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Topic: Metric expansion of space


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 Hubble's law - Wikipedia, the free encyclopedia
When this metric was applied to the Einstein equations, the so-called Friedmann equations emerged which characterized the expansion of the universe based on a parameter known today as the scale factor which can be considered a scale invariant form of the proportionality constant of Hubble's Law.
However, the best way to calculate the recessional velocity and its associated expansion rate of spacetime is by considering the conformal time associated with the photon traveling from the distant galaxy.
It is considered the first observational basis for the expanding space paradigm and today serves as one of the most often cited pieces of evidence in support of the Big Bang.
en.wikipedia.org /wiki/Expansion_of_space

  
 Metric Field
Consequently, galaxies are mass generators due to the expansion of the metric spacetronic field, which field exerts a pressure on all mass units regardless of their size Mass being a field of compressed spacetrons.
The above equation being the fundamental metric form that defines the measure of length of both mass and space.
However, Einstein did not realize that space was in a state of expansion when he produce his theory, nor that for every quantity of space-time- expansion their exist a quantity of mass and that as expansion-time continues so does the increase of mass transpire, and this take place in the center of galaxies.
members.tripod.com /~jimmar/index-5.html

  
 The Intrinsic Motions of Time, Space, and Gravity
A non-local gauge of "infinite" velocity is required to protect energy conservation by ensuring the homogeneity (symmetry) of inertial metric forces and the prevention of uncentered "rogue" gravitational fields, irrespective of the rate of Universal expansion.
The expansion and cooling of space reduces the Universe's capacity for work, hence c is the entropy drive as well as the symmetry gauge of space and free energy.
We can think of the timeline exiting space at right angles to all three spatial dimensions to produce the historic temporal domain; the increase in the age or expansion of this historic temporal domain is the analog of the expansion of space.
www.people.cornell.edu /pages/jag8/motion.html

  
 Discrete space - Wikipedia, the free encyclopedia
However, the discrete metric space is free in the category of bounded metric spaces and Lipschitz continuous maps, and it is free in the category of metric spaces bounded by 1 and short maps.
For instance, a product of countably infinitely many copies of the discrete space of natural numbers is homeomorphic to the space of irrational numbers, with the homeomorphism given by the continued fraction expansion.
The underlying uniformity on a discrete metric space is the discrete uniformity, and the underlying topology on a discrete uniform space is the discrete topology.
en.wikipedia.org /wiki/Discrete_space

  
 Discrete space Information - TextSheet.com
However, the discrete metric space is free in the category of bounded metric spaces and Lipschitz continuous maps, and it is free in the category of metric spaces bounded by one and nonexpansive maps.
For instance, a product of countably infinitely many copies of the discrete space of natural numbers is homeomorphic to the space of irrational numbers, with the homeomorphism given by the continued fraction expansion.
The underlying uniformity on a discrete metric space is the discrete uniformity, and the underlying topology on a discrete uniform space is the discrete topology.
www.shopping.top5miami.com /encyclopedia/d/di/discrete_space.html

  
 Discrete space Information - TextSheet.com
However, the discrete metric space is free in the category of bounded metric spaces and Lipschitz continuous maps, and it is free in the category of metric spaces bounded by one and nonexpansive maps.
For instance, a product of countably infinitely many copies of the discrete space of natural numbers is homeomorphic to the space of irrational numbers, with the homeomorphism given by the continued fraction expansion.
The underlying uniformity on a discrete metric space is the discrete uniformity, and the underlying topology on a discrete uniform space is the discrete topology.
www.shopping.top5miami.com /encyclopedia/d/di/discrete_space.html

  
 Discrete space - Wikipedia, the free encyclopedia
However, the discrete metric space is free in the category of bounded metric spaces and Lipschitz continuous maps, and it is free in the category of metric spaces bounded by 1 and short maps.
For instance, a product of countably infinitely many copies of the discrete space of natural numbers is homeomorphic to the space of irrational numbers, with the homeomorphism given by the continued fraction expansion.
That is, the discrete space X is free on the set X in the category of topological spaces and continuous maps or in the category of uniform spaces and uniformly continuous maps.
en.wikipedia.org /wiki/Discrete_space   (1096 words)

  
 Rietvlei Gazette Page11 New Cosmology
It turns out that an appropriate general relativistic metric for a flat Bedrock Model can be constructed by introducing into the Minkowskian metric of special relativity a scale factor a(t) that increases with time and re-gauging the space coordinates by means of a coordinate transformation.
This is the "expansion" interpretation of change in the metric.
The simplest way of introducing relative change among the metric coefficients would be to set the scale factor a(t) to unity at all times and to preserve the changing ratio of the metric coefficients by introducing a factor b(t) that multiplies c and varies with time, or, equivalently, absorb the time dependency into c.
www.rietvleikzn.co.za /part3.htm   (1096 words)

  
 The Origin of Gravitation
The intrinsic motion of light is therefore explained as the entropy and symmetry conservation drive of metric spacetime, serving energy conservation.
The intrinsic motion of time is the entropy drive of matter, decaying and aging matter, information, and history in a manner analogous to the expansion and cooling of space.
In my view, this deceleration corresponds to the missing spatial entropy of the light which created m, now converted/conserved by gravitational action to the metrically equivalent temporal entropy (time dimension) of m.
www.people.cornell.edu /pages/jag8/Time.html   (5257 words)

  
 Aspects of a theory of gravity with a privileged reference frame
For example, the Robertson-Walker space-time metric of an expanding universe distinguishes a particular class of ‘comoving observers’- that is, comoving with the expansion commonly assumed to explain, as a Doppler effect, the observed red-shift of the spectra emitted by distant galaxies.
In the studied non-linear theory, the coincidence between ‘absolute’ space (or time) metric and physical space (or time) measurements is found only in the first approximation.
is the volume element of the Euclidean metric).
geo.hmg.inpg.fr /~arminjon/ETHER4.htm   (3712 words)

  
 Field Interchange Hypothesis
That, during the expansion phase of these fluctuations, the spacetime curvature would clearly need to be positive, so that there would be a mismatch between the externally measured volume and the internal volume.
This is precisely the recipe for an Alcubierre warpdrive, in which a hypothetical spaceship, enveloped in such a modified space-time metric, would experience a free fall geodesic, even as the whole disturbance is undergoing acceleration relative to external space-time.
These curvature fluctuations of the metric should be highly localized, by virtue of the limited range of the SC photon's field.
starflight1.freeyellow.com /page5.html   (3712 words)

  
 WDT -The Basics of Warp Drive Physics (mathematical)
This metric supposes a contraction of spacetime in front of a body, with a expansion behind it.
What this metric truly suggest is that such a manipulation of space would cause spacetime to propel a localized region of space (refereed to as a warp bubble) by expanding and contracting the metric field.
This is beacuse the basis of the Alcubierre metric requires an enormous amount of negative energy, which according to classical conservation laws shouldn't exist.
members.tripod.com /da_theoretical1/wdtheory.html   (3712 words)

  
 Abstract
The outer automorphism group Out(F_n) of a free group of rank n acts on the Culler Vogtmann moduli space of marked, metric graphs of rank n, known as "outer space" X_n.
Using the structure of Teichmuller space as a guide, we are exploring various questions and conjectures about the structure of outer space.
This action is analogous to the action of the mapping class group of a surface on the Teichmuller space of that surface.
www.math.cornell.edu /~brendle/abstracts/mosher.html   (3712 words)

  
 A non-symmetric space-time metric
In being symmetric in static solutions, the first difference of the vector potential is evidently related to the expansion factor of the gravitational field, which is known to behave similarly to the Newtonian gravitational potential.
The basis of the relationship is that the symmetric part represents the first difference of the vector potential, and the antisymmetric part represents the first difference of the scalar potential.
The symmetric terms are investigated on another page.
www.s-4.com /pulsar/metric.htm   (521 words)

  
 GRADU2.html
Most previous undertakings have supposedly concentrated on weighted generalizations of Sobolev and Hölder-type imbeddings (the latter term refers to imbeddings of Sobolev spaces with p>n) and today most research in this area is concentrated on extending previous results to metric spaces.
is the closure of Ck in the Sobolev space W1,p(see e.g.
The situation was remedied in 1967 when Neil Trudinger found an imbedding of this Sobolev space into an Orlicz space defined by an exponential function.
www.helsinki.fi /~hasto/gradu/gradu.html   (5819 words)

  
 Gravitation, Entropy, and Thermodynamics
The electromagnetic constant c is both the symmetry gauge (regulator) and the entropy drive of light and the "metric" of spacetime; the metric is the relationship of measurement between the dimensions.
Hence the stable metric displays a symmetry (a sameness) with respect to location and orientation in space or time, and this symmetry is a manifestation of energy conservation, perhaps our most fundamental example of Noether's theorem and the connection between symmetry and conservation.
Without a metric, there would be no structure to regulate the expansion of the Universe such that its temperature and volume yield a constant product over time, in satisfaction of the first law.
people.cornell.edu /pages/jag8/thermo.html   (5819 words)

  
 5.1 The matching equation
the multipole expansion of h (for simplicity, we suppress the space-time indices).
Concerning the multipole expansion of the post-Newtonian metric,
The fundamental fact that permits the connection of the exterior field to the inner field of the source is the existence of a ``matching'' region, in which both the multipole and the post-Newtonian expansions are valid.
www.maths.tcd.ie /EMIS/journals/LRG/Articles/Volume5/2002-3blanchet/node13.html   (476 words)

  
 Predmety - Predmety
The notion of a projective space, homogeneous coordinates, projective expansion of an affine space, colinear mapping, double partition ratio, quadrics in projective spaces, projective, affine and metric classification of quadrics, dual space, the principle of duality.
The notion of an affine space, subspaces, the description of the subspaces by the equations, mutual position of subspaces, trasformation of coordinates, the transversal of oblique lines, affine mappings, partition ratio.
Projective space, classification of quadrics with a special emphasis to conic sections in affine and euclidian spaces.
www.mff.cuni.cz /vnitro/is/sis/predmety/kod.php?kod=ALG002   (275 words)

  
 Cantor set - Wikipedia, the free encyclopedia
It is worth noting that as a topological space, the Cantor set is homeomorphic to the product of countably many copies of the space {0, 1}, where each copy carries the discrete topology, as can easily be shown using the ternary expansion used to prove its uncountability.
Since the Cantor set is the complement of a union of open sets, it itself is a closed subset of the reals, and therefore a complete metric space.
As a compact totally disconnected Hausdorff space, the Cantor set is an example of a Stone space.
www.hackettstown.us /project/wikipedia/index.php/Cantor_set   (275 words)

  
 Expanding space - Physics Help and Math Help - Physics Forums
The Robertson-Walker metric describes the expansion of the physical matter in the universe, galaxies separating and moving apart, not the expansion of space.
One instead finds that the metric in a global description is dynamic according to every frame and so globally speaking it is expanding space and not galaxies separating within space that is the accurate description.
However when one considers the global behavior of the metric and the galaxies one can no longer use the special relativistic Doppler formula, nor the special relativistic metric.
www.physicsforums.com /showthread.php?threadid=15225   (275 words)

  
 ARN Board: Creationist Cosmology
In a Klein universe, time is space-like at the center during the early phases of expansion, in the R-W metric, this can only happen if your t imaginary, which Hawking shows is where physical clocks stop.
The metric inside the dust will be similar to that of part of a Robertson-Walker universe, while that outside will be the Schwarzchild metric.
Whereas for an unbounded Robertson-Wakler cosmos, the origin of coodinates can be anywhere, here the origin of coordinates must be at the center of the sphere and nowhere else.
www.arn.org /boards/ubb-get_topic-f-12-t-000036.html   (275 words)

  
 As a matter of fact, not
For example the Alcubierre metric engineering solution of EFE uses the same space expanding mechanism as cosmic expansion to achieve FTL travel, and it has been shown to violate causality in the usual FTL way.
Indeed the causal violation proofs are insensitive to the way you achieve FTL, all they require is that you get from event A to spacially related event B (which is how they say "FTL").
www.superstringtheory.com /forum/timeboard/messages7/61.html   (275 words)

  
 General Relativity & Black Holes
The description of the curvature of space is the mathematically complicated part of general relativity involving "metrics", which describe the way that matter curves space, and tensor calculus.
The General Theory of Relativity is an expansion of the Special Theory to include gravity as a property of space.
In his second calculation, published in 1916, he included the space-time metric, which describes the curvature of space and time caused by gravity and got an answer twice as large as his first calculation.
cassfos02.ucsd.edu /public/tutorial/GR.html   (3331 words)

  
 Expert About co:Compactly
The category of compactly generated Hausdorff spaces is general enough to include all metric spaces, topological manifolds, and all CW complexes.
The paper is devoted to one-dimensional compactly supported wavelets which are of the greatest interest for applications because of the simplest numerical realization of expansion and synthesis algorithms.
In topology, a compactly generated space is a topological space X satisfying the following condition: a subspace A is closed in X if and only if A ∩ K is closed in K for all compact subspaces K ⊆ X. Most topological spaces commonly studied in mathematics are compactly generated.
www.expertsite.biz /dir/co/compactly.htm   (3331 words)

  
 Isometric embeddings of black-hole horizons in three-dimensional flat space
Our method is based on expanding the surface in spherical harmonics and minimizing the differences between the metric on the original surface and on the trial surface in the space of the expansion coefficients.
The geometry of a two-dimensional surface in a curved space can be most easily visualized by using an isometric embedding in flat three-dimensional space.
We have applied this method to study the geometry of black-hole horizons in the presence of strong, non-axisymmetric, gravitational waves (Brill waves).
stacks.iop.org /0264-9381/19/375   (3331 words)

  
 WarpDrive_02.doc
In order to understand the metric further we will need to construct an arbitrary function f as to produce the contraction/ expansion of volume elements as proposed by the Alcubierre Spacetime.
The metric tensor is one of the most important concepts in relativity, since it is the metric which determines the distance between nearby points, and hence it specifies the geometry of a space-time situation.
He has developed a “metric” for General Relativity, a mathematical representation of the curvature of space-time, that describes a region of at space surrounded by a warp or distortion that propels it forward at any arbitrary velocity, including FTL speeds.
www.astrosciences.info /WarpDrive.htm   (3331 words)

  
 Ken Richardson's Publications and Preprints
I show that given a compact Riemannian manifold on which a compact Lie group acts by isometries, there exists a Riemannian foliation whose leaf closure space is naturally isometric (as a metric space) to the orbit space of the group action.
Conversely, given a Riemannian foliation, there is a metric on the basic manifold (an O(q)-manifold associated to the foliation) such that the leaf closure space is isometric to the O(q)-orbit space of the basic manifold via an isometry that preserves the volume of the leaf closures of maximal dimension.
In contrast to the asymptotic expansion of the ordinary heat kernel of a Riemannian manifold, the nature of the expansion at x in M may depend on x, and the coefficients of the powers of t are not necessarily integrable.
faculty.tcu.edu /richardson/pubs.htm   (2094 words)

  
 Ken Richardson's Publications and Preprints
I show that given a compact Riemannian manifold on which a compact Lie group acts by isometries, there exists a Riemannian foliation whose leaf closure space is naturally isometric (as a metric space) to the orbit space of the group action.
Conversely, given a Riemannian foliation, there is a metric on the basic manifold (an O(q)-manifold associated to the foliation) such that the leaf closure space is isometric to the O(q)-orbit space of the basic manifold via an isometry that preserves the volume of the leaf closures of maximal dimension.
In contrast to the asymptotic expansion of the ordinary heat kernel of a Riemannian manifold, the nature of the expansion at x in M may depend on x, and the coefficients of the powers of t are not necessarily integrable.
faculty.tcu.edu /richardson/pubs.htm   (2094 words)

  
 Discrete space - Wikipedia, the free encyclopedia
However, the discrete metric space is free in the category of bounded metric spaces and Lipschitz continuous maps, and it is free in the category of metric spaces bounded by 1 and short maps.
For instance, a product of countably infinitely many copies of the discrete space of natural numbers is homeomorphic to the space of irrational numbers, with the homeomorphism given by the continued fraction expansion.
Certainly the discrete metric space is free when the morphisms are all uniformly continuous maps or all continuous maps, but this says nothing interesting about the metric structure, only the uniform or topological structure.
en.wikipedia.org /wiki/Discrete_space   (1058 words)

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