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).
Mentz114 said:If space doesn't expand, the big-bang is not possible. In the FRW model there is some beginning time when there is no space. I think this depends on choice of coordinates. But observations, particularly the CBR, give strong support to the BB theory. If I remember correctly, FTG does not do as well as GR in explaining observations.
If you're looking for a way to quantize gravity using the standard treatments, you'd do better with teleparallel gravity.
Actually, the (pseudo-Riemannian) manifold is like the map without the coordinates. The manifold defines ideas of connectedness and neighborhoods (topology), i.e, you can talk about small regions of the manifold near a point in the manifold, and also notions of distances and angles (metric).waterfall said:I imagine a manifold as like a map of the Earth with coordinates or latitudes or longitudes.
DaleSpam said:Actually, the (pseudo-Riemannian) manifold is like the map without the coordinates. The manifold defines ideas of connectedness and neighborhoods (topology), i.e, you can talk about small regions of the manifold near a point in the manifold, and also notions of distances and angles (metric).
One of the key features of manifolds is that if you zoom into a small region near any point it looks like Rn where n is the dimension of the manifold (4 in the case of spacetime). So a good example of a 2D manifold is the surface of a sphere. If you zoom into the surface of a sphere you can see that locally it looks like a 2D plane.
On top of the manifold you can add a coordinate system, called a coordinate chart, but the manifold is a topological and geometrical object which is independent of the coordinate chart used to describe it.
waterfall said:Now if cosmological observations prove beyond the shadow of a doubt that space indeed expand. Then spin-2 field over flat spacetime as a priori is falsified. If so. Then all quantum gravity theories that use gravitons in this terms like string theories are falsified. Think of the implications if space indeed expand. What do you think
If spacetime is discrete then in small neighborhoods it does not look like R4, and if it does not look like R4 in small neighborhoods then it is not a (4D) manifold.waterfall said:Thanks. How come they say that if spacetime is discrete, then there is no manifold.
DaleSpam said:If spacetime is discrete then in small neighborhoods it does not look like R4, and if it does not look like R4 in small neighborhoods then it is not a (4D) manifold.
Mentz114 said:I certainly wouldn't come to those conclusions on the basis of what I understand. I see no difficulty in the coexistence of gravitons and expanding space.
[I have a memory of someone posting an arXiv paper about the flat spacetime + spin-2 bosons but I can't find the post nor the paper. Does anyone have the reference ?]
I don't know anything about loop quantum gravity (nor am I very interested in it). But in normal relativistic quantum mechanics spacetime is not discrete, so I would be mildly surprised to learn that it is in LQG. If that is correct then LQG does not have a manifold, although it may approximate one in the classical limit.waterfall said:You mean Loop Quantum Gravity for example doesn't have a manifold?
No, I haven't seen the MTW treatment. FTG is a classical field theory that begins with the Lagrangian which has three terms, one each for the field, one for the matter and crucially one for the interaction between the field and the matter. The exchange boson, if the theory was quantized would be spin-2. All this is done in Minkowski spacetime.waterfall said:Can you enumerate how exactly the Baryshev approach differs to the Misner, Thorne & Wheeler's? It seems MTW's accept of the coexistence of gravitons and expanding space while the former doesn't. What are their main differences in the formalisms? Isn't it that both are about spin-2 field on flat spacetime? How can they differ when they have this in common?
DaleSpam said:Personally waterfall, I think you should learn established physics before attempting to learn speculative physics.
Certainly, but all you need for that is GR. Speculative spin-2 fields are not required, and from your frustration in these threads I think they are also not helpful.waterfall said:right now.. the universe is expanding as shown by the supernova lantern techniques. So space expansion is established physics.
I think that the best way to answer this question is to explain what we mean by saying that spacetime is curved.waterfall said:What I'd like to understand at this point is how come expanding space is automatically curved space. Can't minkowski space expand? maybe something to do with the submanifolds giving appearance of curvature whenever there is space expansion?
DaleSpam said:Certainly, but all you need for that is GR. Speculative spin-2 fields are not required, and from your frustration in these threads I think they are also not helpful.
I think that the best way to answer this question is to explain what we mean by saying that spacetime is curved.
First, let's examine 3 key concepts:
1) Spacetime: space and time are combined into one 4D mathematical space where the time dimension is different from the 3 spatial dimensions.
2) Worldlines: the position of a classical point particle over its lifetime is represented by a 1D curve in spacetime.
3) Inertial: the worldline of an inertial particle (a particle which is not acted on by any real force) is a straight line (aka geodesic).
The above 3 concepts are critical for SR and GR, although they even apply to Newtonian physics. The key difference between GR and Newtonian physics in the above is that in GR, due to the equivalence principle, gravity is considered a fictitious force rather than a real force. This means that, in GR, an inertial particle can be experimentally identified simply by attaching an ideal accelerometer: if it reads 0 then the particle is inertial.
Do you follow so far?
waterfall said:I understood all of the above concepts from my many books on GR like Relativity Visualized, Relativity Explained and even Taylor's Spacetime Physics. So no problem about those concepts.
