Deep space analysis

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Thank you all for clearing my doubt before. There is a question I want to ask on space and time and this time it is not about the absolute time as I have understood fairly that space and time are always relative.
So Here it is according to GR It is very beautifully explained that Very massive objects manipultes space and time , as they bends the space- time fabric and as a consequence give rise to gravity. This shows how gravity actually behaves.
I want to ask you then what we will call or how we will acknowledge that space and time which has not been manipulated or in other words describe something in domain of deep empty spaces in this ever expanding cosmos.?
 
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  • #2
PeterDonis
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I want to ask you then what we will call or how we will acknowledge that space and time which has not been manipulated or in other words describe something in domain of deep empty spaces in this ever expanding cosmos.?
I don't understand the question.
 
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I don't understand the question.
How we will acknowledge that space and time which has not been manipulated i.e the space and time fabric which has not been bend as there is no planet , star or massive object to manipulate the space time fabric or in other words how to describe the domain of deep empty spaces in this ever expanding cosmos.?
 
  • #4
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How we will acknowledge that space and time which has not been manipulated i.e the space and time fabric which has not been bend as there is no planet , star or massive object to manipulate the space time fabric or in other words how to describe the domain of deep empty spaces in this ever expanding cosmos.?
There is no total emptiness. Energy counts, too, and gravitation acts infinitely. But what do you want to describe, if there is nothing to describe?
 
  • #5
Ibix
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How we will acknowledge that space and time which has not been manipulated i.e the space and time fabric which has not been bend as there is no planet , star or massive object to manipulate the space time fabric or in other words how to describe the domain of deep empty spaces in this ever expanding cosmos.?
It's all spacetime. The only difference is how curved it is and in what way it is curved.
 
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I want to ask you then what we will call or how we will acknowledge that space and time which has not been manipulated or in other words describe something in domain of deep empty spaces in this ever expanding cosmos.?
I am not sure what you are asking since you seem to be asking about two different spacetimes.

A spacetime without any mass or energy is called a vacuum spacetime. The simplest vacuum spacetime is the Minkowski spacetime which is flat (no curvature) everywhere.

The spacetime which describes the cosmos as a whole is the FLRW spacetime also called LCDM for a specific equation of state.
 
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PeterDonis
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space and time which has not been manipulated i.e the space and time fabric which has not been bend as there is no planet , star or massive object to manipulate the space time fabric
Ok, then you're talking about the flat Minkowski spacetime of special relativity. Which does not actually exist; it's an idealization only, useful for certain purposes.

how to describe the domain of deep empty spaces in this ever expanding cosmos.?
As an appropriate curved spacetime geometry, since there is matter and energy in the universe. The fact that there might not be matter or energy in some particular region does not mean there is no spacetime curvature in that region; there can be spacetime curvature there due to the presence of matter or energy elsewhere in the universe.
 
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I am not sure what you are asking since you seem to be asking about two different spacetimes.

A spacetime without any mass or energy is called a vacuum spacetime. The simplest vacuum spacetime is the Minkowski spacetime which is flat (no curvature) everywhere.

The spacetime which describes the cosmos as a whole is the FLRW spacetime also called LCDM for a specific equation of state.
So are there actually two dimensions/ models of space-time. One is vaccum space-time and other FLRW. ?
 
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It's all spacetime. The only difference is how curved it is and in what way it is curved.
I'm asking about that space- time which is not curved. i.e what is the nature of that space-time which is not curved.
 
  • #10
Ibix
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So are there actually two dimensions/ models of space-time. One is vaccum space-time and other FLRW. ?
No. There's one model of spacetime, a 4d manifold. Depending on what's in that spacetime it has different curvature, and we give names to the different curvatures we get under circumstances. Spacetime around a non-rotating black hole is called Schwarzschild spacetime. Spacetime in a large enough empty region is flat and is called Minkowski spacetime. Spacetime on a large enough scale that galaxies are too small to see is FLRW spacetime.
I'm asking about that space- time which is not curved. i.e what is the nature of that space-time which is not curved.
It's spacetime with zero curvature. We do not have a more fundamental model, so there isn't any further layer of explanation.
 
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Ok, then you're talking about the flat Minkowski spacetime of special relativity. Which does not actually exist; it's an idealization only, useful for certain purposes.



As an appropriate curved spacetime geometry, since there is matter and energy in the universe. The fact that there might not be matter or energy in some particular region does not mean there is no spacetime curvature in that region; there can be spacetime curvature there due to the presence of matter or energy elsewhere in the universe.
The space - time is always curved is hard to digest. Because the % occupied by matter and energy I'd only 5% of the total cosmos. The respective is dark matter and energy . Can we say that flat or unmanipulated space- time anddark matter and energy are same?
Here is the link of the blog.
https://en.m.wikipedia.org/wiki/Dark_matter
Here some scientific theory have also proved that flat space-time exists. Have a look
https://en.m.wikipedia.org/wiki/Shape_of_the_universe
 
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jbriggs444
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The space - time is always curved is hard to digest. Because the % occupied by matter and energy I'd only 5% of the total cosmos.
Matter, energy, dark matter, dark energy. They all curve space time. The difference between the dark stuff and the non-dark stuff is that we can see the latter. Hence the names.
Can we say that flat or unmanipulated space- time anddark matter and energy are same?
No. Not even close.
Here is the link of the blog.
https://en.m.wikipedia.org/wiki/Dark_matter
Here some scientific theory have also proved that flat space-time exists. Have a look
https://en.m.wikipedia.org/wiki/Shape_of_the_universe
The latter reference does not say what you think it says. Space-time curvature is a tensor, not a scalar. The fact that we live in an expanding universe means that the tensor is not identically zero.

However, we can observe some symmetries. And if we adopt the "co-moving" coordinate system where the expansion is uniform in all directions then we can slice space-time up into spatial slices (each corresponding to a moment in time according to our coordinate system) and ask whether these spatial slices are each flat. The curvature of a 3-dimensional space is a scalar. It can be positive, negative or zero. It is this curvature of these spatial slices which the latter article is speaking of. Not space-time curvature.
 
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So are there actually two dimensions/ models of space-time. One is vaccum space-time and other FLRW. ?
There are an infinite number of models of space-time corresponding to an infinite number of distributions of matter. Some of the more useful or easy to calculate models have names. You were asking about two of those (as far as I could tell).

I'm asking about that space- time which is not curved. i.e what is the nature of that space-time which is not curved.
That is the flat Minkowski solution. However you also asked:
domain of deep empty spaces in this ever expanding cosmos.?
Which is not flat and is the FLRW spacetime instead.

Because the % occupied by matter and energy I'd only 5% of the total cosmos.
This is not correct. In the FLRW spacetime one of the assumptions is homogeneity which means that 100% of the cosmos is occupied by matter at the largest scales. Remember, we are talking about cosmological scales, so at cosmological scales every part of the universe contains a mix of matter, dark matter, energy, and dark energy. The percentages you mention describe the ratio of this mixture, not the spatial distribution which is homogenous.
 
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  • #14
Ibix
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The space - time is always curved is hard to digest.
Gravity has infinite range as far as we are aware. So spacetime will be (possibly very slightly) curved everywhere if it is curved anywhere.
Here some scientific theory have also proved that flat space-time exists. Have a look
https://en.m.wikipedia.org/wiki/Shape_of_the_universe
This says that there are spatially flat FLRW solutions, not that spacetime curvature is zero. These are not the same thing.
 
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There are an infinite number of models of space-time corresponding to an infinite number of distributions of matter. Some of the more useful or easy to calculate models have names. You were asking about two of those (as far as I could tell).

That is the flat Minkowski solution. However you also asked:
Which is not flat and is the FLRW spacetime instead.

This is not correct. In the FLRW spacetime one of the assumptions is homogeneity which means that 100% of the cosmos is occupied by matter at the largest scales. Remember, we are talking about cosmological scales, so at cosmological scales every part of the universe contains a mix of matter, dark matter, energy, and dark energy. The percentages you mention describe the ratio of this mixture, not the spatial distribution which is homogenous.
Can you throw more light on homogeneous spatial distribution and how would our universe look if it was heterogeneous..?
 
  • #16
Ibix
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Can you throw more light on homogeneous spatial distribution and how would our universe look if it was heterogeneous..?
We might see different numbers of galaxies in different parts of the sky, or more galaxies further away than nearby. On average at large scales, we don't see this - the universe is pretty much the same in every direction.
 
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Matter, energy, dark matter, dark energy. They all curve space time. The difference between the dark stuff and the non-dark stuff is that we can see the latter. Hence the names.

No. Not even close.

The latter reference does not say what you think it says. Space-time curvature is a tensor, not a scalar. The fact that we live in an expanding universe means that the tensor is not identically zero.

However, we can observe some symmetries. And if we adopt the "co-moving" coordinate system where the expansion is uniform in all directions then we can slice space-time up into spatial slices (each corresponding to a moment in time according to our coordinate system) and ask whether these spatial slices are each flat. The curvature of a 3-dimensional space is a scalar. It can be positive, negative or zero. It is this curvature of these spatial slices which the latter article is speaking of. Not space-time curvature.
However if the observable universe is expanding which the results shows it is then it's volume must be increasing or the space in the universe is getting increasing.
For analogy we can say that if we put gas into a balloon it's volume get increased and as it volume increases it displaces the air around it. So it takes over air and displaces it as the volume increases.

So in the case of this cosmos as it is expanding then what are the characteristics of that domain in which it is expanding into..?
 
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We might see different numbers of galaxies in different parts of the sky, or more galaxies further away than nearby. On average at large scales, we don't see this - the universe is pretty much the same in every direction.
Okay the universe is same in every direction is an indication of it's isotropic behaviour. What about it's homogeneity?
 
  • #19
Ibix
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Okay the universe is same in every direction is an indication of it's isotropic behaviour. What about it's homogeneity?
Homogeneity means that it's the same everywhere, at all distances. That does imply isotropy too.
 
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Homogeneity means that it's the same everywhere, at all distances. That does imply isotropy too.
Your statement is incorrect.
Isotropy is about exhibiting same properties in every direction while homogeneity is about uniform composition. Here are two examples
1. An example of something that is homogeneous but not isotropic is a space that is filled with a uniform electric or magnetic field. Because the field is uniform it is homogeneous, but because the field has a direction, it is not isotropic.

Similarly, it's easy to see how something can be isotropic but not homogeneous. For example, a spherically symmetric distribution of mass is isotropic for an observer at the center of the sphere, but is not necessarily homogenous.
 
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  • #21
PeterDonis
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Your statement is incorrect.
No, his statement was correct.

Isotropy is about exhibiting same properties in every direction while homogeneity is about uniform composition.
Homogeneity is not just about "uniform composition". It means uniformity everywhere in space, period. And that, as @Ibix said, implies isotropy as well; a universe which is the same at every point in space will also be the same in every direction from every point in space.
 
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No, his statement was correct.



Homogeneity is not just about "uniform composition". It means uniformity everywhere in space, period. And that, as @Ibix said, implies isotropy as well; a universe which is the same at every point in space will also be the same in every direction from every point in space.
Ok Sir. I'm not here to debate anyone. Can you tell me more about spatial distribution of matter as my purpose was to get a clear picture of this.
 
  • #23
PeterDonis
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An example of something that is homogeneous but not isotropic is a space that is filled with a uniform electric or magnetic field.
A region of space can be homogeneous in this sense, but the universe as a whole cannot; it's impossible to have a uniform EM field everywhere in the universe.

Can you tell me more about spatial distribution of matter
For what spacetime? So far we have discussed four possibilities in this thread: flat Minkowski spacetime, Schwarzschild spacetime, FRW spacetime, and our actual universe (which is not exactly described by any of those). Which one are you asking about?
 
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A region of space can be homogeneous in this sense, but the universe as a whole cannot; it's impossible to have a uniform EM field everywhere in the universe.



For what spacetime? So far we have discussed four possibilities in this thread: flat Minkowski spacetime, Schwarzschild spacetime, FRW spacetime, and our actual universe (which is not exactly described by any of those). Which one are you asking about?
How spatial distribution is homogeneous in our actual/ observable universe.
 
  • #25
PeterDonis
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About our actual/ observable universe.
Then, as I said, our actual/observable universe is not described exactly by any of the spacetimes we have discussed, but FRW spacetime is closest. Our actual/observable universe is not exactly isotropic or homogeneous, but it is to a good approximation on scales of about 100 million light-years and larger. So an FRW spacetime is a good approximation to the actual spacetime geometry on these scales.
 

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