neophyte question about hubble's law

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

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

In article , "Nicolaas Vroom"
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.

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

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

In article , "Nicolaas Vroom"
writes:

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

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

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/

In article , "Nicolaas Vroom"
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 he

@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.