If space time began as a singularity it would have been an hypersphere or a 4 sphere formed by gravity. At Time Zero time would start off slow in the extreme of gravity. When space expanded its gravity would become diminished. As gravity weakens space (the hypersurface) would become more flat and time would speed up. I think that inflation rapidly accelerated time soon after time zero.
How does the Big Bang escape the power of its own gravity? There must be a force, I call it inflation, that overcomes the gravity of the Big Bang. What is the escape velocity of the universe at time zero? Perhaps space began first and then matter fluctuated into existence spread out such that gravity was not infinite allowing the universe to unfold. How the universe was created is important.
QUOTE (Nick+May 29 2006, 08:37 PM)
How does the Big Bang escape the power of its own gravity? There must be a force, I call it inflation, that overcomes the gravity of the Big Bang. What is the escape velocity of the universe at time zero?
3 dimensional space is infinite from an inside perspective. There is no center to the universe in 3-D nor was there one if/when the Big Bang occured.
Here are a few things to consider:
1) 3-D space would "wrap around" so there would be no central 3-D location for gravitational forces. Gravitational forces can separate objects as well. Simply being in a deep gravity alone doesn't create a force that pulls (or pushes) everything together. It's the gradient that's more important and there was assumed to be very little of any gradient initially so gravity was pulling more or less equally in 3-D space in all directions.
2) Do we know that gravity is attractive in a 4th dimension as well?
3) Spacial distances are relative to other distances. The universe could be collapsing continually in 3-D and making observations from distant galaxies look like their expanding simply because we're using a smaller ruler than at the time these interactions ocured. We keep finding smaller and smaller particles and no hard core to matter. So what's the correct scale for matter? The Big Bang theory already states that matter didn't exist initially as it does now (there were not atoms or electrons etc. initially) ... so we might have already "collapsed" past a few layers of forces and matter continually exists and interacts with other matter in some manner.
4) Even if we took an older view of black holes as block spots with fossilized gravitational fields left behind disconnected from this universe, that implies gravity is stagnant and fixed, not a propogating force. By this view it seems the universe would have a hard time collapsing into a gravitational singularity as one could never form or alternately they always existed and then nothing should have been able to escape from them in the first place. I'm just throwing out some of the paradoxes and conflicts to the black hole idea and a black hole is a 3-D structure, not a 4-D one.
Anyway, my opinion is simply that as spacial distances are decreased, interactions occur more quickly and that subjective perceptions of time inside a compressed space are still made in a relative fashion that would be unable to determine what the "correct" scaling for the rates of these interactions or spacial distances were.
We haven't found any fundamental unit of mass and from the track record there seems little evidence (and surely no proof yet) that any exists. Instead it seems likely that it's infinitely divisible and even if we did find something that appeared to be finally the fundamental unit of matter, there would still be no way of being certain (as far as I can tell) that with enough scrutiny, further details couldn't emerge.
So there really isn't any absolute scale we can use to measure how large the universe is ... it's whatever size it is and if some view makes it seem too small or too large how could we know without some other universe to compare it too.
3 dimensional space is infinite from an inside perspective. There is no center to the universe in 3-D nor was there one if/when the Big Bang occured.
Here are a few things to consider:
1) 3-D space would "wrap around" so there would be no central 3-D location for gravitational forces. Gravitational forces can separate objects as well. Simply being in a deep gravity alone doesn't create a force that pulls (or pushes) everything together. It's the gradient that's more important and there was assumed to be very little of any gradient initially so gravity was pulling more or less equally in 3-D space in all directions.
2) Do we know that gravity is attractive in a 4th dimension as well?
3) Spacial distances are relative to other distances. The universe could be collapsing continually in 3-D and making observations from distant galaxies look like their expanding simply because we're using a smaller ruler than at the time these interactions ocured. We keep finding smaller and smaller particles and no hard core to matter. So what's the correct scale for matter? The Big Bang theory already states that matter didn't exist initially as it does now (there were not atoms or electrons etc. initially) ... so we might have already "collapsed" past a few layers of forces and matter continually exists and interacts with other matter in some manner.
4) Even if we took an older view of black holes as block spots with fossilized gravitational fields left behind disconnected from this universe, that implies gravity is stagnant and fixed, not a propogating force. By this view it seems the universe would have a hard time collapsing into a gravitational singularity as one could never form or alternately they always existed and then nothing should have been able to escape from them in the first place. I'm just throwing out some of the paradoxes and conflicts to the black hole idea and a black hole is a 3-D structure, not a 4-D one.
Anyway, my opinion is simply that as spacial distances are decreased, interactions occur more quickly and that subjective perceptions of time inside a compressed space are still made in a relative fashion that would be unable to determine what the "correct" scaling for the rates of these interactions or spacial distances were.
We haven't found any fundamental unit of mass and from the track record there seems little evidence (and surely no proof yet) that any exists. Instead it seems likely that it's infinitely divisible and even if we did find something that appeared to be finally the fundamental unit of matter, there would still be no way of being certain (as far as I can tell) that with enough scrutiny, further details couldn't emerge.
So there really isn't any absolute scale we can use to measure how large the universe is ... it's whatever size it is and if some view makes it seem too small or too large how could we know without some other universe to compare it too.
QUOTE (StevenA+May 31 2006, 12:23 AM)
QUOTE (Nick+May 29 2006, 08:37 PM)
How does the Big Bang escape the power of its own gravity? There must be a force, I call it inflation, that overcomes the gravity of the Big Bang. What is the escape velocity of the universe at time zero?
3 dimensional space is infinite from an inside perspective. There is no center to the universe in 3-D nor was there one if/when the Big Bang occured.
Here are a few things to consider:
1) 3-D space would "wrap around" so there would be no central 3-D location for gravitational forces.
Einstein talked of the universe being finite yet unbounded. That it is closed. What he could have said is that the universe curves back on itself in the 4th dimension in the form of the surface of an expanding hypersphere or 4 dimensional sphere. If this wasn't true then the universe would have a boundary where space ends and NO SPACE begins. Which is of course absurd.
As the hypersphere expands we move away from the center of the fourth dimension which is the originating dimension.
3 dimensional space is infinite from an inside perspective. There is no center to the universe in 3-D nor was there one if/when the Big Bang occured.
Here are a few things to consider:
1) 3-D space would "wrap around" so there would be no central 3-D location for gravitational forces.
Einstein talked of the universe being finite yet unbounded. That it is closed. What he could have said is that the universe curves back on itself in the 4th dimension in the form of the surface of an expanding hypersphere or 4 dimensional sphere. If this wasn't true then the universe would have a boundary where space ends and NO SPACE begins. Which is of course absurd.
As the hypersphere expands we move away from the center of the fourth dimension which is the originating dimension.
QUOTE (Nick+May 28 2006, 10:33 PM)
...at Time Zero time would start off slow in the extreme of gravity...
Such stance depends on the role of observer (i.e. the fact, whether is formed by the vacuum or not), but from the inner observer perspective it's correct (compare to Aether Wave theory model of increasing Universe mass/energy density).
Such stance depends on the role of observer (i.e. the fact, whether is formed by the vacuum or not), but from the inner observer perspective it's correct (compare to Aether Wave theory model of increasing Universe mass/energy density).
The Big Bang's time depends on an observing frame? Yiou've got to be kidding.
QUOTE (Nick+May 31 2006, 10:46 PM)
The Big Bang's time depends on an observing frame? You've got to be kidding.
Everything in recursive wave concept depends on the role of observer. For example, I can say easily, our Universe expands by the same way, as it makes itself more dense. Surprisingly enough, both these stances are solely equivalent and if you'll ignore it, you'll never rid of inconsistencies in thinking. Did you ever heard something about imaginary time? Did you ever see such picture in this forum?
Please, consider our time is defined by the light spreading, but at the BigBang's time no light existed yet. When
I'll start kiddin' you, you'll recognize it soon, don't be scared.
Everything in recursive wave concept depends on the role of observer. For example, I can say easily, our Universe expands by the same way, as it makes itself more dense. Surprisingly enough, both these stances are solely equivalent and if you'll ignore it, you'll never rid of inconsistencies in thinking. Did you ever heard something about imaginary time? Did you ever see such picture in this forum?
Please, consider our time is defined by the light spreading, but at the BigBang's time no light existed yet. When
I'll start kiddin' you, you'll recognize it soon, don't be scared.
God is oberver. Who else would be around at Time Zero zeph?
QUOTE (Nick+Jun 1 2006, 03:57 AM)
God is observer. Who else would be around at Time Zero zeph?
From my point of view, the beginning of Universe is poorly conditioned math task. The evolution of Universe from quite nothing is very similar to evolution of next generation of Universe based on recursive model. We should always consider all thinkable possibilities. We can collect some relevant reasons, why our Universe should by cyclic, recursive or very unique both in time, both in context of other parallel Universes possible. This is all, what we can do now.
From my point of view, the beginning of Universe is poorly conditioned math task. The evolution of Universe from quite nothing is very similar to evolution of next generation of Universe based on recursive model. We should always consider all thinkable possibilities. We can collect some relevant reasons, why our Universe should by cyclic, recursive or very unique both in time, both in context of other parallel Universes possible. This is all, what we can do now.
Nick,
When you refer to a 3-D surface on a 4-D sphere, you're implying this sphere is perfect and uniform. If gravity caused space to effectively be contracted then not all surfaces of the spere would collapse at an identical rate and areas where matter was present would contract faster.
We know we're in an area of the universe that contains a higher density of matter than most areas so if you view things as gravity warping spacetime then our area of space would be shrinking faster and make other areas of the universe with less mass appear more expansive (or also delayed/distance areas appear similarly expanded).
So you're talking about a sphere ... but why must it have an equal radius to all parts of the surface when you yourself are questioning how that would be possible.
It may very well be that the only thing that keeps the universe from collapsing into a singularity is ... relativity (in a different sense). If you're making observations within the same space then you can't determine whether that space is shrinking or expanding except in relationship to other distances and sure enough we find that either the universe is expanding ... or more sensibly our local reference is shrinking. This would seem to require to mode of propogation for forces so as to have one space contract versus another and I'd assume it's gravitational versus EMF (this would seem to require that gravity not propogate at light speed so that the effective spaces defined by each could differ and allow for things like dark matter)
When you refer to a 3-D surface on a 4-D sphere, you're implying this sphere is perfect and uniform. If gravity caused space to effectively be contracted then not all surfaces of the spere would collapse at an identical rate and areas where matter was present would contract faster.
We know we're in an area of the universe that contains a higher density of matter than most areas so if you view things as gravity warping spacetime then our area of space would be shrinking faster and make other areas of the universe with less mass appear more expansive (or also delayed/distance areas appear similarly expanded).
So you're talking about a sphere ... but why must it have an equal radius to all parts of the surface when you yourself are questioning how that would be possible.
It may very well be that the only thing that keeps the universe from collapsing into a singularity is ... relativity (in a different sense). If you're making observations within the same space then you can't determine whether that space is shrinking or expanding except in relationship to other distances and sure enough we find that either the universe is expanding ... or more sensibly our local reference is shrinking. This would seem to require to mode of propogation for forces so as to have one space contract versus another and I'd assume it's gravitational versus EMF (this would seem to require that gravity not propogate at light speed so that the effective spaces defined by each could differ and allow for things like dark matter)
QUOTE (StevenA+Jun 1 2006, 07:09 AM)
Nick,
When you refer to a 3-D surface on a 4-D sphere, you're implying this sphere is perfect and uniform. If gravity caused space to effectively be contracted then not all surfaces of the spere would collapse at an identical rate and areas where matter was present would contract faster.
We know we're in an area of the universe that contains a higher density of matter than most areas so if you view things as gravity warping spacetime then our area of space would be shrinking faster and make other areas of the universe with less mass appear more expansive (or also delayed/distance areas appear similarly expanded).
So you're talking about a sphere ... but why must it have an equal radius to all parts of the surface when you yourself are questioning how that would be possible.
Why the radius of the sphere must remain the same is the right question. The hypersphere is expanding because the space in between the galaxies is stretching out an equal amount everywhere. That is why it remains a sphere and is not distorted.
the universe isn't collapsing under its gravity. The hypersphere expansion is the stretching out of space in between the galaxies.
When you refer to a 3-D surface on a 4-D sphere, you're implying this sphere is perfect and uniform. If gravity caused space to effectively be contracted then not all surfaces of the spere would collapse at an identical rate and areas where matter was present would contract faster.
We know we're in an area of the universe that contains a higher density of matter than most areas so if you view things as gravity warping spacetime then our area of space would be shrinking faster and make other areas of the universe with less mass appear more expansive (or also delayed/distance areas appear similarly expanded).
So you're talking about a sphere ... but why must it have an equal radius to all parts of the surface when you yourself are questioning how that would be possible.
Why the radius of the sphere must remain the same is the right question. The hypersphere is expanding because the space in between the galaxies is stretching out an equal amount everywhere. That is why it remains a sphere and is not distorted.
the universe isn't collapsing under its gravity. The hypersphere expansion is the stretching out of space in between the galaxies.
QUOTE (Nick+Jun 1 2006, 10:24 PM)
...the universe isn't collapsing under its gravity. The hypersphere expansion is the stretching out of space in between the galaxies...
If the Universe is formed by stretching space, how is it possible, it doesn't collapse at the same time?
If the Universe is formed by stretching space, how is it possible, it doesn't collapse at the same time?
I don't know. Why don't you ask the astronomers how they measure the space stretch speeding up? The universe is expanding at an increasing rate according to their measurements.
QUOTE (Nick+Jun 1 2006, 07:24 PM)
Why the radius of the sphere must remain the same is the right question. The hypersphere is expanding because the space in between the galaxies is stretching out an equal amount everywhere. That is why it remains a sphere and is not distorted.
the universe isn't collapsing under its gravity. The hypersphere expansion is the stretching out of space in between the galaxies.
Ok, I'll reword it then - why do you restrict this expansion to being equal over all of space? What evidence suggests that it's an equal expansion? Don't we see galaxies inexplicably being pulled or pushed in directions against this general expansion and hypothesize things like dark matter in order to defer the conflict?
the universe isn't collapsing under its gravity. The hypersphere expansion is the stretching out of space in between the galaxies.
Ok, I'll reword it then - why do you restrict this expansion to being equal over all of space? What evidence suggests that it's an equal expansion? Don't we see galaxies inexplicably being pulled or pushed in directions against this general expansion and hypothesize things like dark matter in order to defer the conflict?
Gravity would just move galaxies around on the surface. Can you see that? Matter can move around on the surface of the hypersphere.
QUOTE (Nick+Jun 2 2006, 02:10 AM)
Gravity would just move galaxies around on the surface. Can you see that? Matter can move around on the surface of the hypersphere.
That's possible but if the area (or volume to be more correct) of this surface can vary, what causes this and why is it necessarily uniform?
I'm not against the idea of some forms of information propogating faster than light but what would keep the expansion or contraction in one area of the universe matched to everywhere else? How can the radius be maintained equally without some rather instantaneous communication existing between everything in the universe?
If gravity creates a "warped spacetime" and gravity isn't uniformly distributed, then why wouldn't this effect be non-uniform? Wouldn't a continued local contraction make space elsewhere appear continually expanding in comparison? Wouldn't such an effect also create an appearance of distance, large galaxies orbiting too fast (just as observed) because the distance and size calculations are aged and not reflective of the actual spacial scalings at that time?
You wouldn't need some novel force to pull things apart from the Big Bang either as you could just let whatever fluctuations occur in empty space collapse on their own.
Inflation theory attempts to address the problem of space appearing to become almost instantly very large. What if the universe was already large? Measurements of distances can only be made in a relative sense. If one ruler gets smaller, another looks larger in comparison. What would differentiate between a contraction in local distances versus an overall expansion? Well if we used orbital periods as a means to determine distance scaling then we find gravity acting too strongly elsewhere and this would agree to things not being as large and distant as assumed but instead smaller and closer. If dark matter exists, why wouldn't it speed up the orbits of planets in our solar system? What makes our solar system so unique?
Some of the reasons why I'm arguing this rather strongly is that the ideas that we could effectively be inside a black hole now seem possible ... what would the view from inside a black hole look like? Well for one you'd see light from sources outside it that you could never reach ... we see light from distance galaxies that are assumed to be moving away from us at greater than light speed due to spacial "expansion" ... this seems very much equivalent to being inside an event horizon inside a space contracting at a rate that even light couldn't escape. There's a very repetitive structure to distant observations ... the spacings between galactic "walls" are so regular and periodic that it seems it must be periodic/cyclic ... now imagine light being emitted from inside a black hole and falling back in after a rather fixed delay. Sure enough we inhabit an area of the universe higher in mass than most also which, would seem the most likely locations for a black hole.
If measurements of distances are made in relative sense, then if you made a measurement of the size of even a small space, but from something approaching a singularity, you'd see this small space as effectively infinite. Space would wrap around also, as you'd have no method to escape from a black hole ... all paths lead back to the center.
In the example of the hypersphere, all distances are effectively angular distances. They are cyclic and repeat. I posted a couple times elsewhere regarding how with a very compressed space, the angular relationships between nearby particles becomes very significant - as distances are reduced EMF interactions become more pronounced. This angular components would propogate their influences on neighboring bodies and so on, in a wave like fashion similar to light itself. Light speed has become an abstract, immeasurable definition that more or less signifies the shortest delay between two points ... if gravity ends up effectively operating faster than light speed, they'll just redefine it so gravity travels at light speed but through an alternate smaller dimension than light does (if it's irregular and not simply a scaling factor compared to light, then this would seem appropriate).
Anyway, I'm suggesting that measurements of spacial distances are relative to each other and that the universe might even be seen as having a constant surface area (between matter and space) or volume and that the idea of residing on the surface of hypersphere might actually be closer to being on an irregular surface with some areas pushed in and compressed by gravity and possibly EMF as a complimentary force acting like a surface tension to oppose this. I admit wishing I had a more certain understanding of how it all works (I admire the work Zephir puts into his graphics) but it seems unlikely spacial expansion is as simple as a universal linear scaling factor over time to all of space ... then again, if it's a close approximation maybe that's fine but things like inflation, dark matter, galactic walls etc. just seem to deserve a theory that fits more observations into a simpler model.
That's possible but if the area (or volume to be more correct) of this surface can vary, what causes this and why is it necessarily uniform?
I'm not against the idea of some forms of information propogating faster than light but what would keep the expansion or contraction in one area of the universe matched to everywhere else? How can the radius be maintained equally without some rather instantaneous communication existing between everything in the universe?
If gravity creates a "warped spacetime" and gravity isn't uniformly distributed, then why wouldn't this effect be non-uniform? Wouldn't a continued local contraction make space elsewhere appear continually expanding in comparison? Wouldn't such an effect also create an appearance of distance, large galaxies orbiting too fast (just as observed) because the distance and size calculations are aged and not reflective of the actual spacial scalings at that time?
You wouldn't need some novel force to pull things apart from the Big Bang either as you could just let whatever fluctuations occur in empty space collapse on their own.
Inflation theory attempts to address the problem of space appearing to become almost instantly very large. What if the universe was already large? Measurements of distances can only be made in a relative sense. If one ruler gets smaller, another looks larger in comparison. What would differentiate between a contraction in local distances versus an overall expansion? Well if we used orbital periods as a means to determine distance scaling then we find gravity acting too strongly elsewhere and this would agree to things not being as large and distant as assumed but instead smaller and closer. If dark matter exists, why wouldn't it speed up the orbits of planets in our solar system? What makes our solar system so unique?
Some of the reasons why I'm arguing this rather strongly is that the ideas that we could effectively be inside a black hole now seem possible ... what would the view from inside a black hole look like? Well for one you'd see light from sources outside it that you could never reach ... we see light from distance galaxies that are assumed to be moving away from us at greater than light speed due to spacial "expansion" ... this seems very much equivalent to being inside an event horizon inside a space contracting at a rate that even light couldn't escape. There's a very repetitive structure to distant observations ... the spacings between galactic "walls" are so regular and periodic that it seems it must be periodic/cyclic ... now imagine light being emitted from inside a black hole and falling back in after a rather fixed delay. Sure enough we inhabit an area of the universe higher in mass than most also which, would seem the most likely locations for a black hole.
If measurements of distances are made in relative sense, then if you made a measurement of the size of even a small space, but from something approaching a singularity, you'd see this small space as effectively infinite. Space would wrap around also, as you'd have no method to escape from a black hole ... all paths lead back to the center.
In the example of the hypersphere, all distances are effectively angular distances. They are cyclic and repeat. I posted a couple times elsewhere regarding how with a very compressed space, the angular relationships between nearby particles becomes very significant - as distances are reduced EMF interactions become more pronounced. This angular components would propogate their influences on neighboring bodies and so on, in a wave like fashion similar to light itself. Light speed has become an abstract, immeasurable definition that more or less signifies the shortest delay between two points ... if gravity ends up effectively operating faster than light speed, they'll just redefine it so gravity travels at light speed but through an alternate smaller dimension than light does (if it's irregular and not simply a scaling factor compared to light, then this would seem appropriate).
Anyway, I'm suggesting that measurements of spacial distances are relative to each other and that the universe might even be seen as having a constant surface area (between matter and space) or volume and that the idea of residing on the surface of hypersphere might actually be closer to being on an irregular surface with some areas pushed in and compressed by gravity and possibly EMF as a complimentary force acting like a surface tension to oppose this. I admit wishing I had a more certain understanding of how it all works (I admire the work Zephir puts into his graphics) but it seems unlikely spacial expansion is as simple as a universal linear scaling factor over time to all of space ... then again, if it's a close approximation maybe that's fine but things like inflation, dark matter, galactic walls etc. just seem to deserve a theory that fits more observations into a simpler model.
How "thick" is the three dimensional surface of the 4 dimensional hypersphere? It is the space stretch that forms the hypersphere. The hypersphere is uniform due to the space-stretch. The gravity closes the universe.
Inflation in my opinion happened at time zero. Inflation was necessary to get the universe over its original gravity. Otherwise the universe would have been a black hole. The hypersphere inflated dropping the gravity.
Steven, what form besides the hypersphere could positive curvature take?
Inflation in my opinion happened at time zero. Inflation was necessary to get the universe over its original gravity. Otherwise the universe would have been a black hole. The hypersphere inflated dropping the gravity.
Steven, what form besides the hypersphere could positive curvature take?
QUOTE (Nick+)
How "thick" is the three dimensional surface of the 4 dimensional hypersphere?
How "thick" does it have to be? Kinetic energy seems to require both real and complex components to motion - you need location and velocity, or alternately this might be seen as being composed of 2 planes - where something is now, and where it was, so that motions can be maintained and extrapolated on.
Something I've come to find interesting and more along the lines of Zephirs ideas, is that these two planes might physically operate along the lines of refraction within a surface of relatively uniform spacial density.
Take this for whatever it's worth - imagine in your hypersphere example that there was a varied spacial density from the center outward with densities being highest in the center and expanding and becoming more diffuse outward. A wave propogating through this is most likely to propogate within a plane of similar density - attempting to move to either a higher or lower density space will tend to cause the light to bend and/or reflect back. In this manner planar interactions would naturally arise from a solid with varied density as waves would tend to travel along modes with similar density, though the apparent density in an area would depend upon the observer.
To put this into another analogy - if you look at a topological map that shows loops surrounding a mountain on Earth at different altitudes, and equate higher altitudes with higher densities or compressed areas of space and lower altitudes with lower densities of space, then light would tend to travel in rings around the "universe"/mountain within a topographical line or medium of rather uniform density.
The wavelength of this light might appear to correlate to the gradient of the compression. An area with a higher compression indicates higher potential energy and shorter wavelength.
The interesting thing here is that over time resonances will build and even if light were diffusive, it seems only light propogating at its maximum speed along a path of uniform density would avoid self-interference and cancellation.
So let's say instead that the Big Bang was equivalent to "striking" this medium or otherwise injecting a large amount of energy into it ... waves might propogate in every direction, and not have any directional characteristics - if a wavefront initiating from a specific point in space were to take two slightly different paths and use slower and faster modes of travel, then when they reintersected they wouldn't line up in phase exactly and would slowly cancel themselves. But the very front of the wave that travelled at maximum speed through a path could avoind interacting with itself and cancelling these energies. This would naturally end from an initial high energy chaotic state into a lower energy resonant state with only certain paths (generally along direct poin to point paths of uniform spacial density) being sustainable. This would also seem to agree with the idea of inflation ... the universe never was a point like singularity. Instead that impression is created by the uniformity of the energy stimulating this medium. So the disagreement between the velocity of expansion before and after the Big Bang would be due to trying to extrapolate beyond the actual size of the universe and finding a non-linearity past that.
But again, if gravity closes it, then gravity would seem to be doing the bending/stretching and gravity isn't a uniform force everywhere so why would this be uniform?
Oh, I think there might be a misunderstanding between us. I've been assuming you're comparing spacial expansion to a 3-D surface of a 4-D sphere. Maybe you're thinking of the expansion of a 3-D volume ... yes, that could be the general observation though we'd be unable to actually see the edge of this volume - I assume waves would simply bounce or be diverted away from this edge so there would be no way to actually "see" except in how it distorts otherwise linear spaces.
But again, if gravity closes it, then gravity would seem to be doing the bending/stretching and gravity isn't a uniform force everywhere so why would this be uniform?
Oh, I think there might be a misunderstanding between us. I've been assuming you're comparing spacial expansion to a 3-D surface of a 4-D sphere. Maybe you're thinking of the expansion of a 3-D volume ... yes, that could be the general observation though we'd be unable to actually see the edge of this volume - I assume waves would simply bounce or be diverted away from this edge so there would be no way to actually "see" except in how it distorts otherwise linear spaces.
Inflation in my opinion happened at time zero. Inflation was necessary to get the universe over its original gravity. Otherwise the universe would have been a black hole. The hypersphere inflated dropping the gravity.
Steven, what form besides the hypersphere could positive curvature take?
Any closed surface would seem to work. An elliptical shape could likely be equated as having toroidal characteristics though I must admit that some uniform space needs to be defined in order to measure how non-uniform real spaces are. From that point of view, I would agree that the 3-D surface of a 4-D sphere could be a good reference to compare things with. So I'm recommending considering what observations would be created by "dimples" on this surface. For example, if we see time as the expansion of this sphere and 3-D space passing through expanding spaces over time, then an area where time passed slower (like near large masses) would not be expanding as fast by this perspective ... this would again suggest indentations in space near mass on this surface.
How "thick" does it have to be? Kinetic energy seems to require both real and complex components to motion - you need location and velocity, or alternately this might be seen as being composed of 2 planes - where something is now, and where it was, so that motions can be maintained and extrapolated on.
Something I've come to find interesting and more along the lines of Zephirs ideas, is that these two planes might physically operate along the lines of refraction within a surface of relatively uniform spacial density.
Take this for whatever it's worth - imagine in your hypersphere example that there was a varied spacial density from the center outward with densities being highest in the center and expanding and becoming more diffuse outward. A wave propogating through this is most likely to propogate within a plane of similar density - attempting to move to either a higher or lower density space will tend to cause the light to bend and/or reflect back. In this manner planar interactions would naturally arise from a solid with varied density as waves would tend to travel along modes with similar density, though the apparent density in an area would depend upon the observer.
To put this into another analogy - if you look at a topological map that shows loops surrounding a mountain on Earth at different altitudes, and equate higher altitudes with higher densities or compressed areas of space and lower altitudes with lower densities of space, then light would tend to travel in rings around the "universe"/mountain within a topographical line or medium of rather uniform density.
The wavelength of this light might appear to correlate to the gradient of the compression. An area with a higher compression indicates higher potential energy and shorter wavelength.
The interesting thing here is that over time resonances will build and even if light were diffusive, it seems only light propogating at its maximum speed along a path of uniform density would avoid self-interference and cancellation.
So let's say instead that the Big Bang was equivalent to "striking" this medium or otherwise injecting a large amount of energy into it ... waves might propogate in every direction, and not have any directional characteristics - if a wavefront initiating from a specific point in space were to take two slightly different paths and use slower and faster modes of travel, then when they reintersected they wouldn't line up in phase exactly and would slowly cancel themselves. But the very front of the wave that travelled at maximum speed through a path could avoind interacting with itself and cancelling these energies. This would naturally end from an initial high energy chaotic state into a lower energy resonant state with only certain paths (generally along direct poin to point paths of uniform spacial density) being sustainable. This would also seem to agree with the idea of inflation ... the universe never was a point like singularity. Instead that impression is created by the uniformity of the energy stimulating this medium. So the disagreement between the velocity of expansion before and after the Big Bang would be due to trying to extrapolate beyond the actual size of the universe and finding a non-linearity past that.
QUOTE
It is the space stretch that forms the hypersphere. The hypersphere is uniform due to the space-stretch. The gravity closes the universe.
But again, if gravity closes it, then gravity would seem to be doing the bending/stretching and gravity isn't a uniform force everywhere so why would this be uniform?
Oh, I think there might be a misunderstanding between us. I've been assuming you're comparing spacial expansion to a 3-D surface of a 4-D sphere. Maybe you're thinking of the expansion of a 3-D volume ... yes, that could be the general observation though we'd be unable to actually see the edge of this volume - I assume waves would simply bounce or be diverted away from this edge so there would be no way to actually "see" except in how it distorts otherwise linear spaces.
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| It is the space stretch that forms the hypersphere. The hypersphere is uniform due to the space-stretch. The gravity closes the universe. |
But again, if gravity closes it, then gravity would seem to be doing the bending/stretching and gravity isn't a uniform force everywhere so why would this be uniform?
Oh, I think there might be a misunderstanding between us. I've been assuming you're comparing spacial expansion to a 3-D surface of a 4-D sphere. Maybe you're thinking of the expansion of a 3-D volume ... yes, that could be the general observation though we'd be unable to actually see the edge of this volume - I assume waves would simply bounce or be diverted away from this edge so there would be no way to actually "see" except in how it distorts otherwise linear spaces.
Inflation in my opinion happened at time zero. Inflation was necessary to get the universe over its original gravity. Otherwise the universe would have been a black hole. The hypersphere inflated dropping the gravity.
Steven, what form besides the hypersphere could positive curvature take?
Any closed surface would seem to work. An elliptical shape could likely be equated as having toroidal characteristics though I must admit that some uniform space needs to be defined in order to measure how non-uniform real spaces are. From that point of view, I would agree that the 3-D surface of a 4-D sphere could be a good reference to compare things with. So I'm recommending considering what observations would be created by "dimples" on this surface. For example, if we see time as the expansion of this sphere and 3-D space passing through expanding spaces over time, then an area where time passed slower (like near large masses) would not be expanding as fast by this perspective ... this would again suggest indentations in space near mass on this surface.
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