galaxy. In a sense this is an optical effect, like looking through a magnifying glass. The image is real. The effect is real, but the curvature is only apparent: the galaxy is not physically distorted in it's own frame of reference. We can figure that out by correcting for the distortion.

In the case of global curvature the effect is apparent.

Ok, I can understand an optical effect is real in the sense that the image is real. Like a mirage in the desert, the image, the optical effect is real in the sense that we perceive it, but certainly there is no oasis, no water. So if what you are saying is that the redshift is an optical effect (a mirage) and the global curvature is apparent in the sense that it is nt real (like the oasis in the desert) then I understand it. But if the curvature is just imaginary then you don't really have R>0. Do you?

Part of the difficulties I find might come from the fact that I am not famiiar with the isotropic gravitational fieds and coordinates that seem to solve the global curvature issues for you. So until I get acquainted with them it's hard for me to follow the complete story.

 

 

The observer located at one of those distant galaxies at the superfluous edge of the universe, typing a few key enthralled words on her computer sitting atop a her Lagrangian-like point peering out into the peaceful heavens on her pixelated screen would see the Milky Way as a tiny spec of real estate breaking the speed of light too. Either that or she could conclude that the Milky Way is immersed in a gravitational potential well so deep that the photons emanating from the luminous objects that make up the Galaxy barely escape in time before the gates of hell close for good. :phones:

Hey, you do have a poetic vein! :)

[quantumtopology]

You are essentially saying that matter is not affected by gravity in a isotropic and homogeneous universe yet light is affected.

This is a key point that I had floating in my mind when I read the post. Glad you expressed it so clearly.

 

Your idea breaks the fundamental postulate of GR—the equivalence principle. The nature of curved spacetime is the equivalence between accelerated inertial reference frames and gravity. To say that spacetime is globally curved yet there is no accelerated inertial reference frames just doesn't make sense. By the very definition, global curvature would have accelerated inertial reference frames, and again by definition matter would want to follow those inertial reference frames

 

Again, some of the points I raised with my answers to CC meant to highlight this contradiction. But you are much more specific.

[modest]

Yup :phones: I can see you were concerned with the same thing.

 

 

I've had time to think about it this morning and I have to say, only because it's true, that I fundamentally like the approach. I was previously thinking of this alternative explanation of redshift investigation almost like expansion versus tired light—expansion being curved spacetime and tired light being some other physical factor that would cause redshift in a flat world.

 

Starting from the premise of curved spacetime allows one to say that redshift is not at fault. It behaves as general relativity expects and so wouldn't need an alternative explanation at all. The alternative avenue to approach is the dynamics. Could there possibly be some alternative approach to applying general relativity to cosmology... Some reason that things passed between galaxies are affected by the gravitational field, yet the dynamics of the galaxies themselves is not affected...

 

I think it's an interesting way of framing the issue, CC. I think I understand better where you're coming from now, but I still don't see a practical solution. I would agree with you that seeing some distant clock, or supernova, or galaxy redshifted and time dilated doesn't necessarily imply expansion or recession. But, locally it is so very clear and intuitive that curved spacetime affects mass as well as light. Mass tells spacetime how to curve and curved spacetime tells mass how to move.

 

I'm trying to keep my mind open to the possibility that some misstep has been made in applying GR globally to the case of constant curvature, like you say. But, I think we would need to show definitively where the mistaken assumption is and how exactly the consequences are different in making a new assumption.

 

Perhaps something for us to chew on: radiation pressure acts to stabilize a star against collapse, but globally with the universe as a whole, radiation pressure acts to add to the gravitational field, increasing the curvature, pushing the universe closer to wanting to collapse.

 

It's interesting to think about.

 

~modest

[quantumtopology]

Perhaps something for us to chew on: radiation pressure acts to stabilize a star against collapse, but globally with the universe as a whole, radiation pressure acts to add to the gravitational field, increasing the curvature, pushing the universe closer to wanting to collapse

 

It's apparently contradictory, a new case of local versus global lack of congruence. I would say that also in the local case of the star even if pressure goes against the mass density, both are still increasing the local curvature, curiously in the global picture a universe filled with radiation would have null curvature [according to Friedmann equations: R scalar is proportional to 1/3d-p or to d(1/3-w) with w=p/d making w=1/3 leads to R=0] which is counterintuitive if one thinks that radiation is energy and also curves spacetime.

[modest]

It's apparently contradictory, a new case of local versus global lack of congruence.

 

It's a case where the same laws of physics give a different physical outcome because the physical situation is different. The point is to examine FLRW assumptions. You can't have a non-trivial static FLRW solution, but you can have a static star. The difference is that a star is not homogeneous.

 

I would say that also in the local case of the star even if pressure goes against the mass density, both are still increasing the local curvature

 

GR would agree. Either modeling a universe or a star, radiation pressure adds to the gravitational field. Radiation contributes to the pressure term in Einstein's equation.

 

curiously in the global picture a universe filled with radiation would have null curvature [according to Friedmann equations: R scalar is proportional to 1/3d-p or to d(1/3-w) with w=p/d making w=1/3 leads to R=0] which is counterintuitive if one thinks that radiation is energy and also curves spacetime.

 

I think your intuition is right. I don't see how R=1/3(rho)-P could be right if R is meant to be the Ricci scalar. That would mean that the ricci scalar is zer oin a friedmann universe with one third as much dust as radiation, and that doesn't seem possible. I'd have to see where you got that.

 

The idea that radiation pressure adds to the gravitational field is laid out in ch 3 section 2 here:

 

Relativity, Astrophysics and Cosmology - Google Books

 

Notice the Poisson eq 3.48. Increasing both rho and P increases the strength of the field.

 

~modest

[quantumtopology]

It's a case where the same laws of physics give a different physical outcome because the physical situation is different. The point is to examine FLRW assumptions. You can't have a non-trivial static FLRW solution, but you can have a static star. The difference is that a star is not homogeneous.

 

Exactly

 

I think your intuition is right. I don't see how R=1/3(rho)-P could be right if R is meant to be the Ricci scalar. That would mean that the ricci scalar is zer oin a friedmann universe with one third as much dust as radiation, and that doesn't seem possible. I'd have to see where you got that.

 

Well, I probably didn't put it right( I don't know how to write math formulas here) , I didn't mean R=1/3(rho)-P, as you say that couldn't possibly be right, I said R is related to or in direct proportion to 1/3(rho)-P according to the Friedmann equations if you recast the first four equations in the friedmann equations from wikipedia (after the line element).

I think in the case of pressure= one third of the energy density(not that there is one third as much dust as radiation) you would get a universe with only radiation and R=0.

I don't know if that is possible, I would say you can't have radiation without matter and viceversa, but I think the BBT has a first epoch with only radiation, is that so?

[quantumtopology]

I forgot to say w is the equation of state parameter look here Equation of state (cosmology) - Wikipedia, the free encyclopedia in the "ultrarelativistic matter" paragraph.

[coldcreation]

I would say that curvature is a sufficient cause for redshift and time dilation, but not a necessary cause. The simplest counterexample would be two particles moving away from one another in Minkowski spacetime. They would each see the other as time dilated and redshifted, but the metric is by definition flat.

 

Your conclusion doesn’t follow from the premise. I will grant you that a homogeneous and isotropic metric should treat every observer the same, but that would in no way imply that the physical distance between them cannot be increasing.

 

 

Here, rather than postulate the expansion of actual space to replace a Doppler shift, we postulate the existence of a globally curved spacetime that is independent (to some extent) of local curvature (gravity fields surrounding massive bodies, locally). The global field intensity, or magnitude of curvature does depend, though, on the total mass-energy content of the universe. In that sense their is a relation between local and global curvature.

 

The global curvature is 'apparent' in the sense that each observer is entitled to consider herself atop a Lagrange-like point with an infinite mass at the visible horizon (obviously there is no infinite mass at the horizon, and she's not at and L-point). Yet, an observer located at the horizon may indeed conclude based on observations that she is at an L-point and the we, for example, are located deep inside a gravitational well. Her conclusion is permitted by general relativity (assuming she's familiar with Einstein's general relativity, GR ) yet her conclusion that the field has different values of curvature at different points far-removed from hers (like local fields) and that objects appear to be at their proper distances is erroneous, unless she realizes too that it is only a relative effect.

 

This is similar to your example above, modest, where all observers are entitled to consider themselves on the equator. Certainly other interpretations are permitted, but hers would 'appear' to be consistent with observations, even though we know the conclusion above (that we are deep in a well, or visa versa) is not the case in the real world, i.e., it is a false conclusion. The effect is a relative one.

 

Likewise, our observer at the horizon is entitle to conclude, with her knowledge of special relativity (SR), that the entire Virgo Cluster is racing through space (or with space) close to, or precisely at the speed of light c. This is only an "apparent" affect based on her observations, and which is permitted by relativity, but it too is false, i.e., we are not really moving at the velocity c. That is, the conclusion is false. In order to bypass this problem it had to be invented the notion of expanding space. But general relativity says nothing of the kind. Just as GR says nothing about the existence of an infinite mass at the horizon.

 

Both conclusions above are problematic. Even though derived through methodological analysis of empirical data and interpretation of that evidence within the framework of relativity, both options can be considered equally valid or equally invalid. Only one solution represents the physical universe. General relativity says nothing of the permissibility of either scenario, i.e., GR does not distinguish between the two scenarios.

 

 

_________________

 

 

Quantumtopology had an interesting analogy above: A mirage. Mirages are a natural optical phenomenon that occur where light rays are bent, producing a displaced image of distant objects. They alter proper distances by a distortion process. The observer may incorrectly interpret the actual location of objects, or the shape of the horizon in the background. Light rays coming from a distant object travel through the air layers and all are bent. This is a real physical effect, and the curvature is naturally produced by temperature gradients, but the objects seen and perceived are not really where they appear to be (their position appears to be displaced). Viewed from a different location the mirage will either have a different shape, of will not be present at all.

 

That's as far the analogy goes, but the point is clear: The topology of the visible universe appears to have a particular shape, a geometry with a characteristic negative or positive signature, but in fact, the objects we observe are not affected by this curvature; it is a natural optical effect (a real physical effect) generated as light propagates through a non-Euclidean, homogenous spacetime manifold. The curvature is manifest, clearly apparent and measurable. But it gives the observer an erroneous perception of distance, a false appearance or deceptive impression of reality. What emerges has at least two possible interpretations; one static, one dynamic. Not only can this be interpreted as a curvature of the manifold (with a massive horizon), but observations can also be interpreted as radial motion away form the observer (where objects at the horizon attain c).

 

 

So where does this leave us? We are left with the difficult task to determine exactly what is actually transpiring in the cosmos that gives the impression (and to any observer) that the universe is a truly expanding pseudo-Minkowski spacetime governed by the laws of Newtonian gravitation (with a dash of GR), or that the observer is embedded in a truly curved four-dimensional pseudo-Riemannian spacetime manifold governed entirely by the laws Einsteinian gravitation.

 

 

In an apparently expanding homogeneous and isotropic universe where redshift z is a classical Doppler effect, the conclusion that the physical spatial distance between observers cannot actually be increasing follows from the premise that the metric should treat every observer the same. The interpretation of spectral shifts as a Doppler redshift would be invalid. The only way around the problems created by such an interpretation (e.g., superluminal velocities) would be to hypothesize that objects are not actually moving through space: the idea that space itself must expanding (a change in scale-factor to the metric) has to replace the Doppler interpretation.

 

 

Likewise, in an apparently curved homogeneous and isotropic spacetime manifold, where cosmological spectral shifts are attributed to a gravitational redshift, the conclusion that the physical spatial distances and time intervals between observers cannot actually be changing (or different for each observer) follows from the premise that a metric should treat every observer the same. The interpretation of spectral shifts as a gravitational redshift would be invalid. The only way around the problems created by such an interpretation (e.g., the mass horizon) would be to hypothesize that distances to astronomical objects are actually further or closer than they appear. In that sense, distances are only 'apparent' (objects are not really where they appear to be located). Photons are not actually climbing out of a gravitational well as they propagate towards the observer. So the notion of gravitational redshift must be replaced by the concept of a cosmological redshift z produced as photons propagate through a homogeneous and isotropic globally curved topology.

 

The latter hypothesis would be exemplified by the fact that local distances measured from any rest-frame will appear Euclidean (or quasi-Euclidean, taking into account local inhomogeneities), i.e, when distances are measured locally, the resulting curvature will be deduced as practically "flat" and time intervals will be measured consistent will Euclidean spatial separations. Of course, as distance measurements are made further out (say beyond more or less 1 or 2 Gly), both timelike intervals and spacelike increments will appear to conform increasingly to a non-Euclidean geometry (when comparing redshift to other spatiotemporal measurement indicators: see above).

 

 

In other words, what gives an illusory (or spurious) appearance of radial motion, implying an expanding "flat" manifold, is exactly equivalent observationally to the 'apparent' curvature in a static non-Euclidean manifold. [Note: "static" is meant throughout this thread to mean non-expanding and non-collapsing with respect to the universe as a whole, unless otherwise mentioned].

 

Certainly, according to Einstein, a homogeneous and isotropic metric should treat every observer the same, but that would in no way imply that the physical distance between them must be increasing. Quite au contraire. It would imply that physical distances (globally) do not increase between them. I'll come back to this point.

 

 

So we have, in the look-back time, an image of galaxies and other objects that 'appear' to be at a certain distance, yet that measured distance would be distorted because of curvature. In other words, the objects proper distance is not what we observe. If the distances of objects could be seen in their true location (if curvature were to be removed, or somehow the speed of light instantaneous), they would be seen at their proper distance, further or closer depending on the sign of curvature (before is was removed). Objects would be at their 'Euclidean' distance, if you will. This is why, in a globally curved spacetime, of the general relativistic type discussed in this thread, distances are only apparent; objects are not observed to be located at their true distance. So there is a Euclidean connection inherent in spacetime (perhaps related to every rest-frame). True, or proper distances, would be measured accurately only in a Euclidean or Minkowski spacetime.

 

The idea that the loss of energy associated with photon propagation through curved spacetime can be understood; without having massive objects being affected geodesically by the same global field. That is, a homogenous field would induce loss of energy to the photon but objects would not be accelerated. Objects would not partake dynamically in the globally curved field (as in the case of local fields), since the global field is entirely independent of any inertial rest frame, i.e., there is no slope or gradient; all points on the manifold are equal, with the same magnitude of gravitational potential. (I will expand on this in Explanation 2)

 

 

_______________

 

 

A transitory but nontrivial point to make, related to arguments above, before moving on: When objects such as galaxies are observed at cosmological distances, and in the look-back time, events and phenomena appear to take longer in our frame of reference than in that of the source (a phenomenon observed for relativistic muons that propagate through our atmosphere). In another way, clocks would appear to slow down with increasing distance (just as the de Sitter effect in a static universe). This is the cosmological manifestation of a phenomenon known as time dilation. Source: The Deep Universe, M.S. Longair, page 369. See equation 2.31. The result of this equation gives us the expression for redshift z:

 

This is one of the most important relations in modern cosmology and displays the real meaning of redshift.

Redshift is simply a measure of the scale factor of the Universe when the source emitted its radiation.

[...] Note, however, that we obtain no information about

when

the light was emitted. If we did, we could measure directly from observation the function

R(t)

. [...] Thus, redshift does not really does not really have anything to do with velocities at all in cosmology. The redshift is a beautiful dimensionless number which, as (1 + z)^-1, tells us the relative distance between galaxies when the light was emitted compared with that distance now.

 

The point is, as you may have guessed, there is a direct empirical correlation between redshift z as interpreted by Longair and the interpretation of redshift z as a curved spacetime phenomenon (with both minor and major differences in physical outcome).

 

Both interpretations of redshit z have an associated time dilation factor, and both have nothing to do with velocity at all. All redshift z gives us⎯when interpreted as a general relativistic phenomenon⎯is a clue as to the relative spatial and temporal separation between us (from our rest-frame as we peer into the look-back time) and distant galaxies, when and where the electromagnetic radiation was emitted compared to the actual distance and time now, i.e., redshift z may be seen or interpreted as a measure of curvature, since spatial increments and temporal intervals deviate from linearity with distance in the look-back time.

 

 

 

But, then you would have light following geodesics, but not matter. Matter needs to follow inertial geodesics. In a globally curved manifold where R>0 this means things 'fall' away from one another just as much as in a globally curved manifold where R<0 things would fall toward one another. It isn't just light that gets affected by gravity.

 

Indeed, my claim is that light emitted from distant objects would be affected during the travel time from the observers rest-frame since it would be propagating on a geodesic path through curved spacetime, but material particles (or galaxies) would not participate geodesically, i.e., galaxies would not free-fall toward each other and that they would not radially move away from one another dependent on the sign of the globally curved field.

 

Certainly this is the most nonintuitive, contentious and debatable aspect of the entire premise upon which the interpretation of redshift z rests (as a general relativistic curved spacetime phenomenon). But nevertheless I believe it is a potentially accurate representation of the physical manifold.

 

I will attempt to explain this (again) in two different ways: Explanation 1, and Explanation 2.

 

 

Explanation 1

Apparent curvature of a globally homogeneous isotropic general relativistic spacetime manifold and the stability of the cosmos

 

 

Simply put, in a homogenous and isotropic gravitational field, there is no change or differenece in the physical gradient or 'slope' from one point to another. All points are equal. All points on this manifold have the same value of gravitational potential, and it is nonzero. The fact that the potential would be nonzero implies that light would affected relative to a stationary observer. As light is radiated outwards from the source it is traveling at c. The photon does participate on the global curvature, not because of change in gradient, but because of the continuous curvature. And because of the continuous curvature, light is propagated along a geodesic. The photon would endure a loss energy as it propagates through the homogenous gravitational field; and it would do so progressively with distance from the observer's frame of reference.

 

Locally, gravity fields surrounding massive objects have a gravitational potential that differs depending on the altitude at which the observer is located, away from the surface of the massive body.

 

The global field we are discussing has a potential relative to the total mass-energy density (the mass-energy determines the potential of the homogenous field) of the universe at all points, since it permeates all of spacetime. In a homogenous and isotropic universe the nonzero value of the gravitational potential is virtually the same at all points, even within intergalactic ('empty') space. The gradient does not change depending on the location of the observer.

 

If indeed this global spacetime curvature exists, it is easy to see how objects would not be affected by it. The more pressing issue seems to be why, then, photons would be affected by the field. I've given much thought to this, but unfortunately there are very few links or papers to which I can refer regarding this hypothesis. Not surprisingly so. It is not an area of active research. I think it should be. Between now and the my next post (Explanation 2) I will have had time to research the problem further, and hopefully the proofs that support such claims will emerge.

 

What shows up most often on search engines are solutions such as static isotropic metric, also called a standard isotropic metric which relates to the Schwarzschild solution (or the Schwarzschild vacuum), I think.

 

There was an interesting and related work that popped up. It's entitled On the Physical Interpretation of a Solution of a Nonsymmetric Unified Field Theory, dated 1983, by E.J. Vlachynsky (Deptartment of Applied Mathematic, University of Sydney). This work examines a spherically symmetric static solution of the Einstein-Straus-Klotz non-symmetric field theory, in relation to a background pseudo-Riemannian spacetime, and propose a new physical interpretation of spacetime. The paper mentions G.F.R, Ellis, whom we discussed earlier in this thread, and whom in 1978 suggested that redshift z may be seen in terms of cosmological gravitational redshifts.

 

 

Conclusion: We have shown that the background space-time corresponding to GFT [nonsymmetric unified field theory] solution is equivalent to the SE [Einstein's universe] solution of General Relativity. Thus we must reject the interpretation of ([equation] 1) which asserts that (1) represents an expanding universe. Clearly (1) should be interpreted as representing the exterior geometry of a static black hole (as opposed to a primeval atom) in the background of a static universe. [...]

 

 

What is shown is that the line element (in equation 1) is equivalent to the general relativistic line element which describes a Schwarzschild black hole in the background of Einstein's world model. This solution is identified with a static, spherically symmetric, electric charge.

 

And I'm guessing that the manifold would resemble either Figure D, or Figure 2D above. Or perhaps this:

 

 

 

 

Figure 3D

A reduced dimension schematic diagram representing a constant time equatorial slice through the Schwarzschild solution for a static (non-expanding) spherically symmetric Einstein world-model

 

Figure 3D represents curvature of the Schwarzschild solution with a Flamm-like paraboloid. This diagram differs from diagram A, B and C above in that it is not a look-back time representation; it represents a constant time equatorial slice through the Schwarzschild solution. This manifold has the property that distances measured will match distances in the Schwarzschild metric. This is a cross-section at one moment of time (cosmic time), so all particles moving across it must have infinite velocity. See Schwarzschild metric; Flamm's paraboloid. "Even a tachyon would not move along the path that one might naively expect from a "rubber sheet" analogy: in particular, if the dimple is drawn pointing upward rather than downward, the tachyon's path still curves toward the central mass, not away."

 

Note, I place this diagram here, but it is not the exact same solution that is proposed in this thread. It differs in several respects, that I will try to pin point in the next post. I'm not sure yet, but I'm working on the idea that a constant time equatorial slice through a static (non-expanding) spherically symmetric Einstein world-model may look flat, Euclidean. Only in the look-back time would curvature be manifest. :eek_big:

 

 

...I will just say that it cannot be consistent with general relativity (or the idea of curved spacetime in general). You are essentially saying that matter is not affected by gravity in a isotropic and homogeneous universe yet light is affected.

 

That is more or less what I am saying. Matter is affected by gravity locally, but not globally. See a further explanation below (labeled Explanation 2) in the next post.

 

It will be shown that this assumption is entirely consistent with GR.

 

 

If the universe has constant global curvature then it will behave as if it has constant global curvature. Curved spacetime means that geodesics (the shortest distance between spacetime points) deviate from linearity. [...]

 

Certainly, when referring to what I call local curvature (the intrinsic gravitational fields surrounding massive bodies). See further explanation below (2).

 

While it is true that curved spacetime means that geodesics (the shortest distance between spacetime points) deviate from linearity, it does not imply that the field gradient must differ from one point to another. There is a big difference between a smooth curvature, the potential of which changes inversely and proportionally to the square of the distance from a gravitating body, and a curvature which is smooth and continuous (in the Riemannian or pseudo-Riemannian sense) in a homogenous and isotropic spacetime manifold.

 

 

Your idea breaks the fundamental postulate of GR—the equivalence principle. The nature of curved spacetime is the equivalence between accelerated inertial reference frames and gravity. To say that spacetime is globally curved yet there is no accelerated inertial reference frames just doesn't make sense. By the very definition, global curvature would have accelerated inertial reference frames, and again by definition matter would want to follow those inertial reference frames.

 

What you write is indeed the 'classical' or mainstream view, which leads to instabilities inherent both in Newtonian and Einsteinian mechanics. But this view may not be justified. I will try to show that the idea (global curvature is different from local curvature in that objects are not affected by geodesics, but light will be) is entirely consistent with GR, the equivalence principle, the idea of curved spacetime in general, and the fundamentals principles of non-Euclidean geometry (again below).

 

 

The other direction you take breaks the fundamentals of spherical geometry. In such a geometry both Tom and Sally see parallel geodesics converge with distance. Just because the curvature is global doesn't mean the action can't be reciprocal. Essentially: both Tom and Sally can consider themselves on the top of the world while the other is downhill. This is not a problem.

 

We agree that this is not a problem. The only problem I have with what you write is with the word "action." There is a difference between action and apparent action, just as there is a difference between force and pseudo force. In other words, from the inertial rest-frame of the observer, the 'action' may be considered spurious (nonexistent), at least in the context here. So where you're expecting an 'action' there is none. The distinction is an important one, since the type of action you refer to determines either the structure and evolution of the universe, or the evolution and fate of the universe (i.e., the "action" determines whether the universe is stable or not). I hope that makes sense (pending Explanation 2).

 

 

 

 

CC

[modest]

Well, I probably didn't put it right( I don't know how to write math formulas here)

 

Here's a thread on Latex:

 

http://hypography.com/forums/physics-and-mathematics/6576-latex-fomulas-math-v2-0-a.html

 

and a sandbox for it:

 

http://hypography.com/forums/test-forum/6620-latex-practice-ground.html

 

I didn't mean R=1/3(rho)-P, as you say that couldn't possibly be right, I said R is related to or in direct proportion to 1/3(rho)-P according to the Friedmann equations if you recast the first four equations in the friedmann equations from wikipedia (after the line element).

I think in the case of pressure= one third of the energy density(not that there is one third as much dust as radiation) you would get a universe with only radiation and R=0.

I don't know if that is possible, I would say you can't have radiation without matter and viceversa, but I think the BBT has a first epoch with only radiation, is that so?

 

[math]R \propto \frac{1}{3} \rho + P[/math]

 

would make sense to me (with a plus sign) because I know for a fact that:

 

[math]P < -\frac{\rho}{3}[/math]

 

corresponds to a repulsive force of gravity while

 

[math]P > -\frac{\rho}{3}[/math]

 

is an attractive force. In other words, you need negative pressure to negate positive energy density. Having R = 0 where rho = 3P would not make sense to me.

 

I don't know if that is possible, I would say you can't have radiation without matter and viceversa, but I think the BBT has a first epoch with only radiation, is that so?

 

Yes. "radiation" in that sense means any relativistic particles. As the temp of a universe increases w approaches 1/3.

 

~modest

[quantumtopology]

Having R = 0 where rho = 3P would not make sense to me.

 

Look at equations 89 and 91 in page 18 of this: http://www.nicadd.niu.edu/~bterzic/PHYS652/Lecture_04.pdf

 

Regards

[quantumtopology]

Check this out:

[1006.1270] Lambda-CDM and the WMAP power spectrum beam profile sensitivity

 

http://www.sciencedaily.com/releases/2010/06/100613212708.htm

 

I think that in the end, rather than theoretical or philosophical arguments and preferences, the balance will lean towards a model or another based on some very simple empiric fact.

The CMBR examined with ever more sophisticated means (Planck probe in 2012 for instance) is a good empirical source for either confirmation of the model or else for some interesting surprises.

 

Regards

[modest]

Look at equations 89 and 91 in page 18 of this: http://www.nicadd.niu.edu/~bterzic/PHYS652/Lecture_04.pdf

 

Regards

 

Yep. It looks like,

[math]

R \propto \frac{1}{3} \rho + P

[/math]

is right. There is definitely something I'm not getting. It looks like the time component of the Ricci curvature is all I was considering... :confused:

 

I think that in the end, rather than theoretical or philosophical arguments and preferences, the balance will lean towards a model or another based on some very simple empiric fact.

The CMBR examined with ever more sophisticated means (Planck probe in 2012 for instance) is a good empirical source for either confirmation of the model or else for some interesting surprises.

 

Yep. I do agree Good thing you're not suggesting throwing out the baby with the bathwater ;)

 

CC, I'm wading through your post and may be out of town for a couple days. Will hopefully reply soon.

 

~modest

[quantumtopology]

Yep. It looks like,

[math]R \propto \frac{1}{3} \rho + P[/math]

is right. There is definitely something I'm not getting. It looks like the time component of the Ricci curvature is all I was considering... :confused:

 

You mean

[math]R \propto \frac{1}{3} \rho - P[/math]

is right, don't you?

Well it is also confusing to me, intuitively looks like if you have some energy density from the radiation you can't have R=0.

 

Yep. I do agree Good thing you're not suggesting throwing out the baby with the bathwater ;)

 

I would never do that :naughty:

:D

[modest]

You mean

[math]R \propto \frac{1}{3} \rho - P[/math]

is right, don't you?

 

Yes, thank you. Didn't proof what I was writing.

 

 

 

I would never do that :naughty:

:D

 

:)

 

~modest

[coldcreation]

You mean

[math]R \propto \frac{1}{3} \rho - P[/math]

is right, don't you?

Well it is also confusing to me, intuitively looks like if you have some energy density from the radiation you can't have R=0.

 

Sorry, I've not been following the latest posts here. Could someone explain the significance of the above equation in the context of this discussion?

 

Furthermore, just to let both you know (QT and modest) that Explanation 2 is almost complete. I want to be sure that everything is in order before it is posted: something that will take a little more time. One of the results of this investigation will be that the universe can remain in a state free-of global instability; contrary to the commonly held position that a static universe would be unphysical in that, like a pencil balancing on it's point, gravitational perturbations would cause the universe to either collapse or expand. It will be shown that the global instability conclusion is both erroneous and untenable. Too, it will be shown that the latter interpretation is based on the concept of gravity as an attractive Newtonian force. When gravity is interpreted in accord with general relativity, as a curved spacetime phenomenon, such instability does not exists, globally. :eek:

 

 

CC

[quantumtopology]

Sorry, I've not been following the latest posts here. Could someone explain the significance of the above equation in the context of this discussion?

 

Comes from post 514 in the context of local versus global physics, it seems tha from Einstein and Friedmann equations a universe filled with radiation (no matter) would have R=0 or no curvature but intuitevely one would think that since radiation has energy density the Ricci scalar shouldn't be zero but I am not sure about this, if the Ricci scalar is zero then the Ricci tensor is also zero and therefore the stres energy tensor T should equal zero, is this compatible with a universe filled with radiation, with an energy density three times its pressure. Looks like something is wrong here but I don't know what.

[quantumtopology]

Furthermore, just to let both you know (QT and modest) that Explanation 2 is almost complete. I want to be sure that everything is in order before it is posted: something that will take a little more time. One of the results of this investigation will be that the universe can remain in a state free-of global instability; contrary to the commonly held position that a static universe would be unphysical in that, like a pencil balancing on it's point, gravitational perturbations would cause the universe to either collapse or expand. It will be shown that the global instability conclusion is both erroneous and untenable. Too, it will be shown that the latter interpretation is based on the concept of gravity as an attractive Newtonian force. When gravity is interpreted in accord with general relativity, as a curved spacetime phenomenon, such instability does not exists, globally. :phones:

 

I am curious about how you will do that if you keep your idea of an apparent global positive curvature that clearly ignores the principle of equivalence and arbitrarily affects light but not matter, since you said those problems would be solved in Explanation 2.

 

The notion I'm getting lately is that maybe GR is not suited for a cosmological solution,

it could be that GR only works locally, that is, wherever there is mass there is a local distorsion of spacetime. That would explain the much talked about problems GR has with energy conservation globally. If the universe is infinite, certainly gravitation would be a local phenomenon and GR would describe a local deviation of spacetime but couldn't be applied to the universe as a whole where R would tend to zero as distance from the local perturbation tends to infinite.

Einstein perceived this problem in his 1917 cosmology paper and thus sought to solve it with the cosmolgical constant, that he never liked anyway, when appearance of expansion was found and after the initial resistance, he finally saw expansion as a way to solve his probem with infinty and to get rid of his loathed lambda.