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Author Topic: The Universe and it's Intrinsic Curvature Given Two Ways, One of Them New  (Read 2926 times)

Offline Koki

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First read newbielink:http://www.as.utexas.edu/astronomy/education/spring05/komatsu/lecture15.pdf [nonactive]

The Gaussian curvature for a 3-sphere system with a proper density is actually identified with the square of the reciprocal of the length ee5e5c003694e7cd5ae404923c665edb.gif


45cefa565ff9691ea0e915f670b7a1c2.gif


A three-dimensional hypersphere is


d356b86ba7638b726f188f68a0e25654.gif


Where a5f3c6a11b03839d46af9fb43c97c188.gif is the Gaussian curvature [Appendix] which can be re-written as


701a2d2041337475fe3d1720cec6b946.gif


Our factor of 1679091c5a880faf6fb5e6087eb1b2dc.gif magically disappears when you plug in classical values. Iíll quickly show this proof:

the density of a three dimensional hypersphere should be


8324bcfbec7cd109ecee28ef950f4e6a.gif


The general relativistic relationship to the principle curvatures  is found as


45cefa565ff9691ea0e915f670b7a1c2.gif


sidenote *the term e25a3f84150a4a59ce2a34ff320733a2.gif arises often because it simplified several of the field equations describing gravity


The expression above was noted by Motz on his paper of quantization, and by a reference I will have below this post. Let us plug in and solve the equation. Be careful to remember your algebra when solving, when dividing a whole number by a fraction. I calculate this as


2ec5512e97dfca13e0cc9aa473fcfb88.gif


A three dimensional hypersphere is normally written as  when equated with the Compton wavelength. Equating my expression with this term we have


4a8e187c31e4900d78e8b28876e59ec1.gif
 

Cancelling out the 6's, we end up with a general relativistic interpretation of how the geometry of a 3-sphere relates to the proper The The proper density and the Gaussian Surface Curvature are related as

2a9de6cb0aa215b6921711f13f4932fe.gif


Where the last equality comes about from a knowing that it has dimensions of length over mass. What is the Gaussian curvature of a metric? Refer back now to the cited reference at the beginning:

5f8e977602c742047058f1616e454fad.gif


Where a5f3c6a11b03839d46af9fb43c97c188.gif is the curvature of the universe.


908029a94d8adc762b920de423c9bd47.gif


where


2934696b7b39bcdfe7d08afae9d748e1.gif


is the many body system and now allow 145df3922ebb7674002078760a2a232d.gif (the Hubble Constant) and multiply through by our Schwarzschild constant


19ef0824332a47f7a88141aebd3065c4.gif


because 1057c183727755cdb7d58a2fe2dcd23d.gif as we proved before. We also showed that this equation was actually a length over the mass, in exchange we may think of this as the radius of the universe and entire ensemble of statistical averages so that the equation doesn't hold two identical features on either side of the equal sign, it's just more aesthetic


9e83b1a6b5135bc934a0617574cf8b01.gif


There are of course limits we can look at for variety, the equation above can satisfy a cosmological model. If eff88ca458c0ba299aeb219214f4d0a5.gif then the proper density goes to 55ac65fee4cc530f41ae7a0da1424db1.gif which implies a breakdown in the presence of a singular region within this non-space. In other words, it can be argued for a universe, the disappearance of space itself is unthinkable. Making time disappear is another matter and one completely acceptable. The thing we must keep in mind however is that the equation


e8184b923baeaa905efcf5e3e611e4b0.gif


satisfies the matter-dominated region of the universe. If we really where to make the radius go to zero, with neglecting the range of density to infinite size, we still have the problem of an environment application, it wasn't until 100,000 give or take (according to Susskind) that our universe first appeared to have matter. In later work when investigating Pensrose, he concluded for me a finding I too independently came to, that if matter fields acd0b9a53431f92783e0597d54d13fc9.gif where to vanish in the universe, time ceases to exist. Because matter is in fact emergent, especially under the Wheeler model of Geometrogenesis, matter isn't and must not be fundamental, meaning the equation I derived


e06a7b67e55b99a1df8eebf657ef6fe3.gif


Satisfies the low energy range and emergent geometry with matter... and most of all, time itself. I can prove in a quantum approach how matter is ''given'' time, by finding a relationship between the zitter motion of particle clocks and with local gravity. To show how time emerged when matter is considered, we begin with an equation which is in the strong gravity range using the gravitational fine structure and a timeless action:



03387009a38a7d8beb1a271e1d6df2ce.gif


15367621ae57d148c4a85d589c62e879.gif


We know this because of Maurapitus' principle


839e7ad63cb1c796d5748afe374a23e2.gif


fe7cd034a275cff3e76ada7fc5869ee4.gif


You can find an energy


99c43be552ef74afcaa44ef6d4b74470.gif


Our generalized coordinate 4d33fb4e487aa85e4c53565979df6979.gif has absorbed the time term. You find the clock to matter by distributing a frequency


e672b52dfb9732001d3ce02f75a1cf21.gif


The mass term requires a coefficient: 27c84b3a114c6ea1525025fe30ff0703.gif to become a frequency term itself. This would imply a relativistic change in the wavelength 7b28403f88f2443a1e7901e79b6c927b.gif since frequency and wavelength are related


19074180984cabcbb8f5ee90b7dabd89.gif


303ba50e6df508fd79b4bdca2f358a32.gif


distributing the coefficient we have


3af6da3610ec61c2cf8c2ddf2120fdc5.gif


This gives time to matter! The equation simplifies to


93dd68455a5593571928870607693254.gif


072a5d910f0bb87f5fc36944ba6dc6ca.gif


where c9faf6ead2cd2c2187bd943488de1d0a.gif is the gravitational parameter 64f3bd1741ab8d6ba545a1ae09bb8728.gif. To finish off, we return to my equation of cosmology in the low energy range


9e83b1a6b5135bc934a0617574cf8b01.gif


The term of mass over length is in fact a reciprocal of the linear density expression


e5840886cef387a75803c7d0e6264cc4.gif


Before I go, there are some interesting things we can think upon. A dominated matter universe would have a relation allowed


06ad345295532f40fbb32f9e22bc3045.gif


Notice we can make


acc808d58ecbb0be61bfc14b46fcca54.gif


Is the same LHS expression for the equation


4f5f3331ff87e9ec257d940958d78598.gif for equation


e06a7b67e55b99a1df8eebf657ef6fe3.gif

except for a factor of dfcf28d0734569a6a693bc8194de62bf.gif.
« Last Edit: 20/01/2015 16:48:52 by Koki »


 

Offline Koki

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The latex is a bit sensitive here, I will give you another link to see the equations a bit more clearly and some of them more correctly

newbielink:http://www.physicsdiscussionforum.org/post6906.html#p6906 [nonactive]
 

Offline PmbPhy

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Quote from: Kok
First read http://www.as.utexas.edu/astronomy/education/spring05/komatsu/lecture15.pdf

The Gaussian curvature for a 3-sphere system with a proper density is actually identified with the square of the reciprocal of the length ee5e5c003694e7cd5ae404923c665edb.gif


45cefa565ff9691ea0e915f670b7a1c2.gif
Welcome to the forum! :)

Were did that relationship come from? I can't make heads or tails out of the rest because it makes no sense. I also don't see what Gaussian curvature has to do with Gaussian curvature. It's Riemann curvature that pertains to space and spacetime.

By the way. It's a bad idea to expect members to read a paper that long.
 

Offline Koki

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Hi!


It is derived from a scale length due to a proper density. You obtain it by related a wavelength of reciprocal 2 with the dimensions given.

You said ''It's Riemann curvature that pertains to space and spacetime.''


Yes under the Minkowskian four dimensional symmetry of the theory. But there is now more evidence suggesting that there is no fundamental four symmetry, instead Machian relativity agrees more with General Relativity than Minkowski relativity does with the general. A clear example of this is because General relativity doesn't have a fundamental clock - at least not in any high energy origin range where no matter fields existed. General relativity uses diffeomorphisms to explain the new definition of ''time'' if one can be bold enough to call it that. As Mach himself said, ''Time is an abstraction derived from the changes of things,'' so space-time is likely faulty as unification. Dirac also held this position.
 

Offline JohnDuffield

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Hi Geo. Sorry I've not replied at length. Can I just point out Preliminaries on Baez? See this:

"Similarly, in general relativity gravity is not really a 'force', but just a manifestation of the curvature of spacetime. Note: not the curvature of space, but of spacetime. The distinction is crucial".

Also see Einstein and this and this. Your pencil falls down because spacetime is "tilted" in the room you're in. The spacetime isn't curved, and nor is the space. Instead the space is inhomogeneous.
 

Offline yor_on

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Relativity has a very simple clock. It's related to you local measurement of a 'light speed'. Split that measurement in even chunks and you come to a clock. Wheter it breaks down at Planck scale I don't know, but it's still there, locally measured.
 

Offline yor_on

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And if you think that you can take some 'average' of some 'common universe' defining it , you just lost a constant, called the speed of light in a (perfect) vacuum.
 

Offline yor_on

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My point is that Planck scale is a try for unifying. It that is incorrect you have a 'smooth' universe, if it is correct we have a 'pixilated' universe, or consisting of 'quanta' if you like. But that only means as far as we can measure, or assume. It depends on how you think of 'backgrounds' too. Is that needed? Or can 'quanta' create it?
 

Offline yor_on

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In the end, in what way do you consider it acceptable to ignore time? From personal experience? (I can go with that naively, doubt I'll ever be a grown up :)
 

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