[Erasmus00]

Originally Posted by coldcreation

It is a nonexpanding model, also called de Sitter redshift effect. The radius of curvature can be obtained using the de Sitter model with Einstein's GR equations, 1917. Note that the time dilation with distance seen in redshift z is observtional evidence of spacetime curvature in a stationary universe model, it has a hyperbolic signature.

Emphasis added by me. De Sitter models do expand. While the De Sitter-Schwarzchild metric's space metric is invariant, the cosmological equations show that the universe grows with time.

The simplest De Sitter model is the solution of space made isotropic and homogeneous (remove all the mass). The space of this model does expand with time. The radius is proportional to e^(Ct) where C is sqrt(lambda/3). lambda being the Einstein lambda. This has a constant curvature.

The other De-sitter model I can think of is the so called Einstein-de Sitter model, which is isotropic and homogeneous. It too has constant curvature, and expands, but lambda is 0.

All of these models show evolving universes. Please show me an actual metric where the cosmological equations predict that the size of the spatial universe doesn't change with time, and redshift effects are predicted.

For a general treatment of evolving universes, google Friedmann equation.
-Will

[coldcreation]

Originally Posted by Erasmus00

Emphasis added by me. De Sitter models do expand. While the De Sitter-Schwarzchild metric's space metric is invariant, the cosmological equations show that the universe grows with time.

The simplest De Sitter model is the solution of space made isotropic and homogeneous (remove all the mass). The space of this model does expand with time. The radius is proportional to e^(Ct) where C is sqrt(lambda/3). lambda being the Einstein lambda. This has a constant curvature.

The other De-sitter model I can think of is the so called Einstein-de Sitter model, which is isotropic and homogeneous. It too has constant curvature, and expands, but lambda is 0.

All of these models show evolving universes. Please show me an actual metric where the cosmological equations predict that the size of the spatial universe doesn't change with time, and redshift effects are predicted.

For a general treatment of evolving universes, google Friedmann equation.
-Will

"Our conception of the structure of the universe bears all the marks of a transitory structure. Our theories are decidedly in a state of continuous, and just now very rapid, evolution. It is not possible to predict how long our present views and interpretations will remain unaltered and how soon they will have to be replaced by perhaps very different ones, based on new observational data and new critical insight in their connection with other data." Willem de Sitter, 1932

Everything is in transit...

There is a world-view called the Einstein-de Sitter model: galaxies separate at a critical rate that prevents gravitational attraction from over-powering the expansion. This representation is also referred to as the critical model. As the radius of the universe tends to infinity the velocity of expansion tends to zero. This model is the source of the classic fine-tuning problem. The balance is perfect; why? (Of course this concept is neither Einstein’s nor de Sitter’s, it is a posthumous interpretation of Friedmann’s). Touch E = mc2 with your magic wand and you can go anywhere!

In 1929, the historically correct year that Hubble’s official discovery was made, he published a famous paper entitled A Relation Between Distance and Radial Velocity Among Extra-Galactic Nebula. In this seminal work he writes: “The outstanding feature, however, is the possibility that the velocity-distance relation may represent the de Sitter effect, and hence that numerical data may be introduced into discussions of the general curvature of space.”

Hovering on the brink of complete surrealism, himself, Hubble seemed to have gotten cold feet. Philosophically he found the expanding universe concept “unsatisfactory” and preferred to highlight the “difficulties” and “uncertainties” involved with the observational groundwork. In a 1931 letter to the Dutchman de Sitter, Hubble wrote; “The interpretation, we feel [Hubble and Humason], should be left to you and the very few others who are competent to discuss the matter with authority”

Coldcreation

[Erasmus00]

Originally Posted by coldcreation

There is a world-view called the Einstein-de Sitter model: galaxies separate at a critical rate that prevents gravitational attraction from over-powering the expansion. This representation is also referred to as the critical model. As the radius of the universe tends to infinity the velocity of expansion tends to zero. This model is the source of the classic fine-tuning problem. The balance is perfect; why? (Of course this concept is neither Einstein’s nor de Sitter’s, it is a posthumous interpretation of Friedmann’s). Touch E = mc2 with your magic wand and you can go anywhere!

Yes, the rate of expansion tends to zero as the radius goes to infinity. HOWEVER, it starts quite high. This model represents a universe that expands at a decreasing rate, eventually slowing to a crawl. It still expands. You have made the claim that redshift is related to gravitational effects in a universe that is NOT expanding, but you don't have any metric that can satisfy both those conditions (accounts for redshift and isn't expanding).
-Will

[coldcreation]

Originally Posted by Erasmus00

Yes, the rate of expansion tends to zero as the radius goes to infinity. HOWEVER, it starts quite high. This model represents a universe that expands at a decreasing rate, eventually slowing to a crawl. It still expands. You have made the claim that redshift is related to gravitational effects in a universe that is NOT expanding, but you don't have any metric that can satisfy both those conditions (accounts for redshift and isn't expanding).
-Will

The critical model (or Einstein-de Sitter model, which was neither Einstein's or de Sitter's, but Friedmann's) where omega is equal to 1, has not been confirmed by observation. The universe does not appear to be slowing down. The two other Friedmann models are also in violation of observation: the universe does not appear to be coasting to infinity at a constant rate, and there will be no big crunch. So what gives?

A fourth Friedmann model? I think not. A well endowed cosmological constant that defeat gravity in a one on one battle? I doubt it. Dark (kooky) energy? Why not, but where is it?

The metric: the Einstein-de Sitter metric is one where the universe is in equilibrium. Balanced, albeit delicately, between expansion and collapse. It is a non-expanding model.

In 1977, G. F. R. Ellis wrote a paper titled "Is the Universe Expanding?" Ellis shows that “spherically symmetric static general relativistic cosmological space-times can reproduce the same cosmological observations as the currently favored Friedmann-Robertson-Walker universes.” In this case the systematic redshifts are interpreted as “cosmological gravitational red shifts” and the assumption of spatial homogeneity is replaced by the assumption that the universe is stationary.

You will find a general relativistic metric in this paper. It may not yet be the final metric. The redshift itself is a sign of spatiotemporal curvature.

Coldcreation

[Erasmus00]

Originally Posted by coldcreation

The metric: the Einstein-de Sitter metric is one where the universe is in equilibrium. Balanced, albeit delicately, between expansion and collapse. It is a non-expanding model.

The Einstein- de Sitter model with lambda=0 does expand. Its expansion just slows with time, eventually slowing to a crawl. An Einstein-de Sitter model starts at near 0 volume and grows with time, just with a slowing growth. It is not a non-expanding model.

In 1977, G. F. R. Ellis wrote a paper titled "Is the Universe Expanding?" Ellis shows that “spherically symmetric static general relativistic cosmological space-times can reproduce the same cosmological observations as the currently favored Friedmann-Robertson-Walker universes.” In this case the systematic redshifts are interpreted as “cosmological gravitational red shifts” and the assumption of spatial homogeneity is replaced by the assumption that the universe is stationary.

I am not familiar with the paper, in what journal was it published so that I may find it? Also, I believe spherically symmetric, non-expanding spacetimes only work with a non-zero lambda, which you have stated is not what you believe.
-Will

[coldcreation]

Originally Posted by Erasmus00

The Einstein- de Sitter model with lambda=0 does expand. Its expansion just slows with time, eventually slowing to a crawl. An Einstein-de Sitter model starts at near 0 volume and grows with time, just with a slowing growth. It is not a non-expanding model.

I am not familiar with the paper, in what journal was it published so that I may find it? Also, I believe spherically symmetric, non-expanding spacetimes only work with a non-zero lambda, which you have stated is not what you believe.
-Will

Let’s be clear about what is not going on. It was realize after 1929 that the critical Friedmann model resembled the stable-stationary universes of both Einstein and de Sitter. The original Einstein Models, and the original de Sitter models were all non-expanding worldviews. Recall that these theories were developed from 1917 onward, well before the expansion hypothesis flourished. For those still attached to the old Friedmann models: they have all been excluded on observational grounds. The favored critical model (as it should be called exclusively) was the source of the fine-tuning problem, as well as the flatness problem (don’t forget the age problem: at the outset of expansion theory the age of the universe according to the critical model was 1.2 Gyrs old).

The new-relativists transformed the Einstein-de Sitter solution in such a manner that the universe became non-static, an intellectual construal that solely depends on how the geometrical symbols are conceived and physically interpreted. Neither Einstein nor de Sitter seem to have considered this new expanding model important. They both flatly (no pun intended) rejected it.

A theory is supposed to make predictions that can be tested against results of observations or experiments. The Friedmann equations make three very explicit predictions. 85 years later astronomers were able to obtain data that reconciled non of the predictions. So what to do? Modify the models (create a fourth model) or abandon them altogether. The difficulty is that more than a modification is required. A complete overhaul is more appropriate terminology. The Friedmann models were all based on the idea that gravity would control the fate of the universe, and that depended on the mass, omega. A fourth model, if it is to comply with observations, no longer depends on mass, or gravity. It depends on something else. Something that by definition cannot be studied, observed or detected directly: dark energy, nonbaryonic dark matter, quintessence, a new cosmological term off by 120 orders of magnitude, the most grotesque fudge factor in the history of science.

As far as expansion or staticity is concerned, the situation is by no means settled. The favored Miss Universe contestant is the only stable Friedmann model, where ? = 1. This is neither the most attractive, nor the most repulsive, but by far the most desirable of the three Friedmann models; also known as the critical model or, paradoxically, the Einstein-de Sitter model. Here the universe is the flat, isotropic, homogenous, the metric is Euclidean, it has the linear expansion regime. The expansion of the universe does not accelerate in this model. The velocity of expansion tends to zero as the radius R (the size of the universe) tends to infinity. It will never collapse into a big crunch like the ? > 1 model, although some of her traits are the same: both models inherited the missing mass problem. To maintain this linear regime, most of the matter in the universe must be non-baryonic, not composed of ordinary matter. Ordinary matter refers to elements composed of protons, neutrons and electrons. Visible forms of matter, stars and galaxies, account for less than 1% of the critical density. Even with the additional baryonic dark matter (brown dwarfs, planets, gas, and their constituent protons, neutrons and electrons) the missing mass problem is still as real as ever: a dazzling reminder in dark times of what cosmological dramatists do best.

Since 1990’s supernovae survey, all Friedmann models are ruled out observationally. Non of the Friedmann models predicted an accelerating universe. That option was not, either, considered by the Priest himself, Lemaître, the co-Creator of the big bang, He who resurrected the Friedmann models, or Guth, the co-Creator of inflation, another flat theory, or anybody in between. Galaxies were supposedly going to coast to infinity (or decelerate) not speed-up. That represents a freefall when the clocks are revered. Now the universe puts on the brakes if we reverse time. This idea is not only ugly, it is hideous, it is the worst possible scenario anyone could have hoped for.

See H. Kragh’s exceptional book titled Cosmology and Controversy (1996), and P. Kerszberg’s outstanding study of the Einstein-De Sitter debate The Invented Universe (1989).

Here is the Ellis reference again: Ellis, G.F.R. 1977, Is the Universe Expanding?, General Relativity and Gravitation, Vol. 9, No. 2 (1978), pp. 87-94

Coldcreation

[Erasmus00]

Originally Posted by coldcreation

Let’s be clear about what is not going on. It was realize after 1929 that the critical Friedmann model resembled the stable-stationary universes of both Einstein and de Sitter. The original Einstein Models, and the original de Sitter models were all non-expanding worldviews.

Yes, and these models both have a nonzero cosmological constant. Einstein created the cosmological constant in order to build a static universe. You claim that the universe is static, and lambda is 0, but I don't see how thats possible if you believe GR is essentially the correct description of large scale objects.
-Will

[coldcreation]

Originally Posted by Erasmus00

Yes, and these models both have a nonzero cosmological constant. Einstein created the cosmological constant in order to build a static universe. You claim that the universe is static, and lambda is 0, but I don't see how thats possible if you believe GR is essentially the correct description of large scale objects.
-Will

For specific details regarding the Cold Creation interpretation of Einstein's cosmological constant see the thread titled The Cosmological Constant: A New Law. Indeed your precise question is answered there generally. Here briefly, it can be mentioned that the value of lambda has never been known for sure, though it was presumed to be zero by both Einstein, de Sitter, Eddington, Weyl and others from 1917 onward.

The value of lambda is difficult to determine because of many factors. 0 degrees Centigrade was easy to determine, though the freezing point of water was chosen arbitrarily. The boiling point of Mercury could just as readily been chosen as the zero value. The problem is this: What, in the case of the cosmological term, is being measured? Is it pressure, antigravity, dark energy? Know one really knows.

Before the value is determined with any exactitude, a clear and unambiguous definition must be made. Once defined, empirical evidence must be gathered and compared to the predictions as defined.

There is absolutely no contradiction between the general postulate of relativity and a zero value for lambda in a stationary, evolving, dynamic (non-expanding) universe. On the contrary.

The Cold Creation definition of lambda is straight forward: Lambda is a physical state that describes pure spacetime, i.e., a vacuum state in the absence of curvature (gravity, pressure, energy etc.). Lambda is the Minkowski spacetime that would be left over if all matter energy and field could be removed. It defines the properties not just of space but of what happens when matter, energy and field are present.

One might complain that special relativity and Minkowski spacetime are only special cases of the manifold, and have been replaced by GR, a theory that does include gravity and excludes the existence of Euclidean space (because the field is everywhere present, i.e., according to Einstein there exists no space without field). This is true, though there exist in every gravitational system points that are field-free, called Lagrange points.

The point is that lambda is the ‘opposite’ of the gravity field, thus the common misinterpretation ‘antigravity.’ The opposite of curved space is not a space curved in the opposite direction (that would simply be gravity). Curvature is gravity: there is no positive and negative gravity. Gravity does not carry with it a sign, it has no charge. So what about positive and negative curvature, hyperbolic and spherical curvature? To understand these terms more than non-Euclidean geometry is required. You see, the only way to reconcile observation and physical theory is set an absolute scale for gravity, curvature (just as there is for temperature, and just as there should be for entropy, energy, pressure).

As it turns out, an absolute value for lambda (absolute zero curvature) provides the mechanism for the gravitational interaction: something that has eluded physics since its outset. That is because space is thought of generally as nothing, with no limit.

The implicit argument in all big bang expansion theories is that space is created between galaxy clusters allowing (or causing) expansion. Space is therefore not conserved. Nowhere can it be found in the pertinent literature how space is created, by what physical process space enlarges, grows. There simply is no physical explanation as to how space is created.

The contention here is that lambda is not vacuum energy, negative pressure, gravity with an opposite sign, or a dark unphysical (undetectable) force responsible for expansion with a turbo-charge. It is a physical state that describes spacetime and how that space responds to objects and forces within it. It is essentially ubiquitous and has the same absolute value for all times. The field is a modification of that state. These properties are responsible for the observed quasi-equilibrium between gravitating systems.

Lambda is responsible for maintaining stability not just on scales compatible with super clusters or clusters of galaxies, but also right here in the solar system.

Take a classic two-body system, say, the Sun and Earth (or the Earth and Moon). Between two massive bodies, along the line connecting the centers of each mass, there exists a point called L1 (or the inner Lagrange point). This is a point in space where the two gravity fields cancel. At L1 the value of gravity is zero (absolute). An object, or test particle, placed on either side of L1 will tend to accelerate toward the mass on the side in which it is placed. Visualize a curved space or gravitational well. Both the Sun and Earth are in their own respective wells. If you could ride a bike up the hill and escape from the Earth’s field all the way to L1, you could stop there, rest, then roll, or freefall down to the Sun. The Lagrange point L1 is the top of the hill. Stability is attained because the Earth cannot climb out of its own well, it cannot pass through the top of the hill. Massive bodies maintain a ‘space-cushion’ like two magnets that repel one another. If the Earth and Sun where to stop in their tracks they would not attract each other and merge. Space acts in a way that keeps them apart, without actually being a repulsive force

As it turns out, the value of curvature (or gravity) at the top of the hill between the Earth and Moon is also equal to zero. All field-free points have zero value for the gravity field, not –1 or +1. This fact is not by chance. It is because of a very general law of nature that has never been properly expressed, it is because the cosmological constant poses very definite limits on the curvature of space. It is because of lambda that space cannot be created, that space cannot expand.

This interpretation of lambda is not based on new physics, or founded on some philosophical argument in order to justify a stationary regime. It is based known physics, simply, on the notion that the vacuum, space, is a four-dimensional surface upon which all interactions, fields and material bodies manifest themselves. And, yes, there is a new law of nature that describes how space responds in the presences of all things. Lambda is a fundamental, universal constant.

Coldcreation

[coldcreation]

Originally Posted by Erasmus00

Yes, and these models both have a nonzero cosmological constant. Einstein created the cosmological constant in order to build a static universe. You claim that the universe is static, and lambda is 0, but I don't see how thats possible if you believe GR is essentially the correct description of large scale objects.
-Will

For specific details regarding the Cold Creation interpretation of Einstein's cosmological constant see the thread titled The Cosmological Constant: A New Law. Indeed your precise question is answered there generally. Here briefly, it can be mentioned that the value of lambda has never been known for sure, though it was presumed to be zero by both Einstein, de Sitter, Eddington, Weyl and others from 1917 onward.

The value of lambda is difficult to determine because of many factors. 0 degrees Centigrade was easy to determine, though the freezing point of water was chosen arbitrarily. The boiling point of Mercury could just as readily been chosen as the zero value. The problem is this: What, in the case of the cosmological term, is being measured? Is it pressure, antigravity, dark energy? Know one really knows.

Before the value is determined with any exactitude, a clear and unambiguous definition must be made. Once defined, empirical evidence must be gathered (much is available already) and compared to the predictions as defined.

There is absolutely no contradiction between the general postulate of relativity and a zero value for lambda in a stationary, evolving, dynamic (non-expanding) universe. On the contrary.

The Cold Creation definition of lambda is straight forward: Lambda is a physical state that describes pure spacetime, i.e., a vacuum state in the absence of curvature (gravity, pressure, energy etc.). Lambda is the Minkowski spacetime that would be left over if all matter energy and field could be removed. It defines the properties not just of space but of what happens when matter, energy and field are present.

One might complain that special relativity and Minkowski spacetime are only special cases of the manifold, and have been replaced by GR, a theory that does include gravity and excludes the existence of Euclidean space (because the field is everywhere present, i.e., according to Einstein there exists no space without field). This is true, though there exist in every gravitational system points that are field-free, called Lagrange points.

The point is that lambda is the ‘opposite’ of the gravity field, thus the common misinterpretation ‘antigravity.’ The opposite of curved space is not a space curved in the opposite direction (that would simply be gravity). Curvature is gravity: there is no positive and negative gravity. Gravity does not carry with it a sign, it has no charge. So what about positive and negative curvature, hyperbolic and spherical curvature? To understand these terms more than non-Euclidean geometry is required. You see, the only way to reconcile observation and physical theory is to set an absolute scale for gravity, curvature (just as there is for temperature, and just as there should be for entropy, energy, pressure) where at zero absolute, gravity is no longer present.

As it turns out, an absolute value for lambda (absolute zero curvature) provides the mechanism for the gravitational interaction: something that has eluded physics since its outset. That is because space is thought of generally as nothing, with no limit.

The implicit argument in all big bang expansion theories is that space is created between galaxy clusters allowing (or causing) expansion. Space is therefore not conserved. Nowhere can it be found in the pertinent literature how space is created, by what physical process space enlarges, grows. There simply is no physical explanation as to how space is created.

The contention here is that lambda is not vacuum energy, negative pressure, gravity with an opposite sign, or a dark unphysical (undetectable) force responsible for expansion with a turbo-charge. It is a physical state that describes spacetime and how that space responds to objects and forces within it. It is essentially ubiquitous and has the same absolute value for all times. The field is a modification of that state. These properties are responsible for the observed quasi-equilibrium between gravitating systems.

Lambda is responsible for maintaining stability not just on scales compatible with super clusters or clusters of galaxies, but also right here in the solar system.

Take a classic two-body system, say, the Sun and Earth (or the Earth and Moon). Between two massive bodies, along the line connecting the centers of each mass, there exists a point called L1 (or the inner Lagrange point). This is a point in space where the two gravity fields cancel. At L1 the value of gravity is zero (absolute). An object, or test particle, placed on either side of L1 will tend to accelerate toward the mass on the side in which it is placed. Visualize a curved space or gravitational well. Both the Sun and Earth are in their own respective wells. If you could ride a bike up the hill and escape from the Earth’s field all the way to L1, you could stop there, rest, then roll, or freefall down to the Sun. The Lagrange point L1 is the top of the hill. Stability is attained because the Earth cannot climb out of its own well, it cannot pass through the top of the hill. Massive bodies maintain a ‘space-cushion’ like two magnets that repel one another. If the Earth and Sun where to stop in their tracks they would not attract each other and merge. Space acts in a way that keeps them apart, without actually being a repulsive force

As it turns out, the value of curvature (or gravity) at the top of the hill between the Earth and Moon is also equal to zero. All field-free points have zero value for the gravity field, not –1 or +1. This fact is not by chance. It is because of a very general law of nature that has never been properly expressed, it is because the cosmological constant poses very definite limits on the curvature of space. It is because of lambda that space cannot be created, that space cannot expand.

This interpretation of lambda is not based on new physics, or founded on some philosophical argument in order to justify a stationary regime. It is based known physics, simply, on the notion that the vacuum, space, is a four-dimensional surface upon which all interactions, fields and material bodies manifest themselves. And, yes, there is a new law of nature that describes how space responds in the presences of all things. Lambda is a fundamental, universal constant.

Coldcreation

[Erasmus00]

Originally Posted by coldcreation

There is absolutely no contradiction between the general postulate of relativity and a zero value for lambda in a stationary, evolving, dynamic (non-expanding) universe. On the contrary.

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