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Old 19th November 2009, 09:21 AM   #1
common
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Looking for feedback

Wanted: any research / reference / web blogs / ofeering analysis for or against or neutral the following scenario:



universe is in state of galaxy/galaxy clusters with space between them, space of which its metric is expanding at an accelerated rate, which expansion is not noticed (not occuring) localy within the galaxy clusters, which such galaxy clusters experience this expansion as if each were in the "center" and all others were moving away from it, wich expanding metric is responsible for a particular red shift of electromagnetic waves (light) passing thru it.



There are no known "bubbles" around galaxy clusters that would prevent forces from acting upon its individual bodies of mass



Each body of mass as a member of the galaxy cluster experiences the accl. exp. metric from all directions, although only from non local origins, namely the entire universe except anything within its own galaxy cluster;



relatively, each body of mass in any given galaxy "experiences" "acceleration" in all directions, but does not experience change in distance in any one direction; however this acceleration is expresses by a contraction in the space metric in a field surrounding the body.



The universe is homogonous and isotropic; notwithstanding trivial irregularities, all bodies of mass in each galaxy cluster are in a state of relative equiforce regarding the univesal acceleration, modulo fast moving masses;



Locally, if a small mass wanders close to a much larger mass the equiforce position of each become unbalance and, as the two bodies are local (ie not part of the universal expansion) then the rest of the universe beyond their locality will "treat" them as one mass in that - as the "force" is equal from all directions, one possible outcome would be that the new "center of force" which the 2 masses will now share, will be a location in space between the centers of the 2 bodies that is a representation their respective inertias' - hence the large body will barely move while the small one will "move towards the large body" Similar smaller masses of all values will move toward the large body at the same rate in change of distance due to the equivalancy priciple.



Equally true, and relatively speaking, the above process is described and understood as a field of compressed metric surrounding the body caused by an equal and opposite reaction, in all directions, to universal accelerating expanding space metric, whereby, just as in classic acceleration which creates a "false" force in the opposite direction, such "false" force will maintain a static value of metric compression as a result of an opposite continual acceleratiing metric expansion.

All smaller masses wandering into the field with a previously established momentum, will necesarily follow the path of least distance which is toward the large mass. All smaller masses of varying value that come into large mass' field of compressed metric, will move thru the field at equal rate of chane in distance because, as the "attraction" is a result of the smaller masses moving from a larger space metric to a smaller metric, only distance is at play. Therefore due to classic laws of momentum and inertia, each will convert its energies into kinetic respective to its mass, resulting in equal acceleration rates (another way to know equivelancy principle?)





OK, NOT A THEORY FOR DEBATE. IT IS MOST ASSUREDLY WRONG. VERY LIKELY JUST BABBLE. That is why I am researching it, and the only way to hunt down resources is to explain what you are looking for. Thats it.





Any suggestions as to search words I should be useing?



Thank you.
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Old 20th November 2009, 08:15 AM   #2
Thabiguy
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Hi and welcome to the forum.

What you describe is a bit confusing. Some parts of it are reminiscent of standard physics (like the Big Bang theory), parts of it are unusual - but it's difficult to tell whether that's because it's improperly expressed or because there are actual differences, and which of these differences are important.

Why don't you start by simply telling us how the scenario differs from standard models and pointing out its key features, instead of attempting to describe it in full.

Also, where does this scenario come from? Did you hear it somewhere? Where?

Or is it a creation of your own? In that case, you most likely won't find any research/references/blogs/analyses of it.

Last edited by Thabiguy; 20th November 2009 at 08:23 AM.
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Old 20th November 2009, 08:23 AM   #3
Reality Check
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Originally Posted by common View Post
Any suggestions as to search words I should be useing?
Thank you.
Wikipedia is the answer.
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Old 20th November 2009, 09:06 AM   #4
common
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Originally Posted by Thabiguy View Post
Hi and welcome to the forum.

What you describe is a bit confusing. Some parts of it are reminiscent of standard physics (like the Big Bang theory), parts of it are unusual - but it's difficult to tell whether that's because it's improperly expressed or because there are actual differences, and which of these differences are important.

Why don't you start by simply telling us how the scenario differs from standard models and pointing out its key features, instead of attempting to describe it in full.

Also, where does this scenario come from? Did you hear it somewhere? Where?

Or is it a creation of your own? In that case, you most likely won't find any research/references/blogs/analyses of it.
Thank you for the reply. I will put something together.
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Old 20th November 2009, 10:29 AM   #5
Michael Mozina
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Originally Posted by common View Post
Wanted: any research / reference / web blogs / ofeering analysis for or against or neutral the following scenario:

universe is in state of galaxy/galaxy clusters with space between them, space of which its metric is expanding at an accelerated rate, which expansion is not noticed (not occuring) localy within the galaxy clusters, which such galaxy clusters experience this expansion as if each were in the "center" and all others were moving away from it, wich expanding metric is responsible for a particular red shift of electromagnetic waves (light) passing thru it.
http://arxiv.org/abs/astro-ph/0601171
http://arxiv.org/find/astro-ph/1/au:.../0/1/0/all/0/1

Michal has written extensively about this topic as a critic of the notion of "space" expansion.
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Old 20th November 2009, 08:16 PM   #6
Reality Check
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Originally Posted by Michael Mozina View Post
http://arxiv.org/abs/astro-ph/0601171
http://arxiv.org/find/astro-ph/1/au:.../0/1/0/all/0/1

Michal has written extensively about this topic as a critic of the notion of "space" expansion.
The first paper is interesting. Basically in an empty universe, cosmological redshift is there simply a relativistic Doppler shift.
A pity that we do not live in an empty universe. It would make things so much simpler !
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Old 30th November 2009, 11:04 AM   #7
common
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Originally Posted by Thabiguy View Post
Hi and welcome to the forum.

What you describe is a bit confusing. Some parts of it are reminiscent of standard physics (like the Big Bang theory), parts of it are unusual - but it's difficult to tell whether that's because it's improperly expressed or because there are actual differences, and which of these differences are important.

Why don't you start by simply telling us how the scenario differs from standard models and pointing out its key features, instead of attempting to describe it in full.

Also, where does this scenario come from? Did you hear it somewhere? Where?

Or is it a creation of your own? In that case, you most likely won't find any research/references/blogs/analyses of it.

key features:

1) model implements most of current mainstream view of accelerated expansion of universe including "expanding metric".......except:

where mainstream discounts presence of "normal" behavior of acceleration (because space is expanding rather than actual "movement" of galaxies), this model suggests alternative behavior of acceleraton that is more in harmony with accepted concept of expanding metric, i.e..........an opposing contacted metric (gravity).

2) model treats gravity as a neccecary behavior in an accelerating expansion of universe. Model agrees with Einstein in that aceleration and gravity appear to be of kin.

3) model assumes homogenous, isotropic universe

4) model does not violate Mach

5) model treats galaxies/clusters each as individual "bodies" - and assumes that all bodies within a galaxy/cluster behave (are affected) the same as is its home galaxy/cluster.

6) model assumes that as an equal an opposite partner to the acceleating expanding metric of the space between galaxies/clusters, that each body within a galaxy experiences metric contraction equally from all directions towards its "center of contracted metric", gravity.

7) local gravity is a result of inertial properties of bodies in relation to there location within a galaxy - which such galaxy is being affected upon by universal accelerating metric expansion as if it were an individual body made of smaller parts.
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Old 30th November 2009, 11:44 AM   #8
Reality Check
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What model?
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Old 30th November 2009, 12:24 PM   #9
common
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Originally Posted by Reality Check View Post
What model?
appologies. i should have said "group of ideas" that form the scenario in the OP, about which i am curious seeking information.
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Old 30th November 2009, 12:41 PM   #10
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There is no understandable group of ideas in the OP
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Old 30th November 2009, 12:52 PM   #11
common
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Originally Posted by Reality Check View Post
There is no understandable group of ideas in the OP
I don't doubt it. 9 x out of 10 misunderstanding stems from the one presenting message. Me

I will clarify and post again. Thank you for your candor.
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Old 30th November 2009, 03:07 PM   #12
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Scenario:

Assumes current view of accelerating expansion of galaxy/ galaxy clusters (hereinafter "galaxies") throughout the universe is accurate in that:

Each galaxy perceives all other galaxies are accelerating away from it, and so, perceives itself at the center of this expansion.

Each galaxy perceives itself as accelerating away from all other galaxies in the universe.

There is no local expansion between bodies within a galaxy.

It is the space metric between galaxies that is actually expanding, and galaxies should not be understood as accelerating away from eachother in the classic sense of objects accelerating away from eachother.

A particular type of doppler red shift is caused by the acclerating expansion of the space metric between galaxies.

______________

While a galaxy is made of many things, for simplicity and clarity, this scenario uses only bodies such as the size of our sun, the earth, asteroids, and various moons we know of in our solar system.

A galaxy is comprised of bodies.

If a galaxy is in a state of acceleration, then it's individual bodies are likewise each, independently but in relative uniformity, accelerating at same rate in same direction
.
Just as each galaxy experiences itself as being at the center of expansion of the universe, so does each of it's bodies. While there is a large distance between bodies at opposite ends of a galaxy, compared to each bodies' distance from far reaches of the universe, their local distance from eachother is trivial by comparison* - and each is at the relative center of the universe.

*except that any such body's distance from true "local center" of galaxy may offer insight as to why outer tails of galaxy spirals are not "more spiraled" (layman's term) in proportion to predicted overall gavity of the galaxy - which I am not exploring further here.

Therefore, each body is accelerating away from all other bodies in the universe, in all directions. (notwithstanding other local bodies).

Because a body does not experience more acceleration in any one particular direction ,then it experiences the results of equal acceleration from/in all directions. And so, as opposed to imagining a body accelerating in all directions at once (a real mind blower) , perhaps this omnidirectional acceleration is manifested as omnidirectional contraction of the space surrounding the body.

Such a relationship may explain why clocks close to a massive body will be slower than clocks further away, in that: a clock posesses a certain quantity of energy in order to operate; a clock operating in a contracted metric will require less kinetic energy to operate under its design than the same design clock operating with same overall energy in non-compressed metric; therefore a clock operating in compressed metric will express less (slower) energy thru kinetic.

Furthermore, omnidirectional contraction with a constant value seems a harmonious partner with omnidirectional accelerating expansion : similar to Einsteins explanation of a coordinate system attached to a rope which is pulling it in one direction with constant acceleration, while objects inside system experience a constant "force", and hence motion, in the opposite direction - such motion of all objects at the same speed, regardless of mass.

Local attraction of bodies are a necessary result of this arrangement. I can offer explanation if interested.

Hope this clarifies the scenario I am looking into. It is not a proposal, just an arrangement of ideas I am looking into. I do not claim to have figured anything out. Like most "different" ideas, this one is likely full of holes. I am simply looking for those holes.
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Old 30th November 2009, 03:41 PM   #13
Reality Check
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Originally Posted by common View Post
Scenario:
...
The scenario does not clarify much.
General comment: The expansion of the universe does mean that the distance between all bodies increases. But there is also gravity. It stops this expansion from being measurable until you get to big bodies that are far apart, i.e. galaxies.

Originally Posted by common View Post
While a galaxy is made of many things, for simplicity and clarity, this scenario uses only bodies such as the size of our sun, the earth, asteroids, and various moons we know of in our solar system.
You may as well ignore the "the earth, asteroids, and various moons we know of in our solar system" on galactic scales.

Originally Posted by common View Post
If a galaxy is in a state of acceleration, then it's individual bodies are likewise each, independently but in relative uniformity, accelerating at same rate in same direction.
No. Stars obit in galaxies. They have a component of velocity that is the same as the velocity of the galaxy. Their acceleration though is due to their orbit (like all orbiting bodies).

Originally Posted by common View Post
Just as each galaxy experiences itself as being at the center of expansion of the universe, so does each of it's bodies. While there is a large distance between bodies at opposite ends of a galaxy, compared to each bodies' distance from far reaches of the universe, their local distance from eachother is trivial by comparison* - and each is at the relative center of the universe.
No - see above.

Originally Posted by common View Post
*except that any such body's distance from true "local center" of galaxy may offer insight as to why outer tails of galaxy spirals are not "more spiraled" (layman's term) in proportion to predicted overall gavity of the galaxy - which I am not exploring further here.
Just as well since spiral arms are not what you think they are (physical arms). They are regions of slightly more densely packed stars in galaxies that hove a high proportion of young stars and so are brighter then the rest of the galaxy.

Originally Posted by common View Post
Therefore, each body is accelerating away from all other bodies in the universe, in all directions. (notwithstanding other local bodies).
No 'Thus" needed. This is standard cosmology.

Originally Posted by common View Post
Because a body does not experience more acceleration in any one particular direction ,then it experiences the results of equal acceleration from/in all directions. And so, as opposed to imagining a body accelerating in all directions at once (a real mind blower) , perhaps this omnidirectional acceleration is manifested as omnidirectional contraction of the space surrounding the body.
No. The universe is expanding not contracting.

Originally Posted by common View Post
Such a relationship may explain why clocks close to a massive body will be slower than clocks further away, in that: a clock posesses a certain quantity of energy in order to operate; a clock operating in a contracted metric will require less kinetic energy to operate under its design than the same design clock operating with same overall energy in non-compressed metric; therefore a clock operating in compressed metric will express less (slower) energy thru kinetic.
No. General relativity explains why clocks close to a massive body will be slower than clocks further away using the curvature of spacetime.
There are plenty of people who try this compression of spacetime idea but the idea just does not work: Curved space is not contracted space.

Originally Posted by common View Post
Furthermore, omnidirectional contraction with a constant value seems a harmonious partner with omnidirectional accelerating expansion : similar to Einsteins explanation of a coordinate system attached to a rope which is pulling it in one direction with constant acceleration, while objects inside system experience a constant "force", and hence motion, in the opposite direction - such motion of all objects at the same speed, regardless of mass.
No. Special and general relativity explains relativistic contraction.
Coordinate systems are never attached to ropes.

Originally Posted by common View Post
Local attraction of bodies are a necessary result of this arrangement. I can offer explanation if interested.
Any one can "expalin" thngs, e.g. pixes do it!

Originally Posted by common View Post
Hope this clarifies the scenario I am looking into. It is not a proposal, just an arrangement of ideas I am looking into. I do not claim to have figured anything out. Like most "different" ideas, this one is likely full of holes. I am simply looking for those holes.
The holes are that
  • You are just trying to explain what has already been explained.
  • You are not expressing this mathematically and so have little chance of converting your vague ideas into actual hypotheses.
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Old 30th November 2009, 05:16 PM   #14
common
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Reality Check:

Thank you for the feedback. I am sure in this case I made myself clear I am looking for "any research / reference / web blogs / offering analysis for or against or neutral the following scenario" I was also clear I am a layman looking for learned analysis rather than responses in the form of raw opinion, and, that I am not in a position to present or defend these ideas.

Rather I am "looking into why or why not". I am quite sure I presented my role clearly.

You have presented yourself as an expert on these matters. However, you offered conclusions to these "ideas" upon your opening statement that "The scenario does not clarify much." However poorly I, admitedly, presented the scenario, I can give your responses only as much credit as a source who lacks clarity of subjects upon which it opines.

I thank you for the dialog, but respectfully dismiss your reply, but I will certainly research the subject matter offered by the same. Thank you.

Further, I am unarmed for a learned argument on these subjects and so repectfully decline the same.

Does anyone else have any references to learned research on these matters? Thank you.
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Old 30th November 2009, 06:18 PM   #15
ben m
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Hello common,

RC's responses are quick but not un-learned. I don't think they always quite hit the nail on the head, but it would be just as easy for you to respond as to dismiss the whole thing.

Your idea seems to intend to be an alternative to General Relativity. Physicists have seen a very large number of such proposals go by, and there are some reasonably-well-known subtleties. For example, it's very easy to casually say "space is contracted" but very hard (or, at least, requires exceptional attention to detail) to say exactly what that means---what is smaller than what? According to a ruler placed where? Where does an equation-of-motion care about this contractedness (i.e. how do objects fall through this space?)

Now, I have never seen a terribly useful discussion of such ideas that relied on words. It needs to come down to math. In most cases, descriptions of theories like yours cannot be turned into math, because usually they're fundamentally not theories-of-spacetime at all, they're just visual paintings of grids and trajectories and rubber sheets. (I wish to distinguish this from "it would work if I could get a math expert to sit down and work out all the details.")

Anyway, in terms of "learned research", it's impossible to make progress on "The Theory that Overturns Theory X" without being an expert on Theory X. As you are trying to modify/replace/? General Relativity, you need to understand GR itself first. The old standard graduate textbook is Misner, Thorne, and Wheeler, "Gravitation", but there are now several others as well as (e.g.) online video lectures from MIT.

Almost all "learned discussion" of cosmological spacetime issues is going to rely on GR math and language one way or another. Even people looking for errors, variants, etc., in GR are going to describe those errors by reference to GR and using GR-like language. So: learning GR will open up these discussions to you.
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Old 30th November 2009, 06:24 PM   #16
Reality Check
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Originally Posted by common View Post
Reality Check:

Thank you for the feedback. I am sure in this case I made myself clear I am looking for "any research / reference / web blogs / offering analysis for or against or neutral the following scenario" I was also clear I am a layman looking for learned analysis rather than responses in the form of raw opinion, and, that I am not in a position to present or defend these ideas.
Your scenerio is so badly stated that I had to guess at what you stated. Thus you will not be able to find any "research / reference / web blogs" addressinf these matters.

Originally Posted by common View Post
You have presented yourself as an expert on these matters. However, you offered conclusions to these "ideas" upon your opening statement that "The scenario does not clarify much." However poorly I, admitedly, presented the scenario, I can give your responses only as much credit as a source who lacks clarity of subjects upon which it opines.
I have not presented myself as an expert. I have presented myself as a member of this forum.
I do have a good general knowledge of physics gained from a degree in solid state physics. That makes it clear that what little I can extract from your scenario is wrong.


For example: "contracted metric" explains gravitational time dilation is obviously wrong because
  • As far as I know there is no such thing as a "compressed metric".
    A metric is an extension of the Euclidean concept of length to spacetime (in GR). More generally it is a mapping between elements of a space that defines a distance between the elements.
    Metrics are not compressed or curved. It is the space that they describe that has the property of being compressed or curved.
  • Gravitational time dilation is caused by a curved spacetime.
Originally Posted by common View Post
I thank you for the dialog, but respectfully dismiss your reply, but I will certainly research the subject matter offered by the same. Thank you.

Further, I am unarmed for a learned argument on these subjects and so repectfully decline the same.

Does anyone else have any references to learned research on these matters? Thank you.
You first have to describe "these matters" in such a way that people can understand what you are talking about before they can find any learned research on it.

For example: "similar to Einsteins explanation of a coordinate system attached to a rope which is pulling it in one direction with constant acceleration, while objects inside system experience a constant "force", and hence motion, in the opposite direction - such motion of all objects at the same speed, regardless of mass."
Can you give a citation to where this explanation by Einstein came from?

ETA
It sounds a little like the equivalance principle:
Quote:
Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is actually the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.
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Old 30th November 2009, 06:30 PM   #17
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Originally Posted by common View Post
Does anyone else have any references to learned research on these matters? Thank you.
Concerning the cosmological aspect of things, I suggest you take a look at the Talk Origins website on Evidence for the Big Bang.
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Old 1st December 2009, 06:23 AM   #18
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Hi Common, I will try as a layman i may be able to question your viewpoint in a fashion closer to your level of understanding. I do have to warn you however, you might be restating what Bjarne is already having a hard time stating clearly.
Originally Posted by common View Post
Scenario:

Assumes current view of accelerating expansion of galaxy/ galaxy clusters (hereinafter "galaxies") throughout the universe is accurate in that:
Okay first off you have to understand the data.

the data is that there is an apparent relationshop between distance and redshift reffered to as the Hubble constant. And there is very good reason to feel that it is accurate.

There is very little reason to debate it.

the universe does appear to have this expanion.
Quote:
Each galaxy perceives all other galaxies are accelerating away from it, and so, perceives itself at the center of this expansion.

Each galaxy perceives itself as accelerating away from all other galaxies in the universe.
Not really, the distance is the crucial factor here, in the local group the Huble constant value is low.
HC='160 km/sec per million-light-years'
source

So if Andromeda Galaxy is 2.5 million light years away so 2.5 x 160 km/sec = 320 km/sec but Andromeda is approaching us at 138 km/sec as well so the expansion is very low in astronomical terms. 152 km/sec
source
Quote:
There is no local expansion between bodies within a galaxy.
There is but given the distances and the speed involved it would be very very very low.

.00086 km/sec for Alpha centauri in example.
Quote:

It is the space metric between galaxies that is actually expanding, and galaxies should not be understood as accelerating away from eachother in the classic sense of objects accelerating away from eachother.
Well yes and no. It is easier if we don't expect the universe to meet our expectations and just accept it for what it is. The space itself is currently believed to be expanding or stretching, it makes no difference unless you want to cling to earth bound notions.
Quote:

A particular type of doppler red shift is caused by the acclerating expansion of the space metric between galaxies.

______________

While a galaxy is made of many things, for simplicity and clarity, this scenario uses only bodies such as the size of our sun, the earth, asteroids, and various moons we know of in our solar system.

A galaxy is comprised of bodies.

If a galaxy is in a state of acceleration, then it's individual bodies are likewise each, independently but in relative uniformity, accelerating at same rate in same direction
.
Sort of, the distances for the Hubble constant to be appreciable are rather large, even in terms of a galaxy.
Our milky way is 100,000 ly across source, so at 1/10 of the Hubble constant in scale it is going to have a relative expansion across the galaxy (end to end) of 32 km/sec.
Quote:
Just as each galaxy experiences itself as being at the center of expansion of the universe, so does each of it's bodies. While there is a large distance between bodies at opposite ends of a galaxy, compared to each bodies' distance from far reaches of the universe, their local distance from eachother is trivial by comparison* - and each is at the relative center of the universe.
Not that they are the center of the universe at all, that is a false conclusion right there. But at the center of an appearance of expansion.
Quote:

*except that any such body's distance from true "local center" of galaxy may offer insight as to why outer tails of galaxy spirals are not "more spiraled" (layman's term) in proportion to predicted overall gavity of the galaxy - which I am not exploring further here.
I would avoid that, it is common gravitational motion and there is a huge variety in galaxies.
Quote:

Therefore, each body is accelerating away from all other bodies in the universe, in all directions. (notwithstanding other local bodies).
Not really in the current theory there is an apparent acceleration due to the expansion of the universe, but the effect is the same.
Quote:
Because a body does not experience more acceleration in any one particular direction ,then it experiences the results of equal acceleration from/in all directions. And so, as opposed to imagining a body accelerating in all directions at once (a real mind blower) , perhaps this omnidirectional acceleration is manifested as omnidirectional contraction of the space surrounding the body.
Well, I think I see what you are trying to say here, and while such symmetries are often useful, this one will not work out quite as well because then all of the universe would have already crunched back in and stayed crunched. If a balloon starts to loose the air inside, then it will collapse, but it can not collapse indefinitely.

I understand your concept but I don’t think it will translate well, in one sense yes the opposite of expansion is contraction, so if all bodies are approaching us at 320 km/sec per million ly, it would produce a similar redshift. However in this case because of the passage of time you would collapse the milky way galaxy in about 937 million year (if I did the math right), so that would be a problem.
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Such a relationship may explain why clocks close to a massive body will be slower than clocks further away, in that: a clock posesses a certain quantity of energy in order to operate; a clock operating in a contracted metric will require less kinetic energy to operate under its design than the same design clock operating with same overall energy in non-compressed metric; therefore a clock operating in compressed metric will express less (slower) energy thru kinetic.
Sorry if it takes less energy then the clock would express time more quickly, in a mechanical clock at any rate. The force of the spring would be stronger and with out the governor wheels it would therefore move the hands faster.
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Furthermore, omnidirectional contraction with a constant value seems a harmonious partner with omnidirectional accelerating expansion : similar to Einsteins explanation of a coordinate system attached to a rope which is pulling it in one direction with constant acceleration, while objects inside system experience a constant "force", and hence motion, in the opposite direction - such motion of all objects at the same speed, regardless of mass.

Local attraction of bodies are a necessary result of this arrangement. I can offer explanation if interested.
Nope and again for the same reason, if a body comes in with energy x at angle whatever and needs less energy then it will move faster.

If I understand you correctly.
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Hope this clarifies the scenario I am looking into. It is not a proposal, just an arrangement of ideas I am looking into. I do not claim to have figured anything out. Like most "different" ideas, this one is likely full of holes. I am simply looking for those holes.
Well the issue is that not all symmetries have useful meaning.
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Old 1st December 2009, 08:41 AM   #19
common
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Awesome replies from all. Extremely usefull. I thank you each for your time and consideration. My appologies if I came accross as flippant at any time.

This is a good board.
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