Hubble flow interpretation

[Jacques]

Hubble flow tells us the more distant a galaxy the faster it goes away or an other way to tell is the expansion is a function of distance.

It is based on observation of the redshift and on the distance mesurement of galaxy.

I thaught about it an other way:

The more you go in the past, the faster the galaxy goes a way or the expansion is an inverse function of time.

How can we decide which interpretation is the good one ?

[Spyman]

Image of Expansion over Time -> http://www.space.com/php/multimedia/imagedisplay/img_display.php?pic=070501_matter_universe_02.jpg∩=Measurements+of+the+recessional+velocity%2C+distance+and+age+of+stellar+explosions+called+supernovae+provided+the+first+direct+evidence+that+the+rate+at+which+the+universe+is+expanding+is+increasing.+Credit%3A+NASA

[Martin]

Hubble flow tells us the more distant a galaxy the faster it goes away or an other way to tell is the expansion is a function of distance.

 

that is right. the mathematical form of the Hubble law does not involve redshift, and it does not involve recession speed or distance as they were in the past.

 

the mathematical form of the law only involves quantities at the present instant in time. it says

 

v = H D

 

where v is the recession speed, H is the present value of the Hubble parameter (which has changed by several orders of magnitude over the course of time, it is not a constant)

and D is the distance at the present instant (as a chain of observers might measure it, had they organized and planned to do it in advance.)

 

 

the formal definition of the Hubble parameter is H(t) = a'(t)/a(t)

where a(t) is the scale parameter in the FRW metric (roughly speaking the average distance between galaxies usually normalized so a(present) = 1)

and a'(t) is the time derivative.

 

 

It is based on observation of the redshift and on the distance mesurement of galaxy.

 

that is right, but you cannot naively equate redshift with recession speed at the present moment.

that only works to a good degree of approximation when things are comparatively nearby, the redshift is small, and the light travel time is brief.

the expansion history of the universe (as in Spyman's diagram) has to be RECONSTRUCTED from the data. One has to figure out what a(t) and a'(t) must have been in the past, and therefore what H(t) must have been in the past, in order to produce the redshift/distance data that we see.

 

I thaught about it an other way:

The more you go in the past, the faster the galaxy goes a way or the expansion is an inverse function of time.

How can we decide which interpretation is the good one ?

 

that wouldn't work out very well. you wouldn't get a simple proportionality.

again you could look at the diagram Spyman linked.

what do you mean by "the expansion" is an inverse function of time?

 

do you mean the recession speed of a galaxy at the moment it emitted the light which we are now receiving? and is this supposed to be inversely PROPORTIONAL to some time? and what time do you mean? the age of the universe? or the travel time the light has taken to get here?

 

none of these things are proportional or inversely proportional to each other so it wouldnt make a very good law IMO

 

if you want to see how these quantities change, the simplest way is to find Morgan's COSMOS CALCULATOR and plug in various values of the redshift z.

then it will tell you what the recession speed was at the time the thing emitted the light, and it will tell you the light travel time, and so on.

 

Just google "cosmos calculator". I did that and got:

http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html

 

Morgan makes you put in 0.27 for Omega and 0.73 for Lambda, if you want conventional cosmology. those are the standard numbers for the matter density and the cosmological constant.

Once you do that you can put in various redshift numbers and it will tell the light travel time and the recession speed. It is a good thing to get familiar with.

[Jacques]

OK I will try to explain my question a little bit more.

You observe the redshift of a galaxy and you can calculate that it was recessing at v. In the same galaxy you observe a cepheid and mesure the distance to be d. You do a bunch of galaxies and you build a curve of v over d , and you can deduce that v increse when d increase.

But you can express d in term of time, if d is 1 billion light years we see the galaxy 1 billion year in the pass or you can tell time= -1 billions years.

The closer you get to the present time the lower the recessing speed.

Do you follow me ?

If you take now to 0 time and the pass negative and future positive, it mean that now the recession is stopped.

Is it a valid way to interpret the data?

[Martin]

OK I will try to explain my question a little bit more.

You observe the redshift of a galaxy and you can calculate that it was recessing at v.

 

but how? the cosmological redshift is not a doppler shift and it is not related in any simple way to the recession speed at the time the light was emitted.

 

what formula can you use?

 

you should google *cosmos calculator* and experiment with some redshifts and see what recession speeds they correspond to. I guarantee you will be amazed.

 

In the same galaxy you observe a cepheid and mesure the distance to be d. You do a bunch of galaxies and you build a curve of v over d , and you can deduce that v increse when d increase.

But you can express d in term of time, if d is 1 billion light years we see the galaxy 1 billion year in the pass or you can tell time= -1 billions years.

The closer you get to the present time the lower the recessing speed.

Do you follow me ?

If you take now to 0 time and the pass negative and future positive, it mean that now the recession is stopped.

Is it a valid way to interpret the data?

 

in the Hubble law v = H d

the distance d does NOT correspond to the light travel time!

they can differ by a factor of two or three even.

you are talking as if you could say that if the light travel time is 1 billion years that the distance d which works in the Hubble law should be 1 billion light years. That is totally off.

 

Again you should really experiment either with Ned Wright's calculator (google ned wright) or with Morgan's (google cosmos calculator)

 

The reason that these people who teach Cosmology at universities have these simple redshift calcualators on line for their students is because the quantities are NOT related the way one might naively suppose if you have tried to learn from popularizations.

 

Perhaps you could re-read my post and try one of the online redshift calculators, then get back to me.

 

thanks

[Spyman]

if d is 1 billion light years we see the galaxy 1 billion year in the pass or you can tell time= -1 billions years.

Don't worry Jacques, it's a common mistake, fueled by the definition of the distance "lightyear" and the vast popular science articles written by journalists who doesn't seem to understand the difference.

 

A lightyear is the distance light can reach in a year if the spacemetric is rigid.

 

But according to General Relativity spacetime is dynamic, it can expand or contract.

 

When space is expanding the distance is increasing over time while light is making the journey to us. So you end up with three different values, distance between the objects when the light was emitted, distance between the objects when light is received and the distance light has traversed, (which is flighttime).