# If two galaxies can drift apart in twice the speed of light, how can a third do it?

1. Dec 22, 2012

### cdux

If Galaxy A drifts apart from Galaxy B with twice the speed of light then how could a Galaxy C next to Galaxy A drift apart from Galaxy A at a similar speed?

edit: PS. Wouldn't that need some kind of "universal central observer" to limit Galaxy A from Galaxy C to not drift apart by more than 2*c?

2. Dec 22, 2012

### Staff: Mentor

Re: If two galaxies can drift apart in twice the speed of light, how can a third do i

Head over to the Cosmology subforum and read some of the FAQ's there. I believe one of them should answer your question. If not, look up the Balloon Analogy.

3. Dec 22, 2012

### cdux

Re: If two galaxies can drift apart in twice the speed of light, how can a third do i

It's the same question for points on the balloon.

4. Dec 22, 2012

### Naty1

Re: If two galaxies can drift apart in twice the speed of light, how can a third do i

Not as we currently calculate standard cosmological 'observations'. The 'drift' of two galaxies has nothing to do with the drift of either relative to another galaxy.

Can objects move away from us faster than the speed of light?

Again, this is a question that depends on which of the many distance definitions one uses. However, if we assume that the distance of an object at time t is the distance from our position at time t to the object's position at time t measured by a set of observers moving with the expansion of the Universe, and all making their observations when they see the Universe as having age t, then the velocity (change in D per change in t) can definitely be larger than the speed of light. This is not a contradiction of special relativity because this distance is not the same as the spatial distance used in SR, and the age of the Universe is not the same as the time used in SR. In the special case of the empty Universe, where one can show the model in both special relativistic and cosmological coordinates, the velocity defined by change in cosmological distance per unit cosmic time is given by v = c ln(1+z), where z is the redshift, which clearly goes to infinity as the redshift goes to infinity, and is larger than c for z > 1.718. For the critical density Universe, this velocity is given by v = 2c[1-(1+z)-0.5] which is larger than c for z > 3 .

For the concordance model based on CMB data and the acceleration of the expansion measured using supernovae, a flat Universe with OmegaM = 0.27, the velocity is greater than c for z > 1.407.

http://www.astro.ucla.edu/~wright/cosmolog.htm

5. Dec 23, 2012

### Trenton

Re: If two galaxies can drift apart in twice the speed of light, how can a third do i

One of the common omissions when people are learning about GR is the notion that space itself moves - and that the velocity of space is not limited to c. That limit only applies to entities travelling through space. The space around a dense object is falling into the object at the newtonian escape velocity. This infall is due to the contraction of space due to the presense of the mass. As the space near the mass contracts more space comes in to take it's place. Without this process, a black hole would never become 'black'.

The big bang is the inverse of this process and the space is expanding and this expansion is also not limited to c. It is quite possible for a line of objects all to be moving away from thier adjacent objects faster than than c even if that means they can't observe them.

6. Dec 23, 2012

### Staff: Mentor

Re: If two galaxies can drift apart in twice the speed of light, how can a third do i

Does GR even describe space as "moving"?

7. Dec 23, 2012

### Trenton

Re: If two galaxies can drift apart in twice the speed of light, how can a third do i

As I understand it yes. It is counter-intuative in the extreme but space and time are said to fall into a black hole. Likewise a spinning black hole drags time and space around with it. All of this would be nonsense unless space itself could move. Indeed if this were not part of GR then a black hole could never be black or indeed have an event horizon. A photon originating inside the EH would, if travelling away from the singularity, escape albeit with massive redshift - because light cannot be slowed and the EH is at a finite distance.

But the photon cannot escape because although it is moving outward at c, that is only relative to space. At the EH space is moving inwards at c and so the photon stays at the EH. Further in space is moving inwards at greater than c and this drags the photon back to the singularity.

8. Dec 23, 2012

### Staff: Mentor

Re: If two galaxies can drift apart in twice the speed of light, how can a third do i

I don't think that's how GR labels it. I don't have much experience with GR, but I believe the metric is just describing how space is curved, not that it moves at all. You can't have a frame relative to space, only relative to another object.

9. Dec 23, 2012

### arindamsinha

Re: If two galaxies can drift apart in twice the speed of light, how can a third do i

As far as faraway galaxies receding from us at c in all directions, I understand there is no "movement" of space, but "expansion" of space. It is the velocity of expansion of space that is not limited to c by GR. So perhaps this is a terminology issue.

10. Dec 23, 2012

### Staff: Mentor

Re: If two galaxies can drift apart in twice the speed of light, how can a third do i

Yes, the popular explanation is that the galaxies are being dragged along with space. However I don't know how accurate that terminology is.

11. Dec 24, 2012

### Naty1

Re: If two galaxies can drift apart in twice the speed of light, how can a third do i

Another explanation from a standard reference for these forums:

http://www.astro.ucla.edu/~wright/cosmology_faq.html#MX

12. Dec 24, 2012

### Naty1

Re: If two galaxies can drift apart in twice the speed of light, how can a third do i

Here is an explanation of distance changes from phinds....this BALLOON ANALOGY
was developed among a dozen or so members of these forums in looooong thread.

www.phinds.com/balloonanalogy

http://en.wikipedia.org/wiki/Expansion_of_space

intro paragraph:

13. Dec 24, 2012

### Naty1

Re: If two galaxies can drift apart in twice the speed of light, how can a third do i

Further in the metric expansion discussion in Wikipedia is this:

So a MAJOR concept in cosmology, based on the fact that distance/time, even energy, in GR have no global meaning, is that coordinates determine the result of your measure. The reason 'space expands' has become so popular is that HUBBLE utilized 'proper distance' in his v = HD relationship....This is the one where at the Hubble radius, we see distant objects receding at velocity c.

Here is a more precise explanation from someone in another discussion:

This reference is to curved spacetime in cosmology versus line element distance in flat space. distances in GR are different than in SR. In GR the distance you measure depends on the curve you choose....
edit: Different observes utilize different curves and get different measures.

Last edited: Dec 24, 2012
14. Dec 24, 2012

### Naty1

Re: If two galaxies can drift apart in twice the speed of light, how can a third do i

found it:
the ultimate discussion of expanding space in these forums:

It's long and confusing at times, but worth your time. Wallace who posts there
is a practicing cosmologist....

a few insights:

I did not begin to understand such measurements until I studied these diagrams:
http://en.wikipedia.org/wiki/Metric..._two_points_measured_if_space_is_expanding.3F

Be sure to click on the illustrations to enlarge them.....

15. Dec 24, 2012

### Naty1

Re: If two galaxies can drift apart in twice the speed of light, how can a third do i

Most of that reply is not correct.

While in a novice sense, some consider space itself as 'expanding' I don't think any scientist nor anyone in these forums would agree it 'moves'. That a spinning black hole' drags space and time' is a reference to frame dragging, not any motion. It's an effect our our artifical [theoretical] overlay frame. Read about it in Wikipedia and note the reference to linear frame dragging: do you also think a moving particle 'drags space and time with it?'....or is it curvature that changes??
http://en.wikipedia.org/wiki/Frame_dragging

Black hole characteristics do NOT involve 'space moving'. That is not part of SR, GR nor cosmological understanding. Any observed photon motion is relative to the observer!! Space is NOT moving inwards at C at the event horizon. The only thing that moves at c at the horizon are PHOTONS. Inside the horizon, space is NOT moving towards the singularity at c!! What prevents a photon from escaping is gravitational spacetime curvature.

Check this:

In Fabric of the Cosmos, Brian Greene says in a footnote (Chapter 12, #7,Page 527)

"...It's somewhat of misnomer to speak of the "center" of a black hole as if it were a place in space....Just as you can't resist going from one second to the next in time, you can't resist being pulled to the black holes "center" once you've crossed the event horizon...Thus rather than thinking of the black holes center as a location in space it is better to think of it as a location in time...it may be true that its ...where spacetime comes to an end....if we had equations that don't break down deep inside a black hole we might gain important insights into the nature of time..."

An observer freely falling from a distance outside a black hole [or a particle], never exceeds c and is in fact unaware when she passes the event horizon: nothing happens there except that in passing, the observer loses causal connection with the outside universe. And from a distant observer's perspective, 'time stops' at the horizon so the infalling local observer APPEARS to hang there forever...to future infinity. But that, too, is a coordinate effect, NOT a physical one.

JesseM explained elsewhere:

Once again, different COORDINATES change everything!!!!

So the basic rule to remember is that in GR, curved spacetime, distance, velocity,acceleration and even energy are ill defined. Different [coordinate] observers 'see' [predict] different things...even at different times [non simultaneity] and these effects are magnified in cosmology because of the vast expanses we try to describe.

Hope all this helps.....it sure took me several years to digest what little I know.

Last edited: Dec 24, 2012
16. Dec 24, 2012

### Naty1

Re: If two galaxies can drift apart in twice the speed of light, how can a third do i

This is basically correct. The metric provides one aspect of curvature...and is a distance measure, the metric is a distance measure in curved spacetime. Here are some conventions associated with it which I posted in another discussion trying to develop a summary explanation of why its not like a simple ruler:

Last edited: Dec 24, 2012
17. Dec 24, 2012

### Staff: Mentor

Re: If two galaxies can drift apart in twice the speed of light, how can a third do i

Thanks Naty!

18. Dec 24, 2012

### Trenton

Re: If two galaxies can drift apart in twice the speed of light, how can a third do i

Whoever mention terminology has the key point. Katy1 states that I am incorrect and that space does not move. Curvature of space is the explanation. I have never been truly happy with either concept but for me space moving is the lesser of two evils. The presence of a mass does cause space around the mass to contract so that a given coordinate would move toward the mass would it not? And how can frame dragging occur without space moving? If sapce is not falling into a black hole can someone give a good description of what curved space might mean in geometric terms to put me out of my misery!

I am intruiged that the singularity is located in time rather than position and that the laws of physics break down. The equations break down because a term is missing. Singularity is a math term and a true physical singularity with one or more meaningful values being infinite cannot exist. There are quantum mechanical limits that we have yet to understand and only when we do can we complete the equations!

As for the 'singularity' (for want of a better term) not being at the center, why not? It is accepted that once a body (neutron star) has a radius equal to the EH it must collapse - no matter how much pressure nutonium could withstand. The reason why is that for the star not to collase matter must remain at the EH and this (with the space infalling at the escape velocity which is c) would require the matter to be travelling through space at c. But whatever causes the collapse, collapse of a spherical object means the matter all moves inward. And unless someone cares to redefine geometry all matter moving inwards means everything is going to end up in the center!

19. Dec 25, 2012

### Naty1

Re: If two galaxies can drift apart in twice the speed of light, how can a third do i

Hi Trenton: I provided a number of reputable sources to help you better communicate in these forums. You ARE free to maintain 'space moves' but I'll not be responding again as you repeat this. And it will hamper your communication and further understanding.

I explained 'frame dragging' is NOT dependent on 'space moving' any more than is linear frame dragging. I hope you read the sources so you at least understand mainstream insights from people with a lot more experience and understanding than I.

We all have some misery! Curved space and TIME is not something we can visualize.

Curved spacetime IS the geometric explanation of gravity. For a large black hole, most of the curvature, that is the distortion of spacetime, is time not space. The tidal gravity outside such a large black hole horizon is small while the time dilation is unbounded as seen from afar..time APPEARS to diverge but does not locally.

Perhaps you could consider time versus space. Perhaps thinking about special relativity might help? Consider time dilation and length contraction, distortions of time and space in flat spacetime.....no tidal gravity. Does space have to move there for you too?? I am not looking for you to defend, just asking you THINK about it. If no movement is necessary in SR, why in GR??

And except for a negative sign in relativity, space and time are treated alike. Why do you like space moving but not time? Shouldn't you treat them on an equal footing. Time curves too! good luck.

20. Dec 25, 2012

### Trenton

Re: If two galaxies can drift apart in twice the speed of light, how can a third do i

I shall certainly read further material as I am keen to get to the bottom of these terms. I am not encouraged by your statement that curved space and time is not something we can visualize. The whole ojective for me is to envisage what happens to space and time in the vacinity of mass - which I continue to believe is possible. After all Einstien came up with a set of equations to describe these things and I don't see how he could have done this without a very clear idea of what he though was going on.

I am very happy with the SR concepts of the lorentz contraction applied both to time and to space. And I am very happy with the GR concept that gravity is the result of mass 'curving' spacetime for want of a better word. It is for me, a far more intuative explanation of gravity than gravitons.

And I do not like the idea of space moving either although I should have made clear that it is both space and time (Minkowsky spacetime) that was moving! It is a slick way of arriving at results and certainly, the time dilation at a stationary point in a gravitational well (eg a man stading on the Earth's surface) is the same value as for an object moving through space at the escape velocity at the staionary point - but this is all it is, a slick trick (unless space does move). I also take your point that since movement of space is nessesary in SR it should not be nessesary in GR. The trouble is I have never come across a decent explanation of the term curvature.

21. Dec 25, 2012

### cdux

Re: If two galaxies can drift apart in twice the speed of light, how can a third do i

If I'm not mistaken even your favorite GR visualization of spacetime curvature is an approximation that does not fully describe the mathematics, and it reminds me of physicists admitting they don't understand quantum mechanics beyond their understanding of the math. My basic understanding of the concept of visualization in sciences in general is that if something goes beyond the 4 dimensions in the "middle-cosm" has to be understood via math or via crude approximations on those 4 (uncurved) dimensions. I've been hearing of visualizations of the type of multidimentional manifolds and the more I think of it the more it seems unfathmable and the more I suspect it's wishful thinking for full 4 dimensional understanding. In fact, some popular notions sound almost embarrassing, such as the popularized notion that extra dimensions in string theory are "small dimensions like looking at an ant on a flag pole but then zooming in on it". What does that even mean? If my vision is good I may not have to zoom in to notice the extra dimensions. Notions such as that look at the end of the day non-sensical or at best crude approximations.

Last edited: Dec 25, 2012