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Cosmological Observations Conundrum

by wstrohm
Tags: conundrum, cosmological, observations
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wstrohm
#1
Jan24-13, 08:21 PM
P: 13
Perhaps I am missing something obvious, but here it is anyway.

Observation of an astronomically distant object is essentially observation of a past condition of the object, due to the fixed speed of light. And IIRC, the Hubble constant seems to say that all sufficiently distant objects recede from the observer (any observer, supposedly anywhere in the universe) at a rate of about 77.3 Km/sec per mega-parsec of distance, or 77.3 Km/sec per ~3.28 million light-years.

So if we look at a galaxy 3.28 million light-years distant, we see it receding at 77.3 Km/second. But what we are really seeing is that it was receding at 77.3 Km/second 3.28 million years ago. If we see a galaxy many times that distance receding many times faster, we are (of course) really seeing it much earlier in time. Although Hubble's constant is a d(v)/d(s) value, acceleration is not defined as d(v)/d(s), it is defined as d(v)/d(t).

If the observed recession velocities of galaxies are plotted as a function of time, not distance, the galaxies were decreasing their recession velocities as time progressed.

What does that say about the expansion of the universe "accelerating?"
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Bobbywhy
#2
Jan24-13, 10:08 PM
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Hi wstrohm. Ned Wright's Cosmology Tutorial is one of the most authentic, respected, and well-written sources for information on this subject. You may find a satisfactory explanation at his website. See this FAQ: “Why do we think that the expansion of the Universe is accelerating?”
http://www.astro.ucla.edu/~wright/cosmology_faq.html#CC

Cheers,
Bobbywhy

(edit) If you do not get satisfied using Ned Wright's site, do return here with your doubts and questions. Some members here are highly qualified to answer your doubts/questions.
marcus
#3
Jan25-13, 01:06 AM
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Quote Quote by wstrohm View Post
Perhaps I am missing something obvious, but here it is anyway.

So if we look at a galaxy 3.28 million light-years distant, we see it receding at 77.3 Km/second. But what we are really seeing is that it was receding at 77.3 Km/second 3.28 million years ago...
Hubble law is a statement about today's rate of expansion of today's distances. Where did you get the 77.3 figure? I don't recall ever having seen it before. Nowadays some people are using numbers around 70 and others using 71 and some higher but nothing as high as 77, that I know of.

Hubble law relates the instantaneous distance (if you could stop expansion TODAY to get time to measure it) to the rate that distance is expanding right now, this very day.

The Hubble rate actually evolves over time according to a form of the Einstein equation. The rate at some time t in the past (call it H(t) ) is the corresponding thing for that time. the distance THEN related to the rate it was increasing THEN.

So the cosmology model give you a whole past history of the instantaneous expansion rate. that is what determines the predicted redshifts. And that is what is required to fit the observational data.

Chalnoth
#4
Jan25-13, 10:49 AM
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Cosmological Observations Conundrum

Quote Quote by wstrohm View Post
Perhaps I am missing something obvious, but here it is anyway.

Observation of an astronomically distant object is essentially observation of a past condition of the object, due to the fixed speed of light. And IIRC, the Hubble constant seems to say that all sufficiently distant objects recede from the observer (any observer, supposedly anywhere in the universe) at a rate of about 77.3 Km/sec per mega-parsec of distance, or 77.3 Km/sec per ~3.28 million light-years.

So if we look at a galaxy 3.28 million light-years distant, we see it receding at 77.3 Km/second. But what we are really seeing is that it was receding at 77.3 Km/second 3.28 million years ago. If we see a galaxy many times that distance receding many times faster, we are (of course) really seeing it much earlier in time. Although Hubble's constant is a d(v)/d(s) value, acceleration is not defined as d(v)/d(s), it is defined as d(v)/d(t).

If the observed recession velocities of galaxies are plotted as a function of time, not distance, the galaxies were decreasing their recession velocities as time progressed.

What does that say about the expansion of the universe "accelerating?"
What it says is that we have to be a bit careful when understanding our observational data. When the light from a far-away galaxy was first emitted, the expansion rate was faster but things were closer together. We have to incorporate the rate of expansion over the entire period from the time the light was emitted to now to determine how the distance we measure is related to the object's redshift.
wstrohm
#5
Jan25-13, 12:35 PM
P: 13
Thank you all for your thoughtful answers and references. I have looked at Ned Wright's paragraph in the link above, which for me raises more questions. I was thinking of our basic observations, assuming only speed of light and recession velocity (due to red shift), not even considering whether distance has been determined accurately.

Faraway objects are seen moving away faster than close objects, which inherently means objects were at more ancient times moving away faster than objects at more recent times.

No matter whether the Hubble dv/ds value is a constant over time or not, no matter whether it is correct or not, the curve of recession velocity with time has a negative slope. The curve may be linear or concave upward or even convex upward, but the slope is always negative, if plotted (between all the "snapshots" of our astronomical observations) versus time. I am leaving out altogether the question of accurate distance.

If my text is unclear, I apologize. Think of what I am writing in this way: Consider the red shift of a galaxy as a dot on an x-y plot. Time flows in the +x direction and distance in the -x direction. On this graph, two sets of units or x-axes can be overlaid... light-years for distance increasing to the left, years for time progressing to the right. And because of the choice of units (years and light-years), they are numerically equal at any point. Recession velocity increases in the +y direction. The plot will show the highest red shifts/velocities on the upper left and the lowest red shifts/velocities on the lower right. The curve's y-values increase to the left (per Hubble) and decrease to the right (with time).

The following is all IMHO and subject to change if convinced otherwise:

The logical conclusion from the above is that recession velocities were decreasing as time flowed forward.

Also I question Ned Wright's premise that we can ever know a galaxie's distance "NOW," by any means whatsoever. We can never know anything about an object in space at any more recent time than at that time at which light left it.
Chalnoth
#6
Jan25-13, 06:28 PM
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The problem with that statement is that there is no unique definition of recession velocity, because there is no unique definition for the velocity of a far-away object.
skydivephil
#7
Jan25-13, 06:30 PM
P: 451
Isnt t=0 the moment the scale factor goes to zero and Gr gives infinite answers for pressure, curvature, density etc?
Johninch
#8
Jan28-13, 10:12 AM
P: 96
Quote Quote by wstrohm View Post
The logical conclusion from the above is that recession velocities were decreasing as time flowed forward.
You are right for the first 5bn years when galaxies were being formed and you are wrong for the last 5bn years when expansive dark energy has become much stronger than gravity in intergalactic space. The "cosmic jerk" took place between 5bn and 8bn years ago. Read about it here:

http://www.sdss3.org/press/lyabao.php

.
wstrohm
#9
Jan28-13, 11:51 AM
P: 13
Johninch,

Fascinating article, mostly over my head. But note that in the range of -5 billion years (light-years) to present, objects still appear to be slowing their recession velocity from us as time flows forward. I think I have a basic lack of understanding of time itself, maybe...

Thanks for your response!
marcus
#10
Jan28-13, 01:31 PM
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Quote Quote by wstrohm View Post
... But note that in the range of -5 billion years (light-years) to present, objects still appear to be slowing their recession velocity from us as time flows forward. I think I have a basic lack of understanding of time itself, maybe...
I think the source of your confusion could be that you equate measuring an object's redshift with measuring its recession speed at the time it emitted the light.

That would give a decent approximation for comparatively nearby objects like those studied by Hubble in 1930s and 1940s but overall it does not work. The redshift is NOT determined by the recession speed at the time of emission. So someone who equates those two would inevitably get into a terrible mess of confusion.

I am only guessing. I can't be confident I understand what you have been saying or that I understand your process of reasoning.

However if that is what you are doing, if that is the basis of the problem, then people can easily help by explaining what the observed redshift actually represents mathematically!

1+z = received wavelength/emitted wavelength

1+z = distance now/distance then
(now = when light is received, back then = when light was emitted)

The 1+z ratio is the proportion or ratio by which both wavelengths and distances have increased while the light has been in transit. The convention is to subtract 1 from this ratio and call that "z" the redshift number.

Cosmology is about fitting a math model (of the expansion history) to the observational data and getting the simplest model with the best fit. In that sense it is holistic. You have to make the model fit ALL the data. That is how, for instance, distances of things at various times now and in the past are determined. They are what they have to be in order to get the simplest best fit to the data which we can observe.

Here is a picture of one object's recession history as you vary the model parameters
http://ned.ipac.caltech.edu/level5/M...s/figure14.jpg
the dashed curves and the thin-line curves are what you get from adjusting the parameters differently.
The dark heavy curve is what you get when you adjust the two key parameters how we think is right. The model is derived from 1915 Einstein GR equation, which is our law of gravity (and geometry). There is a lot of confidence in GR because it has been checked and rechecked in many ways at many scales and gives amazingly accurate predictions. The model, once it is derived from GR, has very few adjustable parameters. You can see in the Figure 14 that there are basically just two main numbers being adjusted.

What you see there is the two-decimal-place best fit to ALL the observations as of 2003 when the article was published. At that time the central values of the confidence intervals were .71 and (.27, .73). In the figure you can see the .71 down at the bottom and the (.27, .73) in the legend at the upper left corner labeling the dark split curve.
Tanelorn
#11
Jan28-13, 06:41 PM
P: 711
I presume these supercluster maps show the true relative positions of galaxies where they really are today, rather than the observed positions ie. where they used to be?
http://upload.wikimedia.org/wikipedi...%28JPEG%29.jpg
Chalnoth
#12
Jan28-13, 06:50 PM
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Quote Quote by Tanelorn View Post
I presume these supercluster maps show the true relative positions of galaxies where they really are today, rather than the observed positions ie. where they used to be?
http://en.wikipedia.org/wiki/Virgo_Supercluster
Computing the eventual positions is, for the forseeable future, impossible. Basically what you'd be asking for here is to run a massive N-body simulation without knowing the initial velocities.
Tanelorn
#13
Jan28-13, 07:02 PM
P: 711
Thanks Chalnoth, good to know. Its a bit like seeing a picture map of Gondwana land and trying to work out from this where your house is relative to NYC. They should make this clear more I think.
A very nice pic though:

http://upload.wikimedia.org/wikipedi...%28JPEG%29.jpg

Can we at least produce a rough version of the above which takes into account the hubble expansion of space? It should be just based on how distant objects are away from us.
ConformalGrpOp
#14
Feb1-13, 12:01 PM
P: 40
Quote Quote by marcus View Post
The model is derived from 1915 Einstein GR equation, which is our law of gravity (and geometry). There is a lot of confidence in GR because it has been checked and rechecked in many ways at many scales and gives amazingly accurate predictions. The model, once it is derived from GR, has very few adjustable parameters. You can see in the Figure 14 that there are basically just two main numbers being adjusted.

What you see there is the two-decimal-place best fit to ALL the observations as of 2003 when the article was published. At that time the central values of the confidence intervals were .71 and (.27, .73). In the figure you can see the .71 down at the bottom and the (.27, .73) in the legend at the upper left corner labeling the dark split curve.
Marcus, you always seem to be focused on the heart of the issues at hand. This post is no different. Fig 14, comparing the recession history of an object using different values for the model's parameters is instructive.

(The following has been corrected from the original post)

The ΛCDM model, the one employed to interprete the data in the paper, "Baryon Acoustic Oscillations in the Ly- forest of BOSS quasars", by members of the SDSS III group referenced in Johninch'sr post, is based on GR.

In the model employed by SDSSIII, Λ (Lambda) stands for the cosmological constant which is currently associated with a vacuum energy or dark energy inherent in empty space. This is the plug-in is used to make the model fit the parameters of the current accelerating expansion of space against the attractive (collapsing) effects of gravity from matter. In that model, the cosmological constant is interpreted as the fraction of the total mass-energy density of a flat universe that is attributed to dark energy. Currently, about 73% of the energy density of the present universe is estimated to be dark energy.

That is, according to the ΛCDM model, the amount of dark energy is a direct function of the metrics governing the accelerating expansion of the universe, and therefore, our understanding of the need for/role of dark energy/matter in the model is intimately dependent on our measure of the expansion based on the cosmological redshift.

In essence, everything we think we know about dark matter, dark energy and the expansion of the universe is entirely dependent on our determination of the value of the Hubble constant and the behavior of EM across cosmological distances.

The paper by the SDSS III group is very interesting for the unique techniques used to measure the absorption of light from quasars by the intervening Ly-α gas clouds.
Chalnoth
#15
Feb1-13, 12:47 PM
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Quote Quote by ConformalGrpOp View Post
In essence, everything we think we know about dark matter, dark energy and the expansion of the universe is entirely dependent on our determination of the value of the Hubble constant and the behavior of EM across cosmological distances.
Sorta kinda. Our measurements of all of the parameters are interrelated, and any significant change in one of them impacts all of the others.

However, that said, we now have quite good measurements of the expansion rate.
wstrohm
#16
Feb1-13, 12:49 PM
P: 13
It's good to see the return of phlogiston... (j/k)
marcus
#17
Feb1-13, 02:27 PM
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Conformal,
We don't seem to be communicating. I did not reference a SDSSIII paper. I did not refer to "Baryon Acoustic Oscillations in the Ly-forest of BOSS quasars" which you say I referenced.

I also did not make any reference to "vacuum energy" or "dark energy" which I find is an unnecessary idea. I treat the cosmological constant Lambda simply as a curvature constant that appears naturally in the Einstein GR equation.

There is no evidence AFAIK that this curvature arises from some type of "energy". That way of thinking of it was very popular for a time but now seems to be going out of style--as evidence piles up that we are simply dealing with a constant that appears in the equation which is our law of gravity/geometry.

If you want to pursue the subject I would recommend the article you get by googling "rovelli prejudices". It's written for wide audience, is quite accessible and "down to earth". Worth a serious examination.
Quote Quote by ConformalGrpOp View Post
Marcus, you always seem to be focused on the heart of the issues at hand. This post is no different. You point out that the ΛCDM model, the one employed to interprete the data in the paper, "Baryon Acoustic Oscillations in the Ly- forest of BOSS quasars", by members of the SDSS III group which you referenced in your post, is based on GR, and only has a limited number of adjustable parameters.

In the model employed by SDSSIII, Λ (Lambda) stands for the cosmological constant which is currently associated with a vacuum energy or dark energy inherent in empty space. This is the plug in is used to make the model fit the parameters of the current accelerating expansion of space against the attractive (collapsing) effects of gravity from matter.

The cosmological constant is interpreted as the fraction of the total mass-energy density of a flat universe that is attributed to dark energy. Currently, about 73% of the energy density of the present universe is estimated to be dark energy.

That is, the amount of dark energy is a direct function of the metrics governing the accelerating expansion of the universe, and therefore, our understanding of the need for/role of dark matter in the model is initimately dependent on our measure of the expansion based on the cosmological redshift.

In essence, everything we think we know about dark matter, dark energy and the expansion of the universe is entirely dependent on our determination of the value of the Hubble constant and the behavior of EM across cosmological distances. The paper by the SDSS III group is very interesting for the unique techniques used to measure the absorption of light from quasars by the intervening Ly-α gas clouds. I think this project is likely to bear more rich fruit which may significantly advance our understanding of the universe even beyond the targeted effort to calculate the effects of dark energy, etc.
I don't know what you are talking about when you refer to "the paper by the SDSS III group" maybe you should give a reference, but probably it does not matter. Dark matter and the cosmological constant are very different topics. I don't see the sense in lumping them together. Dark matter can be observed (by weak lensing) and regions of higher and lower density can be mapped---one has contour maps of DM concentration. This does NOT depend critically on precise determination of the Hubble expansion rate! (Contrary to what you suggest.)

For historical reasons people CUSTOMARILY quantify the cosmological constant as an energy density equivalent.
That is a convention, maybe they should change the convention. But in physics that kind of thing is done all the time--energy equivalents are used to express (lengths, inertias) quantities which are not energies.

Quote Quote by wstrohm View Post
It's good to see the return of phlogiston... (j/k)
As I see it, your joke is about 10 years out of date. Back in 2003 various "dark energy" ideas were getting a lot of attention. People were talking about "quintessence" and "big rip". Some mysterious energy field was causing expansion to accelerate. That, I think would have been a witty time to mention "phlogiston". Now after that fad has begun to subside and one sees less and less speculation along those lines, it falls kind of flat.

What I've found is that, for me, a handy way to quantify Lambda is to remember what it's square root is:
the reciprocal of a certain distance. Namely 16.3 Gly.
Tanelorn
#18
Feb2-13, 09:13 AM
P: 711
Quote by ConformalGrpOp

In essence, everything we think we know about dark matter, dark energy and the expansion of the universe is entirely dependent on our determination of the value of the Hubble constant and the behavior of EM across cosmological distances.


Quote by Chalnoth

Sorta kinda. Our measurements of all of the parameters are interrelated, and any significant change in one of them impacts all of the others.

However, that said, we now have quite good measurements of the expansion rate.



This is perpetually at the back of my mind also. Over the past 2000 years we have had several instances where scientific theories have been rewritten in the light of new evidence and understanding. Here we have built an entire intricate cosmology pretty much on the value of the Hubble constant and the behavior of EM across cosmological distances.

I realise that it is rare or perhaps never that we can say anything with absolute certainty, but always at the back of my mind I feel a nagging doubt of a finite element of risk that our observations are somehow deceiving us.

Perhaps if I had taken these measurements myself with instruments that I fully understand I then might reduce these occasional doubts, but we have to rely on others for this and also others for the interpretation of these measurements.

I hope that Cosmologists will keep their minds open to the admittedly remote possibility of alternatives and that means welcoming new ideas and working professionally through they pros and cons without being overly defensive.


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