neophyte question about hubble's law

In article , Thomas Smid
writes:

On 17 Sep, 02:32, dfarr --at-- comcast --dot-- 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.

Phillip Helbig---remove CLOTHES to reply wrote:
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

On 20 Oct, 12:53, Phillip Helbig---remove CLOTHES to reply
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

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.../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.

In article , Hans Aberg
writes:

Phillip Helbig---remove CLOTHES to reply wrote:
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?

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/he...fo/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.

In article , Thomas Smid
writes:

On 20 Oct, 12:53, Phillip Helbig---remove CLOTHES to reply
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.

In article , Stupendous_Man
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.../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.)

"Thomas Smid" schreef in bericht
...
On 20 Oct, 12:53, Phillip Helbig---remove CLOTHES to reply
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 wrote:
What formula is used to compute velocity from redshift?

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/he...fo/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.

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

In article , Hans Aberg
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.