# Traveling in an Expanding Universe

1. Apr 16, 2010

### JWINC

For starters let me say that reading about and pondering cosmology is only a hobby, I have no formal education in this arena, although I am returning to school this spring to do just that. That being said, the following query may be foolish for some basic reasons I have missed, or not come upon yet, but I would be happy to know what they are.

For the sake of this question let us say that the Milky Way Galaxy is at the center of a sphere, the sphere being our expanding universe. As we draw a radial line from the center of the sphere (A) out to its face our line passes through 5 other galaxies (B,C,D,E,F). Each of these galaxies are separated by each other by a decent amount of space, say 10 billion light years, and measures a red shift to its nearest galactic neighbors sufficient to put their speed of separation at 1/4 the speed of light.

Galaxy A being the Milky Way, here are the 6 galaxies connected by a straight line each uniformly spaced.
A----B----C----D----E----F

My understanding is that since we on A measure a redshift of X to B and B measures a redshift of X to C we on A measure a redshift of 2x to C. Therefor we on A would measure a redshift of 5x to F, and since X=1/4 the speed of light galaxy F is "moving away" from A at a speed greater than the speed of light?

If that is the case then even though F is "moving away" from A at greater than the speed of light it is still possible to travel from A to F while moving at only slightly more than 1/4 the speed of light?

2. Apr 16, 2010

### bapowell

That's just about right. What you need here is Hubble's Law:

$$v=Hr$$

where v is the recession velocity of a distant object (one of your galaxies), H is Hubble's constant, and r is its distance. This famous relation indicates that recession velocities grow with distance (more space is expanding between distant objects than objects close together, or, as Gertrude Stein would say, "there's more there there.") You'll notice that there is a distance, r= c/H, at which distant objects begin to recede at light speed. This is perfectly fine and consistent with relativity. Each galaxy is locally at rest (not moving relative to the background spacetime -- this is best visualized by drawing a grid, placing galaxies at points on the grid, and then stretching the grid to simulate expansion). So, there will be no problem with you traveling to one of these far off galaxies. Eventually you will reach a distance from your starting point at which your destination galaxy is no longer receding at light speed.

3. Apr 16, 2010

### pixchips

Very interesting. This prompts the question: is H constant. When B moves with the Hubble flow to the position of C when we started, is it now moving with twice the velocity?

Related question: in special relativity, Einstein tossed out the notion of simultaneity. How does that work in GR? What does it even mean to say "the position of C when we started"?

Just trying to wrap my head around this.

4. Apr 17, 2010

### Chalnoth

The primary issue here is that the there is no strict way to determine the relative velocities of far-away objects. Yes, this is one way to talk about the velocity between, say, galaxy A and galaxy F. And by this definition, yes, most visible galaxies in our universe always are (and always have been) moving away at faster than the speed of light.

But I could merely change coordinates and end up with there being no relative velocity at all (e.g. if my coordinates move along with the expansion: galaxy F is always just as many grid points away from galaxy A as it always was).

In fact, relative velocities are only well-defined in General Relativity at a single point. This means that you can definitively say that galaxies A and F are not outrunning any light rays that pass by them. But you can't say they're not outrunning light rays that are far away.

5. Apr 17, 2010

Just a thought from another hobbyist: Is this really 'compatible'...??
To me it looks like JWINC is talking about the observable universe (46 bly), and bapowell is talking about the Hubble volume (13.8 bly)...?

Surely, there must be galaxies in the observable universe which we can never 'travel' to, or??

Last edited: Apr 17, 2010
6. Apr 17, 2010

### Chalnoth

Provided that there is actually a cosmological constant, yes, even light rays sent out from the Earth today can never reach many galaxies that we can see.

7. Apr 17, 2010

Okay, thanks Chalnoth. And I take it, since the http://en.wikipedia.org/wiki/Supernova_Cosmology_Project" [Broken] has shown that there is not only an expansion, but an accelerating expansion – the 'traveling' gets even tougher...

Last edited by a moderator: May 4, 2017
8. Apr 17, 2010

### Chalnoth

The accelerated expansion is actually necessary for there to be places in the observable universe that will forever be out of reach.

9. Apr 17, 2010

Independent of the speed of the traveler?

Edit: Stupid question, forget it. You are talking about c, right?

10. Apr 17, 2010

### Chalnoth

Yes :)

11. Apr 17, 2010

hehe...

12. Apr 17, 2010

### bapowell

No. It's proportional to the energy density of the universe, and hence is a function of time; however, it's effectively a constant: it's value today is going to be just about its value 100 years from now.

I don't think this adds any complication, as long as we establish a frame of reference. If you are an observer comoving with the expansion, and galaxy C is as well, then the distance between yourself and galaxy C is just the proper distance. No need to worry about issues of simultaneity.

13. Apr 22, 2010

### mehul ahir

can any partical in our universe travell faster than the speed of light ? sir i heared that some time it is found that some paticals are found which emits the rays & speed of rays is 4 times than the speed of light ? sir some time we say that no body can run faster than the light sir i am in totally confusion please email me my answer via email and solve my tension

14. Apr 22, 2010