neophyte question about hubble's law
dfarr --at-- comcast --dot-- net
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'?
I'm not an astronomer or even a physicist, just an aging isolated
mathematics amateur, so go easy on me if this is something all
freshmen astronomy students know. Thanks.
[[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*.
[For present purposes let's ignore the well-known
difficulty of defining "right now" for a distant object
(a.k.a. the "clock synchronization" problem) in the
context of special relativity.]
If you want to ask "does physics say anything meaningful about what
the Sun is doing right now?", then I would say that the answer is still
"yes": If we combine our observations of what the Sun was doing prior
to 8.5 minutes ago, with theoretical models of the Sun's structure,
[note that these *assume* that "things are orderly",
i.e., that the laws of quantum
mechanics, atomic & nuclear structure, thermodynamics,
electromagnetism, and many other aspects of physics
work "properly" in the Sun right now, even though
there can be no causal contact between the Sun-right-now
and any observation we have ever made, or will make
any sooner than 8.5 minutes from now]
then we can infer with (*very*) high certainty that the Sun is still
shining right now, with a total luminosity which is very close to what
it was 8.5 minutes ago.
This same sort of reasoning is necessary in cosmology: we only directly
observe things at places/times such that their light or other signals
can get to us, so aside from assuming that "things are orderly", we
don't know directly what a distant galaxy is doing *now*.
[We can observationally test some cases of whether
"things are orderly",
i.e. whether "physics works the same way everywhere":
For example, we can verify that the spectrum of hydrogen
observed at high redshift looks just like that observed
in Earth-bound laboratories except for an overall redshift.
We can also observationally test these assumptions
for (some) events which are *closer* to us than their
light-distance.
For example, we can measure isotope ratios of the Oklo
uranium deposits
http://en.wikipedia.org/wiki/Natural_nuclear_fission_reactor
to check that nuclear reactions and energy levels were
the same on Earth 2 billion years ago as they are today.
With the exception of some quite-controversial claims
of very small variations in the fine-structure constant,
so far all these tests have come out supporting the
assumptions that things are indeed "orderly".
This makes the extension of these
assumptions to not-directly-observable things,
e.g., the Sun and/or distant galaxies right now,
at least plausible.]
For much more (very clear and insightful) about what Hubble's law does
and doesn't say, see
Edward R. Harrison
"Cosmology: The Science of the Universe", 2nd Edition
Cambridge U.P., 2000,
hardcover ISBN 0-521-66148-X
As Phillip Helbig said later in the same sci.physics.research thread
from which I quoted above, "EVERYONE interested in cosmology should
read this book at least twice.".
-- jt]]
Oh No
>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)
Bear in mind that this applies only for small cosmological distances
>
>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'?
>
>I'm not an astronomer or even a physicist, just an aging isolated
>mathematics amateur, so go easy on me if this is something all
>freshmen astronomy students know. Thanks.
>
Basically we have general relativity, plus a bit of common sense.
General relativity is itself based on the common sense principle that
the laws of physics are locally the same everywhere, and if we can't be
sure of that principle we cannot be sure of anything.
Under the assumption that matter is reasonably uniformly distributed we
can solve the equations of general relativity, and show that if the
universe is expanding now, then it has always been expanding (since the
big bang).
>For much more (very clear and insightful) about what Hubble's law does
>and doesn't say, see
> Edward R. Harrison
> "Cosmology: The Science of the Universe", 2nd Edition
> Cambridge U.P., 2000,
> hardcover ISBN 0-521-66148-X
>
>As Phillip Helbig said later in the same sci.physics.research thread
>from which I quoted above, "EVERYONE interested in cosmology should
>read this book at least twice.".
Perhaps. It's just a pity Harrison's ideas about the expansion of space
time are somewhat inaccurate. I would recommend everyone should read
some real general relativity also.
Regards
--
Charles Francis
moderator sci.physics.foundations.
charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces
and
braces)
Phillip Helbig---remove CLOTHES to reply
<645be291-d735-4aa7...@l13g2000yqb.googlegroups.com>,
dfarr --at-- comcast --dot-- net <df...@comcast.net> writes:
> 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)
That is correct. This is the only possible velocity-distance law for a
universe which is expanding homogeneously and isotropically. However,
the distance is the proper distance and the velocity is the temporal
derivative of the proper distance. Neither of these distances is a
distance which is useful in observational cosmology (examples of the
latter are luminosity distance and angular-size distance).
> 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'?
You are confused. Hubble's Law as stated above is correct, but
describes unobservable quantities. If a galaxy which was moving away
from us 12 billion years ago is now approaching us, then nearby galaxies
would be approaching us as well. Another point: the only thing the
light from the galaxy indicates is the ratio of the scale factor of the
universe compared to the time when the light was emitted. It says
nothing about distance, velocity etc. To convert the observed redshift
into such quantities, we need to know the cosmological parameters.
Phillip Helbig---remove CLOTHES to reply
<No...@charlesfrancis.wanadoo.co.uk> writes:
> Thus spake dfarr --at-- comcast --dot-- net <df...@comcast.net>
> >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)
>
> Bear in mind that this applies only for small cosmological distances
That depends on how one defines Hubble's Law. See my other post in this
thread and the recent thread in sci.physics.research.
> Perhaps. It's just a pity Harrison's ideas about the expansion of space
> time are somewhat inaccurate.
Care to elabourate?
Nicolaas Vroom
news:645be291-d735-4aa7...@l13g2000yqb.googlegroups.com...
[[Mod. note -- 79 excessively-quoted lines snipped. -- jt]]
[[Mod. note --
>
> For much more (very clear and insightful) about what Hubble's law does
> and doesn't say, see
> Edward R. Harrison
> "Cosmology: The Science of the Universe", 2nd Edition
> Cambridge U.P., 2000,
> hardcover ISBN 0-521-66148-X
>
> As Phillip Helbig said later in the same sci.physics.research thread
> from which I quoted above, "EVERYONE interested in cosmology should
> read this book at least twice.".
> -- jt]]
I think this picture is too simple.
We will all agree that the sun is shining right "now"
based on current observations.
And we will also all agree that all our planets will be there
100 years from now, because they were be there 100 years ago.
On the other hand the Andromeda Galaxy M31 is moving towards us
which is in disagreement with Hubble's Law.
In fact this shows that Hubble's Law is only an approximation.
[[Mod. note -- Yes, galaxies have random velocities about the large-scale
Hubble flow, not to mention non-random gravitational motions due to the
mass of superclusters. This is well-known to all cosmologists. Give
or take a bit, Hubble's law refers to the overall *average* velocity
(redshift) of galaxies at a given distance. For a more precise definition,
see the book by Harrison, or his paper
http://adsabs.harvard.edu/abs/1993ApJ...403...28H
-- jt]]
However there is more.
This document by Hilton Ratcliffe
http://vixra.org/pdf/0907.0003v1.pdf
also discusses the validity of Hubble's Law.
The question to what extend his objections are true
requires thoroughly investigation.
[[Mod. note -- Alas, Ratcliffe's paper is very badly flawed.
I'll comment further on it in a following posting.
-- jt]]
Nicolaas Vroom
http://users.pandora.be/nicvroom/
Phillip Helbig---remove CLOTHES to reply
<nicolaa...@pandora.be> writes:
> On the other hand the Andromeda Galaxy M31 is moving towards us
> which is in disagreement with Hubble's Law.
> In fact this shows that Hubble's Law is only an approximation.
Yes, it is an approximation. If the universe were exactly homogeneous
and isotropic, it would hold exactly. (In that case, though, there
would be no galaxies. We can imagine "test particles", though, which
essentially just serve as markers for position.) In reality, galaxies
have their own so-called peculiar motions, which are combined with the
"Hubble flow". For nearby galaxies, the former dominate; for
high-redshift galaxies, the latter dominates. In other words, the fact
that the Andromeda galaxy is approaching us no more and no less
contradicts Hubble's Law than the fact that a person approaches me in
the street. (In the ideal case, Hubble's Law applies to every particle,
whatever its distance. In practice, it applies only at distances large
enough that other velocities are negligible.)
Nicolaas Vroom
schreef in bericht news:h922gc$571$1...@online.de...
> However,
> the distance is the proper distance and the velocity is the temporal
> derivative of the proper distance. Neither of these distances is a
> distance which is useful in observational cosmology (examples of the
> latter are luminosity distance and angular-size distance).
I do not understand this.
As far as I know v = c * z and z is caculated via z = d labda/labda
which both are measured by means of observations.
Why the distiction between proper distance and Luminosity distance ?
None of the books I have studied (Hoyle, Silk, Kaufmann,
and the book Galactic Astronomy Chapter 7) make this distinction.
The last book uses the concept:
Luminosity function as a distance indicator 415-418.
Basically the distance is calculated bij using the formula:
L = 4 * pi * d *d * f (f = flux, d = distance, L = luminosity).
Using those measured and or observed values H is calculated.
Finally if only z is measured the distance d can be inferred.
>> 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?
>
> You are confused. Hubble's Law as stated above is correct, but
> describes unobservable quantities.
I expect you mean an unobservable situation right now.
> If a galaxy which was moving away
> from us 12 billion years ago is now approaching us
This seems highly unlikely.
IMO 6 billion years ago that same galaxy was also moving away from us.
or am I wrong.
The question is did the speed increase or decrease between those two events.
>, then nearby galaxies would be approaching us as well.
>From a local point of view they can move in any direction.
> Another point: the only thing the
> light from the galaxy indicates is the ratio of the scale factor of the
> universe compared to the time when the light was emitted. It says
> nothing about distance, velocity etc.
Is that true ? Again the books I have tell a different story.
> To convert the observed redshift
> into such quantities, we need to know the cosmological parameters.
Is that not the Hubble constant ? Why not mentioned ?
What amazes me the most is if you look at galaxys at very large
distances their shape seems to be much more develloped than you should
expected solely based on their early age. Or are they much older ?
In fact almost all galaxys look like M31
(What you should expect is much more small elliptical than large spirals)
Nicolaas Vroom
[[Mod. note -- The distinction between proper and luminosity distances
is because logically they're different quantities, so it's clearer to
use different names for them.
It is not the case that "amost all galaxies look like M31", either for
nearby galaxies or for very distant galaxies.
-- jt]]
Phillip Helbig---remove CLOTHES to reply
<nicolaa...@pandora.be> writes:
> "Phillip Helbig---remove CLOTHES to reply" <hel...@astro.multiCLOTHESvax.de>
> schreef in bericht news:h922gc$571$1...@online.de...
>
> > However,
> > the distance is the proper distance and the velocity is the temporal
> > derivative of the proper distance. Neither of these distances is a
> > distance which is useful in observational cosmology (examples of the
> > latter are luminosity distance and angular-size distance).
>
> I do not understand this.
> As far as I know v = c * z and z is caculated via z = d labda/labda
> which both are measured by means of observations.
What is "both"? Only the wavelength of a distant object is observed,
and compared to the wavelength in the laboratory. Everything else is
inferred. (I'm assuming we all agree on what c is.)
There is a velocity-distance law and there is a redshift-distance law.
But only at low redshift can one combine them to get a straightforward
relationship between velocity and redshift. What is v? Velocity. That
is distance per time. Which distance (in cosmology there are several,
which at high redshift are different, because a) the universe can be
non-Euclidean and b) non-static)? Which time? We can assume cosmic
time, that measured by someone at rest relative to the CMB. But there
is no distance which is otherwise used in cosmology (luminosity
distance, angular-size distance) whose derivative with respect to cosmic
time (or any other time, except perhaps one specially defined so that
the desired result is achieved) result in a velocity related to the
redshift by the equation above. (And no, at high redshifts it doesn't
help to use the relativistic Doppler formula. Since it contains no
cosmological parameters, that would imply that the velocity---whatever
it is---of an object at high redshift is independent of the cosmological
model.)
(It IS possible to view cosmological redshifts as Doppler redshifts, but
neither the familiar formula nor familiar distances are involved, so
this seems more trouble than it is worth.)
> Why the distiction between proper distance and Luminosity distance ?
> None of the books I have studied (Hoyle, Silk, Kaufmann,
> and the book Galactic Astronomy Chapter 7) make this distinction.
At low redshift, no distinction is necessary. The luminosity distance
is (1+z)^2 times as large as the angular-size distance.
> The last book uses the concept:
> Luminosity function as a distance indicator 415-418.
> Basically the distance is calculated bij using the formula:
> L = 4 * pi * d *d * f (f = flux, d = distance, L = luminosity).
Right. This defines the luminosity distance. But it is not the same as
the distance one would measure with a rigid ruler, neither now nor at
the time when the light was emitted. Nor is it the same as distance
derived from angular size (objects farther away look smaller) nor the
distance derived from parallax nor the distance from the light-travel
time. To convert one type of distance to the other, one needs to know
at least the redshift (for some distances) and perhaps the cosmological
parameters (for other distances).
> Using those measured and or observed values H is calculated.
Yes, but the redshifts at which H is calculated are so small that the
distances all agree.
> Finally if only z is measured the distance d can be inferred.
Assuming one knows H, and if the redshift is small.
> >> 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?
> >
> > You are confused. Hubble's Law as stated above is correct, but
> > describes unobservable quantities.
> I expect you mean an unobservable situation right now.
While your statement is true, I meant unobservable distances. The
distances involved can be calculated from others, if one knows the
cosmological parameters.
> > If a galaxy which was moving away
> > from us 12 billion years ago is now approaching us
> This seems highly unlikely.
> IMO 6 billion years ago that same galaxy was also moving away from us.
> or am I wrong.
> The question is did the speed increase or decrease between those two events.
Depends on the cosmological parameters.
> > Another point: the only thing the
> > light from the galaxy indicates is the ratio of the scale factor of the
> > universe compared to the time when the light was emitted. It says
> > nothing about distance, velocity etc.
> Is that true ? Again the books I have tell a different story.
Yes, it is true. All else can be inferred, IF one knows the
cosmological parameters. Or one can calculate other quantities for
different sets of cosmological parameters and compare them to
observations. This is in practice how the cosmological parameters are
measured.
> > To convert the observed redshift
> > into such quantities, we need to know the cosmological parameters.
> Is that not the Hubble constant ? Why not mentioned ?
That's one of them, but there is also Omega (the density parameter) and
lambda (the cosmological constant). Also, the clumpiness of matter
between ourselves and a distant object can affect some measures of
distance.
> It is not the case that "amost all galaxies look like M31", either for
> nearby galaxies or for very distant galaxies.
> -- jt]]
Once Richard Ellis was showing some strangely shaped galaxies observed
with HST. He remarked that were Gerard de Vaucouleurs in the audience,
he could name some similarly looking nearby galaxies.
Jonathan Thornburg [remove -animal to reply]
> This document by Hilton Ratcliffe
> http://vixra.org/pdf/0907.0003v1.pdf
> also discusses the validity of Hubble's Law.
Unfortunately, this paper has major flaws, and should not be relied
on to convey what is and isn't known about any given research field.
Here are a few flaws in Ratcliffe's paper which I noticed in a brief
perusal:
Ratcliffe (section 5) discusses (favorably) Tifft's work on galaxy
redshift periodicities, and argues that these are a significant
challenge to standard cosmological models.
[For those who haven't seen it, Tifft claimed that if one
looks at binary galaxies, and for each pair tabulates the
*difference* in redshift of the two members of the pair,
the resulting distribution is strongly periodic with a
period of around cz = 72 km/sec. If this were true, it
would indeed be a huge challenge to standard cosmological
models.]
But Ratcliffe makes no mention of the refutation of this work by
Newman, Haynes, and Terzian
http://adsabs.harvard.edu/abs/1989ApJ...344..111N
who showed that Tifft's statistical analysis was horribly flawed:
it would find "periodicities" even in Gaussian random noise!
Ratcliffe also makes no mention of the later work by
Chengalur, Salpeter, and Terzian
http://adsabs.harvard.edu/abs/1993ApJ...419...30C
or Tang & Zhang's study of quasar-galaxy--pair redshift differences
http://adsabs.harvard.edu/abs/2005ApJ...633...41T
In section 2, Ratcliffe writes
| Thus, we may assume that there is something anomalous about the
| redshift of an astrophysical object if:
| 1.1. There is a prevalence of high redshift objects near the
| nucleus of nearby galaxies, or high redshift galaxy-like
| systems associated with low redshift clusters;
The key phrase there is "a prevalence of high redshift objects".
This (of course) only considers *known* high-redshift objects.
The question is, are known high-redshift objects a random sample
of all high-redshift objects? Of course, the answer is "no":
known objects comprise only those which are (among other criteria)
* which are in a part of the sky which has been observed, and
* bright enough to have been observed
Thus you can easily create a spurious apparent prevalence of [known]
high redshift objects in some part of the sky, simply by observing
that part of of the sky a lot. And the sky around nearby galaxies
and low redshift clusters does get observed a lot, probably more than
less "interesting" parts of the sky.
The only way to figure out whether there is a true prevalence of
high redshift objects on a certain part of the sky, is to do a
careful statistical analysis of the selection criteria of whatever
catalogs you're using.
Ratcliffe does not discuss this issue. Indeed, the word "selection"
or the phrase "selection bias" doesn't seem to appear anywhere in his
paper!
In section 3.2, Ratcliffe writes:
| If one plots quasars' redshift against apparent brightness, as
| Hubble did for galaxies, one gets a wide scatter, as compared
| with a smooth curve for the same plot done for galaxies. This
| seems to indicate that quasars do not follow the Hubble law, and
| there is no direct indication that they are at their proposed
| redshift distance.
There are several obvious flaws with this argument:
* First, there seems to be a misunderstanding of just what Hubble's
law is. See
http://adsabs.harvard.edu/abs/1993ApJ...403...28H
for a very clear account, including refutation of some common
misconceptions. For present purposes, the key point is that
Hubble's law (at least as the term is usually used in cosmology)
connectes some measure of distance to either redshift or recessional
velocity. It does *not* say that the brightness of galaxies, quasars,
or any other objects has any necessary relation to their redshift!
* Second, the author seems to think that if one plots galaxies'
redshift against apparent brightness, one gets a tight correlation.
This is only true if one pre-selects the galaxies to be relatively
homogeneous in intrinsic brightness.
["intrinsic brightness" = brightness as measured
at some fixed distance away from the object =
often just called "luminosity"]
Without such a pre-selection, galaxies vary by (plural) orders
of magnitude in intrinsic brightness.
* Third, the author makes no mention of the obvious alternative
hypothesis: quasars' intrinsic brightnesses vary over a wide range
(even wideer than those of galaxies).
Later in section 3.2, Ratcliffe writes:
| Even more onerous was the precision measurement of radial expansion
| rate [[of quasars]] by very long baseline radio interferometry.
| Quasars appeared to be expanding at up to ten times the speed of
| light, with obviously serious implications for underlying theory and
| Einsteinian physics.
However, Ratcliffe doesn't mention the well-known special-relativity
optical illusion that can readily explain such apparent "superluminal"
motions. For a nice brief explanation of how this works, see
http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/Superluminal/superluminal.html
This examples are unfortunately all too typical of Ratcliffe's paper:
he points out apparent problems, without critiquing or even *mentioning*
well-known alternative hypotheses or resolutions of the problems. This
makes his paper a seriously unreliable source of information.
For a much more reliable brief introduction to some of the controversies
(mis-)described by Ratcliffe, see Bill Keel's web page
http://www.astr.ua.edu/keel/galaxies/arp.html
(This is a few years old, but still good.)
--
-- "Jonathan Thornburg [remove -animal to reply]" <jth...@astro.indiana-zebra.edu>
Dept of Astronomy, Indiana University, Bloomington, Indiana, USA
"Washing one's hands of the conflict between the powerful and the
powerless means to side with the powerful, not to be neutral."
-- quote by Freire / poster by Oxfam
Oh No
LOTHESvax.de>
>In article <Im0WT6AC...@charlesfrancis.wanadoo.co.uk>, Oh No
><No...@charlesfrancis.wanadoo.co.uk> writes:
>
>> Thus spake dfarr --at-- comcast --dot-- net <df...@comcast.net>
>> >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)
>>
>> Bear in mind that this applies only for small cosmological distances
>
>That depends on how one defines Hubble's Law. See my other post in this
>thread and the recent thread in sci.physics.research.
Hubble's law is defined as a linear relationship between redshift and
distance. This relationship only holds for small cosmological distances.
For large cosmological distances such a relationship doesn't even make
sense unless you first define what you mean by distance, and there
certainly isn't a natural definition of distance which would give a
linear relationship. You would only get a linear relationship if you
defined distance from Hubble's law - which is tautology, and certainly
an unhelpful measure of large scale structure.
>
>> Perhaps. It's just a pity Harrison's ideas about the expansion of space
>> time are somewhat inaccurate.
>
>Care to elabourate?
I have only dipped into the book, so cannot comment on much of it, but
the discussion of the Hubble sphere on p281 struck me as particularly
misleading. It is absolutely not meaningful to talk about the recession
velocity of a star in the early universe with respect to ourselves now.
Think of the balloon analogy. Cosmological redshift is the consequence
of cosmological expansion, not recession velocities. It just happens
that, for small cosmological distances, cosmological expansion looks
like recession velocity. You can't take that concept too far.
Regards
--
Charles Francis
moderator sci.physics.foundations.
charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces an=
d
braces)
Nicolaas Vroom
>
schreef in bericht news:h9g8vm$ke5$1...@online.de...
> In article <d0qum.83416$H%7.7...@newsfe02.ams2>, "Nicolaas Vroom"
> <nicolaa...@pandora.be> writes:
>
>> I do not understand this.
>> which both are measured by means of observations.
>
> What is "both"? Only the wavelength of a distant object is observed,
> and compared to the wavelength in the laboratory. Everything else is
> inferred. (I'm assuming we all agree on what c is.)
The main problem with c is it also affected by an expanding universe ?
The question is is the distance of one lightyear going in the expanding
direction equal as going in the opposite direction ?
Is forward equal as backward ?
Is this distance the same as using a rigid ruler ?
>> The last book uses the concept:
>> Luminosity function as a distance indicator 415-418.
>> Basically the distance is calculated bij using the formula:
>> L =3D 4 * pi * d *d * f (f =3D flux, d =3D distance, L =3D luminosity).
>
> Right. This defines the luminosity distance. But it is not the same as
> the distance one would measure with a rigid ruler, neither now nor at
> the time when the light was emitted. Nor is it the same as distance
> derived from angular size (objects farther away look smaller) nor the
> distance derived from parallax nor the distance from the light-travel
> time. To convert one type of distance to the other, one needs to know
> at least the redshift (for some distances) and perhaps the cosmological
> parameters (for other distances).
>
>> Using those measured and or observed values H is calculated.
>
> Yes, but the redshifts at which H is calculated are so small that the
> distances all agree.
>
>> IMO 6 billion years ago that same galaxy was also moving away from us.
>> or am I wrong.
>> The question is did the speed increase or decrease between those two
>> events.
>
> Depends on the cosmological parameters.
Anyway what is the answer ?
>> > Another point: the only thing the
>> > light from the galaxy indicates is the ratio of the scale factor of th=
e
>> > universe compared to the time when the light was emitted. It says
>> > nothing about distance, velocity etc.
>> Is that true ? Again the books I have tell a different story.
>
> Yes, it is true. All else can be inferred, IF one knows the
> cosmological parameters. Or one can calculate other quantities for
> different sets of cosmological parameters and compare them to
> observations. This is in practice how the cosmological parameters are
> measured.
>
The more I read the less I understand.
When you observe the distance to the Sun what you measure
is not the true/present position/distance but the historic/past
position/distance roughly 5 minutes in the past.
Based from that position using for example Newton's Law
you can calculate the true or present position.
The method used is for example parallax.
(trigonometric distances)
You can do that also for stars. You measure a distance
in the past and when you know the speed (direction)
you can calculate the true/present position.
A different way to measure the distance is by measuring
the flux but than You use the assumption that stars of the
same type all have the same Luminosity.
This introduces an error but again what you measure is
the past distance.
IMO for the same star the distance should be identical.
The same can be done by using redshifts and the following
three equations:
V =3D H*d d=3Dc*z and z =3D d labda/labda.
The problem is those 3 equations can not be used around
M31. The H constant calculated is not correct.
In order to calculate H by two independent measurements
of V(speed) and d(distance) much further galaxies
should be used.
How is this done in practice ? I expect this is very difficult
specific for the speed. (You need two distances)
Any way what you calculate is the past distance.
You need the present distance. How is this done. ?
What is v going from past to present ?
Is v a constant ?
There is an aditional problem.
What you observe is the present value of d labda.
The question is assuming expanding space that that
value is not identical as when it was emitted.
ie it was smaller. This inturn means that both z and d
are much smaller or is this wrong.
Nicolaas Vroom
http://users.telenet.be/nicvroom/
Hans Aberg
> The main problem with c is it also affected by an expanding universe ?
The idea is that the universe itself expands without changing c. So the
observable universe is at least 47 Gyr in radius, but the expansion
theory claims that the distant objects did not arrive there by actual
traveling on their own, but surfing on the universe expansion, thus
explaining away why one does not see the Big Bang by looking 14 Gyr out.
(Also see the link below.)
The idea comes from GR, but I recall that in original GR claiming that
an object moving by its own or by universe expansion are equivalent. So
the expansion theory would depend on some alteration of GR that destroys
that equivalence - but I could not find any reference for that.
So it would be nice if the experts here would clarify.
Hans
Jonathan Thornburg [remove -animal to reply]
> When you observe the distance to the Sun what you measure
> is not the true/present position/distance but the historic/past
> position/distance roughly 5 minutes in the past.
> Based from that position using for example Newton's Law
> you can calculate the true or present position.
> The method used is for example parallax.
> (trigonometric distances)
> You can do that also for stars. You measure a distance
> in the past and when you know the speed (direction)
> you can calculate the true/present position.
> A different way to measure the distance is by measuring
> the flux but than You use the assumption that stars of the
> same type all have the same Luminosity.
> This introduces an error but again what you measure is
> the past distance.
> IMO for the same star the distance should be identical.
I'm afraid you're mistaken: while they're very close for stars in
our galaxy, they would only be *identical* if we lived in a flat
spacetime (one where Newton's laws hold for slowly-moving objects)....
but we don't live in a flat spacetime.
To be specific, let's consider the simple case of measuring the mean
Earth-Sun distance. Suppose you measure this distance in the following
ways:
(a) Measure this distance by parallax, i.e., by observing how much
the Sun's angular position on the sky shifts when you move (say)
100 kilometers (measured by lining up meter sticks end-to-end,
sighting along them to make sure they're in a straight line)
sideways on the Earth.
(b) Same as (a), but with a larger baseline, say the Earth-Moon
distance (i.e., observe how much the Sun's angular position
on the sky shifts when you move from the Earth to the Moon
at a time when the Sun-Earth-Moon angle is roughly 90 degrees)
(c) Measure the distance by radar, i.e., send a radar signal from
the Earth to the Sun, let some of it bounce off the Sun, and
time how long it takes the echo to get back to the Earth.
(d) Line up meter sticks (sighting along them to make they're all
in a straight line) from the Earth to the Sun, and count how
many meter sticks it takes to span the distance.
(e) Construct a circle centered on the Sun of radius matching the
mean Earth-Sun distance, and measure the circumference of
this circle by lining up meter sticks around the circle and
counting how many meter sticks it takes to go all the way around.
Then compute a radius by dividing that circumference by 2 pi.
[Of course, these are all gedanken measurements; here we're treating
each of the Earth and Sun as point masses, and neglecting assorted
other complications which aren't relevant to the point at hand. For
actual measurements, what we really care about is the mean distance
between the Earth-center-of-mass and the Sun-center-of-mass.]
Contrary to what you might expect, in general these 5 measurements
will give slightly *different* results, typically differing by a few
kilometers. This is because in a curved spacetime, each of these
measures something fundamentally *different* (they use different
trajectories in spacetime). For close-enough objects these measurements
all agree, but the Earth and Sun aren't "close enough" if you care
about a level of accuracy of a few kilometers.
[In case you're wondering, that "a few kilometers"
is really some O(1) constant (in general different for
each measurement method) times the spacetime-curvature
scale near the Sun.]
[Switching from gedanken to real experiments for a
moment, modern experimental measurements of the mean
Earth-Sun center-of-mass distance (the "astronomical unit")
via radar-like techniques are accurate to a few *meters*!
Of course, at that level of accuracy the analysis needs
to be done very carefully, including using a careful
curved-spacetime definition of just what it is that's
being measured, and an analysis of the observational
data that takes curved-spacetime effects into account.]
If we now move to the original poster's example of stars within our
galaxy, then it's certainly true that these curved-spacetime effects
are (*much*) smaller than the other errors involved in astronomical
distance measurements. So for this case, you might reasonably decide
to ignore curved-spacetime effects. But as we'll see, the conceptual
distinction between different notions of "distance" is still important
to keep in mind as preparation for the cosmological case.
In general, all reasonable definitions of "distance" agree for
objects which are much closer than the spacetime curvature scale.
[More precisely, if you Taylor-expand any one reasonable
definition of "distance" in terms of any other one, you'll
get something which looks like the identity function plus
higher order terms in the distance, i.e.,
D =3D d + k_2 d^2 + k_3 d^3 + k_4 d^4 + k_5 d^5 + ...
where d and D are the two distances, and the k_i are coefficients
depending on how the distances are defined, and what the local
spacetime looks like, but not on the numerical values of d or D.
(I suspect, but haven't bothered to check right now, that
in fact k_2 is always zero.)
So, if d is small enough, we can neglect all the higher order
terms in the Taylor series and approximate D =3D d.]
For cosmology, that scale is around 4000 megaparsecs, so (given the
accuracy scales common in astrophysics) for objects closer than (say)
a few hundred megaparsecs, it's generally reasonable to neglect
spacetime curvature and say that "distance" is (within the
approximations we're making) uniquely defined.
[That is, for objects within a few hundred megaparsecs,
the percentage difference between d and D is generally
much smaller than our experimental/observational uncertainties
in measuring d, D, the object's redshift, or most other
properties of the object.
Of course, this "a few hundred megaparsecs" is really a
somewhat fuzzy boundary, depending on just how large or
small our experimental/observational uncertainties are.]
For such objects (distance < 200 megaparsecs or so, or equivalently
redshift z < 0.05 or so, or equivalently cz < 15,000 km/sec or so),
Hubble's law is observed to hold to a good approximation.
[The main deviations from it are the random motions of
galaxies and smaller objects, and the large-scale
gravitational-flow effects of large clusters of galaxies;
both of these effects introduce scatter on the order
of 1000 km/sec or less.]
Now let's move to cosmology, i.e., let's consider observing objects
with redshifts of order unity or larger. Now it's *not* reasonable
to neglect spacetime curvature: there's no simply no unique concept
of "distance" for cosmologically-distant objects. Rather, there
are a bunch of different "distances" (e.g., luminosity distance,
angular-diameter or parallax distance, the distance you'd measure
if you lined up meter sticks in a straight line from us to the object,
the distance you get from measuring the circumference of a big circle
and dividing by 2 pi, etc etc), which can easily differ a lot
(factors of 2 or more) from each other.
It's precisely because of the lack of a unique "distance" that
astronomers almost always use redshift when describing such objects:
redshift is what can be directly observed, and it's readily compared
across objects (& between observations & theoretical models).
For cosmologically-distant objects it's *not* valid to interpret
redshift as simply a flat-spacetime Doppler shift (even with the
special-relativity Doppler-shift formula).
And finally, since we don't have a reasonable definition of "distance"
for cosmologically-distant objects, Hubble's law isn't meaningful for
them.
--
-- "Jonathan Thornburg [remove -animal to reply]" <jth...@astro.indiana-zeb=
Nicolaas Vroom
news:mt2.0-20137...@hercules.herts.ac.uk...
> Nicolaas Vroom <nicolaa...@pandora.be> wrote:
>> A different way to measure the distance is by measuring
>> the flux but than You use the assumption that stars of the
>> same type all have the same Luminosity.
>
> I'm afraid you're mistaken: while they're very close for stars in
> our galaxy,
Fred Hoyle also uses that concept. He also uses that for other galaxies.
> To be specific, let's consider the simple case of measuring the mean
> Earth-Sun distance. Suppose you measure this distance in the following
> ways:
> (a),(b),(c),(d),(e)
>
> Contrary to what you might expect, in general these 5 measurements
> will give slightly *different* results, typically differing by a few
> kilometers.
I also would expect they are all different
> This is because in a curved spacetime, each of these
> measures something fundamentally *different* (they use different
> trajectories in spacetime).
IMO if you are not carefull you measure the distance at different moments.
You have to take the position of the Earth and the Sun into account.
> If we now move to the original poster's example of stars within our
> galaxy, then it's certainly true that these curved-spacetime effects
> are (*much*) smaller than the other errors involved in astronomical
> distance measurements. So for this case, you might reasonably decide
> to ignore curved-spacetime effects.
What you might not ignore that infact you measure the distance in the
past.
When you use parallax for a star and you measure the angle now
what you measure is not angle based on the present position
but the position approx d/c earlier (d =3D distance)
The same for the angle a half year from now and the same
for the calculated distance. (for practical reasons you can ignore this)
If you know the Limunosity of a star and you can measure the flux
than based on the relation L=3D4*pi*d*d*f you can calculate the distance
but again you calculate the past distance.
> For such objects (distance < 200 megaparsecs or so, or equivalently
> redshift z < 0.05 or so, or equivalently cz < 15,000 km/sec or so),
> Hubble's law is observed to hold to a good approximation.
What you need here is curve to show measured z versus measured
Luminosity distance d
The book by Fred Hoyle at page 617 shows such a curve and
the impression is that Hubles Law is at least valid between
z =3D 0.05 and z =3D 0.5
> It's precisely because of the lack of a unique "distance" that
> astronomers almost always use redshift when describing such objects:
> redshift is what can be directly observed, and it's readily compared
> across objects (& between observations & theoretical models).
The issue is what does this red shift mean.
> For cosmologically-distant objects it's *not* valid to interpret
> redshift as simply a flat-spacetime Doppler shift (even with the
> special-relativity Doppler-shift formula).
>
> And finally, since we don't have a reasonable definition of "distance"
> for cosmologically-distant objects, Hubble's law isn't meaningful for
> them.
What is than the meaning of Hubble's Law ?
IMO if Hubble's Law is true between z=3D0.05 and z =3D 0.5
and that there are no exceptions than you can reasonably assume
that this relation is also true for z =3D 1 .
However that is not the most important issue.
The issue is that z=3D0.5 indicates that the star had in the past
a certain distance and speed.
The question is what was the speed of the star when the light was
emitted that we observe now.
If you assume space expansion than that speed was much lower
as c*z.
Even more interesting is the question what is the speed of that star
now (i.e the one of which we measure z=3D0.5 now)
Maybe the speed is zero.
IMO this are all difficult issues
Nicolaas Vroom
http://users.pandora.be/nicvroom/
Nicolaas Vroom
news:mt2.0-27053...@hercules.herts.ac.uk...
> Nicolaas Vroom wrote:
>> The main problem with c is it also affected by an expanding universe ?
>
> observable universe is at least 47 Gyr in radius,
>
>
> http://en.wikipedia.org/wiki/Universe
I do not understand this claim.
IMO the concept of expanding Universe is based on two concepts:
First we measure L and f and than we calculate the distance based
on the equation:
L =3D 4 * pi * d * d * f
Secondly we measure d(labda) and labda
and we calculate z =3D d(labda)/labda =3D "redshift"
Fig 14.13 in the book by Hoyle shows a lineair relation between
those two for z between 0.05 and 0.5. This implies that that concept
can be used to calculate a distance for much larger values of z.
The next step is to multiply z with c and than you get the recession
velocity v of a star based on the measured values L and f.
The problem I have with this approach is that when you use
Luminosity as a measurement you calculate a distance in the past
implying that it is very difficult to claim what the present distant
(position) is.
The same problem you have for the total size of the Universe.
The Second problem is with the equation v=3Dc*z.
If you assume an expanding Univerese than d labda is also
expanded meaning that both z and v (of the origin in the past
when light was emitted) are much smaller.
Nicolaas Vroom
http://users.pandora.be/nicvroom/
Phillip Helbig---remove CLOTHES to reply
<nicolaa...@pandora.be> writes:
> Secondly we measure d(labda) and labda
> and we calculate z =3D3D d(labda)/labda =3D3D "redshift"
> Fig 14.13 in the book by Hoyle shows a lineair relation between
> those two for z between 0.05 and 0.5. This implies that that concept
> can be used to calculate a distance for much larger values of z.
Non sequitur. Why does the former imply the latter?
Phillip Helbig---remove CLOTHES to reply
<nicolaa...@pandora.be> writes:
> The same can be done by using redshifts and the following
> three equations:
> V =3D3D H*d d=3D3Dc*z and z =3D3D d labda/labda.
> The problem is those 3 equations can not be used around
> M31. The H constant calculated is not correct.
No one should ever even think of thinking of redshifts of nearby
galaxies as being cosmological redshifts. There is a component, yes,
but it is swamped by peculiar motion.
> In order to calculate H by two independent measurements
> of V(speed) and d(distance) much further galaxies
> should be used.
And are, in practice.
> How is this done in practice ?
There is a HUGE literature on this. Many people have devoted their
lives to it.
> I expect this is very difficult
> specific for the speed. (You need two distances)
The speed is not calculated by a change in distance with time. It is
inferred, assuming a cosmological model.
One observes the redshift. One observes something such as brightness
which can be used as a proxy for distance. The relationship between
them depends on the cosmological parameters.
Phillip Helbig---remove CLOTHES to reply
<No...@charlesfrancis.wanadoo.co.uk> writes:
> Hubble's law is defined as a linear relationship between redshift and
> distance.
Some people define it as the linear relationship between velocity and
distance, i.e. between the present derivative, with respect to cosmic
time, of the proper distance and the proper distance of the object.
(Hubble OBSERVED a relation between redshift and luminosity, which can
be taken as a proxy for distance. At small redshifts, none of these
distinctions matters.
> >> Perhaps. It's just a pity Harrison's ideas about the expansion of spac=
e
> >> time are somewhat inaccurate.
> >
> >Care to elabourate?
>
> I have only dipped into the book, so cannot comment on much of it, but
> the discussion of the Hubble sphere on p281 struck me as particularly
> misleading. It is absolutely not meaningful to talk about the recession
> velocity of a star in the early universe with respect to ourselves now.
> Think of the balloon analogy. Cosmological redshift is the consequence
> of cosmological expansion, not recession velocities. It just happens
> that, for small cosmological distances, cosmological expansion looks
> like recession velocity. You can't take that concept too far.
Yes, but it does go this far. Assuming a homogeneous and isotropic
expansion, the recession velocity is proportional to
distance---otherwise the homogeneity and/or isotropy are destroyed. At
large redshifts, though, these aren't observable distances and
observable velocities. (Knowing the cosmological parameters, though,
they can still be calculated.)
Nicolaas Vroom
> In article <mt2.0-31051...@hercules.herts.ac.uk>, Nicolaas Vroom
> <nicolaa...@pandora.be> writes:
>
>> The same can be done by using redshifts and the following
>> three equations:
>> In order to calculate H by two independent measurements
>> of V(speed) and d(distance) much further galaxies
>> should be used.
>> I expect this is very difficult
>> specific for the speed. (You need two distances)
>
> The speed is not calculated by a change in distance with time. It is
> inferred, assuming a cosmological model.
Should that not be based on a physical model of the universe ?
> One observes the redshift. One observes something such as brightness
> which can be used as a proxy for distance. The relationship between
> them depends on the cosmological parameters.
Accordingly to the Book by Boyle it goes like this: page 640
"For the relation v=H*d, with v obtained from c*z,
the quantity z being given by d labda/labda (See chapter 14)
and with d obtained (See chapter 8). Hence by determining v
and d values for a number of nearby galaxys the Hubble
constant H is obtained "
I do not know if this description is accordingly to what you call the
cosmological parameters.
Besides that I have a problem with the method explained by Boyle.
What we are observing is a number of galaxies (in the past) which
are moving away from us in an expanding Universe.
The question is can we use v=c*z in order to calculate
the speed (in the past) by measuring d labda now (frequency shift)
which IMO is influenced by the expanding universe itself.
IMO the expanding universe is partly the cause of the frequency
shift, the futher away the more.
That means that the v of the source (in the past) is much smaller
as calculated based from c*z.
A second problem is what is the v of those galaxies now ?
IMO you need at least an answer on both questions in order
to calculate the present size of the Universe.
Nicolaas Vroom
http://users.pandora.be/nicvroom/neophyte.htm
Phillip Helbig---remove CLOTHES to reply
<nicolaa...@pandora.be> writes:
> > The speed is not calculated by a change in distance with time. It is
> > inferred, assuming a cosmological model.
>
> Should that not be based on a physical model of the universe ?
By "cosmological model", what I mean IS a physical model of the
universe, for example General Relativity. In particular, a universe
described by General Relativity with certain values for the cosmological
parameters. One could, of course, also compare other models which are
not based on GR to observations.
> Accordingly to the Book by Boyle it goes like this: page 640
> "For the relation v=3DH*d, with v obtained from c*z,
> the quantity z being given by d labda/labda (See chapter 14)
> and with d obtained (See chapter 8). Hence by determining v
> and d values for a number of nearby galaxys the Hubble
> constant H is obtained "
Fine, no problem. Unstated (apparently by Hoyle) assumptions: the
distance has to be great enough that cosmological redshift is large
compared to that from peculiar motion but not so high that higher-order
effects (depending on the other cosmological parameters but not on the
Hubble constant) need to be taken into account.
(I don't know if that applies here, but Hoyle was a believer in the
steady-state model of the universe and might be deliberately setting up
a straw-man version of more conventional cosmology in order to knock it
down more easily.)
> I do not know if this description is accordingly to what you call the
> cosmological parameters.
In the quote above, the redshift is so low that the velocity can be
calculated as given with only a small error. This doesn't work at
larger redshifts.
> Besides that I have a problem with the method explained by Boyle.
> What we are observing is a number of galaxies (in the past) which
> are moving away from us in an expanding Universe.
> The question is can we use v=3Dc*z in order to calculate
> the speed (in the past) by measuring d labda now (frequency shift)
> which IMO is influenced by the expanding universe itself.
At the low redshifts involved, this is not a problem.
> IMO the expanding universe is partly the cause of the frequency
> shift, the futher away the more.
> That means that the v of the source (in the past) is much smaller
> as calculated based from c*z.
>
> A second problem is what is the v of those galaxies now ?
>
> IMO you need at least an answer on both questions in order
> to calculate the present size of the Universe.
Trust me, it is all very clear and easy, but a bit too much for a usenet
post before breakfast.
Thomas Smid
wrote:
> The 'Hubble's law' Wikipedia article states '...that the velocity at
> their distance from us.'
This is at least historically incorrect (so Wikipedia shouldn't be
writing that): what Hubble discovered was the linear redshift/
distance relationship; the association of the redshift with a
recession velocity was made by others and only adopted by Hubble as a
kind of working hypothesis. Hubble himself believed in the possibility
of a different cause for the redshift (see
http://home.pacbell.net/skeptica/edwinhubble.html
for more regarding the historical facts).
Thomas
Phillip Helbig---remove CLOTHES to reply
<thoma...@gmail.com> writes:
> On 17 Sep, 02:32, dfarr --at-- comcast --dot-- net <df...@comcast.net>
> wrote:
> > The 'Hubble's law' Wikipedia article states '...that the velocity at
> > which various galaxies are receding from the Earth are proportional to
> > their distance from us.'
>
> This is at least historically incorrect (so Wikipedia shouldn't be
> writing that): what Hubble discovered was the linear redshift/
> distance relationship;
To be pedantic, he discovered a linear relationship between redshift and
apparent magnitude. One can interpret apparent magnitude as distance
and redshift as velocity, at least at the low redshifts Hubble was
working at. Then one has a relationship between velocity and distance.
The linear relationship between velocity and distance applies at all
distances and for all velocities (even those greater than the speed of
light) and the constant of proportionality is the Hubble constant, so
some call this Hubble's Law. However, at large redshifts one can't
simply calculate the velocity from the redshift, and the distance
involved is not a "directly observable" distance.
Hans Aberg
> To be pedantic, he discovered a linear relationship between redshift and
> apparent magnitude. One can interpret apparent magnitude as distance
> and redshift as velocity, at least at the low redshifts Hubble was
> working at. Then one has a relationship between velocity and distance.
>
> The linear relationship between velocity and distance applies at all
> distances and for all velocities (even those greater than the speed of
> light) and the constant of proportionality is the Hubble constant, so
> some call this Hubble's Law. However, at large redshifts one can't
> simply calculate the velocity from the redshift, and the distance
> involved is not a "directly observable" distance.
What formula is used to compute velocity from redshift?
Hans
Nicolaas Vroom
> In article <mt2.0-21285...@hercules.herts.ac.uk>, Nicolaas Vroom
> <nicolaa...@pandora.be> writes:
>
>> "For the relation v=H*d, with v obtained from c*z,
>> the quantity z being given by d labda/labda (See chapter 14)
>> and with d obtained (See chapter 8). Hence by determining v
>> and d values for a number of nearby galaxys the Hubble
>> constant H is obtained "
etc
> (I don't know if that applies here, but Hoyle was a believer in the
> steady-state model of the universe and might be deliberately setting up
> a straw-man version of more conventional cosmology in order to knock it
> down more easily.)
Strange sentence.....
>> Besides that I have a problem with the method explained by Hoyle.
>> What we are observing is a number of galaxies (in the past) which
>> are moving away from us in an expanding Universe.
>> The question is can we use v=c*z in order to calculate
>> the speed (in the past) by measuring d labda now (frequency shift)
>> which IMO is influenced by the expanding universe itself.
>
> At the low redshifts involved, this is not a problem.
Where do you draw this border line ?
At 1% of the speed of light ?
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)
(This should cause a redshift, but in reality it has a blue shift resulting
in a relative/peculiar velocity of roughly 300 km/sec towards the Sun)
I have no problem using v=c*z if we lived in an Universe
with no expansion in order to measure the peculiar velocity of
far away galaxies.
I have a problem using that formula as soon as space expansion
becomes involved to measure based on a speed measured here now
to calculate the speed over there in the past.
IMO the speed over there is smaller.
>> IMO the expanding universe is partly the cause of the frequency
>> shift, the futher away the more.
etc
> Trust me, it is all very clear and easy, but a bit too much for a usenet
> post before breakfast.
For high speeds relativistic redshift equations has to be used.
z = sqrt(c+v)/(c-v) -1 (See Box 27.1). Is that the solution ?
I already see a problem at much lower speeds.
Nicolaas Vroom
http://users.pandora.be/nicvroom/
Thomas Smid
<hel...@astro.multiCLOTHESvax.de> wrote:
> To be pedantic, he discovered a linear relationship between redshift and
> apparent magnitude.
The Big-Bang model of the universe rests solely on the interpretation
of the redshift as being due to recessional velocities, so you can
hardly call this issue pedantic. The point is that Hubble's work has
nothing to do with this interpretational step. The latter is an ad-hoc
assumption made by others, so with the formulation as in the Wikipedia
article (and many other publications), Hubble's name and work has
effectively been hijacked to promote this ad-hoc interpretation of the
galactic redshifts.
>One can interpret apparent magnitude as distance
> and redshift as velocity,
Whether one 'can' or not is not the point here. The question here is
whether one *has to*. Only if one could answer this unambiguously with
yes, would this justify the interpretation of the redshifts as
recessional velocities.
[Mod. note: in science, one rarely 'has to' interpret anything as
anything, as Descartes pointed out some time ago -- mjh]
Thomas
Stupendous_Man
(here's a copy of his 1929 paper, for example)
http://spiff.rit.edu/classes/phys240/lectures/expand/hub_1929.html
you'll see that he discusses a relationship between
distance and radial velocity. Note the title of the
paper, for example:
"A RELATION BETWEEN DISTANCE AND RADIAL VELOCITY
AMONG EXTRA-GALACTIC NEBULAE"
Hubble used several methods involving stars
(including Cepheids and luminous blue stars)
to estimate distances to other galaxies.
He converted the shift in apparent wavelength
of their spectra into radial velocities.
It is true that he offered two explanations for the
shift in wavelengths, one of which is motion
(radial velocity) and the other some sort of
scattering.
I recommend that people who argue about
the work of old-timey astronomers actually read
those old-timey papers themselves, rather than
reading an interpretation of those papers on
someone's website.
Phillip Helbig---remove CLOTHES to reply
<haberg_...@math.su.se> writes:
For small redshifts, the Doppler formula. Since you're a mathematician,
I'm sure you understand that all things are linear to first order. :-)
For larger redshifts, the easy part is v = H*D. This is why has the
dimensions of inverse time, or km/s/Mpc. The hard part is calculating D
from the redshift. What you want is the proper distance. This, in the
general case, is rather tricky and involves elliptic integrals. See,
for example,
http://www.astro.multivax.de:8000/helbig/research/publications/info/angsiz.html
The paper is mainly concerned with a general numerical method for
calculating certain distances in the case of a locally inhomogeneous
universe, but for questions like this there is an appendix which
explains the relationships between redshifts and various distances.
Phillip Helbig---remove CLOTHES to reply
<thoma...@gmail.com> writes:
> On 20 Oct, 12:53, Phillip Helbig---remove CLOTHES to reply
> <hel...@astro.multiCLOTHESvax.de> wrote:
>
> > To be pedantic, he discovered a linear relationship between redshift and
> > apparent magnitude.
>
> The Big-Bang model of the universe rests solely on the interpretation
> of the redshift as being due to recessional velocities, so you can
> hardly call this issue pedantic.
But Hubble's discovery came first, the big-bang model as a model for the
real universe came later.
Phillip Helbig---remove CLOTHES to reply
<nicolaa...@pandora.be> writes:
> > (I don't know if that applies here, but Hoyle was a believer in the
> > steady-state model of the universe and might be deliberately setting up
> > a straw-man version of more conventional cosmology in order to knock it
> > down more easily.)
>
> Strange sentence.....
Hoyle was a strange character. Once, he presented a rather
over-simplified model, emphasising its simplicity. Some in the audience
thought it unrealistically simplified, and someone remarked "You'd look
pretty simple, too, Fred, at a distance of 10 parsecs.".
> >> Besides that I have a problem with the method explained by Hoyle.
> >> What we are observing is a number of galaxies (in the past) which
> >> are moving away from us in an expanding Universe.
> >> The question is can we use v=c*z in order to calculate
> >> the speed (in the past) by measuring d labda now (frequency shift)
> >> which IMO is influenced by the expanding universe itself.
> >
> > At the low redshifts involved, this is not a problem.
>
> Where do you draw this border line ?
> At 1% of the speed of light ?
Depends on the cosmological parameters. For some models, the
relationship is exact at all redshifts. For others (though perhaps not
within the framework of GR), it might not even be close in the limit of
small redshifts (but in all GR models, at small redshifts the
approximation is OK).
> I have no problem using v=c*z if we lived in an Universe
> with no expansion in order to measure the peculiar velocity of
> far away galaxies.
> I have a problem using that formula as soon as space expansion
> becomes involved to measure based on a speed measured here now
> to calculate the speed over there in the past.
> IMO the speed over there is smaller.
Depends on the cosmological model. However, for any model in which the
approximation v=cz is valid, the difference between here and now and
there and then is negligible.
> For high speeds relativistic redshift equations has to be used.
> z = sqrt(c+v)/(c-v) -1 (See Box 27.1). Is that the solution ?
Definitely not. To paraphrase Wolfgang Pauli, it is wrong to use the
Doppler formula at low redshifts, it is very wrong to say that the
cosmological expansion is caused by the Doppler effect, and it is not
even wrong to say that the relativistic Doppler formula is appropriate
at high redshifts. Simple argument: This formula makes no reference to
the cosmological parameters, so it will give the same result no matter
what their values are.
Phillip Helbig---remove CLOTHES to reply
<mwr...@rit.edu> writes:
> If you actually read Hubble's work for yourself
> (here's a copy of his 1929 paper, for example)
>
> http://spiff.rit.edu/classes/phys240/lectures/expand/hub_1929.html
>
> you'll see that he discusses a relationship between
> distance and radial velocity. Note the title of the
> paper, for example:
>
> "A RELATION BETWEEN DISTANCE AND RADIAL VELOCITY
> AMONG EXTRA-GALACTIC NEBULAE"
OK, but it is still an interpretation, even if it is Hubble's. I was
merely pointing out that if on the one hand one is discussing whether to
interpret the redshift as velocity, one should or could also
discuss---and I did use the word pedantic---whether to interpret the
magnitude as distance. The latter is actually non-trivial, since it
relies on a "standard candle". Only within the last 10--15 years have
reliable standard candles been found and used to accurately measure the
Hubble constant.
As Mach said: "Every statement in physics has to state relations between
observable quantities." What is observed are magnitude and redshift,
^^^^^^^^^^
distance and velocity are derived. (One could be even more pedantic and
talk about what is actually recorded by the photographic emulsion, which
in practice actually has to be taken into account.)
Hans Aberg
But it is this redshift-velocity interpretation that results in speeds
exceeding c?
And my guess there is no experimental verification of such a formula at
high speeds. Suppose a particle at speed close to c emits a photon, what
is the measured wavelength shift?
Hans
Nicolaas Vroom
news:mt2.0-19629...@hercules.herts.ac.uk...
> On 20 Oct, 12:53, Phillip Helbig---remove CLOTHES to reply
> <hel...@astro.multiCLOTHESvax.de> wrote:
>
>>One can interpret apparent magnitude as distance
>> and redshift as velocity,
>
> Whether one 'can' or not is not the point here. The question here is
> whether one *has to*. Only if one could answer this unambiguously with
> yes, would this justify the interpretation of the redshifts as
> recessional velocities.
>
I have no problem with the statement one can interpret
redshift as velocity.
IMO the issue is how.
The current point of view is that for values of z << 1 one has to
use the equation v = c*z
(Also called the nonrelativistic equation for the Doppler shift)
I have a problem with that equation.
Suppose a galaxy at a far distance in the past is receding from us
with a speed of 0.01c resulting in a value of z of 0.01.
Light from that galaxy in an expanding universe is travelling towards
us at a speed c and is stretched.
Suppose we receive it now. Is it not possible in principle that we measure
a value of z=0.02 implying a speed of v=0.02*c ?
My point is what we measure is not the true speed of the source at the point
of emission. This speed is much lower because the waves are stretched.
Even if we measure a z=2 it does not mean that the source in the past
was travelling at a speed higher than c.
The overall implication is that maybe there is no reason to
use the relativistic equation for the Doppler shift.
A second implication in principle is that the true speed, of a galaxy
with z=2 measured now here, could be zero over there.
A third implication is that the size of the Observable Universe
is much smaller than 47 Gyr. See the posting by Hans Aberg.
Nicolaas Vroom
http://users.pandora.be/nicvroom/neophyte.htm
Phillip Helbig---remove CLOTHES to reply
<haberg_...@math.su.se> writes:
> But it is this redshift-velocity interpretation that results in speeds
> exceeding c?
Yes, but that's not a problem.
See
@BOOK {EHarrison81a,
AUTHOR = "Edward R. Harrison",
TITLE = "Cosmology, the Science of the Universe",
PUBLISHER = "Cambridge University Press",
YEAR = "1981",
ADDRESS = "Cambridge"
}
and
@ARTICLE {EHarrison93a,
AUTHOR = "Edward R. Harrison",
TITLE = "The Redshift-Distance and Velocity-Distance
Laws",
JOURNAL = APJ,
YEAR = "1993",
VOLUME = "403",
NUMBER = "1",
PAGES = "28",
MONTH = jan
}
> And my guess there is no experimental verification of such a formula at
> high speeds. Suppose a particle at speed close to c emits a photon, what
> is the measured wavelength shift?
I'm sure this happens all the time in particle accelerators which
produce synchrotron radiation.
Phillip Helbig---remove CLOTHES to reply
<nicolaa...@pandora.be> writes:
> I have no problem with the statement one can interpret
> redshift as velocity.
> IMO the issue is how.
> The current point of view is that for values of z << 1 one has to
> use the equation v = c*z
> (Also called the nonrelativistic equation for the Doppler shift)
You don't have to use it, but you CAN use it and get the same result as
a more detailed analysis.
> I have a problem with that equation.
> Suppose a galaxy at a far distance in the past is receding from us
> with a speed of 0.01c resulting in a value of z of 0.01.
> Light from that galaxy in an expanding universe is travelling towards
> us at a speed c and is stretched.
OK.
> Suppose we receive it now. Is it not possible in principle that we measure
> a value of z=0.02 implying a speed of v=0.02*c ?
Why should that happen?
> My point is what we measure is not the true speed of the source at the point
> of emission. This speed is much lower because the waves are stretched.
Again, for the low redshifts at which one can use the Doppler formula,
the change in speed between the time of emission and the time of
absorption is negligible.
> Even if we measure a z=2 it does not mean that the source in the past
> was travelling at a speed higher than c.
But it could be.
> The overall implication is that maybe there is no reason to
> use the relativistic equation for the Doppler shift.
Right.
> A second implication in principle is that the true speed, of a galaxy
> with z=2 measured now here, could be zero over there.
Possible. But now you are in the high-redshift regime, where you can't
get a useful answer from the Doppler formula.
> A third implication is that the size of the Observable Universe
> is much smaller than 47 Gyr. See the posting by Hans Aberg.
I don't think that anyone claims that the size of the Observable
Universe is as large as 47 Gyr.
Hans Aberg
>> exceeding c?
>
> Yes, but that's not a problem.
But it would appear as though you arrive at two different, non-unified
concepts of velocity: of relativity which excludes FLT for massive
objects, and of universe expansion of unclear independent verification.
> See
....
> @ARTICLE {EHarrison93a,
> AUTHOR = "Edward R. Harrison",
> TITLE = "The Redshift-Distance and Velocity-Distance
> Laws",
> JOURNAL = APJ,
> YEAR = "1993",
> VOLUME = "403",
> NUMBER = "1",
> PAGES = "28",
> MONTH = jan
> }
This one is avilable here:
http://tinyurl.com/ygq7aq2
expanded might appear as broken:
http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?bibcode=1993ApJ...403...28H&db_key=AST&page_ind=0&data_type=GIF&type=SCREEN_VIEW&classic=YES
It does not seem to discuss redshift-velocity formulas, though, only
formulas depending on distance.
>> And my guess there is no experimental verification of such a formula at
>> high speeds. Suppose a particle at speed close to c emits a photon, what
>> is the measured wavelength shift?
>
> I'm sure this happens all the time in particle accelerators which
> produce synchrotron radiation.
So how are the redshift-velocity formulas used in astronomy derived from
that?
Hans
Nicolaas Vroom
> In article <mt2.0-4565...@hercules.herts.ac.uk>, Nicolaas Vroom
> <nicolaa...@pandora.be> writes:
>
>> I have no problem using v=c*z if we lived in an Universe
>> with no expansion in order to measure the peculiar velocity of
>> far away galaxies.
>> I have a problem using that formula as soon as space expansion
>> becomes involved to measure based on a speed measured here now
>> to calculate the speed over there in the past.
>> IMO the speed over there is smaller.
>
> Depends on the cosmological model. However, for any model in which the
> approximation v=cz is valid, the difference between here and now and
> there and then is negligible.
>
Finally I found a document which describes the problem.
See http://wapedia.mobi/en/Hubble's_law
Specific paragraph 2. 2. "Observability of parameters"
Here we read:
"For relatively nearby galaxies (redshift z much less than unity),
v and D will not have changed much, and v can be estimated
using the formula v=zc where c is the speed of light.
This gives the empirical relation found by Hubble."
The book Universe Box 26.2 has an example:
for NGC 4889.
Normally wavelength 3933A measured 4018 A
z = (4018-3933)/3933= 65/3933= 0,0216
Next we read:
The galaxy is therefore moving away
from us with a speed of: v=zc= 6500 km/sec
Also at this small value of z there is an issue exactly
what is the definition of v?
Is this a speed measured over here now
or
is this the speed of the galaxy over there in the past.
To write this slightly different.
What was the difference in wavelength at the moment
of transmission at the source:
1) 0 A or close to zero
2) inbetween 0A and 65A for example close to 32A
3) 65 A or close to 65
People who believe in the retarded light concept
are in favour of option 1 (ie no space expansion)
I place the above sentence
> the difference between here and now and
> there and then is negligible.
as option 3
I have a problem with this.
IMO the difference in wave length can have two causes:
By a speed of the galaxy away from us at the moment of
emission.
By space expansion during its traveling from source to destination.
The question is how much is this and how do we know ?
How much is this when d labda = 65 A
How much is this when d labda = 3933 A resulting z=1
Why can not it be 50% already in the case of 65 A
Using H = 70, NGC 4889 is roughly 90 million lightyears
away from us.
Nicolaas Vroom
http://users.pandora.be/nicvroom/neophyte.htm
Hans Aberg
> Phillip Helbig---remove CLOTHES to reply wrote:
>>> But it is this redshift-velocity interpretation that results in speeds
>>> exceeding c?
>> Yes, but that's not a problem.
>
> But it would appear as though you arrive at two different, non-unified
> concepts of velocity: of relativity which excludes FLT for massive
> objects, and of universe expansion of unclear independent verification.
Actually, I noticed after making the post that
http://en.wikipedia.org/wiki/Redshift#Expansion_of_space
indicates it is a metric expansion of space.
>>> And my guess there is no experimental verification of such a formula at
>>> high speeds. Suppose a particle at speed close to c emits a photon, what
>>> is the measured wavelength shift?
>> I'm sure this happens all the time in particle accelerators which
>> produce synchrotron radiation.
>
> So how are the redshift-velocity formulas used in astronomy derived from
> that?
And the link above also indicates different redshift formulas, for
example, a gravitational one.
Hans
Thomas Smid
If you had fully read the web reference http://home.pacbell.net/skeptica/edwinhubble.html
, you would have found there
"To the best of my knowledge Hubble�s 1929 paper (3) is the only
published paper where the reader is left with the view by Hubble, and
now apparently universally adopted, that the linear law of redshifts
applies only as a velocity-distance relation. It is no wonder that
this is the paper that is usually cited by itself in astronomy
textbooks."
and also the quote from Hubble's book 'The Realm of the Nebulae':
"Meanwhile, red-shifts may be expressed on a scale of velocities as a
matter of convenience. They behave as velocity-shifts behave and they
are very simply represented on the same familiar scale, regardless of
the ultimate interpretation. The term �apparent velocity� may be used
in carefully considered statements, and the adjective always implied
where it is omitted in general usage. --pp. 122-123"
As is well known, the interpretation of the redshift in terms of
velocities was already suggested much earlier by Vesto Slipher, and
even he considered other causes possible. I quote from from
http://en.wikipedia.org/wiki/Vesto_Slipher : Slipher first reports on
the making the first Doppler measurement on September 17, 1912 in The
radial velocity of the Andromeda Nebula in the inaugural volume of the
Lowell Observatory Bulletin, pp.2.56-2.57. In his report Slipher
writes: "The magnitude of this velocity, which is the greatest
hitherto observed, raises the question whether the velocity-like
displacement might not be due to some other cause, but I believe we
have at present no other interpretation for it."
Thomas
Phillip Helbig---remove CLOTHES to reply
<nicolaa...@pandora.be> writes:
> The galaxy is therefore moving away
> from us with a speed of: v=zc= 6500 km/sec
>
> Also at this small value of z there is an issue exactly
> what is the definition of v?
> Is this a speed measured over here now
> or
> is this the speed of the galaxy over there in the past.
Again, for the redshifts involved, the difference is negligible.
> To write this slightly different.
> What was the difference in wavelength at the moment
> of transmission at the source:
> 1) 0 A or close to zero
> 2) inbetween 0A and 65A for example close to 32A
> 3) 65 A or close to 65
0. The wavelength gets stretched out as the universe expands.
Phillip Helbig---remove CLOTHES to reply
<haberg_...@math.su.se> writes:
> Phillip Helbig---remove CLOTHES to reply wrote:
> >> But it is this redshift-velocity interpretation that results in speeds
> >> exceeding c?
> >
> > Yes, but that's not a problem.
>
> But it would appear as though you arrive at two different, non-unified
> concepts of velocity: of relativity which excludes FLT for massive
> objects,
Within the constraints of special relativity, i.e. Minkowski space-time.
> >> And my guess there is no experimental verification of such a formula at
> >> high speeds. Suppose a particle at speed close to c emits a photon, what
> >> is the measured wavelength shift?
> >
> > I'm sure this happens all the time in particle accelerators which
> > produce synchrotron radiation.
>
> So how are the redshift-velocity formulas used in astronomy derived from
> that?
There are two possibilities. One, imagine the expansion of space
stretching the wavelength of light. This provides a quantitatively
correct interpretation, and underlines the fact that, without further
assumptions, the redshift tells us ONLY the ratio of the scale factor of
the universe now to that at the time the light was emitted. Or, do the
the full-scale GR derivation, which is too much for a usenet post.
Thomas Smid
> As is well known, the interpretation of the redshift in terms of
> velocities was already suggested much earlier by Vesto Slipher, and
> even he considered other causes possible. I quote from fromhttp://en.wikipedia.org/wiki/Vesto_Slipher: Slipher first reports on
> the making the first Doppler measurement on September 17, 1912 in The
> radial velocity of the Andromeda Nebula in the inaugural volume of the
> Lowell Observatory Bulletin, pp.2.56-2.57. In his report Slipher
> writes: "The magnitude of this velocity, which is the greatest
> hitherto observed, raises the question whether the velocity-like
> displacement might not be due to some other cause, but I believe we
> have at present no other interpretation for it."
>
> Thomas
Just an add-on to this: in case of the Andromeda Nebula (and some
other close galaxies), the line shift is of course actually a blue-
shift, and thus is not representable by the Hubble law. But
nonetheless, it seems that both Slipher and Hubble potentially
questioned the interpretation of all these shifts in terms of radial
velocities.
Thomas
Hans Aberg
>>>> But it is this redshift-velocity interpretation that results in speeds
>>>> exceeding c?
>>> Yes, but that's not a problem.
>> But it would appear as though you arrive at two different, non-unified
>> concepts of velocity: of relativity which excludes FLT for massive
>> objects,
>
> Within the constraints of special relativity, i.e. Minkowski space-time.
As in the link of my other post (which probably did not appear before
you made your post), it is called metric expansion of space.
http://en.wikipedia.org/wiki/Redshift
This is perfectly logical, but falls in the same category as for example
MOND: one has incomplete information as to why something is happening,
and adjust the questions so that known data fits. This is the problem of
retrodiction without genuine prediction.
>>>> And my guess there is no experimental verification of such a formula at
>>>> high speeds. Suppose a particle at speed close to c emits a photon, what
>>>> is the measured wavelength shift?
>>> I'm sure this happens all the time in particle accelerators which
>>> produce synchrotron radiation.
>> So how are the redshift-velocity formulas used in astronomy derived from
>> that?
>
> There are two possibilities. One, imagine the expansion of space
> stretching the wavelength of light. This provides a quantitatively
> correct interpretation, and underlines the fact that, without further
> assumptions, the redshift tells us ONLY the ratio of the scale factor of
> the universe now to that at the time the light was emitted. Or, do the
> the full-scale GR derivation, which is too much for a usenet post.
Metric expansion is easy to understand from the mathematical point of
view: just let it depend on time, as here
http://en.wikipedia.org/wiki/FLRW_metric
But then sort of the very physics principles change, because the metric
is not a directly measurable quantity, but an intermediate used to
explain connections between physically measurable quantities.
I like the gravitational redshift more. If background radiation is
produced by black hole, that would explain the heavy redshift there. I
think such possibilities were in the past excluded because the GR
predict the universe cannot be stable. But at that time, one did not
know that only a small fraction of the mass is not visible.
Hans
Phillip Helbig---remove CLOTHES to reply
<thoma...@gmail.com> writes:
> Just an add-on to this: in case of the Andromeda Nebula (and some
> other close galaxies), the line shift is of course actually a blue-
> shift, and thus is not representable by the Hubble law. But
> nonetheless, it seems that both Slipher and Hubble potentially
> questioned the interpretation of all these shifts in terms of radial
> velocities.
Hubble did so, IIRC, due to a misunderstanding of the K-correction.
Alan Sandage detailed this in his Saas-Fee lecture notes from the 1993
summer school. I have the proceedings, but haven't unpacked them since
having recently moved house, but if there is interest I can post a short
summary in a couple of weeks. Sandage, of course, was Hubble's
assistant (at the same time that he was Baade's doctoral student).
Ironically, when Hubble died he probably doubted that the expansion of
the universe was real.
(A note of caution to readers of historical literature: the modern
definitions are often different than the ones used by authors in the
first half of the 20th century. Caveat lector! (A similar situation
exists with regard to 17th- and 18th-century physics literature.))
Phillip Helbig---remove CLOTHES to reply
<haberg_...@math.su.se> writes:
> As in the link of my other post (which probably did not appear before
> you made your post), it is called metric expansion of space.
> http://en.wikipedia.org/wiki/Redshift
> This is perfectly logical, but falls in the same category as for example
> MOND: one has incomplete information as to why something is happening,
> and adjust the questions so that known data fits. This is the problem of
> retrodiction without genuine prediction.
Historically, it was exactly the opposite. The universe was believed to
be static, Einstein saw that this was not what his theory predicted. So
first the expanding space, and then, more than 10 years later, the
observations to support it. (Einstein modified his theory---not just by
introducing the cosmological constant, which someone else might have
included from the outset, but by introducing it with a special, finely
tuned value (the distinction is important)---to allow a static universe,
but disowned this when observations confirmed his original prediction.
> I like the gravitational redshift more. If background radiation is
> produced by black hole, that would explain the heavy redshift there.
It's not just the redshift. Cosmology, today, is a data-driven science.
(This wasn't the case until quite recently.) There are a lot of data to
explain. Any alternative theory has to explain the CMB observations in
detail.
Hans Aberg
>> you made your post), it is called metric expansion of space.
>> http://en.wikipedia.org/wiki/Redshift
>> This is perfectly logical, but falls in the same category as for example
>> MOND: one has incomplete information as to why something is happening,
>> and adjust the questions so that known data fits. This is the problem of
>> retrodiction without genuine prediction.
>
> Historically, it was exactly the opposite. The universe was believed to
> be static, Einstein saw that this was not what his theory predicted. So
> first the expanding space, and then, more than 10 years later, the
> observations to support it.
Did his analysis say that the universe must have a metric expansion? - I
thought it just said that it could not be stable.
>> I like the gravitational redshift more. If background radiation is
>> produced by black holes, that would explain the heavy redshift there.
>
> It's not just the redshift. Cosmology, today, is a data-driven science.
> (This wasn't the case until quite recently.) There are a lot of data to
> explain. Any alternative theory has to explain the CMB observations in
> detail.
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?
Hans
Phillip Helbig---remove CLOTHES to reply
<haberg_...@math.su.se> 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. You need to take into account H, Omega and
lambda and their errors to get an age with an error. Also, 13.2 Gy is
not something seen in the spectrum of the start; it is inferred, also
with some error bar. Keeping these caveats in mind, if a star were
found which had an age which was, say, older than the age of the
universe by 3 sigma, then one of the age estimates is probably wrong.
Probably, since many other lines of argument support the values of the
cosmological parameters, not just the age of the universe, and since it
is just ONE star (the fact that all of the billions and billions of
other stars are younger than the universe is of course also evidence
which should not be ignored), most people would probably doubt the age
determination of the star. Extraordinary claims require extraordinary
evidence. One would have to make a really good case that that star is
really that old. (And this would not sound credible from someone who
has claimed in the past that we know so little about stars that there is
no way that supernovae can be used as standard candles.)
Hans Aberg
>> thought it just said that it could not be stable.
>
> Define "metric expansion".
I gave some links:
http://en.wikipedia.org/wiki/Redshift#Expansion_of_space
http://en.wikipedia.org/wiki/Metric_expansion_of_space
http://en.wikipedia.org/wiki/FLRW_metric
Briefly, GR is expressed using a Lorentz manifold, and one assumes that
its metric can be expressed to that the spatial component is time dependent.
Take the picture the universe of a balloon with some raisins stuck on
it, illustrating the galaxies. If you blow up the balloon, the
raisins/galaxies move apart - there is no difference telling whether the
galaxies moves apart as result of a motion of their own, or by them
being stuck on the expanding balloon/universe.
Now, instead keep the balloon fixed, and let the measurement rulers
shrink over time. This is metric expansion of the universe. Since the
metric is used by all physical objects at a certain spatial slice at
each point in time, one will measure the objects moving apart. But when
comparing objects of different time slices, things like speeds higher
than c become possible. Objects get another velocity component, which is
due to the change of the average metric over time.
>> 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. You need to take into account H, Omega and
> lambda and their errors to get an age with an error. Also, 13.2 Gy is
> not something seen in the spectrum of the start; it is inferred, also
> with some error bar. Keeping these caveats in mind, if a star were
> found which had an age which was, say, older than the age of the
> universe by 3 sigma, then one of the age estimates is probably wrong.
> Probably, since many other lines of argument support the values of the
> cosmological parameters, not just the age of the universe, and since it
> is just ONE star (the fact that all of the billions and billions of
> other stars are younger than the universe is of course also evidence
> which should not be ignored), most people would probably doubt the age
> determination of the star. Extraordinary claims require extraordinary
> evidence. One would have to make a really good case that that star is
> really that old. (And this would not sound credible from someone who
> has claimed in the past that we know so little about stars that there is
> no way that supernovae can be used as standard candles.)
So if you would device an experiment able to determine if the BB model
is true or false, what would it be?
Hans
Phillip Helbig---remove CLOTHES to reply
<haberg_...@math.su.se> writes:
> So if you would device an experiment able to determine if the BB model
> is true or false, what would it be?
A theory cannot be proven true, only proven false. An object which is
unquestionably older than a robust age of the universe derived from the
big-bang theory would be a disproof, for example.
Hans Aberg
>> is true or false, what would it be?
>
> A theory cannot be proven true, only proven false.
Yes, that is what I meant. Sorry for the unclarity.
Hans
Hans Aberg
>> is true or false, what would it be?
>
> A theory cannot be proven true, only proven false.
Yes, that is what I meant. Sorry for the unclarity.
Hans
[Mod. note: reposted to, hopefully, fix broken References: line -- mjh]
Thomas Smid
> Phillip Helbig---remove CLOTHES to reply wrote:
>
> >> 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".
>
> I gave some links:
> � �http://en.wikipedia.org/wiki/Redshift#Expansion_of_space
> � �http://en.wikipedia.org/wiki/Metric_expansion_of_space
> � �http://en.wikipedia.org/wiki/FLRW_metric
> Briefly, GR is expressed using a Lorentz manifold, and one assumes that
> its metric can be expressed to that the spatial component is time dependent.
>
> Take the picture the universe of a balloon with some raisins stuck on
> it, illustrating the galaxies. If you blow up the balloon, the
> raisins/galaxies move apart - there is no difference telling whether the
> galaxies moves apart as result of a motion of their own, or by them
> being stuck on the expanding balloon/universe.
>
> Now, instead keep the balloon fixed, and let the measurement rulers
> shrink over time. This is metric expansion of the universe. Since the
> metric is used by all physical objects at a certain spatial slice at
> each point in time, one will measure the objects moving apart. But when
> comparing objects of different time slices, things like speeds higher
> than c become possible. Objects get another velocity component, which is
> due to the change of the average metric over time.
I haven't heard of that definition of metric expansion before. In
fact, in the very Wikipedia link you gave above (
http://en.wikipedia.org/wiki/Metric_expansion_of_space ) the expanding
balloon is given as an analogy for the metric expansion. I can't see
any reference to a static balloon and a shrinking measurement ruler
here.
Anyway, what measurement ruler are you talking about? Where is it
supposed to be in context of the balloon model, and why should it be
shrinking? Without a clear definition in this sense, you can't define
metric expansion.
Thomas
Hans Aberg
>> Take the picture the universe of a balloon with some raisins stuck on
>> it, illustrating the galaxies. If you blow up the balloon, the
>> raisins/galaxies move apart - there is no difference telling whether the
>> galaxies moves apart as result of a motion of their own, or by them
>> being stuck on the expanding balloon/universe.
>>
>> Now, instead keep the balloon fixed, and let the measurement rulers
>> shrink over time. This is metric expansion of the universe. Since the
>> metric is used by all physical objects at a certain spatial slice at
>> each point in time, one will measure the objects moving apart. But when
>> comparing objects of different time slices, things like speeds higher
>> than c become possible. Objects get another velocity component, which is
>> due to the change of the average metric over time.
>
> I haven't heard of that definition of metric expansion before. In
> fact, in the very Wikipedia link you gave above (
> http://en.wikipedia.org/wiki/Metric_expansion_of_space ) the expanding
> balloon is given as an analogy for the metric expansion. I can't see
> any reference to a static balloon and a shrinking measurement ruler
> here.
>
> Anyway, what measurement ruler are you talking about? Where is it
> supposed to be in context of the balloon model, and why should it be
> shrinking? Without a clear definition in this sense, you can't define
> metric expansion.
Strictly speaking, none of the balloon models are mathematically
correct, as they embed the (two dimensional) space into a three
dimensional Euclidean space (R^3) - GR does not come with any such
embeddings. (Neglecting the dimension issue.)
If you are in one spatial time-slice, then you can't tell the difference
between a (conformal) change in the metric and the change in the size of
space, because the distance measurements are relative. You have one
physical object used as a rules, and measure another object relative
that measurement unit. Suppose your rules is certain number of
wavelengths of a certain Cesium atom transition. When the GR metric is
deformed, looking at it from the outside, distance will change. But from
the inside, distances will all change in proportion, so it cannot be
detected.
So this interpretation of the GR metric is not a physically measurable
quantity. Only relative measurements within the spatial component are
measurable.
Now the metric expansion theory says that this conformal factor changes
over time. It cannot be detected within any time-slice, but it affects
certain aspects between the time-slices, like the redshift. Because the
physical measurements of the past were smaller relative than those now,
the light gets stretched, or redshifted. By developing formulas, one can
indirectly compute formulas for the change in the metric. You can't
detect this change in your measurement rod, as the number of wavelengths
from the Cesium atom above, because it is not transported sufficiently
much through time - the effect is probably too small to be measured.
Now to the balloons. Because it is not possible to tell the difference
between the expansion of space and in the metric, it is natural to use
the first model for both. But then it becomes hard to understand why
objects can move at speeds higher than c. And I think that possibly, if
the GR metric is just the usual time-space distance all through space,
at all times, then speeds higher than c may indeed be impossible. - This
would then be an alteration of the original GR model, where one admits a
deformation of the GR metric through time.
So I then wanted to illustrate this with the second picture above. When
looking from the outside, one will see that the metric changes, so that
those inside will se an expansion of the universe, but from the outside,
the objects are stuck in their places. They do not move physically at
all: the expansion is in fact just an illusion, due to the metric
expansion. This can the be explained as a perceived velocity of the
objects, caused by a perceived expansion of the universe.
I think there might be another difference between these illustrations.
If the first picture was valid, one could shrink it down to zero size.
But in the second picture, no matter how much the metric is deformed,
one could not get down to 0. It will behave as a singularity. So no
matter how extreme measurements you put into model, it will only adjust
closer to this singularity.
Anyway, that is my rather cursory interpretation if it. The experts here
will surely clarify.
Hans
Hans Aberg
>> Take the picture the universe of a balloon with some raisins stuck on
>> it, illustrating the galaxies. If you blow up the balloon, the
>> raisins/galaxies move apart - there is no difference telling whether the
>> galaxies moves apart as result of a motion of their own, or by them
>> being stuck on the expanding balloon/universe.
>>
>> Now, instead keep the balloon fixed, and let the measurement rulers
>> shrink over time. This is metric expansion of the universe. Since the
>> metric is used by all physical objects at a certain spatial slice at
>> each point in time, one will measure the objects moving apart. But when
>> comparing objects of different time slices, things like speeds higher
>> than c become possible. Objects get another velocity component, which is
>> due to the change of the average metric over time.
>
> I haven't heard of that definition of metric expansion before. In
> fact, in the very Wikipedia link you gave above (
> http://en.wikipedia.org/wiki/Metric_expansion_of_space ) the expanding
> balloon is given as an analogy for the metric expansion. I can't see
> any reference to a static balloon and a shrinking measurement ruler
> here.
First model: in R^3 with standard metric, take the sphere S_t = {(x, y,
z)| x^2 + y^2 + z^2 = t^2} with radius the parameter t > 0. The sphere
gets its metric induced by that of R^3.
Second model: in R^3, take the unit sphere S = {(x, y, z)| x^2 + y^2 +
z^2 = 1}, but give it the distance function d_t(x, y) = t|x - y[, t > 0.
Two points on the unit sphere will get a larger distance with increased
t, even though their position on the sphere isn't changing.
The unit sphere S with metric d_t can be mapped isometrically onto S_t.
So one would think that the models would be equivalent. But when
speaking about metric expansion, one uses the second model, and by that
one somehow can arrive at speeds higher than c. This speed is then due
to a change in d_t.
Hans
jacob navia
[snip]
> If you are in one spatial time-slice, then you can't tell the difference
> between a (conformal) change in the metric and the change in the size of
> space, because the distance measurements are relative.
"The size of space"...
I am astonished by seeing those words in writing and that nobody cares to
explain what that could *possibly* MEAN!
"Size" as it is normally understood, means meters, i.e. space. When I say
"My size is 1.72 meters" I mean that there is a FIXED quantity of a measure
of space that would fit 1.72 times between my toes and my head.
What is "the SIZE of space?" How can we measure the "size of space?"
in meters? Obviously impossible.
Each second (I read that in this incredible thread) there are 174 Km
more of space between Andromeda and me.
WHERE are those 174 Km?
Uniformly spread between here and Andromeda?
Or at the middle of the distance?
Or uniformly spread between the border of the milky way and
the border of Andromeda?
Or at the middle of a straight line between the center of gravity of the
milky way and Andromeda?
What is the kinetic energy of Andromeda? m*v*v?
But v is meters / second. If Andromeda is approaching at (say) 300 Km/sec
its kinetic energy is m*(300+174)*(300*174)?
And at a certain point of distance (if we believe BB theory) the expansion of
space between Andromeda and us will CEASE since they will be too close to
be separated each second by space expansion.
At what point will that happen?
When they touch?
When the borders are less than 1 light year apart?
WHEN?
Nobody has ever given an answer to this question.
Astronomy must make SENSE. It can't just ignore the most elementary bases
of science: metrics.
Hans Aberg
> 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/Andromeda-Milky_Way_collision
Hans
jacob navia
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
Hans Aberg
> 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
Oh No
CLOTHESvax.de>
>In article <mt2.0-31162...@hercules.herts.ac.uk>, Hans Aberg
><haberg_...@math.su.se> 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)
Hans Aberg
>> 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
Nicolaas Vroom
news:645be291-d735-4aa7...@l13g2000yqb.googlegroups.com...
> 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
Phillip Helbig---undress to reply
<nicolaa...@pandora.be> writes:
> "dfarr --at-- comcast --dot-- net" <df...@comcast.net> schreef in bericht
> news:645be291-d735-4aa7...@l13g2000yqb.googlegroups.com...
> > 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/helbig/research/p/abstracts/angsiz.html
Nicolaas Vroom
schreef in bericht news:mt2.0-22470...@hydra.herts.ac.uk...
> In article <mt2.0-31925...@hydra.herts.ac.uk>, "Nicolaas Vroom"
> <nicolaa...@pandora.be> writes:
>
>> "dfarr --at-- comcast --dot-- net" <df...@comcast.net> schreef in bericht
>> news:645be291-d735-4aa7...@l13g2000yqb.googlegroups.com...
>> > 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/helbig/research/p/abstracts/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
Phillip Helbig---undress to reply
<nicolaa...@pandora.be> 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/helbig/research/p/abstracts/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.
Nicolaas Vroom
> In article <mt2.0-9608...@hydra.herts.ac.uk>, "Nicolaas Vroom"
> <nicolaa...@pandora.be> 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/
Phillip Helbig---undress to reply
<nicolaa...@pandora.be> writes:
> "Phillip Helbig---undress to reply" <hel...@astro.multiCLOTHESvax.de>
> schreef in bericht news:mt2.0-6207...@hydra.herts.ac.uk...
> > In article <mt2.0-9608...@hydra.herts.ac.uk>, "Nicolaas Vroom"
> > <nicolaa...@pandora.be> 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.
Nicolaas Vroom
> In article <mt2.0-31513...@hydra.herts.ac.uk>, "Nicolaas Vroom"
> <nicolaa...@pandora.be> writes:
>
>> "Phillip Helbig---undress to reply" <hel...@astro.multiCLOTHESvax.de>
>> schreef in bericht news:mt2.0-6207...@hydra.herts.ac.uk...
>> > In article <mt2.0-9608...@hydra.herts.ac.uk>, "Nicolaas Vroom"
>> > <nicolaa...@pandora.be> writes:
>> >
>> >> 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.
In fact the way I see it there are two proper distances in volved:
1. The proper distance in the past at the moment of emission.
2. The proper distance now. This is the distance we are looking for.
Suppose I call the proper distance: D, the parallax distance pd
and the luminisity distance: ld
The law above then becomes: D=v/H or v=H*D
The first low, how should it be defined ?
1) D = c/H*z or 2) pd= c/H*z or 3) pl = c/H*z ?
I expect either 2 or 3.
If I am correct then Hubble constant H describes the relation between
z and pd or pl.
The important question is: (assuming that the second law uses
the proper distance D) are the two Hubble constants H the same ?
( are both Hubble relations the same ?)
>> 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.
I expect you mean contamation caused by the expansion of space.
> 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.
That is the situation within the Milky Way or at maximum
between us and Andromeda Galaxy.
> 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.
Does that mean that the speed of 7772 km/sec is the present speed NOW ?
Nicolaas Vroom
Phillip Helbig---undress to reply
<nicolaa...@pandora.be> writes:
> In fact the way I see it there are two proper distances in volved:
Yes.
> 1. The proper distance in the past at the moment of emission.
> 2. The proper distance now. This is the distance we are looking for.
OK.
> Suppose I call the proper distance: D, the parallax distance pd
> and the luminisity distance: ld
> The law above then becomes: D=v/H or v=H*D
Right. If you think about it, this is trivial. There is no physics
involved. This law HAS TO hold as long as the universe expands
homogeneously and isotropically; any other velocity-distance law would
not be compatible with such an expansion.
> The first low, how should it be defined ?
> 1) D = c/H*z or 2) pd= c/H*z or 3) pl = c/H*z ?
If the redshift is low enough so that the distance is (nearly)
proportional to it, then the differences between the various definitions
of distance are small enough to be ignored (especially considering the
fact that the redshift has a non-cosmological component as well which at
low redshift might not be negligible. However, in general NONE of your
equations is correct.
Look at it this way. All your equations have a LINEAR relationship
between distance and redshift. However, in general distance is NOT
linear with redshift; it is a more complicated function of redshift.
This is true for all distances. However, at low redshifts, all the
distances are roughly equal, and all your equations are roughly right.
> I expect either 2 or 3.
> If I am correct then Hubble constant H describes the relation between
> z and pd or pl.
No; see above.
> The important question is: (assuming that the second law uses
> the proper distance D) are the two Hubble constants H the same ?
>
> ( are both Hubble relations the same ?)
There is but one Hubble constant. However, it might not be appropriate
to use it in all contexts.
> > 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.
>
> I expect you mean contamation caused by the expansion of space.
No; the cosmological redshift is caused by the expansion of space.
However, in addition, the galaxy can be moving through space, which also
produces a redshift (or blueshift).
> > 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.
> That is the situation within the Milky Way or at maximum
> between us and Andromeda Galaxy.
Quite the opposite. Within the Milky Way, there is no cosmological
redshift. The peculiar velocity of the Andromeda galaxy dwarfs its
cosmological redshift (it actually has a net blueshift).
> > Assuming we know the Hubble constant, and we know the distance, then we
> > get the velocity NOW.
> Does that mean that the speed of 7772 km/sec is the present speed NOW ?
Yes, if a) we are talking about the proper distance now and its
derivative with respect to cosmic time as measured now and b) if this
redshift is due only to the cosmological redshift.
Nicolaas Vroom
>> Suppose I call the proper distance: D, the parallax distance pd
>> and the luminisity distance: ld
>> The law above then becomes: D=v/H or v=H*D
>
> Right. If you think about it, this is trivial. There is no physics
> involved. This law HAS TO hold as long as the universe expands
> homogeneously and isotropically;
It is 100 % physics.
The question is: Is this law a correct description
of the physical reality ?
The physical reality being the state over there now.
Not the state over there in the past which we can observe.
>> The first low, how should it be defined ?
>> 1) D = c/H*z or 2) pd= c/H*z or 3) pl = c/H*z ?
>
> If the redshift is low enough so that the distance is (nearly)
> proportional to it, then the differences between the various definitions
> of distance are small enough to be ignored
The proper distance D versus the parallax distance (and ld) are fundamental
different. The first being defined as the distance using rigid rulers (ie
between
two present positions) and the second as the distance between the present
and the past.
> (especially considering the
> fact that the redshift has a non-cosmological component as well which at
> low redshift might not be negligible. However, in general NONE of your
> equations is correct.
This are not my equations.
See for example the book "Astronomy and Cosmology" by Fred Hoyle
page 617 which discusses the relation between redshift z and distance d
>> > 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.
>>
>> I expect you mean contamation caused by the expansion of space.
>
> No; the cosmological redshift is caused by the expansion of space.
> However, in addition, the galaxy can be moving through space, which also
> produces a redshift (or blueshift).
Okay.
The real issue is how typical is your example of 600 km/s.
If you go towards larger distances could this typical value not be much
larger
implying that contamination increases with distance ? (in time)
Secondly how do you measure this so called contamination ?
>> > Assuming we know the Hubble constant, and we know the distance, then
we
>> > get the velocity NOW.
>> Does that mean that the speed of 7772 km/sec is the present speed NOW ?
>
> Yes, if a) we are talking about the proper distance now and its
> derivative with respect to cosmic time as measured now and b) if this
> redshift is due only to the cosmological redshift.
And what is the verdict ?
Are both a and b correct ?
I have great problems with both, but ofcourse my opinion is
of no importance.
http://users.telenet.be/nicvroom/Hubble-Faq.htm#ol9
See comments near Document 9
Nicolaas Vroom
Phillip Helbig---undress to reply
<nicolaa...@pandora.be> writes:
> "Phillip Helbig---undress to reply" <hel...@astro.multiCLOTHESvax.de>
> schreef in bericht news:mt2.0-2685...@hydra.herts.ac.uk...
> > In article <mt2.0-21368...@hydra.herts.ac.uk>, "Nicolaas Vroom"
> > <nicolaa...@pandora.be> writes:
>
> >> Suppose I call the proper distance: D, the parallax distance pd
> >> and the luminisity distance: ld
> >> The law above then becomes: D=v/H or v=H*D
> >
> > Right. If you think about it, this is trivial. There is no physics
> > involved. This law HAS TO hold as long as the universe expands
> > homogeneously and isotropically;
>
> It is 100 % physics.
> The question is: Is this law a correct description
> of the physical reality ?
> The physical reality being the state over there now.
> Not the state over there in the past which we can observe.
We can only observe what is happening around us now. Everything else
might have ceased to exist. Actually, our brain only responds to
signals---they might be generated by something other than external
reality. Or we might be dreaming. However, if we talk about cosmology
the way we talk about day-to-day life, we have a model (an expanding
homogeneous and isotropic universe) and we can observe some things and
infer others.
> > (especially considering the
> > fact that the redshift has a non-cosmological component as well which at
> > low redshift might not be negligible. However, in general NONE of your
> > equations is correct.
> This are not my equations.
> See for example the book "Astronomy and Cosmology" by Fred Hoyle
> page 617 which discusses the relation between redshift z and distance d
Yes, but it is JUST AN APPROXIMATION FOR REDSHIFT. Even if it's Fred's
and not yours, it's still just an approximation.
> > No; the cosmological redshift is caused by the expansion of space.
> > However, in addition, the galaxy can be moving through space, which also
> > produces a redshift (or blueshift).
> Okay.
> The real issue is how typical is your example of 600 km/s.
> If you go towards larger distances could this typical value not be much
> larger
> implying that contamination increases with distance ? (in time)
It might have been larger in the past, but at large redshift the
RELATIVE contribution is much less. (If that weren't the case, then the
framework of a universe which is homogeneous and isotropic at large
scales wouldn't be valid.)
> Secondly how do you measure this so called contamination ?
All we measure is the redshift; we don't know, without further
assumptions, how much of it is cosmological and how much due to peculiar
motion.
> >> > Assuming we know the Hubble constant, and we know the distance, then
> we
> >> > get the velocity NOW.
> >> Does that mean that the speed of 7772 km/sec is the present speed NOW ?
> >
> > Yes, if a) we are talking about the proper distance now and its
> > derivative with respect to cosmic time as measured now and b) if this
> > redshift is due only to the cosmological redshift.
>
> And what is the verdict ?
> Are both a and b correct ?
A is something we can choose to talk about. B is an approximation which
is not very useful at low redshift.
Nicolaas Vroom
> In article <mt2.0-24861...@hydra.herts.ac.uk>, "Nicolaas Vroom"
> <nicolaa...@pandora.be> writes:
>
>> It is 100 % physics.
>> The question is: Is this law a correct description
>> of the physical reality ?
>> The physical reality being the state over there now.
>> Not the state over there in the past which we can observe.
>
> We can only observe what is happening around us now.
> the way we talk about day-to-day life, we have a model (an expanding
> homogeneous and isotropic universe) and we can observe some things and
> infer others.
Correct
The issue is between observe and infer.
IMO the law V = H * D is inferred assuming you mean proper speed
and proper distances. See below.
>> The real issue is how typical is your example of 600 km/s.
>> If you go towards larger distances could this typical value not be much
>> larger
>> implying that contamination increases with distance ? (in time)
>
> It might have been larger in the past,
I agree and most probably it is.
This is in line which the concept of the Big Bang which allows for much
higher speeds in the past compared to the present.
> but at large redshift the
> RELATIVE contribution is much less. (If that weren't the case, then the
> framework of a universe which is homogeneous and isotropic at large
> scales wouldn't be valid.)
>
>> Secondly how do you measure this so called contamination ?
>
> All we measure is the redshift; we don't know, without further
> assumptions, how much of it is cosmological and how much due to peculiar
> motion.
That is correct.
>> >> > Assuming we know the Hubble constant, and we know
>> >> > the distance, then we get the velocity NOW
>> >> Does that mean that the speed of 7772 km/sec
>> >> is the present speed NOW ?
>> > Yes, if a) we are talking about the proper distance now and its
>> > derivative with respect to cosmic time as measured now and
>> > b) if this redshift is due only to the cosmological redshift.
>>
>> And what is the verdict ?
>> Are both a and b correct ?
>
> A is something we can choose to talk about. B is an approximation which
> is not very useful at low redshift.
I want to talk about this.
As I already remarked there are two Hubble Laws.
The first Hubble Law establishes a relation between redshift z
and distance d with d the distance between the observer
and the Galaxy in the past.
This Law is expressed as z = (H/c) * d (1)
d can be measured as parallax distance or luminosity distance.
If I'am correct than we can measure d for the following galaxies:
M31, NGC 4258 (z=0.002), UGC 3789 (z=0.011)
and NGC 6323 (z =0.026)
Using that information we can find the relation H/c.
Using the equation v = z * c (2)
and by multiplying both sides of (1) with c we get
the second Hubble's law: v = H * d (3)
There is also a second version of this law: V = H * D (4)
In equation (3) v and d are the past speed and the past distance.
In equation( 4) V and D are the present speed and the proper distance
Equation (4) is the equation that is used to calculate the
"proper speed" of 7772 km/sec of NGC 6323
Equation (2) is standard used to calculate Galaxy rotation curves
by observing the red shift value z. For example of M31
It is important to note that in this case v represents the past
speed of a certain region of M31.
In equation (3) the v is also past speed. The question is what
does it physical represents ?
In equation (4) the speed and the distance represent the speed
and the distance of the Galaxy NOW..
But here we have a new problem:
Is the relation between in equation 3 and 4 the same ?
Assuming that the realation is linear, the problem is:
Is the Hubble constant H in both equations the same ?
I have great doubts.
To read more see:
http://users.telenet.be/nicvroom/Hubble-Faq-PH.htm
There are two problems:
1) first neither V nor D (present values) can be measured directly.
2) What is the physical meaning of z.
Let us go back to equation (1) what does the measured
value in z represent ?
Exactly as written above:
> All we measure is the redshift; we don't know, without further
> assumptions, how much of it is cosmological and how much due to peculiar
> motion.
That means z represents partly the peculiar velocity of the Galaxy
in the past and partly space expansion.
What the ratio is between those two numbers I do not know.
For M31 this can easily be 90 to 10
For NGC 6323 for example 30 to 70
The important question to answer is:
what is the evolution of the speed of a Galaxy after emission
of light that we can observe now ?
IMO assuming a big bang (which implies space
expansion) the speed became smaller in time
and the distance between the galaxies became larger.
However the frequency of the light changed and
became larger. This increase, observed as a redshift
is only a function of distance (travel time)
but does not reflect the actual speed of the Galaxy.
IMO there is not something like:
"action at a distance involved"
which allows me to calculate the present speeds
based on redshifts.
As such I disagree with the idea that 7772 km/sec
is the proper speed of NGC 6323.
This picture is in line with the idea that the Universe
is homogeneous.
Nicolaas Vroom
http://users.telenet.be/nicvroom/
Phillip Helbig---undress to reply
<nicolaa...@pandora.be> writes:
> > We can only observe what is happening around us now.
> > However, if we talk about cosmology
> > the way we talk about day-to-day life, we have a model (an expanding
> > homogeneous and isotropic universe) and we can observe some things and
> > infer others.
>
> Correct
> The issue is between observe and infer.
> IMO the law V = H * D is inferred assuming you mean proper speed
> and proper distances. See below.
Yes. However, it follows trivially from isotropic and homogeneous
expansion. If you don't grant that, then much of standard cosmological
theory isn't valid. (It's not a matter of belief; there is good
observational evidence for homogeneous and isotropic expansion.)
> >> >> > Assuming we know the Hubble constant, and we know
> >> >> > the distance, then we get the velocity NOW
> >> >> Does that mean that the speed of 7772 km/sec
> >> >> is the present speed NOW ?
> >> > Yes, if a) we are talking about the proper distance now and its
> >> > derivative with respect to cosmic time as measured now and
> >> > b) if this redshift is due only to the cosmological redshift.
> >>
> >> And what is the verdict ?
> >> Are both a and b correct ?
> >
> > A is something we can choose to talk about. B is an approximation which
> > is not very useful at low redshift.
>
> I want to talk about this.
>
> As I already remarked there are two Hubble Laws.
> The first Hubble Law establishes a relation between redshift z
> and distance d with d the distance between the observer
> and the Galaxy in the past.
> This Law is expressed as z = (H/c) * d (1)
> d can be measured as parallax distance or luminosity distance.
> If I'am correct than we can measure d for the following galaxies:
> M31, NGC 4258 (z=0.002), UGC 3789 (z=0.011)
> and NGC 6323 (z =0.026)
> Using that information we can find the relation H/c.
Yes, but there is scatter because in practice only luminosity distances
can be used at this distance, but the absolute luminosity is not
precisely known.
> Using the equation v = z * c (2)
> and by multiplying both sides of (1) with c we get
> the second Hubble's law: v = H * d (3)
Yes, valid in the limit of low redshifts.
> There is also a second version of this law: V = H * D (4)
> In equation (3) v and d are the past speed and the past distance.
NO. In (3) it is an approximation valid in the limit of low redshifts;
at such low redshifts, any difference between various distances, or
distance now and distance then, is lost in the uncertainties due to
other factors.
> In equation( 4) V and D are the present speed and the proper distance
> Equation (4) is the equation that is used to calculate the
> "proper speed" of 7772 km/sec of NGC 6323
Assuming that the redshift is purely cosmological.
> Equation (2) is standard used to calculate Galaxy rotation curves
> by observing the red shift value z. For example of M31
> It is important to note that in this case v represents the past
> speed of a certain region of M31.
This is not a cosmological redshift. Still, the equation is valid in
the limit. Again, in this case it doesn't make any practical difference
if you say it is the past speed or the present speed. Such distinctions
are important only at large cosmological redshift.
> In equation (3) the v is also past speed. The question is what
> does it physical represents ?
Velocity. What else?
> In equation (4) the speed and the distance represent the speed
> and the distance of the Galaxy NOW..
OK.
> But here we have a new problem:
> Is the relation between in equation 3 and 4 the same ?
> Assuming that the realation is linear, the problem is:
> Is the Hubble constant H in both equations the same ?
Yes, it is the same number. However, it doesn't have the same
"function" in that in one case it is an exact theoretical quantity and
in the other it is a constant of proportionality in an approximately
linear relation.
> I have great doubts.
> To read more see:
> http://users.telenet.be/nicvroom/Hubble-Faq-PH.htm
> There are two problems:
> 1) first neither V nor D (present values) can be measured directly.
> 2) What is the physical meaning of z.
I think you're making a mountain out of a molehill.
All you need to know is here:
@ARTICLE {EHarrison93a,
AUTHOR = "Edward R. Harrison",
TITLE = "The Redshift-Distance and Velocity-Distance
Laws",
JOURNAL = APJ,
YEAR = "1993",
VOLUME = "403",
NUMBER = "1",
PAGES = "28",
MONTH = jan
}
Please read it.