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WaxRubiks
2015-Apr-04, 07:46 PM
All the matter(and dark matter) in the Universe must surely give the space we see a curvature, wouldn't it?

And if matter just goes on and on into space, then it must curve back on itself.....although that wouldn't mean it joined up to form a 3-sphere, I suppose.

Cougar
2015-Apr-04, 09:00 PM
All the matter(and dark matter) in the Universe must surely give the space we see a curvature, wouldn't it?

No, actually all the matter and dark matter do not add up to enough mass to slow the expansion to an eternal standstill (flat overall curvature), much less provide enough gravitational curvature to stop the expansion and turn it around into a contraction (positive curvature). About 68% of the needed mass to yield a flat universe is missing. But measurements of the largest temperature fluctuations on the CMB, and a little trigonometry, indicate the overall curvature is indeed very nearly flat. Dark energy is called upon to fill the hole of that missing 68% (and also to somehow cause the expansion to accelerate).

Noclevername
2015-Apr-04, 09:03 PM
All the matter(and dark matter) in the Universe must surely give the space we see a curvature, wouldn't it?

And if matter just goes on and on into space, then it must curve back on itself.....although that wouldn't mean it joined up to form a 3-sphere, I suppose.

Observational evidence says otherwise; The result we get back from the CMB says that the observed universe is flat.

Oops, I missed that Cougar said that already.

John Mendenhall
2015-Apr-04, 09:10 PM
R
No, actually all the matter and dark matter do not add up to enough mass to slow the expansion to an eternal standstill (flat overall curvature), much less provide enough gravitational curvature to stop the expansion and turn it around into a contraction (positive curvature). About 68% of the needed mass to yield a flat universe is missing. But measurements of the largest temperature fluctuations on the CMB, and a little trigonometry, indicate the overall curvature is indeed very nearly flat. Dark energy is called upon to fill the hole of that missing 68% (and also to somehow cause the expansion to accelerate).

Agreed. And while we're at it, let's make note that there is no physical evidence of any spatial dimensions beyond three, and one time dimension.

Swift
2015-Apr-05, 02:35 AM
And don't call me Shirley! :D

Noclevername
2015-Apr-05, 04:41 AM
And don't call me Shirley! :D

Shirley, you jest.

WaxRubiks
2015-Apr-05, 06:09 AM
I hope I'm not getting all ATM, but maybe we can't see the full picture of the Universe because we are part of it. What looks curved from one perspective, may look flat from another.

Shaula
2015-Apr-05, 07:04 AM
I hope I'm not getting all ATM, but maybe we can't see the full picture of the Universe because we are part of it. What looks curved from one perspective, may look flat from another.
If all our models and measurements come back with flat as an answer then that is our answer. We see curvature due to masses, we see no overall curvature due to an underlying geometry. So there doesn't really seem to be a compelling case to claim that there is a hidden curvature that is still caused by mass but isn't like any other curvature we see.

It is a bit like saying that the Earth is flat. Sure, is seems spherical to us but we are part of it. But in some other perspective it is flat.

Cougar
2015-Apr-05, 12:53 PM
...maybe we can't see the full picture of the Universe because we are part of it.

Actually, we cannot see the full picture of the Universe, but it's not because we are part of it. The Universe is likely larger than the visible part of the Universe that we can see. Much larger. We cannot see beyond the visible Universe because the light from there has not had time to reach us (and with the accelerating expansion, it looks like it'll never get here). Yes, we are decidedly part of the Universe, but by definition, the Universe is everything - there is nothing that is not part of the Universe. To imagine looking down on our Universe from the 'outside' is an impossible view. There can be no such view. Nevertheless, we can see quite a bit of the Universe from our necessarily internal viewpoint. Especially with telescopes. :D

kevin1981
2015-Apr-05, 04:22 PM
Or, it could be curved but because the size of the whole universe is so gigantic it looks as our observable "patch" is flat. But without evidence, which we have none of, it is purely speculative.

mkline55
2015-Apr-06, 11:54 AM
How exactly would you measure universal curvature in three dimensions?

Shaula
2015-Apr-06, 12:05 PM
How exactly would you measure universal curvature in three dimensions?
WMAP did this by looking at the angular scale of the fluctuations in the CMBR. The results came out as near to flat (less than half a percent deviation from what was expected from flat).

mkline55
2015-Apr-06, 12:28 PM
Thanks Shaula. My mistake in thinking cosmological "curvature" was related to the English word "curve".

Shaula
2015-Apr-06, 12:45 PM
Thanks Shaula. My mistake in thinking cosmological "curvature" was related to the English word "curve".
It is, although the cosmological version is currently intrinsic rather than extrinsic. Essentially the WMAP measurements were measurements of the amount of curvature along the path of the light from the early universe to us. See: http://map.gsfc.nasa.gov/mission/sgoals_parameters_geom.html

Cougar
2015-Apr-06, 12:46 PM
How exactly would you measure universal curvature in three dimensions?

Basically, you 'construct' a very large triangle, measure the sides, and calculate the angles. If the angles add up to 180o, the curvature is flat. If the sum is less than or greater than 180o, then the curvature is negative or positive, respectively. As Shaula said, the angular size of the largest CMB temperature fluctuations was used as the base of a very tall and skinny isosceles triangle (with the sides being the distance to the CMB). The sum of angles comes back very close to 180o.

mkline55
2015-Apr-06, 05:46 PM
Thanks Cougar. I wasn't aware that temperature fluctuations could only occur along absolutely straight lines. Now it makes sense.

ShinAce
2015-Apr-06, 06:58 PM
If the universe had positive curvature, we would expect temperature variations of a certain 'size'. Likewise for negative curvature, and zero curvature. The pattern we see matches zero curvature.

I can't find the image I'm looking for. However, all three cases look pretty similar, it's just the size of the 'blotches' which are slightly different for each case.

Flat means 2 things:
1) triangles have internal angles adding up to 180 degrees --> geometric interpretation
2) the universe has critical energy density --> physical interpretation

WayneFrancis
2015-Apr-07, 03:45 AM
I hope I'm not getting all ATM, but maybe we can't see the full picture of the Universe because we are part of it. What looks curved from one perspective, may look flat from another.

But there are test we can and have done that will let us know if the universe is flat or not. Just because we are stuck to the surface of the universe doesn't mean we can't test the curvature. All this is also mathematical. We can say a torus is mathematically flat. We can look at a doughnut and say it isn't in 3 dimensions. But say the universe's topology was a torus that doesn't mean there needs to be a higher dimension that exists for our universe to be a torus.

WayneFrancis
2015-Apr-07, 03:52 AM
How exactly would you measure universal curvature in three dimensions?

one way to measure curvature is the following. Take a satellite with gyroscopes to keep it pointing in one direction. Have the satellite travel in closed path. Compare the direction the satellite is pointing at the beginning and end of the journey and the difference, if any, will give you the curvature of that region of spacetime. There are lots of experiments that can and have been done that test the curvature of space/time. Forgetting all the local curvature due to various massive bodies the universe keeps coming up as flat using various unrelated testing mechanisms.

ShinAce
2015-Apr-07, 04:11 AM
Wayne is talking about parallel transport:
http://en.wikipedia.org/wiki/Parallel_transport

Indeed, if the universe is very much larger than what we see(which is likely) and curved, we may not be able to tell. Current limits on the curvature parameter indicate that if the universe is curved, it's at least 1000 bigger (in terms of radius) than what we see.

The fact that all tests say it is flat may not be a coincidence. This is called the 'flatness problem'. For it to be exactly flat seems quite a coincidence. There could be some underlying physics that makes it so that only a flat universe is possible. However, that's conjecture without any evidence.

WayneFrancis
2015-Apr-07, 07:31 AM
Thanks ShinAce. I've watched lectures by Susskind and someone else who I can't remember where they presented the experiment. I couldn't remember the name and definitely could not point anyone at the specific lectures :)

malaidas
2015-Apr-07, 11:37 AM
however there are two ways there could be curvature beyond our measurement, one that our visible universe is such a small % of the total sphere that the curvature is smaller than we can measure. 2 the curvature is not apparent in the dimensions we have available to measure, but neither is demonstrable and thus have no scientific meaning.

mkline55
2015-Apr-07, 12:57 PM
one way to measure curvature is the following. Take a satellite with gyroscopes to keep it pointing in one direction. Have the satellite travel in closed path. Compare the direction the satellite is pointing at the beginning and end of the journey and the difference, if any, will give you the curvature of that region of spacetime. There are lots of experiments that can and have been done that test the curvature of space/time. Forgetting all the local curvature due to various massive bodies the universe keeps coming up as flat using various unrelated testing mechanisms.
If you are using gyroscopes to "keep it pointing in one direction", it seems that you are just using a circular argument to support itself, because if the universe were curved, then the gyroscope would turn with it, and keep the same relative orientation with regard to all other objects in that curving universe, or any attempt to prove that the satellite remained in a perfectly continuous orientation would require that you first assume the universe is flat, then upon seeing the gyroscope having the same orientation, conclude that the universe is flat.

Although the examples given so far may indeed demonstrate flatness, they have not been presented in a convincing manner. I suspect that important details are missing. Essentially what I've seen so far amounts to this: Draw a straight line of length x then measure it. If it is x in length and the line is straight, then the universe is flat.

ShinAce
2015-Apr-07, 01:17 PM
Suppose an ant had a 2D gyroscope and was walking around the surface of the earth. We must also assume the gyroscope must point along the surface of the Earth(2D) and not keep its heading in 3D.

Now, spin the gyroscope and have it point 'North'. Tell the ant to start at the equator, then follow the gyroscope's heading until the north pole. At the north pole, it turns 90 degrees to the left and goes straight until the equator. Now it turns left again at the equator, and walks back to where it started. The gyroscope is now pointing East.

There's a drawing of that right at the beginning of the article:
http://en.wikipedia.org/wiki/Parallel_transport

ShinAce
2015-Apr-07, 01:21 PM
Thanks ShinAce. I've watched lectures by Susskind and someone else who I can't remember where they presented the experiment. I couldn't remember the name and definitely could not point anyone at the specific lectures :)

Welcome. I was introduced to this by my cosmology professor. The idea of parallel transport was a step towards 'covariant derivatives', or the calculus in curved space. I work as a teaching assistant and always stress how much geometry is involved in doing calculus.

Susskind is great. Even if he doesn't teach you the terms, he does an amazing job at covering the important physics. His lecture on the Higgs mechanism is a gem.

mkline55
2015-Apr-07, 01:49 PM
Suppose an ant had a 2D gyroscope and was walking around the surface of the earth. We must also assume the gyroscope must point along the surface of the Earth(2D) and not keep its heading in 3D.

Now, spin the gyroscope and have it point 'North'. Tell the ant to start at the equator, then follow the gyroscope's heading until the north pole. At the north pole, it turns 90 degrees to the left and goes straight until the equator. Now it turns left again at the equator, and walks back to where it started. The gyroscope is now pointing East.

There's a drawing of that right at the beginning of the article:
http://en.wikipedia.org/wiki/Parallel_transport

Okay. So by "flatness", you mean the universe does not appear to consist of more than 3 spatial dimensions?

ShinAce
2015-Apr-07, 02:12 PM
No. By flatness I mean that the universe has critical density. If there was any more matter/radiation/dark energy, then it would be positively curved like a sphere. If there was any less matter/radiation/dark energy, then it would be negatively curved like a saddle.

The other, and equivalent meaning, is that if you draw out big enough triangles and add up the angles, then you get 180 degrees.

The gyroscope thing is to help point you towads 'there is no such thing as pointing in a well defined direction when curvature is involved'. Just trying to clear up a misconception. Look at the Gravity Probe B mission. It used gyroscopes in orbit to measure curvature of space due to Earth's gravity. They did this by measuring how much the 'pointing' of the gyroscopes changed with time.

ShinAce
2015-Apr-07, 02:34 PM
Allow me to add that the definition of flatness is not obvious. The geometric version, the triangle, is the standard one that anyone familiar with high school geometry can relate to. After all, we were taught that all triangles add up to 180 degrees. Because we did geometry on flat pieces of paper. If we did geometry on globes instead, we would be familiar with geometry with positive curvature. The sums of the angles would always be more than 180 degrees. The area of a triangle would always be more than base*height/2. There is even a relationship between the 'extra' surface area of the triangle and its extra 'angle'.

What I call critical density is actually a parameter, omega, being equal to 1.
http://en.wikipedia.org/wiki/Big_Bang#/media/File:End_of_universe.jpg

That image shows omega>1, omega=1, and omega<1 and the corresponding curvature of space. Note that to make an image of it, they're forced to draw space as being some 2D object viewed in 3D. We can still view a flat 2D universe in 3D. Flat does not equal 3D. The only reason the gyroscope can't keep its heading in 3D(when we're concerned with living on a 2D surface) is relativity. If the globe isn't moving, then maybe the 3D space is moving. If the 3D space isn't moving, maybe the globe is. How do you define which way the gyroscope should point without defining an absolute north, which you can't do if you wan't relativity. It's an aether problem. Aether = bad physics. That part is history.

It's geometry, geometry and more geometry. Have a look at the definition of flatness in mathematics just to see how abstract the concept is:
http://en.wikipedia.org/wiki/Flatness_%28mathematics%29

Surface. Manifold. These are the playthings of geometry.

John Mendenhall
2015-Apr-08, 03:11 AM
Suppose an ant had a 2D gyroscope and was walking around the surface of the earth. We must also assume the gyroscope must point along the surface of the Earth(2D) and not keep its heading in 3D.

Now, spin the gyroscope and have it point 'North'. Tell the ant to start at the equator, then follow the gyroscope's heading until the north pole. At the north pole, it turns 90 degrees to the left and goes straight until the equator. Now it turns left again at the equator, and walks back to where it started. The gyroscope is now pointing East.

There's a drawing of that right at the beginning of the article:
http://en.wikipedia.org/wiki/Parallel_transport

Isn't the ant in the diagram turning right?

The center pieces on a rubix cube illustrate this nicely also.

ShinAce
2015-Apr-08, 03:20 AM
The wiki diagram is when the ant takes right hand turns. I was saying left hand turns, which gives the opposite change to the gyroscope direction.

In other words, going around the triangle forward or backward is not the same. This highlights that parallel transport is 'path dependent'.

mkline55
2015-Apr-08, 11:55 AM
No. By flatness I mean that the universe has critical density. If there was any more matter/radiation/dark energy, then it would be positively curved like a sphere. If there was any less matter/radiation/dark energy, then it would be negatively curved like a saddle.

Like a sphere? You mean only at the surface, which is where a sphere is curved? That example is not anything like the universe. The curvature of a sphere is only because you treat the surface as a two-dimensional plane wrapped around a three-dimensional shape. If you drew a straight line from any point on the surface to any other point on the surface, it is still a straight line, and it passes through some portion of the sphere. If you insist that the test determines whether the universe is "curved like a sphere", then either 1) the universe must be two-dimensional wrapped around some three-dimensional shape, or it is three-dimensional wrapped around some fourth or higher dimension. So, exactly how does the sphere example match up to the universe? For the universe, in which direction would positive curvature occur? In which direction would negative curvature occur?

Shaula
2015-Apr-08, 12:46 PM
Like a sphere? ...So, exactly how does the sphere example match up to the universe? For the universe, in which direction would positive curvature occur? In which direction would negative curvature occur?
No, a higher dimension is not required. There are two forms of curvature - extrinsic (which is what you are describing - curvature involving dimensions other than the surface) and intrinsic (which is essentially manifested in the way each point in space is connected to each other point and does not require extra dimensions)

Cougar
2015-Apr-08, 12:46 PM
So, exactly how does the sphere example match up to the universe?

I'm sure ShinAce means just the surface of a sphere, discounting any inside or outside of that surface. It's a 2-D analogy of a 3-spatial-dimension universe. And the curvature of the universe is intrinsic to the 3-D space (due to overall gravity and dark energy effects, I expect) - it need not be embedded in a higher dimension.

mkline55
2015-Apr-08, 01:17 PM
Thanks for clearing that up. So the sphere analogy with the ant really has nothing to do with universal curvature, it's just a fun example of 2-D vs. 3-D measurements. Perhaps the analogy should not be used at all since it does nothing to explain how universal curvature is measured except to confuse the issue.

So what the tests measure is, "curvature of the universe is intrinsic to the 3-D space (due to overall gravity and dark energy effects, I expect) - it need not be embedded in a higher dimension." That appears to be the final answer, though it is extremely vague and unsatisfying (at least to me).

How do we know that the lines used to measure the angles of the theoretical triangle are perfectly straight, in the precise directions reported, of exactly the lengths measured?

Cougar
2015-Apr-08, 02:00 PM
...it's just a fun example of 2-D vs. 3-D measurements.

Have you ever read Flatland? The surface-of-a-sphere is not just a fun example, but a pretty good analogy that illuminates some qualities. No analogy is completely satisfying.


How do we know that the lines used to measure the angles of the theoretical triangle are perfectly straight, in the precise directions reported, of exactly the lengths measured?

With the triangle using the largest-CMB-fluctuations, the length of the base of the isosceles triangle is a deduction based on the amount of time gravity has had a chance to propagate (380,000 years). The long sides of the triangle are basically constructions, like a thought experiment. We know how long such lines should be based on the age of the Universe.

mkline55
2015-Apr-08, 03:01 PM
With the triangle using the largest-CMB-fluctuations, the length of the base of the isosceles triangle is a deduction based on the amount of time gravity has had a chance to propagate (380,000 years). The long sides of the triangle are basically constructions, like a thought experiment. We know how long such lines should be based on the age of the Universe.

Just trying to fill in the details here. So someone pointed to a spot in the sky and said that distant point is exactly 13.xxx billion light years away (or it was when the image we see now was created). Then they moved their pointer Y degrees and pointed at another spot and said it is also exactly 13.xx billion light years away because . . . just because. Then they said gravity from the first spot took exactly 380,000 years to travel to the second spot because . . . again just because, so, because of all the becauses, it's a triangle whose angles all add up to 180. How again did they measure the remote angles?

Shaula
2015-Apr-08, 03:18 PM
Just trying to fill in the details here. So someone pointed to a spot in the sky and said that distant point is exactly 13.xxx billion light years away (or it was when the image we see now was created). Then they moved their pointer Y degrees and pointed at another spot and said it is also exactly 13.xx billion light years away because . . . just because. Then they said gravity from the first spot took exactly 380,000 years to travel to the second spot because . . . again just because, so, because of all the becauses, it's a triangle whose angles all add up to 180. How again did they measure the remote angles?
They took a high resolution image of the CMBR. They took the angular power spectrum of the fluctuation data. This yielded a mean angular size of fluctuation. The fluctuations are associated with density fluctuations in the early universe. We know the size of these fluctuations fairly accurately from physical theory. We know the time since they were imprinted on the CMBR. Therefore we can work out if the sizes we are seeing are consistent with flat or curved geometries.

mkline55
2015-Apr-08, 03:48 PM
I see. At least the theory maintains self-consistency. It's clear that none of the conclusions are used as the basis for themselves.

ShinAce
2015-Apr-08, 06:10 PM
Correct. The theory is based on deriving the Friedman equations from general relativity. There is a term which is the curvature term. To actually measure that term is difficult. But the physics is solid. If you don't like the idea of curvature, take it up with general relativity.

mkline55
2015-Apr-08, 06:17 PM
I am fine with "curvature". It's just another term that physicists have taken out of common language and given an alternate meaning, like "spin" and "color". In this case it turns out "curvature" does not mean "curves in one of the three spatial dimensions" like people usually mean when they talk about a pitcher throwing a curve or the curvature of an arc.

Shaula
2015-Apr-08, 06:25 PM
I am fine with "curvature". It's just another term that physicists have taken out of common language and given an alternate meaning, like "spin" and "color". In this case it turns out "curvature" does not mean "curves in one of the three spatial dimensions" like people usually mean when they talk about a pitcher throwing a curve or the curvature of an arc.
The curvature of an arc is just one example of the more general notion of curvature. What mathematicians have done is generalise the term to include more than just basic 2-3D versions of what is at its root a more fundamental concept.

mkline55
2015-Apr-08, 06:37 PM
Care to explain the fundamental concept?

Shaula
2015-Apr-08, 06:48 PM
See: http://en.wikipedia.org/wiki/Riemann_curvature_tensor

The key part is:

It associates a tensor to each point of a Riemannian manifold (i.e., it is a tensor field), that measures the extent to which the metric tensor is not locally isometric to that of Euclidean space. The curvature tensor can also be defined for any pseudo-Riemannian manifold, or indeed any manifold equipped with an affine connection.

ShinAce
2015-Apr-08, 08:32 PM
You have a choice.

A) You can say that the baseball follows a straight line since it's free falling (no forces on it), and then space has the curvature built into it by gravity.

B) Or you can say that space is flat, and the baseball follows an arc because the force of gravity causes it to curve.

Common experience gives you B. Physics gives you A.

Jeff Root
2015-Apr-09, 12:51 AM
The spacetime curvature of general relativity seems to be a
"real" curvature, both similar to and intimately related to the
kinds of curvature we see in 3-D objects. So I'm saying it is
more than just an analogy. It is actual curvature. But is a
curvature of spacetime, not just space, so it is different from
ordinary 3-D curvature. When matter causes spacetime to
curve, it causes some of the 3-D space to curve in the time
direction. Some of the space becomes time. So because we
are near the Earth, we have slightly less space and slightly
more time than we would have if we were far from Earth.
The obvious effect of that difference is gravity.

The event horizon of a black hole is the location where the
black hole's matter has curved the space it is in halfway
toward being pure time. Close to the center, the curvature
approaches being pure time.

-- Jeff, in Minneapolis

ShinAce
2015-Apr-09, 03:58 AM
The first paragraph of the wiki article speaks of extrinsic vs intrinsic curvature:
http://en.wikipedia.org/wiki/Curvature

Extrinsic curvature is the curvature we know. A cylinder has extrinsic curvature. A donut has extrinsic curvature.

Intrinsic curvature is the geometrical property of Riemannian manifolds. A cylinder has no intrinsic curvature. It is flat. Similarly, the torus can be made to be flat.

ShinAce
2015-Apr-11, 02:05 PM
Let me add that the flatness of a cylinder can be made obvious.

Take a piece of paper and draw a triangle. The triangle was drawn on a flat piece of paper, so the angles add up to 180 degrees. Now curl the paper into a cylinder. You haven't stretched or compressed the paper's 'grid'. Therefore, the triangle is still the same. But that triangle indicated flatness. Therefore, the cylinder is 'geometrically' flat.

Jeff Root
2015-Apr-11, 02:57 PM
Can you explain why curving the paper in one dimension
leaves it geometrically flat, but then curving it in a second
dimension (or trying to...) stretches and compresses it so
that it is no longer flat? It is obvious that it does so, but
I can't imagine how to explain it in words. Why should
doing something once have no effect, but doing it again
(in a different direction) changes everything?

-- Jeff, in Minneapolis

ShinAce
2015-Apr-11, 03:52 PM
You already have your answer. If you can do it without stretching/compressing the paper, the geometry will stay flat. Otherwise, you need to move into the geometry of manifolds to know whether it is still flat. That's why I used the cylinder as an example, instead of the torus. It's not related to the number of times you bend the paper. You could have rippled the paper into a bizarre shape and it's still 'flat'. You're not limited to curling it.

Jeff Root
2015-Apr-11, 04:14 PM
Huh. Somehow while typing that last post I forgot that the
torus is "flat", even though you just said so in post #46.
If I curve the paper a second time into a torus, it will have
to stretch and compress (which is why I said "or trying to"
in post #48). So I know less now than I did a few minutes
ago. Nothing makes sense. I can't make a torus without
stretching and compressing the paper, yet it is "flat" like
a cylinder. A "flat" cylinder I have no problem with at all.
A "flat" torus is just complete nonsense. It has more
curves than a sphere does!

-- Jeff, in Minneapolis

ShinAce
2015-Apr-11, 05:51 PM
There is no intuitive way to see that a cylinder can be bent into a torus without altering its flat geometry. Because in the material world, you do need to stretch/compress the cylinder to make the torus.

Mathematics is just not intuitive. It is logical and owes no debt to intuition. For example, if I take the exponential number, e, and raise to any power(ex), is the answer(/solution):
a)positive
b)negative
c) imaginary
d) a single solution
e) infinite, periodic, solutions

If you allow the exponent to be an imaginary number, you can get an infinite set of negative solutions. Whereas a real exponent (the one we're used to), is a single positive solution.

If you don't believe me, look at Euler's identity.

Exposed
2015-Apr-14, 12:15 AM
Observational evidence says otherwise; The result we get back from the CMB says that the observed universe is flat.

Oops, I missed that Cougar said that already.

I don't think that's what the CMB says at all.

From what I've read, it only indicates that any curvature, if it exists, is beyond our ability to measure it in our visible universe.

If you just take a square inch part of the earth's surface, would you be able to detect the earth's curvature with a laser?

If the visible universe is only 1^100000000000000000000 part of the "entire universe", and let's assume it's curved into itself into some kind of hypersphere, would that curvature be detectable in our tiny visible universe?

WayneFrancis
2015-Apr-14, 12:52 AM
I don't think that's what the CMB says at all.

From what I've read, it only indicates that any curvature, if it exists, is beyond our ability to measure it in our visible universe.

If you just take a square inch part of the earth's surface, would you be able to detect the earth's curvature with a laser?

If the visible universe is only 1^100000000000000000000 part of the "entire universe", and let's assume it's curved into itself into some kind of hypersphere, would that curvature be detectable in our tiny visible universe?

Correct, kevin1981 and ShinAce both have mentioned that but we can still talk about the observable universe is essentially flat. If all measurements essentially give you an answer of 1 then why speculate that the actual number is off by orders of magnitude under your margin of error.

No scientist I know would claim that it is definitely flat but in a situation like this it can often confuse the issue if you say "We think it is flat but it may not be". For all intensive purposes, at this time, we can treat the universe, not only the visible universe, essentially flat.

Shaula
2015-Apr-14, 05:07 AM
If the visible universe is only 1^100000000000000000000 part of the "entire universe", and let's assume it's curved into itself into some kind of hypersphere, would that curvature be detectable in our tiny visible universe?
I hate to be pedantic but one raised to any power is one. So strictly the answer to your question is "Yes".

Also I think Noclevername meant that the observable universe is flat, which is exactly what the observations of the CMB say.

mkline55
2015-Apr-14, 11:45 AM
I hate to be pedantic but one raised to any power is one. So strictly the answer to your question is "Yes".

Also I think Noclevername meant that the observable universe is flat, which is exactly what the observations of the CMB say.

I don't mind being pedantic if it leads to greater accuracy and understanding. The observations of the CMB say nothing. They are interpreted to mean that the observable universe is flat enough within the limits of observation.

ShinAce
2015-Apr-14, 02:50 PM
Let's pretend the universe has positive curvature. Then there will be a big crunch in the future. Calculate when this will happen based on the current Hubble parameter and associated deceleration parameter.

I got you!

See? If the universe is flat, it will expand forever. If it's positively curved, it will eventually stop expanding and collapse. While no physicist can strictly say if it is flat or just much bigger than what we observe, we can make predictions about the future expansion. They do not currently jive with a positively curved universe.

Shaula
2015-Apr-14, 03:50 PM
They are interpreted to mean that the observable universe is flat enough within the limits of observation.
MDR thread is that way.

Every observation, every measurement, everything is seen through the filter of a theory. In fact even the observations are based on the theory of how a sensor reacts to incident radiation. And that theory is based on... So I am not sure what qualifying every single measurement, observation, deduction etc adds.

mkline55
2015-Apr-14, 04:11 PM
Here's the issue with the description of the flatness measurements. First, we measure the distance to two remote objects to be exactly the same. Then we calculate the distance between those two distant objects. We do that not by measuring the distance, but by applying the assumption that the universe is flat, and the distances are perfectly measured to be exactly the same. Then we calculate the angles between the adjacent sides using the previous assumptions of flatness and lengths, and come up with a consistent total which shows flatness. It certainly sounds like circular reasoning. We first assume flatness then conclude flatness based on the assumption. The problem is that no one can measure the remote distance between those two objects and no one can measure the resultant angles without first making some assumptions of flatness.

ShinAce
2015-Apr-14, 04:28 PM
Actually, we infer from theory how big the temperature fluctuations would be for (flat, positive, negative curvature) universes. We then take a picture of the microwave background. Then we match it up to theory. From that, the universe appears flat.

We do not physically measure triangles. That would be nice, though.

The method you are alluding to is baryon acoustic oscillations:
http://en.wikipedia.org/wiki/Baryon_acoustic_oscillations
I still don't fully grasp it, but I'm told by my cosmology prof that it is pretty solid.

Shaula
2015-Apr-14, 04:30 PM
Here's the issue with the description of the flatness measurements. First, we measure the distance to two remote objects to be exactly the same. Then we calculate the distance between those two distant objects. We do that not by measuring the distance, but by applying the assumption that the universe is flat, and the distances are perfectly measured to be exactly the same. Then we calculate the angles between the adjacent sides using the previous assumptions of flatness and lengths, and come up with a consistent total which shows flatness. It certainly sounds like circular reasoning. We first assume flatness then conclude flatness based on the assumption. The problem is that no one can measure the remote distance between those two objects and no one can measure the resultant angles without first making some assumptions of flatness.
As I said in post 37 that is not how they do it. And in the following post you agreed that the method as described was self-consistent. What new piece of information has changed your mid?

mkline55
2015-Apr-14, 05:46 PM
As I said in post 37 that is not how they do it. And in the following post you agreed that the method as described was self-consistent. What new piece of information has changed your mid?

Nothing I said has changed. Self-consistent = circular reasoning. You said, " We know the size of these fluctuations fairly accurately from physical theory." Are you certain that theory does not depend on a flat universe to come up with the size?

Shaula
2015-Apr-14, 06:27 PM
Nothing I said has changed. Self-consistent = circular reasoning. You said, " We know the size of these fluctuations fairly accurately from physical theory." Are you certain that theory does not depend on a flat universe to come up with the size?
Yes I am sure. The sizes were calculated as a function of curvature, not just for a value of zero. It would be a rather elementary mistake to so otherwise. The results were consistent with a near zero curvature.

WayneFrancis
2015-Apr-15, 01:50 AM
Nothing I said has changed. Self-consistent = circular reasoning. You said, " We know the size of these fluctuations fairly accurately from physical theory." Are you certain that theory does not depend on a flat universe to come up with the size?

Just an aside. Self-consistent != circular reasoning. Self consistent means that the parts don't contradict each other not that they start off with the premise that they want to end with. In a logical sense I can make a totally untrue self consistent statement that is also not circular reasoning.

Here we have the ability to calculate what something would look like with 3 different topologies. 1 with positive curvature (closed) , 1 with negative curvature (open) and 1 with zero curvature (flat). We then compare actual observation to those 3 results and it matches the flat universe. We didn't make the observation, say that is what it would look like if the universe is flat, create a model that produced that result, used that model to produce a result for positive and negative curvature, compaired the 3 and declared the universe was flat.

The fact is that science is often very hard. People, including some scientists, think that any concept should be easily described to a lay person. The problem is many concepts are very counter intuative. Many are just out right complicated. With simplified explanations comes inaccuracies. It is like models in general. Generally the more simplified you make a model the more it deviates from reality. Here we have simplified explanations of how various observations are made because many of us probably can't even properly describe the real methedology used. Taking those simplified explanations and trying to find holes in them to invalidate the real methedology isn't useful because the people involved in almost every situation would have already thought of those problems long before any of us did.

Note the "physical theories" involved are not dependent on the universe being flat or not. So if you are thinking "the physical theories, that are dependent on the universe being flat, indicate that the universe is flat" then your thinking is not correct.

ShinAce
2015-Apr-15, 03:18 AM
As an example, there's a theory that is the Sakharov conditions:
http://phys.columbia.edu/~dvp/dvp-sakharov.pdf

We know the universe contains matter but no antimatter, and LOTS of photons.

If all three of the conditions are proven to exist in the lab and quantified, we can calculate how much matter the universe should contain. We can then compare that calculation to the known universe. If so, the theory looks good. Or better yet, it hasn't been disproven.

Just because the universe contains matter, and people are looking for a reason why, doesn't mean finding a theory which matches the matter asymmetry would be circular. The theory itself does not require that there be an matter-antimatter asymmetry. It only allows for one.

Cougar
2015-Apr-15, 03:32 PM
First, we measure the distance to two remote objects to be exactly the same.

Well, the distance to the surface of last scattering (the CMB) is the same, no matter in which direction we look. It is all at a redshift of about 1089.


Then we calculate the distance between those two distant objects. We do that not by measuring the distance, but by applying the assumption that the universe is flat....

No, and no. We observe the angular size of the largest temperature fluctuations on the CMB. That angular size is restricted by the amount of time that gravity has had a chance to act on the expanding primordial plasma since the Beginning of the expansion. That amount of time is 380,000 years, since that is the amount of time needed for the expansion to cool the plasma enough for the hydrogen and helium nuclei to be able to capture and hold the loose electrons, forming electromagnetically neutral atoms (thus allowing the CMB photons to travel freely without continually interacting with charged bare nuclei and loose electrons). So gravity has had 380,000 years to work at that point, and its effect will span 380,000 lightyears (in all directions) on the CMB. The only assumption in this exercise is that the effect of gravity travels at light speed.

Now, please note that the radiation from the CMB we are now detecting left the surface of last scattering when our location in space was only ~42,000,000 lightyears from it! So the angular size (http://en.wikipedia.org/wiki/Angular_diameter_distance#Angular_size_redshift_re lation) that we measure now, reflects what that size was from that earlier time.

During the 1990s, the largest temperature variations were measured with increasing sensitivity, and by 2000 the BOOMERanG experiment (http://en.wikipedia.org/wiki/BOOMERanG_experiment) reported that the highest power fluctuations occur at angular scales of approximately one degree.

So, if we have a large isosceles triangle with a vertex angle (here on Earth) of one degree, a base of (380,000 x 2) lightyears (gravity propagates in all directions), and legs of 42,000,000 lightyears, we should be able to check if that triangle is laid out in Euclidean (flat) space... or not.

Using the law of sines, the sine of 1o is ~.01745 and the sine of 89.5o is .9999, so essentially .01745 times 42 million comes in at 733,000. That is very close to (380,000 x 2). That's why the curvature is said to be (not exactly but) very nearly flat. It's within the error bars.

ShinAce
2015-Apr-15, 04:41 PM
Cougar has summed up the 'triangle' method of measuring cosmic curvature nicely.

The same method allows an independent test of the CMBR:
http://en.wikipedia.org/wiki/Cosmic_microwave_background#Primary_anisotropy

Notice just how well the experimental observations(points) line up with the red line(theory). The theoretical curve alone has a non-trivial shape. You get several measurements in one. The location and size of the first bump(the curvature), plus the location and size of the other bumps. To think that odd looking function magically lines up with observations requires much imagination.

As we refine the measurements, the case of a flat universe can not be ruled out. Yet the 'radius' of a curved universe keeps getting bigger and bigger.

There are theoretical reasons for wanting a flat universe. Just like there are theoretical reasons for wanting a massless photon. However, we can only measure a limit on the photon mass. Just like we only measure a limit on the curvature of the universe.

Jeff Root
2015-Apr-15, 04:51 PM
Cougar,

I think it is quite a lot more complicated than that. There are
oodles of assumptions behind all the measurements and how
they relate to each other. The extent to which the results hang
together pretty much determines the extent to which we are
confident that the assumptions are correct. And there is room
for differing opinions about how well they hang together.

-- Jeff, in Minneapolis

mkline55
2015-Apr-15, 05:47 PM
I am sure all of you are trying to accurately represent the current status of mainstream theory.

Shaula
2015-Apr-15, 05:52 PM
And there is room for differing opinions about how well they hang together.
Science is not supposed to be about peoples' opinions. If you want to critique the model show that the assumptions are flawed. And show that the results are critically dependent on them. Just saying "Oh I have a gut feeling that the theory is built on shaky ground" is not an evidence based statement about the science. If you want people to listen to your critique on a theory then you should understand it in sufficient detail to do so in a constructive way - and present that constructive critique.

ShinAce
2015-Apr-15, 06:47 PM
+1 to what Shaula said.

If you claim there are oodles of assumptions, say what they are, how they relate to each other, and how that can affect the prediction.

Jeff Root
2015-Apr-15, 06:49 PM
Shaula,

I am not critiquing and don't want to critique any model.

The point of my post was that Cougar's explanation only
touches on a few aspects of the question of whether we can
tell from the available evidence what overall curvature the
Universe might have. It leaves out discussion of a lot of
assumptions. Those assumptions may all be completely
reasonable, but they make the difference between a good
theory and a not-good theory.

-- Jeff, in Minneapolis

EigenState
2015-Apr-15, 06:51 PM
Greetings,

I am in full agreement with Shaula and ShinAce.

Best regards,
ES

mkline55
2015-Apr-15, 07:20 PM
+1 to what Shaula said.

If you claim there are oodles of assumptions, say what they are, how they relate to each other, and how that can affect the prediction.

That would be pointless. It's not my theory. What started as a simple question got the old, 'WMAP proved it" response. Asking how so, I got the "we laid out a big triangle and and measured it. Questioning how it was "measured" I got, we theorized how big it would be. Asking whether that theory was based on any assumptions that the universe was flat, I got, "sure not".

I think the next question should be, what assumptions went into those theories that are the basis for determining that WMAP measured an exact triangle with precise dimensions?

Shaula
2015-Apr-15, 07:24 PM
The point of my post was that Cougar's explanation only touches on a few aspects of the question of whether we can tell from the available evidence what overall curvature the Universe might have. It leaves out discussion of a lot of assumptions. Those assumptions may all be completely reasonable, but they make the difference between a good theory and a not-good theory.
ShinAce provided a link to the Wikipedia page on the topic which has a number of references which discuss the models and assumptions made, assuming people wish to go into that level of detail. A lot of cosmology and a lot of tested predictions are based on the same assumptions. Hence my objection to this sudden desire to consider a range of opinions on how valid they are. These are not purely hypothetical models, yielding no testable predictions. These are testable scientific models. Consequently discussing what is and isn't a reasonable assumption is largely moot unless someone can present evidence that other assumptions also fit the data. The assumptions built into these models have been validated by observational evidence and I see no value in engaging in a discussion about them without alternative models or hypotheses to test. Because the perceived reasonableness of the assumptions is not what makes or breaks a model. It is the predictions it makes, the tests it passes. What humans happen to feel about it is pretty irrelevant.

One of the reasons I like science is that I don't have to listen to other peoples' opinions if they cannot back them up with evidence.

Shaula
2015-Apr-15, 07:26 PM
I think the next question should be, what assumptions went into those theories that are the basis for determining that WMAP measured an exact triangle with precise dimensions?
Have you read the Wikipedia article referenced by ShinAce? It lays out the steps fairly clearly.

Edit: This reference is particularly worth reading: http://arxiv.org/pdf/0910.5224v1.pdf

ShinAce
2015-Apr-15, 07:47 PM
That would be pointless. It's not my theory. What started as a simple question got the old, 'WMAP proved it" response. Asking how so, I got the "we laid out a big triangle and and measured it. Questioning how it was "measured" I got, we theorized how big it would be. Asking whether that theory was based on any assumptions that the universe was flat, I got, "sure not".

I think the next question should be, what assumptions went into those theories that are the basis for determining that WMAP measured an exact triangle with precise dimensions?

You did not claim 'oodles of assumptions'. The burden of proof is Jeff's.

As for measuring triangles, we've recently been going into detail about what that process involves, and I'm confident the topic has been covered.

mkline55
2015-Apr-15, 08:07 PM
Have you read the Wikipedia article referenced by ShinAce? It lays out the steps fairly clearly.

Edit: This reference is particularly worth reading: http://arxiv.org/pdf/0910.5224v1.pdf

Have you read the arxiv article? It discusses how BAO is determined. Did you see this:

We now discuss the relevant cosmological observables that are derived from standard rulers in general, and the BAO in particular. The Baryon Acoustic Oscillations in
the radial and tangential directions provide measurements of the Hubble parameter and angular diameter distance respectively. where a is the scale factor of the universe – can be written in dimensionless form using the Friedmann equation as (formula not shown here)
where f (z) is the dimensionless dark energy density and ... is the density parameter of curvature with Ωk = 0 corresponding to a flat cosmos.

I interpret this to say BAO assumes a flat universe to define the standard candle that WMAP subsequently uses to conclude that the universe is flat.

ShinAce
2015-Apr-16, 12:11 AM
Nope.

There is a quantity called the critical density. We express all densities as fractions of the critical density. If the density of matter, radiation, and dark energy add up to the critical density, there's nothing left over for curvature, and you have a flat universe. In the event that those densities add up to less (or more) than critical density, then the universe is not flat.

They said that if you plug those 3 densities as adding up to the critical density, then you get a flat universe. We know the ratio of the matter, radiation, and dark energy densities, but then you must choose if they add up to less than critical, exactly critical, or more than critical. In each case, you can predict what the BAO would look like. They've done all three, and then compared observations to those 3 predictions.

If the universe is curved, the radius must be so large that it looks flat to us.

ToSeek
2015-Apr-16, 02:58 AM
Since this has turned into a discussion instead of a question-and-answer, I've moved to from Q&A to Astronomy. Carry on.

EigenState
2015-Apr-16, 03:35 AM
Greetings,


I interpret this to say BAO assumes a flat universe to define the standard candle that WMAP subsequently uses to conclude that the universe is flat.

I do not think that your interpretation is correct.

The cosmological parameters are determined by fitting a theoretical model to the power spectra of the CMB temperature nd polarization anisotropies. The model is Lambda-CDM which assumes General Relativity, but to the best of my knowledge does not assume a shape for the universe. Using that model, the analysis of the Planck observations of temperature and polarization anisotropies yield a spatial curvature of \left\vert{} {\Omega}_{K } \right\vert{} < 0.005.

For a more comprehensive discussion see Planck 2015 results. XIII. Cosmological parameters (http://xxx.lanl.gov/abs/1502.01589).

Best regards,
ES

Cougar
2015-Apr-16, 04:37 AM
Asking how so, I got the "we laid out a big triangle and and measured it. Questioning how it was "measured" I got, we theorized how big it would be.

Apparently you did not understand the explanation. What crucial step are you thinking was "theorized"?

Shaula
2015-Apr-16, 05:01 AM
Have you read the arxiv article? It discusses how BAO is determined. Did you see this:
I would hardly have recommended it otherwise.


I interpret this to say BAO assumes a flat universe to define the standard candle that WMAP subsequently uses to conclude that the universe is flat.
As has been pointed out you have misread what they are saying. That sentence is defining omega and saying that if it turns out to be zero then the universe is flat. It then goes on to show how you can test for this. Omega is never assumed to be zero.

mkline55
2015-Apr-16, 11:57 AM
Apparently you did not understand the explanation. What crucial step are you thinking was "theorized"?
Perhaps this from ShinAce:

Actually, we infer from theory how big the temperature fluctuations would be for (flat, positive, negative curvature) universes. We then take a picture of the microwave background. Then we match it up to theory. From that, the universe appears flat.

We do not physically measure triangles. That would be nice, though.

mkline55
2015-Apr-16, 12:00 PM
I would hardly have recommended it otherwise.


As has been pointed out you have misread what they are saying. That sentence is defining omega and saying that if it turns out to be zero then the universe is flat. It then goes on to show how you can test for this. Omega is never assumed to be zero.
I don't disagree with what you say. Do you realize that you just agreed that the "measurement" of BAO already depends on a flat universe? How does using the measurement of BAO to conclude that the universe is flat not become a circular argument?

Cougar
2015-Apr-16, 01:03 PM
Perhaps this from ShinAce: "Actually, we infer from theory how big the temperature fluctuations would be for (flat, positive, negative curvature) universes. We then take a picture of the microwave background. Then we match it up to theory. From that, the universe appears flat."

I see. Yes, you do misunderstand. What about the following process do you have a problem with, or think is circular?

Based on straighforward physics, scientists hypothesize that IF the largest CMB temp fluctuations have an angular size of 1o, then space is flat. IF the angular size is less than or greater than 1o, then it's not flat. Well, let's look and see! Oh! The angular size is right around 1o. This \Rightarrow flat.

mkline55
2015-Apr-16, 01:34 PM
I see. Yes, you do misunderstand. What about the following process do you have a problem with, or think is circular?

Based on straighforward physics, scientists hypothesize that IF the largest CMB temp fluctuations have an angular size of 1o, then space is flat. IF the angular size is less than or greater than 1o, then it's not flat. Well, let's look and see! Oh! The angular size is right around 1o. This \Rightarrow flat.
Yes, leaving out the details makes it appear to be reasonable.

EigenState
2015-Apr-16, 04:11 PM
Greetings,


I don't disagree with what you say. Do you realize that you just agreed that the "measurement" of BAO already depends on a flat universe? How does using the measurement of BAO to conclude that the universe is flat not become a circular argument?

You are essentially doing nothing more than repeating your interpretation that fitting the Lambda-CDM model to the Planck power spectra assume a flat universe. Time to provide support for your assumption. Please provide objective evidence consistent with your assumption.

I have already provide a manuscript from the Planck collaboration that discusses the cosmological parameters derived from the Planck data, including the derived value for \left\vert{} {\Omega}_{ K} \right\vert{} that is consistent with a flat universe. Thus, where within their analysis do they assume a flat universe only to later corroborate that assumption?

Best regards,
ES

ShinAce
2015-Apr-16, 05:23 PM
You are essentially doing nothing more than repeating your interpretation that fitting the Lambda-CDM model to the Planck power spectra assume a flat universe. Time to provide support for your assumption. Please provide objective evidence consistent with your assumption.

Best regards,
ES

+1. Neither Shaula, nor Eigenstate, nor Cougar, nor I have agreed that "the "measurement" of BAO already depends on a flat universe?"

As an example, when Eratosthenes measured the circumference of the Earth, he assumed it was round. If it was football shaped, we would have been off. I guess he got lucky that the Earth was the same shape as the other major bodies in the sky(Moon, Sun, Venus).

Here, we are assuming that either the universe: is round, is flat, or is saddle shaped. We also assume that physics here is the same as physics there. Lastly, we assume that physics back then is the same as physics today. The same laws, always. There is no reason for a fancy assumption like a pretzel shape. But if you can work it out, and the universe is consistent with a pretzel shape, that theory is sound. But as explained, curvature is defined differently geometrically(instead of with shapes like sphere and saddle). So a 4D donut can be made flat in 3D. The normal 3D grid we imagine as space is flat. The geometry of the whole thing is solid. Very solid. Mathematicians worked hard to prove it.

If the universe is round, then there is too much energy density(with all forms added up) compared to a flat universe. This has a measurable 'circumference', the BAO, which is positive but not infinite .
If the universe is saddle-shaped, then there is not enough energy density(with all forms added up) compared to a flat universe. This has a measurable 'circumference', the BAO, which is negative but not infinite.
If the universe is flat, it has EXACTLY that critical density. The measurable circumference, the BAO, is infinite. That translates to a specific BAO size, which is what has been measured to within current limits.

If the universe is flat and a closed manifold, you can create it starting with 0 energy. The positive energy from matter is balanced by the negative gravitational energy. Otherwise, where did all this energy come from? That's what it boils down to. When the simplest explanation appears to be the right one, why would you reject it on the grounds that it appears self evident?

edit: We've shown you where the trails begin and you can choose to walk them. I'm not going to debate you over your 'disbelief'. You're free to believe what you want, even if empirical knowledge disagrees with you.

mkline55
2015-Apr-16, 05:41 PM
You are essentially doing nothing more than repeating your interpretation that fitting the Lambda-CDM model to the Planck power spectra assume a flat universe. Time to provide support for your assumption. Please provide objective evidence consistent with your assumption.

I have already provide a manuscript from the Planck collaboration that discusses the cosmological parameters derived from the Planck data, including the derived value for \left\vert{} {\Omega}_{ K} \right\vert{} that is consistent with a flat universe. Thus, where within their analysis do they assume a flat universe only to later corroborate that assumption?

Best regards,
ES

No. I already did that. I see no point in allowing you and anyone else to demand that I examine whatever random article you throw at me to see if it also has the same flaw.

mkline55
2015-Apr-16, 05:45 PM
+1. Neither Shaula, nor Eigenstate, nor Cougar, nor I have agreed that "the "measurement" of BAO already depends on a flat universe?"

As an example, when Eratosthenes measured the circumference of the Earth, he assumed it was round. If it was football shaped, we would have been off. I guess he got lucky that the Earth was the same shape as the other major bodies in the sky(Moon, Sun, Venus).

Here, we are assuming that either the universe: is round, is flat, or is saddle shaped. We also assume that physics here is the same as physics there. Lastly, we assume that physics back then is the same as physics today. The same laws, always. There is no reason for a fancy assumption like a pretzel shape. But if you can work it out, and the universe is consistent with a pretzel shape, that theory is sound. But as explained, curvature is defined differently geometrically(instead of with shapes like sphere and saddle). So a 4D donut can be made flat in 3D. The normal 3D grid we imagine as space is flat. The geometry of the whole thing is solid. Very solid. Mathematicians worked hard to prove it.

If the universe is round, then there is too much energy density(with all forms added up) compared to a flat universe. This has a measurable 'circumference', the BAO, which is positive but not infinite .
If the universe is saddle-shaped, then there is not enough energy density(with all forms added up) compared to a flat universe. This has a measurable 'circumference', the BAO, which is negative but not infinite.
If the universe is flat, it has EXACTLY that critical density. The measurable circumference, the BAO, is infinite. That translates to a specific BAO size, which is what has been measured to within current limits.

If the universe is flat and a closed manifold, you can create it starting with 0 energy. The positive energy from matter is balanced by the negative gravitational energy. Otherwise, where did all this energy come from? That's what it boils down to. When the simplest explanation appears to be the right one, why would you reject it on the grounds that it appears self evident?

edit: We've shown you where the trails begin and you can choose to walk them. I'm not going to debate you over your 'disbelief'. You're free to believe what you want, even if empirical knowledge disagrees with you.

my bold
And you do it again. Your measurement of BAO is dependent on a flat universe. You cannot then use BAO to measure something else and claim that those measurements prove the universe is flat.

EigenState
2015-Apr-16, 05:57 PM
Greetings,


No. I already did that. I see no point in allowing you and anyone else to demand that I examine whatever random article you throw at me to see if it also has the same flaw.

Random article?! That article was one of the series prepared by the Planck Collaboration (http://www.cosmos.esa.int/web/planck/publications)--that non-random set of scientists that developed the Planck mission and had first crack at the data.

Best regards,
ES

EigenState
2015-Apr-16, 06:03 PM
Greetings,


my bold
And you do it again. Your measurement of BAO is dependent on a flat universe. You cannot then use BAO to measure something else and claim that those measurements prove the universe is flat.

Emphasis added. Again incorrect. The temperature and polarization anisotropies are physical observables. The power spectra of those anisotropies are analyzed utilizing a Lambda-CDM model. Simply put--there is absolutely no assumption of a flat universe. Flatness is a conclusion drawn from the analysis.

Best regards,
ES

mkline55
2015-Apr-16, 06:09 PM
Random article?! That article was one of the series prepared by the Planck Collaboration (http://www.cosmos.esa.int/web/planck/publications)--that non-random set of scientists that developed the Planck mission and had first crack at the data.

Respectfully, yes, random. It is not specific to this conversation. The issue has to do with Shaula's claim in post #12 regarding WMAP data:

WMAP did this by looking at the angular scale of the fluctuations in the CMBR. The results came out as near to flat (less than half a percent deviation from what was expected from flat).

The issue (once again for anyone who missed it and does not care to read the whole chain) is that WMAP claimed to proved the universe is nearly flat. That was done by measuring a very large triangle. That length of the distant side of that triangle was based on BAO size. BAO is dependent on the universe being flat. Since is depends on the universe being flat, it seems invalid to use that as part of the proof that the universe is flat. It is using a circular argument to prove itself, which is a false argument. It does not mean that the universe is or is not flat. All it means is that this particular argument is invalid.

EigenState
2015-Apr-16, 06:30 PM
Greetings,


Respectfully, yes, random. It is not specific to this conversation. The issue has to do with Shaula's claim in post #12 regarding WMAP data:

On the contrary, it is exceedingly germane to the conversation. WMAP and Planck both measured the temperature anisotropies in the CMB. The Planck data is superior to that from WMAP. The resultant power spectra of the temperature anisotropies are the best method for characterizing the angular size distributions of those anisotropies.


The issue (once again for anyone who missed it and does not care to read the whole chain) is that WMAP claimed to proved the universe is nearly flat. That was done by measuring a very large triangle. That length of the distant side of that triangle was based on BAO size. BAO is dependent on the universe being flat. Since is depends on the universe being flat, it seems invalid to use that as part of the proof that the universe is flat. It is using a circular argument to prove itself, which is a false argument. It does not mean that the universe is or is not flat. All it means is that this particular argument is invalid.

Incorrect yet again! Both WMAP and Planck analyzed the full power spectra of the CMB temperature anisotropies. There were no initial assumptions regarding the flatness of the universe. There was no direct measure of triangles. The full cosmological model was fit to the observational power spectrum and that analysis affords the cosmological parameters one of which is \left\vert{} {\Omega}_{ K} \right\vert{}, the derived value of which is consistent with a flat universe to high precision.

Best regards,
ES

mkline55
2015-Apr-16, 06:51 PM
See post 12.

ShinAce
2015-Apr-16, 07:02 PM
Your measurement of BAO is dependent on a flat universe.

That is your belief, not mine.

mkline55
2015-Apr-16, 07:10 PM
From Planck 2015 results. XIII. Cosmological parameters (http://xxx.lanl.gov/abs/1502.01589) :

Baryon acoustic oscillation (BAO) measurements are a particularly important astrophysical data set. Since BAO surveys involve a simple geometrical measurement, these data are less prone to systematic errors than most other astrophysical data. As in PCP13, BAO measurements are used as a primary astro-physical data set in combination with Planck to break parameter degeneracies
Note the dependency on BAO measurements.

ShinAce
2015-Apr-16, 07:16 PM
How does that say that using BAO means you've assumed a flat universe? It does not.

Jerry
2015-Apr-16, 08:00 PM
"Flatness" eliminates a number of geometries that would imply finite size, but places no constraints upon how large or how old the universe is. It can be argued that flatness eliminates many types of 'multiverses' as well, but certainly not all.

EigenState
2015-Apr-16, 09:23 PM
Greetings,


From Planck 2015 results. XIII. Cosmological parameters (http://xxx.lanl.gov/abs/1502.01589) :

Note the dependency on BAO measurements.

There is still no initial assumption of flatness.

Best regards,
ES

Reality Check
2015-Apr-17, 12:43 AM
my bold
And you do it again. Your measurement of BAO is dependent on a flat universe. ...
Sorry, mkline55, but you actually do it again :D.
ShinAce's explanation does not start with a flat universe no matter how many times you highlight one case out of 3. It starts with a universe that is either positively curved, flat or negatively curved. It is the measurements that pick out one of the cases.

What WMAP actually did was measure that the universe was nearly flat. The really complex explanation of this is in the scientific literature that you are free to read. The "lie to children" is simple trigonometry. The fluctuations in the CMB (not baryon acoustic oscillations) provide one leg of the triangle and the other two are the lines from us to either side of the fluctuations.

BAO are standard rulers - see for example What the hell are Baryon Acoustic Oscillations? (They’re our best measurement of dark energy, even better than supernovae!)
(https://medium.com/starts-with-a-bang/what-the-hell-are-baryon-acoustic-oscillations-cfee6d726538)

Shaula
2015-Apr-17, 05:28 AM
Note the dependency on BAO measurements.
As has been pointed out repeatedly just because something has a measurement of the BAO doesn't mean they assumed a flat universe. Please point out which part of the calculation assumes this. Bearing in mind we already pointed out the bit you had misinterpreted was not doing this.

mkline55
2015-Apr-17, 12:20 PM
What the hell are Baryon Acoustic Oscillations? (They’re our best measurement of dark energy, even better than supernovae!)
(https://medium.com/starts-with-a-bang/what-the-hell-are-baryon-acoustic-oscillations-cfee6d726538)

Ten years ago, we knew that the Universe was dominated by dark energy, but the uncertainties on w, the dark energy equation-of-state parameter, were huge. (For a cosmological constant, w = -1, exactly.) We could say that w was between about -0.5 and -3.0, which is a huge range. Today? Thanks to baryon acoustic oscillations, we can say that w is between about -0.87 and -1.15, which is an incredible improvement! Future surveys, such as the one that the LSST will perform, will get this uncertainty down to just a few percent: we should be able to say that w is somewhere between -0.98 and -1.03 if that goes well.
And once again, showing that using BAO as a standard of measure is already using a presumption of flatness in the WMAP measurements. To conclude from those measurements that the universe is flat is a bad conclusion.

EigenState
2015-Apr-17, 01:52 PM
Greetings,


What the hell are Baryon Acoustic Oscillations? (They’re our best measurement of dark energy, even better than supernovae!)
(https://medium.com/starts-with-a-bang/what-the-hell-are-baryon-acoustic-oscillations-cfee6d726538)

And once again, showing that using BAO as a standard of measure is already using a presumption of flatness in the WMAP measurements. To conclude from those measurements that the universe is flat is a bad conclusion.

Where exactly is the presumption of a flat universe?

Best regards,
ES

mkline55
2015-Apr-17, 02:02 PM
Greetings,



Where exactly is the presumption of a flat universe?

Best regards,
ES

I highlighted it for your convenience in the previous quote.

EigenState
2015-Apr-17, 02:12 PM
Greetings,


I highlighted it for your convenience in the previous quote.

The highlighted portion: Thanks to baryon acoustic oscillations, we can say that w is between about -0.87 and -1.15,

where w is the dark energy equation-of-state parameter.

So how exactly does that range of values for the dark energy equation of state parameter amount to the asserted initial assumption of a flat universe?

Best regards,
ES

mkline55
2015-Apr-17, 02:32 PM
So how exactly does that range of values for the dark energy equation of state parameter amount to the asserted initial assumption of a flat universe?


From here: (http://en.wikipedia.org/wiki/Cosmological_constant#.CE.A9.CE.9B_.28Omega_Lambda .29)

ΩΛ (Omega Lambda)

Instead of the cosmological constant itself, cosmologists often refer to the ratio between the energy density due to the cosmological constant and the critical density of the Universe, the tipping point for a sufficient density to stop the universe from expanding forever. This ratio is usually denoted ΩΛ, and is estimated to be 0.692 ± 0.010, according to the recent Planck results released in 2013.[2] In a flat universe ΩΛ is the fraction of the energy of the Universe due to the cosmological constant; what we would intuitively call the fraction of the universe that is made up of dark energy. Note that this value changes over time: the critical density changes with cosmological time, but the energy density due to the cosmological constant remains unchanged throughout the history of the Universe: the amount of dark energy increases as the universe grows, while the amount of matter does not.

Equation of state

Another ratio that is used by scientists is the equation of state, usually denoted w, which is the ratio of pressure that dark energy puts on the Universe to the energy per unit volume.[3] This ratio is w = −1 for a true cosmological constant, and is generally different for alternative time-varying forms of vacuum energy such as quintessence.

Put two and two together.

ShinAce
2015-Apr-17, 03:36 PM
Ummmm.... w(omega) is used to say how much pressure something exerts.
Matter(dust) does not exert pressure because it is sitting still(w=0). Photons exert some pressure inward(w=1/3). Dark energy exerts pressure outward(w= -1).
Since we don't know what dark energy is, we need to find its energy density and pressure.

But I guess it's still ok to put terms you're not familiar with together and say 'Aha!, the universe is curved".

This thread has gone ATM. I'm out.

mkline55
2015-Apr-17, 03:49 PM
But I guess it's still ok to put terms you're not familiar with together and say 'Aha!, the universe is curved".

This thread has gone ATM. I'm out.

No. I never stated that. I am merely showing that the WMAP results claiming the they show the universe is flat are dependent on a measurement that already claims the universe is flat. It appears to be bad science.

ShinAce
2015-Apr-17, 03:56 PM
I am merely showing that the WMAP results claiming the they show the universe is flat are dependent on a measurement that already claims the universe is flat.

The parameter w does not show this. How are you showing this?

mkline55
2015-Apr-17, 04:03 PM
The parameter w does not show this. How are you showing this?

Please reread the bolded parts of post #107.

ShinAce
2015-Apr-17, 04:25 PM
The two things you bolded are not related to each other. Just because you don't realize it, does not mean you have no onus to explain what you're saying.

Just a few months ago I had numerous cosmology assignments. Some concerning the energy densities, some concerning the curvature and some concerning the equation of state parameter.

As an example, what we call dark energy has w = -1. There was another theory at some point called quintessence, where w varies with time and is between 0 and -1. In both cases, the shape of the universe would be unaffected.

I'm sorry, but it is clear you do not understand how these terms are defined in cosmology. You cannot make your point when the rest of us agree what those words mean, but your definition is different.

Shaula
2015-Apr-17, 05:17 PM
Please reread the bolded parts of post #107.
Everyone telling you that you are wrong has, they have pointed out why you are wrong and yet you just keep repeating yourself. I suggest you go back through the source and work through the model they are presenting in sufficient detail that you can show which parts of it rely on a flat universe. Because you seem to be the only person here who thinks that this dependency is there.

mkline55
2015-Apr-17, 06:02 PM
Everyone telling you that you are wrong has, they have pointed out why you are wrong and yet you just keep repeating yourself. I suggest you go back through the source and work through the model they are presenting in sufficient detail that you can show which parts of it rely on a flat universe. Because you seem to be the only person here who thinks that this dependency is there.
Are we now accepting argument by popularity as science, too? So far, since that post, "Everyone" is you and ShinAce. I don't know how you can determine that every other poster has read that post, nor that they would agree with you. But that is not the point. I have already made my point. I have already provided documented evidence of that point. I have already answered the questions.

ShinAce
2015-Apr-17, 06:18 PM
I have already provided documented evidence of that point. I have already answered the questions.

Your documented evidence does not say what you think it says. Nor have you answered any questions directly.

Let's pretend that the concept of BAO assumes a flat universe. In this case, the universe we see looks flat and you now have a bunch of physicists working on a 'flatness problem'. Why is the universe so flat?

Now let's pretend that the concept of BAO does not assume a flat universe. In this case, the universe we see looks flat and you now have a bunch of physicists working on a 'flatness problem'. Why is the universe so flat?

Remember that there are other tests for flatness. A summary of the whole thing is here:
http://www.symmetrymagazine.org/article/april-2015/our-flat-universe?email_issue=725

You should write your own summary, as it is unique and original.

Cougar
2015-Apr-17, 06:46 PM
I have already made my point.

Yes, and it has been pointed out that your point is in error. As far as I'm concerned, the angles of the triangle from here to the CMB add pretty close to 180, so that space is pretty flat. This is also consistent with an early inflationary period.

Exposed
2015-Apr-17, 06:53 PM
I think the issue is really about semantics. I don't have an issue with someone stating "WMAP/Planck data shows the universe is nearly flat", because it's pretty much proven.

What I would have an issue with, is someone stating "WMAP/Planck data shows the universe IS flat."

There is no way we will ever know if the universe is completely flat, or just appears flat in our visible universe but is actually curved on a much, much larger scale. Not in mine or your lifetimes at least.

EigenState
2015-Apr-17, 07:09 PM
Greetings,


Are we now accepting argument by popularity as science, too? So far, since that post, "Everyone" is you and ShinAce. I don't know how you can determine that every other poster has read that post, nor that they would agree with you. But that is not the point. I have already made my point. I have already provided documented evidence of that point. I have already answered the questions.

No, we are not doing science via a popularity contest, but I must wonder why I was excluded from the list of "everyone".

More germane to the discussion is that you have by no means either made your point, provided documented evidence, or answered the questions posed.

From the WIkipedia page you quoted above (post #107) regarding the cosmological constant {\Omega}_{ \Lambda} with emphasis added:


Instead of the cosmological constant itself, cosmologists often refer to the ratio between the energy density due to the cosmological constant and the critical density of the Universe, the tipping point for a sufficient density to stop the universe from expanding forever. This ratio is usually denoted ΩΛ, and is estimated to be 0.692 ± 0.010, according to the recent Planck results released in 2013.[2] In a flat universe ΩΛ is the fraction of the energy of the Universe due to the cosmological constant; what we would intuitively call the fraction of the universe that is made up of dark energy. Note that this value changes over time: the critical density changes with cosmological time, but the energy density due to the cosmological constant remains unchanged throughout the history of the Universe: the amount of dark energy increases as the universe grows, while the amount of matter does not.

Note especially "is estimated to be 0.692 ± 0.010, according to the recent Planck results released in 2013.[2]" The reference cited is: Planck 2013 results. XVI. Cosmological parameters (http://lanl.arxiv.org/abs/1303.5076), another one of those pesky "random" manuscripts from the Planck Collaboration.

Table 2 (page 12 of the PDF file) is instructive. Scrutiny of that table shows clearly that {\Omega}_{ \Lambda} was a derived parameter and shows clearly that the best fit value of {\Omega}_{ \Lambda} varies slightly depending upon the inclusion of lensing data and/or WMAP polarization data.

Section 2 (page 5ff of the PDF file) presents a comprehensive discussion of Model, parameters, and methodology. Nowhere do I see the assumption of a flat universe.

Unless you can demonstrate unambiguously that the analysis of either the WMAP or the Planck data explicitly assumed a flat universe and constrained the analysis to that flat universe as clearly implied by your prior commentary, then I believe that objectively we are done here.

Best regards,
ES

mkline55
2015-Apr-17, 07:33 PM
No, we are not doing science via a popularity contest, but I must wonder why I was excluded from the list of "everyone".


Really? Me in post 111 in response to ShinAce: "Please reread the bolded parts of post #107." Your response now was to my post 114.
Posts between 107 and 114 were: 108 - ShinAce, 109 - Me, 110 - ShinAce, 111- Me, 112 - ShinAce, 113 - Shaula, 114 - Me, and you wonder why you were not included in that list? Do you see your name in that list? Although I respect you a lot, it is clear that you are either misreading my posts or just starting with your own prejudices and assuming you already know what I am writing without reading them at all.

ShinAce
2015-Apr-17, 08:24 PM
He's simply saying that he agrees with our point of view, therefore he should be added to the list. It was innuendo.

You said:
"So far, since that post, "Everyone" is you and ShinAce."

Eigenstate is saying that should be "you, ShinAce, and Eigenstate".

Cougar
2015-Apr-17, 08:35 PM
From the WIkipedia page you quoted above...

"the energy density due to the cosmological constant remains unchanged throughout the history of the Universe: the amount of dark energy increases as the universe grows, while the amount of matter does not."



Yes, it's interesting that the ratio of their contributions to the critical density changes with time. I can't quite do the math in my head; :rolleyes: how is the flatness affected?

ShinAce
2015-Apr-17, 08:51 PM
The flatness is unaffected, because if the universe is flat, it will stay flat. If it's positively curved, it will stay positively curved. If it's negatively curved, it stays negatively curved. The shape of the universe was determined at the big bang, and does not change.

The energy density for dark energy is a constant regardless of the size factor(a) of the universe. Energy density from matter scales as a-3. Energy density from radiation scales as a-4. Where 'a' is taken to be 1 today. To get 'a', you divide the size of the universe 'then' by the size of the universe 'now'. Last but not least, curvature. If the universe is not exactly flat, curvature's 'energy density' scales as a-2.

Curvature is already accounted for in the terms for energy density, so the relationship is surprisingly simple. That's why mkline's argument fails. The curvature term was included, then found to be consistent with being zero.

EigenState
2015-Apr-17, 09:25 PM
He's simply saying that he agrees with our point of view, therefore he should be added to the list. It was innuendo.

You said:
"So far, since that post, "Everyone" is you and ShinAce."

Eigenstate is saying that should be "you, ShinAce, and Eigenstate".

I was just trying to weasel my way onto the list of authors of the forthcoming manuscript. :doh:

ShinAce
2015-Apr-17, 09:39 PM
I actually weaseled my way OUT of a manuscript as an undergrad. I was asked to review a grad student's work and when I realized there were no results because he did no work(despite claiming otherwise), I informed the prof and told her that I simply did not have time to do the experiment myself.

After that, the prof and I wrote a paper together. The publishing world is a strange creature.

Shaula
2015-Apr-18, 04:45 AM
Are we now accepting argument by popularity as science, too? So far, since that post, "Everyone" is you and ShinAce. I don't know how you can determine that every other poster has read that post, nor that they would agree with you. But that is not the point. I have already made my point. I have already provided documented evidence of that point. I have already answered the questions.
Ah, I see you have misread what I wrote too. I said "Everyone telling you that you are wrong has, they have pointed out why you are wrong and yet you just keep repeating yourself." That is not the same as "Everyone has pointed out why you are wrong and yet you just keep repeating yourself."

My point is that the people you keep telling to read your quotes (the ones telling you that you are wrong) have read your quotes and are telling you that you are misinterpreting them. I also asked you to go beyond just picking a few words and deciding what they mean and find some actual science. So you have not answered that question at all.

mkline55
2015-Apr-19, 02:12 PM
I have read through a number of summaries, reports, results, etc. of the WMAP release 9 data where curvature was reported. What I have been unable to locate is a detailed description of the derivation of curvature in those reports. Does anyone here have a link to a detailed description of the precise method and inputs used to derive the reported curvature range?

Shaula
2015-Apr-19, 03:02 PM
The subject is probably too large for a single paper, it takes in large amounts of big bang cosmology, high energy plasma physics and so on. The reference I provided has much of the method in, along with reference to papers and a bibliography. You could start there.

ShinAce
2015-Apr-19, 03:57 PM
See section 6.2:
http://arxiv.org/pdf/astro-ph/0302209.pdf

As it is a scientific paper, familiarity with the terms and methods discussed are the reader's responsibility.

mkline55
2015-Apr-19, 04:13 PM
The subject is probably too large for a single paper, it takes in large amounts of big bang cosmology, high energy plasma physics and so on. The reference I provided has much of the method in, along with reference to papers and a bibliography. You could start there.

I assume your link to a NASA site.

Two things stand out to me in this reference. First, is this:

A central feature of the microwave background fluctuations are randomly placed spots with an apparent size ~1 degree across. These are produced by sound waves that travel through the hot ionized gas in the universe at a known speed (the speed of light divided by the square root of 3) for a known length of time (375,000 years). By using the relation: distance = rate * time, we can infer the distance the sound travels, and thus the actual size of a typical hot (compressed) or cold (rarefacted) spot.
While distance = rate * time in an unchanging environment, weren't those initial 375,000 years a time of tremendous expansion? I think the formula is being oversimplified (at least in this presentation). Whether or not that is what they really did is unclear.

The second thing is that the one degree of arc measurement between energy spikes should be more easily verified by rotating the view 360 degrees and counting the spikes. The result should be real close to 360. Easier yet, rotate it just 10 degrees and see if all eleven spikes still line up. So I find it hard to imagine that they were testing to see if the angle was one degree like the drawing seems to show. Were they instead testing to see if the distance between WMAP and the CMD matched what they expected?

mkline55
2015-Apr-19, 04:25 PM
See section 6.2:
http://arxiv.org/pdf/astro-ph/0302209.pdf

As it is a scientific paper, familiarity with the terms and methods discussed are the reader's responsibility.

Thanks. That is actually a much more useful paper.

Shaula
2015-Apr-19, 04:28 PM
No, the NASA site is way to basic for the level of detail you want to go into. I meant http://arxiv.org/pdf/0910.5224v1.pdf - sorry, should have reposted the link.

I'll warn you now that unless you are already about undergraduate level in your physics background there is a lot to cover. When I did this topic at uni it was about two weeks of lectures in a larger cosmology module. And that was expecting everyone to have two years of a degree as their background knowledge.

EigenState
2015-Apr-19, 04:55 PM
Greetings,


I have read through a number of summaries, reports, results, etc. of the WMAP release 9 data where curvature was reported. What I have been unable to locate is a detailed description of the derivation of curvature in those reports. Does anyone here have a link to a detailed description of the precise method and inputs used to derive the reported curvature range?

References already posted here provide detailed discussions of the theoretical analyses including the requisite literature citations:

Planck 2013 results. XVI. Cosmological parameters (http://arxiv.org/abs/1303.5076)

Planck 2015 results. XIII. Cosmological parameters (http://xxx.lanl.gov/abs/1502.01589)

Best regards,
ES

ShinAce
2015-Apr-19, 06:28 PM
I'll warn you now that unless you are already about undergraduate level in your physics background there is a lot to cover. When I did this topic at uni it was about two weeks of lectures in a larger cosmology module. And that was expecting everyone to have two years of a degree as their background knowledge.

I'll warn that even if you've recently completed a physics undergrad(like me), there's still some work to be done before you can soak it all in.

I linked to the WMAP equivalent of what Eigenstate just linked(Planck). Same idea, same result. Planck is just the newer, more sensitive, version.

Reality Check
2015-Apr-20, 12:41 AM
And once again, ..
Sorry but that is a bit ignorant about the citation, mkline55.
What the hell are Baryon Acoustic Oscillations? (They’re our best measurement of dark energy, even better than supernovae!) (https://medium.com/starts-with-a-bang/what-the-hell-are-baryon-acoustic-oscillations-cfee6d726538) is not about WMAP or even the flatness of the universe.

This distance scale — the scales at which galaxies are correlated — is known as the acoustic scale, because it’s the baryons (things like protons) that are oscillating in-and-out of these overdense regions. The phenomenon that causes this distance correlation is called baryon acoustic oscillations (BAO), and we can use this at all redshifts to measure how the Universe’s expansion rate has changed over time.
Just 20 years ago, this was barely a feasible method to measure anything in the Universe. But with the advent of surveys like the two-degree field galaxy redshift survey (2dFGRS) and, currently, the Sloan Digital Sky Survey (SDSS), we’ve measured the positions and redshifts of enough galaxies to see this effect in unprecedented detail.
... Today? Thanks to baryon acoustic oscillations, we can say that w is between about -0.87 and -1.15, which is an incredible improvement! Future surveys, such as the one that the LSST will perform, will get this uncertainty down to just a few percent: we should be able to say that w is somewhere between -0.98 and -1.03 if that goes well.
where w is the dark energy (or cosmological constant) equation-of-state parameter.

ETA: This is measuring the positions of galaxies and thus w.
The limits on w from BAO are then used in Planck modeling of the CMB to break degeneracies of parameters. This is where you use a model to fit data. The model has a parameter X with values x1, x2 and x3 that all fit the data. That is a degeneracy. To break it you need a separate measurement of X (or something X depends on) that excludes 2 of the values.

Reality Check
2015-Apr-20, 12:56 AM
Put two and two together.
Obviously some simple math is not being done by you mkline55.
"In a flat universe ΩΛ is the fraction of the energy of the Universe due to the cosmological constant;" + "This ratio is w = −1 for a true cosmological constant" = a flat universe is 2 + 2 = undefined!

You need to read what you quote, mkline55: Cosmological constant (http://en.wikipedia.org/wiki/Cosmological_constant#.CE.A9.CE.9B_.28Omega_Lambda .29)

ΩΛ (Omega Lambda)
Instead of the cosmological constant itself, cosmologists often refer to the ratio between the energy density due to the cosmological constant and the critical density of the universe, the tipping point for a sufficient density to stop the universe from expanding forever. This ratio is usually denoted ΩΛ, and is estimated to be 0.692 ± 0.010, according to the recent Planck results released in 2013.[2] In a flat universe ΩΛ is the fraction of the energy of the universe due to the cosmological constant; what we would intuitively call the fraction of the universe that is made up of dark energy. Note that this value changes over time: the critical density changes with cosmological time, but the energy density due to the cosmological constant remains unchanged throughout the history of the universe: the amount of dark energy increases as the universe grows, while the amount of matter does not.
Equation of state
Another ratio that is used by scientists is the equation of state, usually denoted w, which is the ratio of pressure that dark energy puts on the universe to the energy per unit volume.[3] This ratio is w = −1 for a true cosmological constant, and is generally different for alternative time-varying forms of vacuum energy such as quintessence.

w is not ΩΛ :doh:!

Reality Check
2015-Apr-20, 01:08 AM
Really? Me in post 111 in response to ShinAce: "Please reread the bolded parts of post #107."

Asking someone to read posts that display an inability to understand English as she is written is not a good response, mkline55.
You quote the scientific definitions of 2 different quantities (ΩΛ and w) and assert that what you highlight is the assumption of a flat universe.
What you actually highlight are two irrelevant phrases. The first is a statement of what ΩΛ is for a flat universe. The second is what w is for a true cosmological constant.
The Planck value of ΩΛ = 0.692 ± 0.010 is basically how much of the universe is dark energy.
The two-degree field galaxy redshift survey (2dFGRS) and the Sloan Digital Sky Survey (SDSS) values of w between -0.87 and -1.15 is dark energy acts like a cosmological constant (w=-1) which constrains theories like quintessence.

mkline55
2015-Apr-20, 11:57 AM
Obviously some simple math is not being done by you mkline55.
"In a flat universe ΩΛ is the fraction of the energy of the Universe due to the cosmological constant;" + "This ratio is w = −1 for a true cosmological constant" = a flat universe is 2 + 2 = undefined!

You need to read what you quote, mkline55: Cosmological constant (http://en.wikipedia.org/wiki/Cosmological_constant#.CE.A9.CE.9B_.28Omega_Lambda .29)

w is not ΩΛ :doh:!

Right. I should never have expected anyone to see any connection whatsoever between the two phrases "w = -1 for a true cosmological constant" and "In a flat universe ΩΛ is the fraction of the energy of the universe due to the cosmological constant", nor that one of them so clearly includes the "In a flat universe" phrase.

ShinAce
2015-Apr-20, 03:50 PM
Honestly, yes. Not without first knowing what a cosmological constant and ΩΛ mean.

A cosmological constant is something that has energy per cubic metre everywhere, but that density of energy doesn't change with time, where w is < 0. It acts like anti-gravity, you could say.

ΩΛ is how much if the universe's energy is in the form of dark energy. For the total amount of energy to make a flat universe, call that 100%. What is the % for dark energy? That's ΩΛ.

The only reason it says 'in a flat universe' is because the energy densities have to be compared to some pre-determined amount. That amount is the critical density, and represents a flat universe. So they used the wording 'in a flat universe' instead of 'dividing the energy densities by the critical density'. If the energy components added up to 270%, we would clearly live in a closed universe. It we found 27% total, we'd be looking at an open universe.

How can someone claim that a sentence says 'this or that' when they are unfamiliar with the terms used?

mkline55
2015-Apr-20, 06:31 PM
How can someone claim that a sentence says 'this or that' when they are unfamiliar with the terms used?

The same way someone can declare that identical terms mean different things in consecutive sentences.

Shaula
2015-Apr-20, 07:30 PM
OK lets focus on exactly what you are hung up on. The first part:

In a flat universe ΩΛ is the fraction of the energy of the Universe due to the cosmological constant
This doesn't mean that ΩΛ assumes a flat universe. All it means is that IF the universe is flat the quantity ΩΛ is equal to the fraction of the energy in the universe due to the cosmological constant. If the universe is not flat then it is a more complex beast to describe, in essence it is the pseudo-tensor associated with the cosmological constant (which becomes path dependent so can no longer be called a true energy) with possible extra terms introduced due to the curvature. For experiments this is irrelevant as you are just measuring the number, not the components of it. This number is inferred from the different histories of the baryonic, non-baryonic and 'left over' components of the model. These are not dependent on the initial assumption of flatness.

Then:

This ratio is w = −1 for a true cosmological constant
Implies that for a simple cosmological constant, unmodified by quintessence or second order curvature effects, w=-1. It does not mean we assume a flat universe to calculate w.

There is simply no indication here that the underlying methods or models are dependent on the assumption of a flat universe. As has been pointed out it simply would not make any logical sense to come up with a way to test for a flat observable universe that started off with the assumption that the observable universe is flat. And you would imagine that given the amount of peer review this work has undergone someone would have called them on that by now if it was there. You are misunderstanding what is said, that is all.

mkline55
2015-Apr-20, 08:21 PM
I'm not certain whether the issue is that I ask too many questions or if I demand too much precision. Some of the responses I got here were unnecessarily vague and others were just repetitive. I read all the responses. There was no need to repeat one another. The need was to clarify one another. My intention is drawing this out so long was to make this thread informative. Leaving it at "WMAP determined curvature by measuring angles" was just leaving it at a hand-waving level. Now, if someone else wants to chase through this thread, they can find some useful links with much better detailed explanations.

Thanks.

ShinAce
2015-Apr-20, 08:31 PM
The same way someone can declare that identical terms mean different things in consecutive sentences.

Which sentences? Which terms? That's a little vague.

It appears you don't understand the concept.

The Universe may have something in it which has positive energy, like light and matter. However, it would have negative pressure. Matter exerts no pressure, light exerts positive pressure. That thing is called the cosmological constant.

It's often convenient to talk about things in relation to a known quantity. Like the dollar. Everything is priced in dollars, but the initial amount of a dollar was arbitrarily set. That doesn't mean the universe costs one dollar. We just have a definition for a universe worth one dollar.

You then measure how much matter, radiation and dark energy there is. You can measure matter by counting galaxies. You can measure dark matter from galaxy cluster motions. You can measure radiation by measuring light flux and neutrino flux. You can measure dark energy by measuring the Hubble constant throughout time with supernovae. That is a measure of the universe's worth. It's consistent with being one dollar.

See:
http://en.wikipedia.org/wiki/Flatness_problem#Measurement

At this point though, this thread is becoming repetitive.

ShinAce
2015-Apr-20, 08:43 PM
Now, if someone else wants to chase through this thread, they can find some useful links with much better detailed explanations.

Thanks.

The explanations are all there if you read through the thread. As for better explanations, that depends on your background. If you're not comfortable with calculus, nobody will be able to show you better yet detailed explanations. John Baez has some good stuff. So does Ned Wright.

But you have to learn to walk before you can run. You need to understand Newton's gravity, from which you can derive the Friedmann equations, if you know calculus. Once you have that, you need a second equation to be able to solve it. You then use the pressure-energy relationship for different types of energies coupled with thermodynamics. That's the equation of state parameter. Then you're off to the races.

Reality Check
2015-Apr-20, 10:04 PM
Right. ...repeated ignorance snipped....
Basic English should tell you that a description of ΩΛ is not a description of w, mkline55 - they are two different things!
Basic English should tell you that the phrase "In a flat universe" in Cosmological constant (http://en.wikipedia.org/wiki/Cosmological_constant#.CE.A9.CE.9B_.28Omega_Lambda .29) is not a assumption that leads to a calculation of a flat universe, mkline55 :eek:!
Cosmological constant (http://en.wikipedia.org/wiki/Cosmological_constant#.CE.A9.CE.9B_.28Omega_Lambda .29) is describing what ΩΛ and w are.

Reality Check
2015-Apr-20, 10:15 PM
The same way someone can declare that identical terms mean different things in consecutive sentences.
Who has said that, mkline55? For someone who is demanding precision that is really vague :D!
We have pointed out the obvious to you which is precisely:
* Cosmological constant (http://en.wikipedia.org/wiki/Cosmological_constant#.CE.A9.CE.9B_.28Omega_Lambda .29) is describing two different things (ΩΛ and w).
* Nowhere in that article is a calculation of the curvature of the universe.
* Actual calculations of the curvature of the universe start with the assumption that the universe has either positive, zero or negative curvature. There is no assumption that the universe is flat.
* "WMAP determined curvature by measuring angles" is the "lies to children" version as in their web page WMAP : Shape of the Universe (http://map.gsfc.nasa.gov/universe/uni_shape.html):

The WMAP spacecraft can measure the basic parameters of the Big Bang theory including the geometry of the universe. If the universe were flat, the brightest microwave background fluctuations (or "spots") would be about one degree across. If the universe were open, the spots would be less than one degree across. If the universe were closed, the brightest spots would be greater than one degree across.

Recent measurements (c. 2001) by a number of ground-based and balloon-based experiments, including MAT/TOCO, Boomerang, Maxima, and DASI, have shown that the brightest spots are about 1 degree across. Thus the universe was known to be flat to within about 15% accuracy prior to the WMAP results. WMAP has confirmed this result with very high accuracy and precision. We now know (as of 2013) that the universe is flat with only a 0.4% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe.

* Actual calculations of the curvature of the universe are complex as in the links within this thread.

Ken G
2015-Apr-21, 03:33 AM
Every observation, every measurement, everything is seen through the filter of a theory. In fact even the observations are based on the theory of how a sensor reacts to incident radiation. And that theory is based on... So I am not sure what qualifying every single measurement, observation, deduction etc adds.
The point there is, there is a time to not bother to add the qualifications, and there is a time to notice that they are there all the same. The only problem is when people claim the qualifications don't exist-- as people sometimes do claim. When we can be sure everyone knows the qualifications are there, they don't need to be repeated. When we are not at all clear that everyone knows the qualifications are there, we need to repeat them from time to time. What that adds is a healthy dose of skepticism-- the beating heart of scientific inquiry.

In regard to the flatness of the universe, if everyone knows that we can only say that the observable universe is very nearly flat, then we can just say "the universe is flat" and be confident people understand what that means. When people say "this means the universe is infinite in size" or something like that, they need to be reminded of the qualifications.

mkline55
2015-Apr-21, 11:42 AM
Which sentences? Which terms? That's a little vague.

Post 107. See the bolded parts. I will not repost, having already been accused of repeating myself. See that "cosmological constant" according to everyone here who disagrees with me has a different meaning in the two sentences. Because, if it had the same meaning, then you should be able to substitute the values from one sentence into the other.

mkline55
2015-Apr-21, 11:44 AM
* Cosmological constant (http://en.wikipedia.org/wiki/Cosmological_constant#.CE.A9.CE.9B_.28Omega_Lambda .29) is describing two different things (ΩΛ and w).

Is the meaning of "cosmological constant" the same in both instances?

Ken G
2015-Apr-21, 02:25 PM
Post 107. See the bolded parts. I will not repost, having already been accused of repeating myself. See that "cosmological constant" according to everyone here who disagrees with me has a different meaning in the two sentences. Because, if it had the same meaning, then you should be able to substitute the values from one sentence into the other.You are mistaken, those are exactly the same cosmological constant. The cosmological constant can be described in three different ways, that are all equivalent. It can be included as a constant term in Einstein's field equation (that's how Einstein did it), it can be included as a constant mass density in the Friedmann equation (or equivalently, a varying ratio of the density to the critical density in the dimensionless form of the Friedmann equation that cosmologists like because it involves order-unity numbers like 0.69 and so on), or it can be included in the equation of state (by the w parameter) that shows up in the acceleration equation that can be derived from the Friedmann equation. Those might sound like different things to you, but they are all exactly the same.

ShinAce
2015-Apr-21, 02:36 PM
Again, w=-1 refers to the fact that it has negative pressure. This does not imply a flat universe. It is the equation of state parameter for dark energy.

ΩΛ is the ratio of dark energy in the universe divided by total energy of a flat universe. If all the Ω's add up to 1, then you have a flat universe. It is the energy density for dark energy.

mkline55
2015-Apr-21, 02:58 PM
You are mistaken, those are exactly the same cosmological constant. The cosmological constant can be described in three different ways, that are all equivalent. It can be included as a constant term in Einstein's field equation (that's how Einstein did it), it can be included as a constant mass density in the Friedmann equation (or equivalently, a varying ratio of the density to the critical density in the dimensionless form of the Friedmann equation that cosmologists like because it involves order-unity numbers like 0.69 and so on), or it can be included in the equation of state (by the w parameter) that shows up in the acceleration equation that can be derived from the Friedmann equation. Those might sound like different things to you, but they are all exactly the same.

Why then would it not be valid to merge the statement: "In a flat universe ΩΛ is the fraction of the energy of the Universe due to the cosmological constant"

with this statement: "This ratio is w = −1 for a true cosmological constant"

to get "In a flat universe ΩΛ is the fraction of the energy of the Universe due to the ratio where w = −1"?

Ken G
2015-Apr-21, 03:43 PM
Why then would it not be valid to merge the statement: "In a flat universe ΩΛ is the fraction of the energy of the Universe due to the cosmological constant"

with this statement: "This ratio is w = −1 for a true cosmological constant"

to get "In a flat universe ΩΛ is the fraction of the energy of the Universe due to the ratio where w = −1"?Because although the first two statements are correct and clear, the "merged statement" is quite confusing. As just pointed out, w=-1 is always true of a cosmological constant, regardless of whether or not it makes the universe flat. Also, your merged sentence does not make it clear what "ratio" is being referred to (w is the ratio of the pressure to the energy density for that effect). But in principle, the sentences could certainly be merged, it seems like a stylistic choice to me.

Shaula
2015-Apr-21, 04:15 PM
to get "In a flat universe ΩΛ is the fraction of the energy of the Universe due to the ratio where w = −1"?
How does a ratio convert to an energy? That sentence doesn't really make sense - you omit the physical basis for both components. Plus as Ken says w=-1 is not dependent on a flat universe, nor does a flat universe require w=-1.

Reality Check
2015-Apr-22, 12:56 AM
Is the meaning of "cosmological constant" the same in both instances?
Yes, :doh:!
It is the meaning of ΩΛ and w that are different - read the different symbols used to represent these different things, mkline55. They even have different units of measurement.

PetersCreek
2015-Apr-22, 04:48 PM
:doh:

This is just one example (and not the worst) of the tone on both sides of the table that needs to improve significantly and immediately. The volume of reports from a number of members is more typical of an ATM train wreck than an astronomy thread.