## Comments about Hubble's law - part II

### Introduction

In usenet newsgroup sci.asctro.research there is a discussion with the title:neophyte question about hubble's law. We are lucky that people share their time with us to explain the current understanding of Hubble's Law. In this document I express my own opinion.
Hubble's Law describes a (linear) relation between the distance (d) of a galaxy and the (radial) speed (v) of the galaxy, expressed as: v = H * d , with H being the Hubble Constant
In this document this is called: the second Hubble's Law

The question of course is what means v, H and d
In message 36 is explained that d is the proper distance. For more Detail see: neophyte question about hubble's law #36. In that document the proper distance is defined as: the distance you could measure instantaneously with a rigid ruler. That means that the proper distance between the Earth and the Sun is: the distance between present positions of the Earth and present position of the Sun. This is not the distance between the present position of The Earth and the observed position of the Sun. That is a distance in the past. For Example: if we look at the Earth we See the Sun 8,3 minutes in the past. The Andromeda Galaxy we see at a position 2.5 Million Years in the past.
The consequence of this if you want to know the present or proper distance based on observations you have to take relative speed between the Earth and Andromeda into account.

In message 42 is explained that if d is the proper distance and red shift z is only due to cosmological redshift then v is the speed now (the present speed). For more detail see: neophyte question about hubble's law #42

What in theory is meant, that if redshift z is only due to the expansion of space than you can use the equation v = c * z in order to calculate the present velocity. In the Case of NGC 6323 with a redshift z of 0.026 when you multiply this with 300000 km/sec you get a speed of 7772 km/sec which is the present speed of NGC 6323.

I have great problems with this interpretation.

### The law v = c * z

The classical interpretation of this law is that there exists a linear relation between the speed of the light source and the measured redshift. There is nothing wrong with this assuming that distance between source and observer has completely no influence on the measured redshift. In fact this method is used to measure the galaxy rotation curves. One half of such a curve shows a red shift which means that the stars rotate away from the observer and the other half show a blue shift which means that the stars rotate towards the observer.

A different interpretation is that the redshift is solely from cosmological origin and from expansion of space.
The following sketch shows this:

```  <----z---->
1         2                             .G
t5| 1        2                          .---->v5
|   1       2                       .
t4|     1      2                    .--->v4
|       1     2                 .
t3|         1    2              .-->v3
|           1   2           .
t2|             1  2        .->v2
|               1 2     .
t1|                 12  .> v1
0-------------------G---------
distance        d1

Figure 1
```
Figure 1 shows:
• A galaxy G at t1, a distance d1 away from the Observer moving away from the origin. The distance d1 is the parallax distance or luminosity distance in case they can be measured.
• The same galaxy G at present position t5, but now at a different distance d5 and with a different speed v5.
• The path of the Galaxy between t1 and t5. This is the dotted line.
• Light emitted from the star at t1.
In fact the sketch shows two light paths (frequencies) identified as 1,and 2 assuming that the star emits only one frequency (Is a "laser")
1. Light (line 1) emitted at t1 from a certain frequency f1. Light has a speed c and moves in a straight line towards the Observer and reaches the Observer at t5.
2. Light (line 2) emitted at t1 but with a variable frequency from f1 to f2. Line 2 shows a frequency shift caused by the expansion of space between t1 and t5.
• The sketch shows that there exist a linear relation between z and v, with z being the difference between line 1 and line 2.
• The sketch shows that there exist a linear relation between proper distance d and v, with distance being the difference between line 1 and the dotted line (between the path of the light ray and the path of the Galaxy).
What the sketch shows is that the Hubble constant is a constant in time. The question is, is this accordingly to the physical reality i.e. observations.

The following sketch shows a different reality:

 ``` <----z----> 1 2 .G t5| 1 2 .---->v5 | 1 2 . t4| 1 2 .--->v4 | 1 2 . t3| 1 2 .-->v3 | 1 2 . t2| 1 2 .->v2 | 1 2 . t1| 12 .> v1 0-------------------G--------- distance d1 Figure 2 ```
The only difference between Figure 1 and 2 is that the proper distance shows acceleration. This is caused by the increasing value of v.
Suppose at t1 the proper distance between G and Observer is d1 and the speed of G is v1. At t5 we have d5 and v5.
For H1 at t1 we get v1/d1 and for H5 at t5 we get v5/d5. With v5 being 5 times as large then v1 and d5 more than 5 times as large this means that H5 is smaller than H1 or that the Hubble constant was larger in the past.

The question again is: is this accordingly to observations.

• One problem is you can not measure the speed v directly.
• A second even larger problem, what this sketch suggests, is that presently at this very moment, the furthest galaxies have the largest expansion speeds. This does not match the concept that presently the Universe is homogeneous.

### The First Hubble's law: z = (H/C) * d

The first Hubble's Law establishes a relation between z and distance d.
In fact you can consider two versions of this law:
• The first version in which the distance d is a distance in the past. This distance can be measured by trigonometric means i.e. as parallax, or as a luminosity distance. Both distances if they represent the same instant of the observer should be identical (within an error range)
• The second version in which the distance d represent the past. This is the proper distance. This distance can only be calculated if the parallax distance can be established over a period of time, which allows you to calculate the speed of the object involved. In reality this can only be done for stars in the Milky way and Cepheid variables in certain Galaxies. This does not mean that you know the speed of the Galaxies as a whole.
If you study both figure 1 and 2 than you can see that the H constant or better the Hubble relation in both versions is completely different.
• In the first version, with d a distance in the past, the Hubble relation is linear and H is a constant. The same in both figure 1 and 2.
• In the second version, with d a proper distance, the Hubble relation is linear in figure 1 and non linear in figure 2. In figure 1 the Hubble Constant is smaller than in the first version (because the present distances are larger). In figure 2 the Hubble relation it not linear.
Specific what figure 2 shows is assuming there exists a linear relation between z and the parallax distance that that is no guarantee that there also exists a linear relation between z and the proper distance.

The following sketch also shows a different reality:

 ``` <---z---> 1 2 .G t5| 1 2 .>v5 | 1 2 . t4| 1 2 .->v4 | 1 2 . t3| 1 2 .-->v3 | 1 2 . t2| 1 2 .--->v2 | 1 2 . t1| 1 2.----> v1 0-------------------G--------- distance d1 Figure 3 ```
The above sketch is based on the following principles:
• That the galaxies, which are the furthest and which we presently can see, have the highest expansion speed.
• That z increases. This increase in z is caused by the expansion of space.
• That z currently increases less than in the past. This decrease is caused by an diminishing space expansion.
• That the current value of z does not reflect the present speed of the Galaxy.
• That the relation between z and past distance in general is non linear. Locally the relation between z and past distance is linear.
• The present state of the universe is homogeneous, in the sense that the universe is everywhere the same now and all the Galaxies have the roughly the same speed (close to zero).
Figure 3 is in line with the following article in Nature:
Cosmology: Dark is the new black by Richard Massey, which starts with: Since the Big Bang, the Universe's initial expansion has been gradually slowed down etc.

Figure 3 is in line that with the concept that in the past the universe also was homogeneous. This does not exclude change. Starting from the moment of the Big Bang the whole Universe is changing all the time. One aspect of this is, called: galaxy evolution. We can observe this change because what we see from the past (high values of z) is different than what we see from the present (low values of z). For an article which describes this concept See: The Build-Up of the Hubble Sequence in the COSMOS Field

### Space Expansion

The whole idea behind the Big Bang is that the most distant galaxies have the largest red shift or z values. Those red shift values can be larger than 1 indicating speeds larger than c. The question is: do those large values of z really mean high speeds or could there be an other explanation.
IMO there is. At the moment of emission the Galaxy already has (relative to the observer) a speed consisting of two components: space expansion and peculiar motion. The peculiar motion of a galaxy is the. speed component relative to the average speed of Galaxies in its immediate neighbourhood.
From that moment light travels in a straight line towards the Observer and is stretched, resulting in an increase in its z value. This increase has no influence on the actual speed of the source. In actual fact the speed of the Galaxy can even decrease.
This opinion is also expressed in Comments about Hubble's Law part I and in figure 3 above.

### Conclusion

In both figure 1 and 2 the speed relative to the Observer is not taken into account. IMO it should.
In both figure 1 and 2 the speed of the Galaxy is increasing continuous. IMO there is no evidence for this. In fact the speed can also be decreasing.
IMO the best solution to explain high z values is figure 3. This solution is simple. No extreme high speeds and no "difficult" mathematics are involved. Figure 3 predicts that the presently assumed high speed young objects at z = 5 could be much older.

### Feedback

None

Created: 20 December 2009
Modified: 20 Februari 2016 Back to my home page Index