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waterfall
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In FRW universe, is space expanding or spacetime expanding? If the former... but I know that only spacetime can curve and expand. "Space" doesn't do that. Well?
Matterwave said:If space-time can curve and expand, why can't space? How would you quantify this result?
DaleSpam said:When we say that space is expanding we are talking about a foliation of the spacetime manifold along the time coordinate. We are then comparing different distances in different foliated sub-manifolds.
Since there is only one spacetime manifold I don't know what meaning could be ascribed to the phrase "expanding spacetime". What comparison is possible?
DaleSpam said:I don't know if my terminology is "proper". I certainly don't have any supporting references.
How is that different from "expanding space"? What do you mean by "expanding spacetime"? It sounds like your description of "expanding spacetime" is the same as my description of "expanding space". I just don't understand the distinction you are trying to make between the two terms.waterfall said:So in expanding spacetime, what comparison is it made with. How about matter. If the universe was as big as the earth. We would know we can't see far. If it expands further. We can see more distance from earth. Hence it is in comparison to matter.
DaleSpam said:How is that different from "expanding space"? What do you mean by "expanding spacetime"? It sounds like your description of "expanding spacetime" is the same as my description of "expanding space". I just don't understand the distinction you are trying to make between the two terms.
DaleSpam said:Manifolds don't expand or contract in any meaningful sense that I can envision. You can foliate a manifold into a parameterized set of submanifolds and talk about expansion of the submanifolds as a function of the parameter. That would be what I was describing, i.e. expansion of space as a mathematical concept, not a physical concept.
The corresponding physical concept would be that the distances between unbound systems was increasing compared to the size of the bound systems.
Khashishi said:Space can expand because it is scaling up as time passes. Space-time can't be evolving in time because it already includes time, so it makes no sense to say it is expanding.
If you want an analogy with an orange, try this. Take an orange and draw a small circle round its "North Pole". Then draw a larger circle around that. Then draw an even larger circle around that. Keep going until you get to the "equator".waterfall said:Do you know of sites with the illustrations of what you are talking about? They seldom describe this in Big Bang expansion illustrations. So it's like an orange being a manifold and the pieces inside the submanifolds expanding regionally... or a direct site graphics would say a thousand words. Thanks.
DrGreg said:If you want an analogy with an orange, try this. Take an orange and draw a small circle round its "North Pole". Then draw a larger circle around that. Then draw an even larger circle around that. Keep going until you get to the "equator".
Now the orange skin is a manifold representing spacetime, and each circle is a submanifold representing a snapshot of space at a particular time. You could describe what you have as an "expanding circle". You wouldn't describe it as an "expanding orange-skin".
P.S. spacetime isn't really orange-shaped, it's more like a trumpet.
waterfall said:The thing is this (and to Dalespam too), we are taught that Big Bang is like the baloon expanding and the surface like spacetime, therefore everywhere expand at the same time, so how can any comparison be done when all is expanding together.
Abstract said:While it remains the staple of virtually all cosmological teaching, the concept of expanding
space in explaining the increasing separation of galaxies has recently come under fire as a dangerous idea whose application leads to the development of confusion and the establishment of misconceptions.
In this paper, we develop a notion of expanding space that is completely valid as a framework for the description of the evolution of the universe and whose application allows an intuitive understanding of the influence of universal expansion.
DaleSpam said:Manifolds don't expand or contract in any meaningful sense that I can envision. You can foliate a manifold into a parameterized set of submanifolds and talk about expansion of the submanifolds as a function of the parameter. That would be what I was describing, i.e. expansion of space as a mathematical concept, not a physical concept.
The corresponding physical concept would be that the distances between unbound systems was increasing compared to the size of the bound systems.
waterfall said:Also does this expanding space only works for curved spacetime? Or is it not related to whether curved or flat? Meaning flat spacetime can expand too?
My orange analogy is different from the balloon analogy.waterfall said:The thing is this (and to Dalespam too), we are taught that Big Bang is like the baloon expanding and the surface like spacetime, therefore everywhere expand at the same time, so how can any comparison be done when all is expanding together.
Going to the orange analogy (I'm familiar with the relativity of simultaneity and it's related to it). But if the entire orange expands, the orange-skin would expand too so we can describe it as "expanding orange-skin". Note that all circles you draw from the pole to the equator expands at the same time. So it has same relationship. It's like the Earth expanding and every object, the ground, you and I expanding forever. Can we tell? No. Because we will have same relationship to each other. (btw.. some guy produced a theory where this is what produced gravity because the expanding Earth and us keep us close to the ground.. of course I don't believe this but just mentioning this because I just recalled it).
waterfall said:I think what atyy is saying is this.
Expanding space produces our universe.
Expanding curved spacetime doesn't produce our universe because it is invalid.
Expanding flat spacetime doesn't produce our universe because it is invalid (Milne).
Hence. Expanding space can either have curved spacetime or flat spacetime embedded in it.
Is this correct analysis?
I looked around a bit and was a little disappointed, I didn't really find anything that jumped out at me. There is an example on page 4 of this link, but it is a little technical.waterfall said:Do you know of sites with the illustrations of what you are talking about? They seldom describe this in Big Bang expansion illustrations. So it's like an orange being a manifold and the pieces inside the submanifolds expanding regionally... or a direct site graphics would say a thousand words. Thanks.
DrGreg said:My orange analogy is different from the balloon analogy.
In the expanding balloon analogy, the 3 dimensions of space are represented by the 2 dimensions of the balloon surface, and time is represented by time.
In my orange analogy, the 3 dimensions of space are represented by just one dimension (circumference) of a circle, and time is represented by the "latitude" of the circle. The 4 dimensions of spacetime are represented by the 2 dimensions of the orange skin. The "North Pole" represents the big bang. The circle expands as it moves down but the orange is static.
waterfall said:spacetime expanding is the differential manifold expanding.
bcrowell said:Could you tell us what your background is in math and physics? I didn't get the impression that you were at the level where you knew what a manifold was. If you don't know what it means, don't throw the word around.
pervect said:1) Once upon a time, it was thought that you could measure the "ether velocity", but we now expect any experiment that we can perform not to be able to detect the motion of space will have a null result. So, if special relativity is right, there is no apparatus that can detect empty space moving. So it's possible to imagine an experiment that could detect moving space, but relativity says that all such experiments will show that it's not moving.
2) None - as far as I know, at least, there isn't any experiment (at least none compatible with relativity) to tell whether or not empty space is expanding or not. This may be debatable, I suppose - just because I've never seen it doesn't mean it exists. But if we can't tell that empty space is moving, how would we tell that it's expanding?
3) A lot of people aren't aware of the details, but this can in fact be measured. To tell if a plane is curved, for example, you'd construct a quadrilateral with four equal sides and equal diagonals, and measure the diagonals to make sure they're sqrt(2).
This presuposes that you do know how to measure distances - it's necessary to define how you measure distances before you can measure curvature.
A good example is using this technique to detect the fact that the surface of a sphere is curved.
You should be able to do something similar with the diagonals of a cube in 3d - check if they are both sqrt(3).
Someone posted a good reference in the literature about a different geometric construction to measure spatial curvature by measuring only distances, but I'm forgetting both the poster. ((I think it was some book by Synge))
It's also easy to to find constructions if you're confident in your ability to measure angles, but measuring distances is really more fundamental IMO.
waterfall said:Hi, I have read your shared paper "Expanding space - the root of all evil" for more than an hour. But it still hasn't answered my simple question.. which is...
Since expanding space is automatically curved spacetime (right?).. and since curved spacetime is just spin-2 field on flat spacetime. Then expanding space is composed of spin-2 field and flat spacetime. Therefore expanding space is related to expanding space&spin-2 field and expanding space&flat spacetime. How does one imagine or model expanding space&spin-2 field for example? Or expanding space&flat spacetime which is a Milne model that isn't valid. Can one say that when one adds spin-2 to Milne model. It becomes valid? Does anyone see if there is something wrong with my analysis and directly address what I'm talking about. Thanks.
DaleSpam said:I looked around a bit and was a little disappointed, I didn't really find anything that jumped out at me. There is an example on page 4 of this link, but it is a little technical.
http://luth.obspm.fr/~luthier/gourgoulhon/fr/present_rec/pohang08-1.pdf
Mentz114 said:I think your logic is wrong in that not all curved spacetime is expanding. The expanding spacetimes of GR are a special class where spatial parts of the metric depend on t.
Also field gravity is not the same as GR. They are two different theories, both claim to explain the observed cosmological phenomena but in different ways. In fact I don't think FTG needs expanding space but supposes a fractal distribution of mass.
So you can't talk about splicing them together in the way you suggest.
waterfall said:Yes, that's what I'm asking how to imagine space expanding in Field Theory of Gravitation. I think atyy didn't understand my question that's why he kept mentioning about the milne universe and stuff. But in FTG if space didn't expand. Then in the first Planck milliseconds from the Big Bang where space was still just the size of a football field. How then does space expanded when there was nothing out there. Unless you are assuming space already existed? But I think this was already refuted by say the redshift and other matters (think why else would they propose space indeed expands if they could just state space already existed).