Universe Expansion & The Speed of Light

[jskirvin]

How is it possible for the rate of universe expansion to surpass the speed of light? (According to the Big Bang theory, and according to the model of an accelerating universe, hasn't/won't the universe surpass the speed of light?)

 

[marcus]

How is it possible for the rate of universe expansion to surpass the speed of light? (According to the Big Bang theory, and according to the model of an accelerating universe, hasn't/won't the universe surpass the speed of light?)

Hi jskirvin,
in a curved 4D geometry there is some freedom in how spatial (3D) distance is defined and astro/cosmo people have some different ways of defining and gauging it.

When people talk about expansion of spatial distances there are usually some unstated assumptions, so it is good to get acquainted with some background. Then some of the puzzlement seems to go away.

What is meant by expansion is basically a PERCENTAGE increase in largescale distances between things that are not are not hooked together by gravity----not distances in our solar system or in our galaxy or local group of galaxies (which are bound in a small cluster) but really large scale.

the current rate distances are increasing is 1/140 of a percent per million years.

So you can see if you take a large enough distance it is going to be increasing at a rate > c.

You can work it out. Any distance bigger than 14 billion lightyears is going to increase by a over a million lightyears (1/140 of a percent) in a million years, so that is by over one lightyear per year. Greater than c. But only really big distances do that. For smaller ones, a mere 1/140 percent per million years is a barely noticeable rate of increase.

It's not a violation of special relativity because that is about points within the same local flat frame of reference. In a large curved geometry you can't assume that it's covered by a single flat frame.

Hopefully other people will jump in with their own best intuitive suggestions for understanding. No galaxy, in its own local reference frame, is ever going faster than light . No galaxy actually ever passes a photon. In fact in their own local neighborhood the galaxies we have measured are only going a few hundred km/s. Not even close to the speed of light!

 

[marcus]

jskirvin,
you might want to get into it more technically. This is just in case you or anybody else wants. In talking about expansion stuff you usually have the Hubble law
v = Hd
in the back of your mind, or anyway it will likely come up in the discussion.
In that law, the distance "d" is a type of distances the pros call "proper"
and the rate "v" is the rate that proper distance is increasing.

The intuitive idea of proper distance (the kind that goes with the Hubble law) is that it is the freeze-frame distance. It is what you would measure if you could freeze the expansion of the universe at a certain moment---and then use any old conventional means like a chain of radar measurements or a huge long tapemeasure. It is the conventional idea of distance but with the universe frozen in a certain instant.

Measuring by light travel time is different because the universe expands while the light is traveling---the measurment is spread out over an interval of time.

Then (digging down into unspoken assumptions) there is the question of how you define "now" or any given moment, when you are going to freeze expansion at that moment in order to measure.

For practical purposes that goes back to the most ancient light---by now extended out to microwave (millimeter) wavelengths and called the cosmic microwave background (CMB).

Astronomers have the idea of the CMB rest frame---you are at rest relative to the ancient light if you don't see a doppler hotspot ahead of you. Then the whole microwave sky looks approximately the same temperature. It's a useful idea and they use it a lot.

You can imagine the present moment as populated by a whole bunch of observers scattered all over the universe, all at rest relative CMB, and all measuring the same CMB sky temperature---all agreeing about the age of the universe. They all say expansion is 13.7 billion years old. Observing the CMB is one of the main ways we determine the age of the universe---in other words it is how we "tell time".

And all those guys would agree. (I am not worrying about small differences in gravitation potential, this is broad brush.) So that is the present moment. The distances between those stationary observers are increasing, of course. But then we imagine freezing. And measuring by any conventional means, like radar or yardsticks. That then defines the proper distance at that moment. Then we unfreeze and let expansion proceed.

It is a bit elaborate, but in an expanding universe what else can you do?

 

[jskirvin]

Thank you for your response! However, I fear I may have asked a question with answers too big for my britches. I will follow up soon, once I have a chance to really delve into your response.

 

[Chalnoth]

Thank you for your response! However, I fear I may have asked a question with answers too big for my britches. I will follow up soon, once I have a chance to really delve into your response.

Maybe I can try a (somewhat) shorter response.

Look at the units of expansion. Expansion has units of velocity per distance, which can be converted into units of inverse time.

So expansion just isn't a speed, and thus can't obey any sort of speed limit. The units are just wrong. It's somewhat similar to saying that a car can't travel faster than 6000 rpm's (the engine might not be able to revolve that fast, but that doesn't tell you anything about how fast the car can or cannot go).

And then, in General Relativity, relative speed is only well-defined at individual points. For instance, I can definitively say how fast you are going when you pass by me, but in General Relativity, if you're approaching me from a mile away, what speed I infer depends entirely upon what coordinates I use. If I change the coordinates, I can get a different speed.

So similarly, there can be no speed of light limitation for distantly-separated points in General Relativity, because I could always just rewrite my equations so that the relative speeds are zero. Or infinity. If I so choose.

The only limitation comes in at single points: no object can outrun a light ray. And all objects in the universe satisfy that criterion.

Does that help?

 

[bcrowell]

The short answer is that general relativity does not have a well-defined notion of the relative velocity of two objects that are distant from one another. Therefore there is no unambiguous way to say whether cosmological expansion causes velocities greater than c.

 

[John232]

So then wouldn't the addition of velocity formula when applied to galaxies be wrong since the equation itself doesn't allow for faster than light travel?

 

[jskirvin]

I think my confusion resides in my flawed understanding of an accelerating universe. The framework through which the galaxies exist is expanding; the galaxies themselves are moving apart but not physically accelerating. At some point, two galaxies relative to one another may appear to break the light barrier ("appear" being relative because they actually would disappear), but neither would "outrun a light ray." Is this correct?

 

[bapowell]

I think my confusion resides in my flawed understanding of an accelerating universe. The framework through which the galaxies exist is expanding; the galaxies themselves are moving apart but not physically accelerating. At some point, two galaxies relative to one another may appear to break the light barrier ("appear" being relative because they actually would disappear), but neither would "outrun a light ray." Is this correct?

Not quite. In an accelerating spacetime, once two galaxies are a Hubble distance apart, they will lose causal contact -- a light signal sent by one will not reach the other. The cosmological horizon in accelerating spacetimes is in fact an event horizon.

 

[George Jones]

Not quite. In an accelerating spacetime, once two galaxies are a Hubble distance apart, they will lose causal contact -- a light signal sent by one will not reach the other. The cosmological horizon in accelerating spacetimes is in fact an event horizon.

For a flat universe that exponentially expands for all time, the Hubble radius is the cosmological event horizon, but (as in all universes) we never see anything cross horizon, so we never see anything on the Hubble sphere.

In our universe, the Hubble sphere and the cosmological event horizon don't correspond, even in the distant future. If we can see galaxy A now, it will never disappear. At some future time, A will be "receding" with a speed greater than the speed of light, but, even after this time, we will see A with (exponentially) increasing redshift, and with increasing faintness. In principle, we will never lose sight of A. In fact, some stuff that we see now (for example, the CMB from the (near) the surface of last scattering) was outside the Hubble sphere when the light we now see started its journey.

 

[GowthamDaas]

if the universe is expanding , then why can't it can happen in the reverse manner simultaneousy or one after other?

 

[marcus]

... In fact, some stuff that we see now (for example, the CMB from the (near) the surface of last scattering) was outside the Hubble sphere when the light we now see started its journey.

Glad you made that point! It doesn't seem widely appreciated. Indeed I think any galaxy with redshift > 2 was outside the Hubble sphere when the light started its journey. I will go check that to be sure.

Yes, I checked. More exactly with parameters 0.27, 0.73, 71 plugged in for matter density, cosmological constant, and current Hubble constant, any galaxy we see with redshift greater or equal to 1.7 was receding faster than c when the light set out on its journey to us. The light would at first not have been getting nearer.

 

[jskirvin]

For a flat universe that exponentially expands for all time, the Hubble radius is the cosmological event horizon, but (as in all universes) we never see anything cross horizon, so we never see anything on the Hubble sphere.

In our universe, the Hubble sphere and the cosmological event horizon don't correspond, even in the distant future. If we can see galaxy A now, it will never disappear. At some future time, A will be "receding" with a speed greater than the speed of light, but, even after this time, we will see A with (exponentially) increasing redshift, and with increasing faintness. In principle, we will never lose sight of A. In fact, some stuff that we see now (for example, the CMB from the (near) the surface of last scattering) was outside the Hubble sphere when the light we now see started its journey.

As a pure matter of human perception, I disagree. With an "exponentially increasing redshift," at some point it will become so close to invisible that it will be invisible...but this point is moot. As I see it, at some point in an accelerating universe the rate of acceleration between two points will surpass a threshold, and light emitted from point A cannot travel fast enough to ever reach point B. See the following quote for a more elegant explanation. :)

If you still disagree, can you explain why in more specific terms? If there's something I'm missing, please enlighten me.

Not quite. In an accelerating spacetime, once two galaxies are a Hubble distance apart, they will lose causal contact -- a light signal sent by one will not reach the other. The cosmological horizon in accelerating spacetimes is in fact an event horizon.

I tend to agree with this line of thought.

 

[jskirvin]

Glad you made that point! It doesn't seem widely appreciated. Indeed I think any galaxy with redshift > 2 was outside the Hubble sphere when the light started its journey. I will go check that to be sure.

Yes, I checked. More exactly with parameters 0.27, 0.73, 71 plugged in for matter density, cosmological constant, and current Hubble constant, any galaxy we see with redshift greater or equal to 1.7 was receding faster than c when the light set out on its journey to us. The light would at first not have been getting nearer.

I understand the implications, but I don't understand the logic behind it. Can someone explain/elaborate?

 

[marcus]

I think my confusion resides in my flawed understanding of an accelerating universe. The framework through which the galaxies exist is expanding; the galaxies themselves are moving apart but not physically accelerating. At some point, two galaxies relative to one another may appear to break the light barrier ("appear" being relative because they actually would disappear), but neither would "outrun a light ray." Is this correct?

BTW you can address questions to specific people. Like if Chalnoth said something that interested you and you want to follow up on you can quote him and then as about it.
That way you get more focus, your question has more definite focus.

My impression is that George J, Chalnoth, and B Crowell are all academic folk and expert in Gen Rel, so if you can grab one's attention you can reliably find out stuff.

My impression of you from your post is that you are trying to visually IMAGINE. So instead of explaining verbally (which the others can do as well or better). I will advise you to do this visual exercise:

google "wright balloon analogy" and watch this a couple of times:
http://www.astro.ucla.edu/~wright/Balloon.html
it is a 2d analog of 3d space, there is no inside the balloon or outside the balloon, all existence is on that spherical 2d surface

notice that in a sense none of the galaxies move, they stay at the same latitude and longitude (if those are your coordinates they are stationary, just getting farther apart)

Then put photons of light into the picture by typing a "2" into the URL so it says
http://www.astro.ucla.edu/~wright/Balloon2.html
Then you will see that the photons of light are all traveling at a constant speed.
They do move. The galaxies do not.

What you said in your post is CORRECT. No galaxy ever outruns a photon.
The visualization can help get that in order in one's imagination. There are other things it illustrates but I'll keep this short.

 

[bapowell]

In all spacetimes there is a Hubble distance, the significance of which is that it marks the distance at which recession velocities reach the speed of light. However, in non-accelerating spacetimes, the Hubble distance grows faster than the spacetime expands, and so objects that were once outside the horizon (with v > c) will at some point come within the horizon. In contrast, in accelerating spacetimes the horizon grows more slowly than the spacetime expands, and so objects outside the horizon will forever remain so.

 

[marcus]

Glad you made that point! It doesn't seem widely appreciated. Indeed I think any galaxy with redshift > 2 was outside the Hubble sphere when the light started its journey. I will go check that to be sure.

Yes, I checked. More exactly with parameters 0.27, 0.73, 71 plugged in for matter density, cosmological constant, and current Hubble constant, any galaxy we see with redshift greater or equal to 1.7 was receding faster than c when the light set out on its journey to us. The light would at first not have been getting nearer.

I understand the implications, but I don't understand the logic behind it. Can someone explain/elaborate?

sure, but I still think watching those short balloon animations is a good idea. Use visualization as well as logic.

You are asking how it happens that we look out today and see a galaxy with redshift z = 2 and we know that when the light left that galaxy it was receding at, say 1.1c. About 10% faster than c.

How could the light have gotten to us?

That is a good question. It and a lot of other common questions people have was answered very clearly Charley Lineweaver's March 2005 Sci Am article. I have the link in my sig.
It is a really really good article about basic expansion cosmology and the questions most people have about it.

I'll give you my answer but still advise reading Lineweaver's.

The way I put it is that H is the expansion rate and the Hubble radius is basically the RECIPROCAL c/H. It is the distance which is expanding exactly at rate c.

And in the past H used to be much much larger----like 10 or 100-fold. So as H was decreasing---to get down to the piddling 71 that it is today---the Hubble radius was increasing dramatically. So it could reach out and take in light that was initially getting swept away from its destination.

So even though the photon coming from the galaxy was at first being "swept back" away from us by the expansion, it was making a valiant effort and hanging in there and pretty soon the Hubble radius got big enough to include it. (IOW the expansion rate slowed) and then it was within the Hubble sphere where distances do not expand at rates > c. and it began to make real progress towards us.
Different people will say this different ways (maybe George, Crowell, or Chalnoth would say it differently, more to your liking)

 

[marcus]

In all spacetimes there is a Hubble distance, the significance of which is that it marks the distance at which recession velocities reach the speed of light. However, in non-accelerating spacetimes, the Hubble distance grows faster than the spacetime expands, and so objects that were once outside the horizon (with v > c) will at some point come within the horizon. In contrast, in accelerating spacetimes the horizon grows more slowly than the spacetime expands, and so objects outside the horizon will forever remain so.

I generally agree with you BA, still people should be careful (in the accelerating case) not to equate the Hubble radius with the cosmological event horizon. The meaning of horizon wasn't clear to me from your post.

For us now, the Hubble radius is a bit less than 14 billion LY and our cosm. ev. horiz. is somewhat more than 15 billion LY. I think I'm saying what you know but some others might not, so I'll elaborate.

Despite acceleration, H is still decreasing (asympt. towards about sqrt(.73) of its current value)
Because H is decreasing, the Hubble radius c/H is still increasing.
So there still are photons out there in the v>c who are trying to get to us and losing ground, who will still eventually make it. A kind of shell between 14 and 15, roughly speaking.

 

[bapowell]

Thanks for the clarification marcus. I was inappropriately referring to de Sitter expansion in my explanation rather than, you know, the *actual* universe

 

[marcus]

de Sitter is certainly a good approximation, and it's getting better all the time

 

[George Jones]

If you still disagree, can you explain why in more specific terms? If there's something I'm missing, please enlighten me.

Are you familiar with spacetime diagrams? As illustration of what marcus and I said, take a look at Figure 1 (particularly, the third diagram of Figure 1) from

http://arxiv.org/abs/astro-ph/0310808.

 

[George Jones]

Something related. Figure 1 from another paper,

http://arxiv.org/abs/0802.1532,

plots redshift versus time. The three red curves are for objects in our universe. As we watch (over many years) a distant, high redshift object, A, we will see the object's redshift decrease, reach a minimum, and then increase. If we watch a much closer, lower redshift object, B, we see the object's redshift only increase.

Roughly, when light left A, the universe was in a decelerating matter-dominated phase, and when light left B, the universe was in the accelerating dark energy-dominated phase.

 

[knightEknight]

Here is the link to Lineweaver's article referenced by marcus above:

http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf

... as well as a couple of other related articles:

http://scienceblogs.com/startswithabang/2011/01/q_a_how_is_the_universe_so_big.php
http://scienceblogs.com/startswithabang/2009/07/the_size_of_the_universe_a_har.php