Hubble's Law And A Question Of Time

[pjn2000]

One thing that really bothers me about Hubble's law is the question of time. Was this ever taken into account? When we observe large distances in space we are also looking way back in time. Sure Galaxies appear to be moving faster at a greater distance but how do we know how fast they are moving now when really we are just observing them further back in time the further away they are located?

If someone made a slow motion video of a bomb exploding and played it in reverse, sure the speed of particles moving away from the centre of the explosion would be faster the further back we played the video. How can we be certain that this is not what we are seeing when we observe distant Galxies and use these results to derive Hubble's law? It could be argued that a constant value for Hubble's constant is just another way of saying that matter under went constant deceleration after the Big Bang. If so it could easily predict the maximum size our Universe could achieve. How can we prove otherwise?

 

[marcus]

Hubble law does indeed take account of time. The version of time it is based on is sometimes called "universe time" or "Friedmann time". It is the time that you see in the Friedmann equation which is what most cosmologists use to model the cosmos.

Universe time is implicit in the law, which says
v(t) = H(t) d(t).

suppose that t = present moment. Then it says if d(t) is the present distance (if you could freeze expansion and measure it today) and H(t) is the present value of the Hubble ratio, then v(t) is the rate that distance is increasing at the present moment and v = Hd.

The law is explicitly based on that kind of "freeze-frame" distance, which we can only estimate and know approximately by a process of modeling and fitting data. The mathematical meaning of the law, if you look at it rigorously, has things in it which are not directly measureable---that's just how it is. For galaxies not too far away the approximation is so close you can just apply it naively.

As you go further out you realize that the REDSHIFT does not correspond in any simple way to either the speed which the object had when it emitted the light, or to the speed which we infer that it has today. The redshift that you measure corresponds to in a simple precise way (not to any speed but rather) to the ratio by which the universe's distances expanded during the period of time the light was traveling to us.

In discussing Hubble law I am always using the "freeze frame" idea of distance. What you would measure (by radar or yardsticks or string, but really by light travel time) if you could freeze the expansion process at a certain moment in time. It is often called the "proper" distance by astronomers. The speed we are talking about is the instantaneous rate of increase of distances defined that way.

You might enjoy playing around with some of the online calculators that model the universe.
One I like is morgan's "cosmos calculator". I have the link in my sig at the end of the post.
You can also just google "cosmos calculator" and get it. When you get there first type in .27 for matter density, and .73 for cosmological constant or dark energy density, and 71 for the presentday value of Hubble parameter. Put in redshift 1000 if you want, and try other redshifts. It will tell you speeds (distance increase rates) both back then and now. It will tell you past values of Hubble ratio. It will tell you freeze-frame distances both back when the light was emitted, and now on the day the light is received by us. The nice thing about morgan's online calculator is it doesn't have a lot of extra frills. Just focuses on a few things without distraction. If you want other ones ask.

 

[pjn2000]

Many thanks for this excellent response Marcus and for the fabulous detail.
I find this subject intriguing - I think there is a lot of scope here for enhancing understanding of how the universe came about and much to discover.

Best Wishes,

Patrick Naughton

Hubble law does indeed take account of time. The version of time it is based on is sometimes called "universe time" or "Friedmann time". It is the time that you see in the Friedmann equation which is what most cosmologists use to model the cosmos.

Universe time is implicit in the law, which says
v(t) = H(t) d(t).

suppose that t = present moment. Then it says if d(t) is the present distance (if you could freeze expansion and measure it today) and H(t) is the present value of the Hubble ratio, then v(t) is the rate that distance is increasing at the present moment and v = Hd.

The law is explicitly based on that kind of "freeze-frame" distance, which we can only estimate and know approximately by a process of modeling and fitting data. The mathematical meaning of the law, if you look at it rigorously, has things in it which are not directly measureable---that's just how it is. For galaxies not too far away the approximation is so close you can just apply it naively.

As you go further out you realize that the REDSHIFT does not correspond in any simple way to either the speed which the object had when it emitted the light, or to the speed which we infer that it has today. The redshift that you measure corresponds to in a simple precise way (not to any speed but rather) to the ratio by which the universe's distances expanded during the period of time the light was traveling to us.

In discussing Hubble law I am always using the "freeze frame" idea of distance. What you would measure (by radar or yardsticks or string, but really by light travel time) if you could freeze the expansion process at a certain moment in time. It is often called the "proper" distance by astronomers. The speed we are talking about is the instantaneous rate of increase of distances defined that way.

You might enjoy playing around with some of the online calculators that model the universe.
One I like is morgan's "cosmos calculator". I have the link in my sig at the end of the post.
You can also just google "cosmos calculator" and get it. When you get there first type in .27 for matter density, and .73 for cosmological constant or dark energy density, and 71 for the presentday value of Hubble parameter. Put in redshift 1000 if you want, and try other redshifts. It will tell you speeds (distance increase rates) both back then and now. It will tell you past values of Hubble ratio. It will tell you freeze-frame distances both back when the light was emitted, and now on the day the light is received by us. The nice thing about morgan's online calculator is it doesn't have a lot of extra frills. Just focuses on a few things without distraction. If you want other ones ask.