[coldcreation]

Originally Posted by Erasmus00

There are no solutions to Einstein's field equations with non-zero lambda that don't imply universes that grow (or shrink) with time. As much as you want to make the claim otherwise, you haven't produced a metric. The cosmological constant was, in fact, invented in order to make models with 3 space static.
-Will

Now you understand why lambda had to be defined and what is the mechanism behind the gravitational interaction.

There are solutions to the field equasions that provide static solutions (see the references I provided earlier, then we'll talk).

With this knowledge it is shown that the universe cannot expand. There is no new physics. The theory you support is laoded with new physics, i.e., not physics.

Yes, you arew correct. With Einstein's cosmological term staticity was provisional. That's because there was no absolute value given to it (and that's because no one new what it was, and they still do not (Eddinton was closest to actually illuminating it's true essence). See my previous text for it's proper definition. It is pure spacetime. Nothing more, and nothing less. It has a zero value for all times. There are no negative or positive values for it. It is thus, not a parameter.

Coldcreation

[coldcreation]

Originally Posted by Erasmus00

There are no solutions to Einstein's field equations with non-zero lambda that don't imply universes that grow (or shrink) with time. As much as you want to make the claim otherwise, you haven't produced a metric. The cosmological constant was, in fact, invented in order to make models with 3 space static.
-Will

There is at least one solution to the field equations with a zero value for lambda.

Deviations in the local spacetime metric due to gravitational fields in the presence of massive bodies is well known, but the large-scale effects of gravitation on the global curvature of space and time remain unknown.

According to modern cosmology the Doppler redshift is due to a time-dependent scale factor to the metric, i.e., the expansion of the universe. The standard hot big bang model left open the possibility that the global geometry of the universe might not be flat—depending on its gravitating contents, the Minkowski spacetime metric of special relativity, with its invariance under a Lorentz transformation and its interval for isotropic and homogenous space of constant 3-space curvature, where the spatial metric in non-Euclidean, the signature of space curvature—whereas inflation generically predicts a flat universe today: an unfortunate contention that is in flat contradiction with current observational evidence (and in my opinion, with general relativity as well).

During the 1930’s, at the peak of observational cosmology, a full-scale program had been launched to determine the redshift-distance relation. The most important problem set out at the time was to resolve the question; whether expansion was real—the z–distance relation had to be linear if the expansion scenario was to be adopted—or whether z was an effect on light as it passed through a stationary universe with the parabolic metric of de Sitter (1917).

The field equations provided by general relativity show us how much spacetime curvature is generated by a given distribution of mass-energy density. The EEP determines how matter in the gravitational fields responds to the spacetime metric. The processes involved in the deflection or bending of light generated by gravitational fields, the gravitational redshift and time dilation (the time delay of light) are all closely related, even though the exact mechanism that describes each of these effect is not identical; all are caused by the non-Euclidean, geometric, topological, curvature or deformation of the spacetime metric.

General relativity impels us to reconsider the linear expansion hypotheses and come to terms with the fact that the general geometrical properties of the spacetime manifold depend upon the energy and pressure along with the gravitating mass-density of the universe. This principle strikes a mortal blow to the quasi-Euclidean, neo-Newtonian, pseudo-special-relativistic system that has been suckled and weaned for the past seventy-five years. The dual nature of the expanding model conception remains unsatisfactory—it considers gravitational phenomenon as a local deviation of the spacetime metric, whereas, on the largest scales the associated gravitational influences are entirely done away with, or reduced to trivial insignificance.

The Hubble law considers space and time separately in determining the space-time coordinates in other coordinate systems, i.e., those of other galaxies—a clear violation of the principle of general relativity, which states that the world of events forms a four-dimensional continuum. Modern cosmology describes a Newtonian world of events as a dynamic inertial picture changing in time and hurled onto the background of three-dimensional space, rather than as a static picture on the background of a four-dimensional spacetime continuum, where Einstein’s gravitation plays the key role.

Coldcreation

[coldcreation]

Simply:

The universe is either stable against collapse, expansion or unstable.

Let's assume for a moment that it is stable.

It follows that redshift z is non-Doppler.

If indeed it is not due to a Doppler effect, then it has a different explanation.

A curved spacetime effect is the only other possibility.

It is well known that light (in the 19 octaves of the spectrum) is redshifted (or blueshifted) as it passes through curved spacetime (a gravitational field).

The degree of curvature (as seen in redshift z) depends on the mass-energy density of an extremely large portion of the universe (larger than the visible universe).

It is well known the idea that the universe is non-Euclidean (see general relativity).

Next: this interpretation of redshift z needs to be fully explored if our understanding of the universe (the forces and material contained within it) is to move forward.

Coldcreation

[Erasmus00]

Originally Posted by coldcreation

Simply:

The universe is either stable against collapse, expansion or unstable.

Let's assume for a moment that it is stable.

It follows that redshift z is non-Doppler.

If indeed it is not due to a Doppler effect, then it has a different explanation.

A curved spacetime effect is the only other possibility.

But the spacetime that would best model the red shift effect is De-Sitter space. However, De-Sitter space models an expanding universe, and you have violated your first assumption. You could fix it with a non-zero lambda, but as far as I understand, you don't want a nonzero lambda in your theory.
-Will

[coldcreation]

Originally Posted by Erasmus00

But the spacetime that would best model the red shift effect is De-Sitter space. However, De-Sitter space models an expanding universe, and you have violated your first assumption. You could fix it with a non-zero lambda, but as far as I understand, you don't want a nonzero lambda in your theory.
-Will

The redshift shows us that light (emission throughout the entire spectrum) is being affected by the nonzero mass-energy density of the universe. The displacement of spectral lines towards the red is truly a large-scale gravitational phenomenon. The redshift is observational proof that space is not flat.

Contrary to the simple linear relationship with which the Doppler interpretation enables us to estimate distance and apparent velocity of recession, the complex world of hyperbolic curved space-times collides head-on with the archaic notions that have dominated modern cosmology for the past seventy-five years.

Both well-known de Sitter models (the empty one, and the one with matter) were non-expanding models. Expansion came later, as a result of the Priest Lemaître and his transmutation of the Friedmann equations.

We must further develop the law of gravitation (Einstein’s serves the purpose once lambda is defined) applicable to an environment that is, at first approximation, homogenous. The Hubble constant, with its peculiar dimensions of kilometers per second per megaparsec, must be replaced with the general relativistic concept of spatial coordinates and time coordinates whose deviation from linearity (based on the absolute zero value of the cosmological constant) is perceived as embedded in a stationary four-dimensional continuous manifold.

What that means Erasmus00 is that the interpretation of redshift z must change from the Doppler effect to redshift as a quantity or degree of curvature in a non-Euclidean continuum. And, lambda has to be defined as empty space, not vacuum energy.

If only Einstein could have witnessed the revivification (in 1998 when acceleration was 'discovered') of a significantly grotesque version of lambda: “If the cosmological term exists, then away with expansion.” He might have said. He is actually known for having said almost the exact opposite when Weyl and Eddington (1923) found that test particles recede from one another in the de Sitter world. In a letter to Weyl, Einstein wrote: ‘If there is no quasi-static world, then away with the cosmological term.’ Practically the only man in the world that could have in the early thirties wreaked serious havoc in the growing expansionist camp was Einstein himself; using the potentially significant cosmological constant as an innate pivotal feature of the observed cosmic stability, along with his general conception of curved spacetime as a replacement for the Doppler interpretation to explain the global redshift.

It should be restated that even in a completely empty world model, whether it be de Sitter’s or the Milne model, the global geometry of the universe is hyperbolic, as related by the standard Lorenz transformation (Longair, 1993, p. 384). Certainly when that hyperbolicity is included into the calculation of redshift (in addition to the curvature caused by the mass-density of the universe) the missing mass problem is diminished.

There is no apparent contradiction between a zero value for the cosmological constant and a stable nonexpanding hyperbolically curved universes where redshift is due to a de Sitter-like effect.

Coldcreation

[coldcreation]

Only since the late 1990s has it become evident observationally the degree to which 'curvature' of the spacetime manifold deviates from Euclidean linearity on the largest scales visible. (to be discussed further)

Coldcreation

[Little Bang]

Coldc, how could you possibly hope to explain this so called coldcreation without knowing how and what makes up matter? If you do know that, it would save the entire scientific community a great deal of work. Please enlighten the world.

[coldcreation]

Originally Posted by Little Bang

Coldc, how could you possibly hope to explain this so called coldcreation without knowing how and what makes up matter? If you do know that, it would save the entire scientific community a great deal of work. Please enlighten the world.

Actually, LittleB, this thread is about redshift z and its interpretation as a spacetime curvature phenomenon, it is one that does not imply expansion, one that does not lead to a singular creation event some time (-13.7 Gyrs) in the past.

I take it from your handle that you would agree there was no singular creation event but a series of little bangs (if this is the case you seem to have keeped it to yourself, at least I've never been able to find your ideas posted anywhere: it seems all you have is a long series of questions, but that is ok. Even your Diracian thought experiment thread was a question. Please do not take this as a critique. Well, you can if you like).

The term little bang(s) has often been used in the literature to describe material creation in spurts, usually as ejecta from active galactic nuclei, or C-fields (vis the Quasi-Steady Staters, Arpians, Nernst, MacMillan, Millican, etc.).

Coldcreation, like any other theory, hypothesis or concept, is a work in progress. You're right, no one has ever explained the creation of matter. I will try to do so in the thread called Material Creation: see you there....

Keep cool in the mean time...

[infamous]

Originally Posted by coldcreation

Actually, LittleB, this thread is about redshift z and its interpretation as a spacetime curvature phenomenon, it is one that does not imply expansion, one that does not lead to a singular creation event some time (-13.7 Gyrs) in the past.

Hey Coldc......haven't touched base with you for a while. I've been following a couple other threads that I believe can add value to your theory. A while back, a thread titled 'Gravity is the 4th dimension' was introduced to Hypography. I noticed that both your theory and his have a few things in common even though large parts also do not. The reason I'm bringing this up is I feel that the truth lies somewhere inbetween. Not to discredit your theory, I've suspected for some time now that the universe did not come about by what is commonly referred to as the Big Bang. On this I tend to agree with your point of view. I also think that the thread 'Gravity is the 4th dimension' has some interesting observations to make. As a result, I have been encouraged to believe that both theories can be combined into a hybrid version. I know this would necessitate your theory to also include some form of expansion but not necessarilly due to the Big Bang. This is just a thought Coldc. , I hope you don't take this as a personal attack, I have always considered your theory to have great value. My gut feeling is, that there is also some reason to believe that little bangs, as you call them, might be responsible for the observed expansion we see. I think That Rascal Puff makes a good observation when he points out that if space is expanding, then it is highly likely that matter is doing the same, matter is afterall, little more than nothing but space anyway. I'm curious, what you think about these possibilities?................Infy.

[Erasmus00]

Originally Posted by coldcreation

Both well-known de Sitter models (the empty one, and the one with matter) were non-expanding models. Expansion came later, as a result of the Priest Lemaître and his transmutation of the Friedmann equations.

Now that simply isn't true. In either model, move along the time dimension and take 3D "slices" at a given instant in time. You'll notice that the 3D slices get progressively larger as you move up the time axis. This is the very deffinition of an expanding universe.
-Will