There are only two possible interpretations for cosmological redshift z that show wavelength independence over 19 octaves of the spectrum.
(1) A change in the scale factor to the metric (often called Doppler effect, (implying the expansion of space and the recession of objects in it, i.e., the radius of the universe changes with time t).
(2) The general relativistic curved spacetime interpretation (implying a stationary yet dynamic and evolving universe.
If indeed the Doppler interpretation (1) is not correct, a wholesale revision of cosmology is required.
Coldcreation
Last edited by coldcreation; 12-19-2006 at 10:30 AM.
Just for the sake of this discussion, lets say that the universe has an edge and that we are located on that edge. If by some miracle we happen to look at the center of the universe, wouldn't the light coming toward us be red shifted because of the gravity well it was climbing out of?
Just for the sake of this discussion, lets say that the universe has an edge and that we are located on that edge. If by some miracle we happen to look at the center of the universe, wouldn't the light coming toward us be red shifted because of the gravity well it was climbing out of?
The entire universe, whatever its extent, is a gravitational well if you will. So in trying to answer your hypothetical little bang, even though your edge is not consistent with cutting edge technology based observations, yes, light would be redshifted on its way toward you on the edge of your torus.
Remark, light is redshifted from the perspective of any observer even without an edge. The question is what is what causes the décalage towards the less refrangible end of the spectrum.
All ‘tired light’ scenarios are ruled out by observational data; there is no significant scattering, refracting, or absorption on the line of sight. Absorption would cause part of the incoming energy to be extracted into the interstellar or intergalactic medium; as a result, dimming would occur over a broad range of the spectrum. Scattering alters the direction of the photons, but the wavelength would remain the same. Refraction would cause a change in the direction or a bending of the wave, as light propagates through matter.
The only possible causes are Doppler shifts due to the recession of objects away from the observer, or due to a general relativistic phenomenon of spacetime dilation that increases with distance. Why should it increase with distance? After all, viewed from Earth, gravity fields diminish with distance according to the inverse square law. And why should light, as it passes through the hills and valleys of spacetime, be just as blueshifted as redshifted.
Einstein’s general principle of relativity characterizes the metric properties of space by the gravitational field (curvature). We are familiar with the idea that local gravitational fields are analogous to hills and valleys (in two dimensions), which are obviously not flat. The average quantity of curvature in a homogenous field is nonzero. Light rays follow ‘curved’ geodesic paths that depend on the variations in the fields they traverse, locally. The actual departure from linearity is derived from the propagation of light as it crosses every hump and wrinkle in the metric. All the matter and energy in the universe introduces a deviation from globally flat space, thus redshift is greater with distance. It would no doubt be ludicrous to envisage an infinite (or finite) Euclidean universe where local non-Euclidean features merely cancel other curved protuberances in the spacetime metric.
General relativity impels us to reassess the geometrical configuration of the large-scale spacetime manifold as it does with the properties of the local environment. Redshift z needs to be reassessed.
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 reshift is observational proof that space is not flat.
Note that an observer located on the edge of our visible universe sees too the redshift increasing with distance from her point of reference. So z is entirely a relative phenomenon. Clocks tick slower there from our perspective and they tick slower here from her viewpoint. Cool.
Today, questioning validity of the Doppler redshift interpretation is symptomatic of the fact that recurrent difficulties continually call for new-fangled conceptions. These conceptions lead to the break-down of all natural laws, of general relativity and of quantum mechanics.
Features in the spectra of distant astronomical objects are shifted to longer wavelengths (toward the red end of the spectrum) by a fractional amount due to curved spacetime phenomenon: not because space is expanding.
The prospect that the universe may perhaps be non-Euclidean has to some extent been previously considered: Recall that Lobachevsky developed the concept of hyperbolic space between 1823 and 1826; Einstein of course (1917, in the General relativity theory) and de Sitter who suggested that the redshift was due to time dilation in a static universe; Weyl’s transitory suggestion of 1921 was along the same lines; Segal’s 1976 chronometric redshift stems from partial differential equations which are hyperbolic relative to a given causal orientation; and the suggestion made by Ellis that redshift may be seen in terms of cosmological gravitational redshifts.
In 1977, G. F. R. Ellis inscribed a seminal, but virtually unknown 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. He adds that for this model to be viable “it is essential that local thermodynamic nonequilibrium processes be able to take place continually.” The key idea is that “there could be a continual circulation of matter taking place,” in this case it is possible to have nonequilibrium processes in a static universe.
There is a close analogy between the Friedmann models and the model proposed by Ellis, but the differences are astounding. What was previously ascribed to a time variation in an expanding frame is now ascribed to a spatial variation in properties of a static universe, as we observe the past light cone (in the look-back time). Herman Weyl had considered this possibility in 1921, when he still sought a middle ground between the Einstein and de Sitter models. Ellis urges “a closer investigation of the field equations and astrophysical aspects of these models” and considers that the interpretation of an expanding universe (an idea that was first put forth by de Sitter) “is based on the assumption of spatial homogeneity, which is made on philosophical rather than observational grounds.”
He also adds (in a manuscript note) that it is difficult to fit the mass-redshift observations well within a static universe. Meaning that there does not appear to be enough mass m in the universe to attribute the redshift z to a gravitational effect, and so considers this evidence against the stationary models. But at the same time, Ellis questions whether with a more detailed investigation, one could fit the mass-z relations accurately with observation, so that the results obtained are not implausible. (See Ellis, G.F.R. 1977, Is the Universe Expanding?, General Relativity and Gravitation, Vol. 9, No. 2 (1978), pp. 87-94).
Note that there are several attractive features of a universe where redshift is a cosmological spacetime curvature effect. These features are lacking (and in fact detrimental) in the Doppler redshift model. Explicitly, there is no horizon problem, or flatness problem. Implicitly, there is no galaxy problem, monopole problem, antimatter problem, entropy problem, age problem or singularity problem.
Whereas the Doppler interpretation model is governed by Newtonian mechanics and special relativity, the cosmological redshift zgrav is entirely based on Einstein’s general principle of relativity in a non-Euclidean continuum with a very specific value for the cosmological constant.
This possibility needs to be explored further. The mathematics of mass-energy density vs. redshift as a metric function of the manifold needs to be calculated. A solution for missing mass too needs to be found for the zgrav interpretation.
Note that the zgrav effect requires a loss of energy independent of the wavelength, in accord with observations showing wavelength independence over 19 octaves of the spectrum. This is the only interpretation besides the Doppler effect that has energy loss with such a constant fractional wavelength shift. Certainly there are intrinsic motion shifts and intrinsic gravitational shifts in the mix.
So this interpretation is not pitted against Halton Arp’s discoveries of discordant redshifts.
The deviation from linearity observed in the spectrum of distant supernovae Type Ia is evidence of hyperbolic curvature (not accelerated expansion). With a Doppler interpretation, distant supernovae and their host galaxies appear to be receding slower than permitted by Hubble’s Law. Unexpected dimness of early supernovae gives the impression they are further away than their redshifts indicate, altering the predicted structure of the cosmos. The large shells of radiation and material emitted by distant supernovae appear to have a greater area than they would in a topologically flat space, making the source look very faint.
What we have is general relativistic spacetime dilation increasing with distance from the observer.
One of these interpretation is likely wrong (unless both effects are superimposed). The choice today cannot be made with certainty. More investigation into the relativistic possibility is required before a decision can be made. My personal choice, though possibly premature, and perhaps biased, is in favor of the curvature approach, for the reasons mentioned above (the problems of modern cosmology are simply not there), and because it is founded on a theory (general relativity) that has passed every test (except for the gravitational wave prediction), rather than on two classical theories (Newton’s, or special relativity) that are known to be limited or special cases of the general theory. GR should be used in global considerations where distances are large, light speed is great and mass-energy density of huge portions of space is large.
ColdCreation
Last edited by coldcreation; 07-08-2005 at 10:38 AM.
Reason: forgot an 's' on conception
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 reshift is observational proof that space is not flat.
We will find both time dilation (time delay or retardation of light signal) and increased spatial (metric) increments the greater the distance of the observed source in comparison with our own reference frame (clock appear to slow down and distances appear greater at cosmological distances, i.e., global redshift is a measurement which tests the existence of spatial dependence judging against the locally measured rates of atomic frequency standards, or clocks). Thus, redshift is a relative frequency shift as a function of distance in a curved spacetime continuum.
With respect to the geometrical nature of the four-dimensional continuum (from the quantum realm to the large-scale), before the Prussian Academy of Sciences, January 21, 1921, Einstein expressed the following viewpoint:
“It appears less problematic to extend the concepts of practical geometry to spaces of cosmic order of magnitude. It might, of course, be objected that a construction composed of solid rods departs the more from ideal rigidity the greater its spatial extent. But it will hardly be possible, I think, to assign fundamental significance to this objection. (Einstein, 1954, 1982, pp. 238-239)
The translation from German may seem rather peculiar, but the essence of Einstein’s point is as clear as it is obvious: Locally the universe looks Euclidean, but the further one looks out into the universe the greater the deviation from Euclidean geometry.
How do you get the universe in the shape of a hyperbola.
BTW what is decalage, I thought it had something to do with an airplane?
Good question Little Bang, I will keep this as short as possible:
The shape of the universe appears hyperbolic from the perspective of any observer. Why?
Lobachevsky had already pondered and written about this possibility between 1823 and 1826. After having realized the universal character of his new non-Euclidean geometry, Lobachevsky’s research led him to a series of calculations of the sums of angels of triangles, the vertices of which were two diametrically opposed points on the orbit of the Earth and one of the fixed stars, Sirius, Rigel or 28 Eridani. He was unable to determine the deviation from linearity, due to the margin of error in observation. (The experiment was not carried out). In 1908, Minkowski considered this complex space in connection with Einstein’s special principle of relativity (now called pseudo-Euclidean space).
Further developments of Lobachevsky’s geometry came from Riemann, in 1854 (published in 1866). It subsequently became clear that Lobachevskian space (hyperbolic space) would find itself embedded in the Riemann space of constant ‘negative’ curvature. This is the idea that led to Klein’s quadratic conic section of multidimensional or four-dimensional projective metric, where in Über die sogenannte nicht-euklidische Geometrie (1871) he chose to reflect on Euclidean, elliptical and hyperbolic geometry from a single perspective within the realm of transformations in projective space. A new stage in the expansion of physics had been set in motion; one where the Euclidean geometry of The Middle Ages and antiquity was replaced with modern geometry of variable magnitudes.
But it was Albert Einstein’s incorporation of non-Euclidean geometry within the framework of GR that would unlocked the door to our understanding of the curvature of the real world. According to Einstein, the spacetime metric is determined by the mass-energy density of the universe. Though the average density of visible matter in the universe is extremely low, the total mass of the universe remains unknown.
De Sitter realized that redshifts for stars like the Sun, as an effect due to gravitation, could easily be confused with a receding motion. He believed that the units of space and time would change as a consequence of gravitation. It was clear that the motion of clocks depended on the gravitational potential, but also on where the clocks were located within the field. Consequently, the frequencies of light vibrations are constant when expressed in proper time, and are variable when expressed in coordinate time. This is in essence the principle responsible for the gravitational redshift and time dilation.
‘Time-like intervals’ dependence on distance mean that clocks would appear to slow down depending on distance (the further away, the slower the clock), manifesting itself as a redshift; called the de Sitter effect, in a stationary universe.
There is obviously confusion between spurious motion in an expanding universe, and the impression of motion in a stable universe, between gravity as a globally attractive force, and gravity as a geometric curvature of the manifold. A striking parallel can be observed between the chronometric redshift law (see Segal, I.E. 1976, Mathematical Cosmology and Extragalactic Astronomy) and the early de Sitter model of 1917, where the time-like interval is dependent on distance; again, meaning that clocks would appear to run slower with increasing distance. In a static universe this would manifest itself as a redshift that increases with distance (the de Sitter effect).
The chronometric redshift also resembles Weyl’s transitory suggestion of 1921, in which time variation in the non-static case is interpreted as spatial variations in the static case. An analogous situation arises when comparing the spherically symmetric static general relativistic cosmological spacetimes of Ellis (1977-78), with Segal’s four-dimensional globally hyperbolic (curved), pseudo Riemannian temporal evolution of the spacetime manifold.
Check this out. 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. (Today this is erroneously interpreted as an accelerating universe).
In the 1930’s, modern science had not yet unchained itself from the faith that was concealed from the senses, inaccessible to experiment or observation and implicit in Newtonian gravitation. By limiting its field of action to a highly dubious interpretation of observable quantities and simple calculations, the Doppler effect was erroneously attributed to the galactic redshifts. In the place of non-Euclidean spatial variations, which, at the time, were nothing but words, in the place of global hyperbolicity and gravitational time variations, which were nothing but mathematical constructions, cosmology erected its own edifice. Bearing in mind the experience of the last century, it is today as inadmissible to maintain that the large-scale structure of spacetime is Euclidean, as to assert that the Earth is flat.
Progress in this domain is far from complete. 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.
So why hyperbolic? Redshift itself, with its spacetime dilation interpretation is arguably due to hyperbolic curvature from the perspective of an observer, but the departure from linearity suggested by the recent supernovae data. These SN observations show that spacetime is hyperbolic in the sense that the spatial increments and time-like variations become increasingly larger with distance and volume. Before 1998, redshift was thought to be increasing linearly with distance. Now, it has been shown that distant SN are further away than their redshift would otherwise suggest. That is more than a hyperbolic signature, it is definitive proof of hyperbolicity. (In passing, it is also proof of evolution in the look-back time. I can elaborate if anyone is interested).
There is a fundamental question we must ask ourselves today: How does one measure the large distances between two points of a curved manifold; correspondingly, how does one measure the rate of clocks with respect to a sufficiently large neighborhood of points starting from the base metric of ordinary Euclidean space, and how is differentiation possible between large-scale special relativistic motion away from an observer and global general relativistic curvature of the spacetime continuum in a stationary, dynamic and evolving universe?
The shape of the universe appears hyperbolic from the perspective of any observer.
No winner this time, please try again.
You make a statement as a fact even though no one can observe the universe from the outside an never will. Any curvature of spacetime within would not require it to have a particular shape anyhow.
Based on the Wilkinson Microwave Anisotropy Probe (WMAP) many theorize the shape as a soccer ball. What makes your theory any more certain than theirs?
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No winner this time, please try again.
