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Encyclopedia > Milne model
Milne's model follows the description from special relativity of an observable universe's spacetime diagram containing past and future light cones along with "elsewhere" in spacetime.

## Contents

The Milne Metric is flat space. It is not similar to Einstein's static universe, however, because in Milne's model, the particles are moving apart. In Einstein's static universe, the particles were all standing still.

Friedmann's solution to the Einstein Field Equations requires that a constant uniform density somehow affects the curvature of three dimensional space in a higher dimensional space. Milne argues against this idea, repudiating the assumptions that led to the Friedmann solution.

Even so, cosmologists like to see what Milne's model says as viewed through the FLRW model, and it says the following:

The more general Friedmann, Lemaitre, Robertson, Walker Metric (FLRW metric) reduces to the Milne universe for a spacetime that is a pure vacuum without matter, radiation, or a cosmological constant. Milne cosmology therefore corresponds to a cosmological solution to the Einstein equations for In physics, spacetime is a model that combines three-dimensional space and one-dimensional time into a single construct called the space-time continuum, in which time plays the role of the 4th dimension. ... Matter is commonly defined as the substance of which physical objects are composed. ... Electromagnetic radiation can be conceptualized as a self propagating transverse oscillating wave of electric and magnetic fields. ... The cosmological constant (usually denoted by the Greek capital letter lambda: Î›) occurs in Einsteins theory of general relativity. ...

Tab = 0.

The Milne metric follows when the scale factor of the FRLW metric is a constant over time, yielding: The scale factor, parameter of Friedmann-LemaÃ®tre-Robertson-Walker model, is a function of time which represents the relative expansion of the universe. ...

ds2 = c2dt2dr2r2dΩ2

where:

dΩ2 = dθ2 + sin2θdφ2
r gives the proper motion distance between points in the universe.

and appropriate constants are subsumed into relevant coordinates. The Milne metric is therefore simply a restatement of the Minkowski metric. In physics, proper length is the length of an object or a contour as measured in the reference frame of the object itself in the context of special relativity. ... In physics and mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einsteins theory of special relativity is most conveniently formulated. ...

There are two types of motion in the galaxy. That which goes along with Hubble flow and Peculiar velocity which is motion of a freely projected particle or galaxy relative to the Hubble flow. In cosmology, the Hubble expansion is the motion of galaxies away from each other, due to the expansion of the universe. ... The term peculiar velocity refers to the components of a receding galaxys velocity that cannot be explained by Hubbles law. ...

Whereas the FLRW metric explains all of the redshift associated with the Hubble flow by the metric expansion of space, Milne's model has no expansion of space, thus all of the Hubble flow redshift is explained by the recessional velocity associated with the hypothetical explosion. The metric expansion of space is a key part of sciences current understanding of the universe, whereby space itself is described by a metric which changes over time. ... Recessional Velocity is a term used to describe the rate at which an object is moving away, typically from Earth. ...

## Milne's density function

Milne proposed that the universe's density changes in time because of an initial outward explosion of matter. Milne's model assumes an inhomogeneous density function which is Lorentz Invariant (around the event t=x=y=z=0). When rendered graphically Milne's density distribution shows a three-dimensional spherical Lobachevskian pattern with outer edges moving outward at the speed of light. Every inertial body perceives itself to be at the center of the explosion of matter (see observable universe). From such a perspective, the universe appears isotropic though not homogeneous. The observable Universe is a term used in cosmology to describe a ball-shaped region of space surrounding the Earth that is close enough that we might observe objects in it. ...

Unless the universe modeled has zero density, Milne's proposal does not follow the predictions of general relativity for the curvature of space caused by global matter distribution, as seen in, for example statistics associated with large-scale structure. General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. ... To meet Wikipedias quality standards, this article or section may require cleanup. ...

## Differences between Milne model and other models

In order to explain the existence of matter in the universe, Milne proposed a physical explosion of matter which would not affect the universe's geometry. This is in contrast to the metric expansion of space that is the hallmark feature of many of the more famous cosmological models including the Big Bang and Steady State models. Milne's universe shares a superficial similarity to Einstein's static universe in that the metric of space is not time-dependent They are superficially similar in the sense that an explosion in a room is superficially similar to a bunch of cobwebs in a room. i.e. the room is the same.) The metric expansion of space is a key part of sciences current understanding of the universe, whereby space itself is described by a metric which changes over time. ... According to the Big Bang theory, the universe emerged from an extremely dense and hot state (bottom). ... For alternative meanings see steady state (disambiguation). ... Basic description The theory of a static universe is the rival theory to an expanding universe and all of its subvarieties. ... See: International System of Units, colloquially called the Metric System, and also metrication. ... Space has been an interest for philosophers and scientists for much of human history, and hence it is difficult to provide an uncontroversial and clear definition outside of specific defined contexts. ...

Unlike Einstein's initial cosmology, Milne's proposal directly contradicts the Einstein equations for cosmological scales. Special relativity becomes a global property of Milne's universe while general relativity is confined to a local property. The reverse is true for standard cosmological models, and most scientists and mathematicians agree that the latter is self-consistent while the former is mathematically impossible. The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. ... General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. ...

Milne held up his model as an existence proof that these mathematicions were incorrect.

Edward Arthur Milne predicted a kind of event horizon through the use of this model, as can be seen clearly in the last sentence of the plate. "The particles near the boundary tend towards invisibility as seen by the central observer, and fade into a continuous background of finite intensity." Edward Arthur Milne (February 14, 1896 – September 21, 1950) was a British mathematician and astrophysicist. ... This article or section is in need of attention from an expert on the subject. ...

At the time Milne proposed his model, observations of the universe did not appear to be in a homogeneous form. This, to Milne, was completely compatible with both his own model, and the competing cosmological models which relied on the cosmological principle that demanded a homogeneous universe. What he disliked about the competing models was that they assumed that this homogeneity extended for eternity in all directions, whereas he felt that there was definitely not enough data to support such an assumption. “This conventional homogeneity is only definite when the motion of the particles is first prescribed.” With present observations of the homogeneity of the universe on the largest scales seen in the cosmic microwave background and in the so-called "End of Greatness", questions about the homogeneity of the universe have been settled in the minds of most observational cosmologists. However our observations only extend out to about 10 or 15 billion light years. At these distances, it is unclear whether the density is the same as it is here, or if it is affected by the effects of high recession velocity which would be predicted by Special Relativity. Milne's model says that the universe at these distances is younger and denser than it is locally. Look up Homogeneous in Wiktionary, the free dictionary. ... The Cosmological Principle is a principle invoked in cosmology that severely restricts the large variety of possible cosmological theories: On large scales, the Universe is homogeneous and isotropic. ... WMAP image of the CMB anisotropy,Cosmic microwave background radiation(June 2003) The cosmic microwave background radiation (CMB) is a form of electromagnetic radiation that fills the whole of the universe. ... Observational cosmology is the study of the structure, the evolution and the origin of the universe through observation, using instruments such as telescopes and cosmic ray detectors. ...

## References

Milne, "Relativity, Gravitation and World Structure"

http://world.std.com/~mmcirvin/milne.html ("Milne Cosmology, and Why I Keep Talking About It," by Matt McMirvin.")

http://www.phys-astro.sonoma.edu/BruceMedalists/Milne/MilneRefs.html Here is a list of further reading on Milne's life and work.

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