neophyte question about hubble's law

Hans Aberg a écrit :
jacob navia wrote:
Each second (I read that in this incredible thread) there are 174 Km
more of space between Andromeda and me.

The Andromeda Galaxy is closing in towards our Milky Way galaxy at a
speed of about 300 km/second, though one does not know for sure there
will be a collision.
http://en.wikipedia.org/wiki/Andromeda_Galaxy
http://en.wikipedia.org/wiki/Androme..._Way_collision

Hans

Excuse me but in this same thread and this same discussion group
"Nicolaas Vroom" said (message of Oct 21st, 14:38)

quote
If you start from Andromeda Galaxy with speed of 2,2 Myr
(From the book Universe Box 26.1) you get using H=70
from: http://en.wikipedia.org/wiki/Hubble's_law
v = H*d = 154 km/sec (Using box 26.2)
end quote

I was quoting from memory. I dig out the article and it was 154, not 174
as I wrongly supposed.

I note too that all the relevant questions of my post are left unanswered
and you limit yourself to "correcting" a detail.

Can you try a more substantive answer?

Thanks

jacob navia wrote:
I note too that all the relevant questions of my post are left unanswered
and you limit yourself to "correcting" a detail.

Can you try a more substantive answer?

It looks as though you are addressing me, though this is a public forum:

Your questions are for experts on physical interpretations of
cosmological models making use metric expansion of space. I'm curious
about that too.

In the GR I know, objects cannot move faster than c, and it is
formulated as a coordinate independent Lorentz manifold.

So I'm curious on how metric expansion models with objects having speeds
above c relate to that.

Hans

Thus spake Phillip Helbig---remove CLOTHES to reply
CLOTHESvax.de
In article , Hans Aberg
writes:

Did his analysis say that the universe must have a metric expansion? - I
thought it just said that it could not be stable.

Define "metric expansion".

The problem is that there is only retrofitting of data, and the theory
seems designed so that it can't be refuted. For example, HE 1523-0901 is
a 13.2 Gy old generation two star in the Milky Way and the BB universe
13.73 Gy. Suppose one would find a star older that this theoretical age,
would the BB theory be judged wrong and scrapped? If not, what is the
litmus test of this theory?

13.73 Gy is not exact.

No measured figure is exact, but this one cannot be far out. It is not
just found from calculations of cosmological parameters, but in my view,
it is rather more certainly found from the rate of expansion in the
early universe which gives rise to the relative proportions of light
elements via big bang nucleosynthesis. In answer to the OP's question,
it just ain't gonna happen. Or rather, it actually has happened, but it
shows something wrong with the method of aging stars (which is known to
be a bit dodgy in certain respects), not with the age of the universe.


Regards

--
Charles Francis
moderator sci.physics.foundations.
charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces and
braces)

http://www.rqgravity.net

Oh No wrote:
13.73 Gy is not exact.

No measured figure is exact, but this one cannot be far out. It is not
just found from calculations of cosmological parameters, but in my view,
it is rather more certainly found from the rate of expansion in the
early universe which gives rise to the relative proportions of light
elements via big bang nucleosynthesis. In answer to the OP's question,
it just ain't gonna happen. Or rather, it actually has happened, but it
shows something wrong with the method of aging stars (which is known to
be a bit dodgy in certain respects), not with the age of the universe.

What that has happened will not happen? A change in the value? The OP is
about inferring movements 12 My ago and now of the same object.

Hans

"dfarr --at-- comcast --dot-- net" schreef in bericht
...
The 'Hubble's law' Wikipedia article states '...that the velocity at
which various galaxies ARE receding from the Earth IS proportional to
their distance from us.' (emphasis added)

My question is about the tense of the two verbs in all caps above.
Aside from assuming things are orderly,
do we have any way of inferring that a galaxy that was moving away
from us 12 billion years ago is still doing so? The light from the
galaxy which is reaching us now indicates it was moving away, but do
we have any way of inferring that it has not slowed down or started to
approach us, or disappeared off the 'edge'?



[[Mod. note -- The following is quoted with only slight changes
from a recent posting of mine in sci.physics.research, and seems
relevant here too:

The Earth is roughly 149 million
kilometers = 8.5 light-minutes away from the Sun. So, if we look
outside during daylight hours, we have observational data that the
Sun was shining 8.5 minutes ago. But we have *no* observational
data about what the Sun is doing right *now*.


The more I read the less I understand.
By measuring the parallax of an object we can calculate the past
distance of that object.
Q: Is it also possible to calculate the present position and velocity
of that object?
Within our solar system the answer is yes because we can perform
a sequence of observations and use Newton's law.
Within our Galaxy the answer is also Yes.
Outside Our Galaxy the Answer is No

For individual stars (Cepheids) at that distance we use luminosity
to calculate the past distance.

By measuring the redshift (z) we can calculate the velocity of an object
in the past.
Q: Can we use redshift also the calculate the past distance
and what about the present distance and present velocity ?.
Using redshift we can calculate the past velocity of stars within
Andromeda Galaxy but we cannot use z to calculate the past
position nor the present position and present velocity.

Galaxy NGC 4258 (at a larger distance) the same problems exists.

For a Galaxy like UGC 3789 (again at a larger distance) the problems
become worse.
At the moment of emission this Galaxy has a radial speed away from us
resulting in a certain value of z. However that is not the measured
value of z, which will be larger, being caused by the expansion of space.
The question is now: Which part is caused by movement of source
(in the past) and which part by expansion of space
(going from past to present)
Assuming we can solve that we are left with the Question:
What is the current position and velocity of UGC 3789 ?
IMO we cannot answer that.
(Only that its position will be further away)

For more details and documents studied read:
http://users.telenet.be/nicvroom/Hubble-Faq.htm

Nicolaas Vroom

In article , "Nicolaas Vroom"
writes:

"dfarr --at-- comcast --dot-- net" schreef in bericht
...
The 'Hubble's law' Wikipedia article states '...that the velocity at
which various galaxies ARE receding from the Earth IS proportional to
their distance from us.' (emphasis added)

True, though keep in mind that some people use the term "Hubble's Law"
to mean something different. See

http://adsabs.harvard.edu/abs/1993ApJ...403...28H

In the sense in which you use it above, this means that the velocity
(defined as the change in proper distance (which is the distance you
could measure instantaneously with a rigid ruler) per cosmic time
(essentially time as measured by someone at rest with respect to the
microwave background) as measured now) is proportional to the proper
distance. However, these are not quantities which can be "directly
observed" This law is a trivial consequence of homogeneous and
isotropic expansion.

My question is about the tense of the two verbs in all caps above.

In the sense above, it refers to the present value of all the
quantities, at this moment in cosmic time.

Aside from assuming things are orderly,
do we have any way of inferring that a galaxy that was moving away
from us 12 billion years ago is still doing so?

Yes (see below).

The light from the
galaxy which is reaching us now indicates it was moving away,
^^^
Why do you say this? You uppercased the terms referring to the present
tense.

but do
we have any way of inferring that it has not slowed down or started to
approach us, or disappeared off the 'edge'?

Yes (see below).

The Earth is roughly 149 million
kilometers = 8.5 light-minutes away from the Sun. So, if we look
outside during daylight hours, we have observational data that the
Sun was shining 8.5 minutes ago. But we have *no* observational
data about what the Sun is doing right *now*.

Strictly speaking, true. But we have good reason to believe that we can
extrapolate 8 minutes into the future.

The more I read the less I understand.
By measuring the parallax of an object we can calculate the past
distance of that object.

If you mean parallax in the traditional sense, then this is true only
for objects which are quite close, well within our galaxy, not at
cosmological distances, with light-travel times of a few years.

Q: Is it also possible to calculate the present position and velocity
of that object?

Yes (see below).

Within our solar system the answer is yes because we can perform
a sequence of observations and use Newton's law.

Right.

Within our Galaxy the answer is also Yes.

Right.

Outside Our Galaxy the Answer is No

You are answering your own question here. Why do you say "no"? The
answer is "yes".

For individual stars (Cepheids) at that distance we use luminosity
to calculate the past distance.

Distances which can be measured using Cepheids are extremely small,
cosmologically, so all distances are equivalent.

By measuring the redshift (z) we can calculate the velocity of an object
in the past.

At low redshift this is true, but not at high redshift, unless you have
a really bizarre definition of "velocity". See the paper by Harrison
mentioned above.

Q: Can we use redshift also the calculate the past distance
and what about the present distance and present velocity ?.

Yes (see below).

Using redshift we can calculate the past velocity of stars within
Andromeda Galaxy but we cannot use z to calculate the past
position nor the present position and present velocity.

The Andromeda galaxy is so close that the cosmological redshift is
negligible. The redshift is due to its peculiar velocity and hence
can't be used to calculate the past velocity.

At the moment of emission this Galaxy has a radial speed away from us
resulting in a certain value of z. However that is not the measured
value of z, which will be larger, being caused by the expansion of space.

Wrong. If the redshift is large enough to be cosmologically
interesting, then you cannot use it to infer the velocity. There is a
small range where cosmological redshifts are larger than those due to
other causes (primarily peculiar velocity) but still small enough to use
a linear approximation and calculate the velocity as if the redshift were
due to a Doppler effect. In this case, the difference between the
distance now and distance then (at the time of light emission), or
velocity now and velocity then, is negligible.

The question is now: Which part is caused by movement of source
(in the past) and which part by expansion of space
(going from past to present)

The cosmological redshift is due only to the expansion of space. The
galaxy might have a peculiar velocity which will make an additional
contribution.

Assuming we can solve that we are left with the Question:
What is the current position and velocity of UGC 3789 ?
IMO we cannot answer that.
(Only that its position will be further away)

If it is close enough so that one can approximate its velocity from
measuring the redshift, then the difference between these two distances
is negligible.

In the general case (arbitrarily large redshift), we can calculate the
distance (however it is defined) both now and at the time the light was
emitted.

The redshift, by itself, tells us the ratio of the scale factor now to
that at the time the light was emitted. It tells us NOTHING ELSE. At
low redshift, one can show that one can approximate the velocity by
using the Doppler formula. At high redshift this is not possible (and
don't even think about the relativistic Doppler formula; it is
irrelevant here). To get further, one has to know the cosmological
parameters. If they are known, then one can calculate any distance at
any time from the redshift for the given cosmological parameters. See,
for example,

http://www.astro.multivax.de:8000/he...ts/angsiz.html

"Phillip Helbig---undress to reply"
schreef in bericht ...
In article , "Nicolaas Vroom"
writes:

"dfarr --at-- comcast --dot-- net" schreef in bericht
...
The 'Hubble's law' Wikipedia article states '...that the velocity at
which various galaxies ARE receding from the Earth IS proportional to
their distance from us.' (emphasis added)

True, though keep in mind that some people use the term "Hubble's Law"
to mean something different. See

http://adsabs.harvard.edu/abs/1993ApJ...403...28H

In the sense in which you use it above, this means that the velocity
(defined as the change in proper distance (which is the distance you
could measure instantaneously with a rigid ruler) per cosmic time
(essentially time as measured by someone at rest with respect to the
microwave background) as measured now) is proportional to the proper
distance. However, these are not quantities which can be "directly
observed" This law is a trivial consequence of homogeneous and
isotropic expansion.

I fully agree that there two Hubble Laws.
See also: http://users.telenet.be/nicvroom/Hubble-Faq.htm
The first law describes the relation between Distance and redshift (z)
Expressed as D = c/H * z
The second law describes the relation between Distance and speed
and uses the relation v = c * z
and then you get: D = v/H or v = H *d

I have a problem with this second law specific with the definition
of what means v ?
a) Is v the speed of the Galaxy in the past at moment of emission.
or b) is the v the present speed of the Galaxy ?

For example what means the speed of 7772 km/sec for NGC 6323
calculated using z = 0.026 and H = 72 km/sec/Mpc ?

I have no problem with the relation v = c * z only at very small
distances, implying that the second law does not apply.

The more I read the less I understand.

Q: Can we use redshift also the calculate the past distance
and what about the present distance and present velocity ?.

Yes (see below).

At the moment of emission this Galaxy has a radial speed away from us
resulting in a certain value of z. However that is not the measured
value of z, which will be larger, being caused by the expansion of space.

Wrong. If the redshift is large enough to be cosmologically
interesting, then you cannot use it to infer the velocity.
I agree if you mean the velocity of the galaxy in the past at emission.

The question then remains what does z at those distance represent ?
Does z then represent distance ?
what is this relation ?
based on which observations is this relation demonstrated ?
and what means large enough ? z =0.023 ?

If z = 0.023 is the minimal boundary than you need indepent measurments
in order to establish this relation.

The question is now: Which part is caused by movement of source
(in the past) and which part by expansion of space
(going from past to present)

The cosmological redshift is due only to the expansion of space. The
galaxy might have a peculiar velocity which will make an additional
contribution.

The issue is that contribution will be larger the further the galaxy is
and the further you go back in time.
Making it more and more difficult to calculate its distance.

Assuming we can solve that we are left with the Question:
What is the current position and velocity of UGC 3789 ?
IMO we cannot answer that.
(Only that its position will be further away)

If it is close enough so that one can approximate its velocity from
measuring the redshift, then the difference between these two distances
is negligible.

UGC 3789 has a redshift of 0.011 i.e. below 0.023

That means you can not use it to establish the first Hubble Law
(ie the z versus distance relation)

The redshift, by itself, tells us the ratio of the scale factor now to
that at the time the light was emitted. It tells us NOTHING ELSE. At
low redshift, one can show that one can approximate the velocity by
using the Doppler formula. At high redshift this is not possible (and
don't even think about the relativistic Doppler formula; it is
irrelevant here). To get further, one has to know the cosmological
parameters.
Based on which observations ?
Is one of those parameters density ?

If they are known, then one can calculate any distance at
any time from the redshift for the given cosmological parameters. See,
for example,


http://www.astro.multivax.de:8000/he...ts/angsiz.html

I can not read that document.
angsiz.tar-gz shows an error message:
It does not appesr to be a valid zip file etc

Nicolaas Vroom

In article , "Nicolaas Vroom"
writes:

The first law describes the relation between Distance and redshift (z)
Expressed as D = c/H * z

Fine for low redshift.

The second law describes the relation between Distance and speed
and uses the relation v = c * z

Fine for low redshift.

and then you get: D = v/H or v = H *d

Fine for all redshifts, except you have to keep in mind that this D is
not necessarily the same as the one above.

I have a problem with this second law specific with the definition
of what means v ?
a) Is v the speed of the Galaxy in the past at moment of emission.
or b) is the v the present speed of the Galaxy ?

In the form in which you present it, it is valid only in the limit of
low redshifts, so it doesn't matter. If the redshift is high enough
that it does matter, the equation isn't valid.

The question then remains what does z at those distance represent ?
Does z then represent distance ?
what is this relation ?

Without any additional information, 1+z is the ratio of the size of the
universe now to the size of the universe when the light was emitted.

The redshift, by itself, tells us the ratio of the scale factor now to
that at the time the light was emitted. It tells us NOTHING ELSE. At
low redshift, one can show that one can approximate the velocity by
using the Doppler formula. At high redshift this is not possible (and
don't even think about the relativistic Doppler formula; it is
irrelevant here). To get further, one has to know the cosmological
parameters.
Based on which observations ?

Have a look for "cosmological parameters" att arXiv.org. You will get
hundreds or thousands of papers from within the last 15 years.

Is one of those parameters density ?

Yes.

http://www.astro.multivax.de:8000/he...ts/angsiz.html

I can not read that document.
angsiz.tar-gz shows an error message:
It does not appesr to be a valid zip file etc

It's not a ZIP file, it's a gzipped tar file. You should be able to get
a PDF of the paper from ArXiv.org, though.

"Phillip Helbig---undress to reply"
schreef in bericht ...
In article , "Nicolaas Vroom"
writes:

The first law describes the relation between Distance and redshift (z)
Expressed as D = c/H * z

Fine for low redshift.

The second law describes the relation between Distance and speed
and uses the relation v = c * z

Fine for low redshift.

and then you get: D = v/H or v = H *d

Fine for all redshifts, except you have to keep in mind that this D is
not necessarily the same as the one above.

Do you mean d as trigonometric distance (parallax) versus
d as luminosity distance ?

I have a problem with this second law specific with the definition
of what means v ?
a) Is v the speed of the Galaxy in the past at moment of emission.
or b) is the v the present speed of the Galaxy ?

In the form in which you present it, it is valid only in the limit of
low redshifts, so it doesn't matter.
What do you mean with: it does not matter ?
Does it matter in the case of NGC 6323 ?

In the case of NGC 6323 we get a speed of 7772 km/sec
using z = 0.026 and H = 72 km/sec/Mpc.
The distance is 110 Mpc.

The question is what does this speed of 7772 km/sec mean ?
1. Is this the speed of NGC 6323 in the past, when light was
emitted ?
2. Is this the speed of NGC 6323 now ?
3. Or is it something else ?

See also: http://users.telenet.be/nicvroom/Hubble-Faq.htm
This document shows you the litterature where you can find
more detail information.

Nicolaas Vroom
http://users.telenet.be/nicvroom/

In article , "Nicolaas Vroom"
writes:

"Phillip Helbig---undress to reply"
schreef in bericht ...
In article , "Nicolaas Vroom"
writes:

The first law describes the relation between Distance and redshift (z)
Expressed as D = c/H * z

Fine for low redshift.

The second law describes the relation between Distance and speed
and uses the relation v = c * z

Fine for low redshift.

and then you get: D = v/H or v = H *d

Fine for all redshifts, except you have to keep in mind that this D is
not necessarily the same as the one above.

Do you mean d as trigonometric distance (parallax) versus
d as luminosity distance ?

Neither. The D is proper distance, i.e. the distance which one could
theoretically measure at the present instant of cosmic time with a rigid
ruler. It is, in general, not the same as the luminosity distance, nor
the parallax distance, nor the distance from light-travel time, nor the
proper-motion distance, nor the angular-size distance.

In the case of NGC 6323 we get a speed of 7772 km/sec
using z = 0.026 and H = 72 km/sec/Mpc.
The distance is 110 Mpc.

The question is what does this speed of 7772 km/sec mean ?
1. Is this the speed of NGC 6323 in the past, when light was
emitted ?
2. Is this the speed of NGC 6323 now ?
3. Or is it something else ?

A "typical" value for the peculiar velocity of a galaxy is 600 km/s. So
there is a substantial contamination from a non-cosmological redshift.
This effect is much greater than the difference between the speed now
and the speed at the time the light was emitted.

Assume no contamination, i.e. the ideal case. The Doppler formula is
exact as the redshift approaches zero, i.e. it is a limit. For larger
redshift, it gives NEITHER the speed now NOR the speed when the light
was emitted.

Assuming we know the Hubble constant, and we know the distance, then we
get the velocity NOW. This holds at any redshift. But the distance is
the proper distance (not something "directly observable" like luminosity
distance) (see above) and the velocity is its derivative with respect to
cosmic time as measured now.