I Any direct measure of Universe expansion via galaxy subtended angles?

[Bandersnatch]

Thank you for the additional detail. I am seeing your point now. A part that is still not clear to me though, is that my understanding of OU was all that can at some point be seen while Visible Universe (VU) is all that we can currently see. I am not sure if you are talking about OU above or VU. There are many galaxies in our OU that have given off light that has not had sufficent time to reach us here on Earth and so would be in the OU but not the VU. I did not see much distinction in the article between VU and OU.

Judging by the above, I think what you call OU is the event horizon according to standard nomenclature. While your VU would be OU (or past light cone, or particle horizon). VU doesn't function in standard usage. See if the articles and the discussion above make more sense in this light.

 

[phinds]

Thank you for the additional detail. I am seeing your point now. A part that is still not clear to me though, is that my understanding of OU was all that can at some point be seen while Visible Universe (VU) is all that we can currently see. I am not sure if you are talking about OU above or VU. There are many galaxies in our OU that have given off light that has not had sufficent time to reach us here on Earth and so would be in the OU but not the VU. I did not see much distinction in the article between VU and OU.

As far as I am aware "visual universe" is a pop-science term not actually used by physicists but I would expect it to be just the OU by another name.

EDIT: I see Bandersnatch beat me to it. I didn't see his post before posting.

 

[alantheastronomer]

Summary: Is there anyone examining a large sample of galaxies' subtended angles over time, as an independent test of the universe's supposed expansion?

As indicated in the title and summary, I'm wondering if there is any large scale astronomical effort to assess directly the universal spatial expansion assumed by the Doppler interpretation of the redshift/distance relationship, by measuring individual galaxy subtended angles over time. The predicted decreases in size over time should be small, to be sure, but with a large enough sample size and good enough telescopes, may be measurable over a 5-, 10-, or 20-year period.

If you're interested in doing it yourself, you can access data from the Sloan Digital Sky Survey (SDSS) and the 2 Micron All Sky Survey (2MASS)…have at it! - But be forewarned, the limitations that Bandersnatch and Vanadium 50 pointed out will most likely make it futile...

Are you seriously questioning the expansion of the universe?

Even though he said he supposes so, I think he's just proposing an additional method to nail down the expansion rate, in addition to the cosmological distance ladder and the distances to SNIa explosions, if it were only observationally viable!

 

[mfb]

There is one way we can measure the expansion of the universe directly as change over time with near future instruments: We can measure the change of the redshift of a source over time. ELT will be able to do it, although this task will require hundreds or even thousands of observation hours - it is unclear if that much time will be spent on a single project.

 

[Vanadium 50]

Even though he said he supposes so, I think he's just proposing an additional method to nail down the expansion rate

Gosh, I usually go with what someone actually said instead of something else which is almost the opposite of what he actually said.

 

[Buzz Bloom]

I suggest it might be possible that a measurement across a combination of galaxies in relatively nearby cluster group (but not one that we are gravitationally connected with) might have a large enough angle to notice a angular shrinking over say a hundred years.

Well I found it quite difficult, but I will report what I did find out.
First, I confirmed that the local group is not gravitationally bound to M82 group.
The distance from the Earth to the M81 group is given as 1.174 x 10⁷ ly.
The criteria I used is that
(1) at the distance D from the gravitation body (the local group) has an an attraction gravitational acceleration of
[1] A_G = GM/D²,
and at distance D the universe expansion acceleration is
[2] A_H = H₀²D.
The value of D when
[3] A_G = A_H
is the threshold between being gravitationally bound and not.
From [1], [2], and [3], this distance is
[4] D_GB = (GM/H₀²)^1/3.
Converting the units for G from
m² kg^-1 s^-2
to the units
ly³ M_S-1 (solar mass) yr^-2
gives
[5] G = 1.75976 x 10^-17 ly³ M_S^-1 y^-2.
The mass of the local group is
[6] M_LG = 1.03 x 10¹² M_S.
The reciprocal of the Hubble constant is
[7] 1/H₀ = 1.44 x 10¹⁰ y.
From [5], [6] and [7] the following is the calculated value
[8] D_GB = 1.94 x 10⁵ ly.
This is much less than the distance between Earth and M81
[9] D_E-M81 = 1.174 x 10⁷ ly.

OK, now I will discuss two galaxies in the M81 group: M81 and M82.
Galaxies M81 and M82 are 36 arc minutes (= 2160 arc seconds) apart.
[10] α = 2160 arc seconds
The expansion speed at which M81 and M82 are moving away from Earth is
[11] V = H₀ D_E-M81 = 8.15 x 10^-4 ly/yr.
The distance moved in 100 years is
[12] ΔD = 8.15 x 10^-2 ly.
The distance ratio is
[13] ΔD/D = 8.15 x 10^-2 / 1.174 x 10⁷ ly = 6.942 x 10^-9.
This means that after 100 years the angular distance between M81 and M82 will shrink by
[14] Δα = α ΔD/D = 1.76 x 10^-5 arc seconds.

I apologize for not including references. My wide has just told me it is time for us to leave for a previous commitment. I hope to have time to add some more details and references in several days.

Regards,
Buzz

 

[PeterDonis]

The criteria I used is that
(1) at the distance D from the gravitation body (the local group) has an an attraction gravitational acceleration of
[1] AG = GM/D2,
and at distance D the universe expansion acceleration is
[2] AH = H02D.
The value of D when
[3] AG = AH
is the threshold between being gravitationally bound and not.

There are at least two things wrong with this.

First, if we ignore for the moment the effect of dark energy, the correct criterion for whether a pair of objects are gravitationally bound is whether their relative recession velocity is greater than escape velocity. The recession velocity is $V_H = H_0 D$ and the escape velocity is $V_E = \sqrt{2 M / D}$, so $V_E = V_H$ gives

$$
D = \left( \frac{2 M}{H_0^2} \right)^{\frac{1}{3}}
$$

Your formula happens to be within a factor of $2^{1/3}$ of this (once we add back the corrections for using conventional units instead of the "natural" units I used), but that just means you were lucky to get an answer close to the right one using wrong logic.

Second, if we are talking about "universe expansion acceleration", we are talking about dark energy, which adds an extra correction to the above formula. The easiest way to add that correction is to modify the escape velocity formula from the one for Schwarzschild spacetime, which is what we were using above, to the one for Schwarzschild-de Sitter spacetime; that gives us

$$
V_E = \sqrt{\frac{2 M}{D} - \frac{D^2}{\alpha_0^2}}
$$

where $\alpha$ is the distance to the cosmological horizon "now". Plugging that into $V_E = V_H$ gives

$$
D = \left( \frac{2 M}{H_0^2 + \frac{1}{\alpha_0^2}} \right)^{\frac{1}{3}}
$$

As you can see, this decreases $D$ compared to the formula above that ignored dark energy, so for your purposes here the above formula (assuming your math is correct when the factors for conventional units are added back in) is fine. But you still need to use correct reasoning to get to it.

 

[mfb]

M81 and M82 have some relative velocity. All you'll measure by tracking their angular separation is their relative velocity. 1.76 x 10^-5 arc seconds in 100 years at 12 million light years distance is just 3 km/s.

 

[Buzz Bloom]

There are at least two things wrong with this.

Hi Peter:

I do appreciate the time you took to point out my errors about gravitational boundedness relative to the
expanding universe. I find that your corrections raise more questions in my mind which I would like to pursue. However, these questions seem to me to not be related to the topic of this thread, so I plan to start a new thread specifically about gravitational boundedness relative to the expanding universe.

Regards,
Buzz

 

[dabunting]

I appreciate this discussion very much!
Except for those who ask, "Are you seriously questioning...?"
If we're not questioning, we're not scientists.

hkyriazi asked:
"Is there anyone examining a large sample of galaxies' subtended angles over time, as an independent test of the universe's supposed expansion? I'm wondering if there is any large scale astronomical effort to assess directly the universal spatial expansion assumed by the Doppler interpretation of the redshift/distance relationship... A Doppler shift is one interpretation of the redshift/distance relationship. Others are possible. I'd be happy to see any direct confirmation of the expansion..."

There's a lot we don't know about the universe: Is there anything beyond our observed universe? Or do we assume it infinite?
Could the entire observed universe be within the singularity or very tiny space origin of the Big Bang?
Do we make the questionable assumption that we are at the singularity or very tiny space origin of the Big Bang?
The explanation seems very concocted for the observation that the space between galaxies increases and accelerates with time while the size of galaxies (or gravitationally bound space) does not increase or accelerate.
Explanations also seem concocted or non-existent regarding the Great Attractor in the direction of the Shapley Supercluster and the Dipole Repeller, the two comprising the CMB Dipole.
The CMB spectral radiance contains small anisotropies that match what would be expected if small thermal variations generated by quantum fluctuations of matter in a very tiny space had expanded to the size of the observable universe we see today.
I ask again: Is the entire observed universe WITHIN the "very tiny space," or singularity, the origin of the Big Bang?
We postulate or concoct dark matter and energy with peculiar characteristics that conveniently explain(?) all.
But yes...
We question.

 

[PeterDonis]

If we're not questioning, we're not scientists.

Questioning things that are still open questions is indeed part of science.

Questioning things that are nailed down by data is not.

There's a lot we don't know about the universe

But there's also a lot we do know, and you can't usefully speculate about what we don't know until you have a firm, thorough grasp of what we do know. The rest of your post is speculation without such a firm grasp, and such speculation is not allowed per the PF rules.