Universe expanding faster than light

[marcus]

Your explanation quoted in post #25 says it a lot better:
I had not seen that simple synopsis before...that makes it unambiguous...

Chalnoth's post #25 was:

... Using $$\Omega_m = 0.27$$ and $$\Omega_\Lambda = 0.73$$, I get $$r = 1.12 \frac{c}{H_0}$$. So objects currently receding up to about 12% higher than the speed of light are emitting photons that we will detect at some point...

I will augment that post some and add a detail or two.

Recession rate c corresponds to a current distance which is by definition equal to the Hubble distance c/H. With the new 2009 parameters (see the Riess thread) that c/H distance is 13.2 billion lightyears. (This is not "light travel time" it is actual proper distance).

So 12 percent faster increase that Chalnoth is talking about corresponds to 12 percent larger distance. 1.12 * 13.2 = 14.8
So it is the galaxies which are today 14.8 billion lightyears from us which can, if they act immediately, send us a message which will eventually reach us. If the distance is any more than 14.8, then they have lost their chance.

This is according to Chalnoth's figure of 1.12 c. It sounds right to me but I didn't check in detail.

What does this mean in terms of redshift? Again using the new cosmic parameters that were published this year (Riess et al 2009) that Sylas gave the link to, we can say that if a galaxy has redshift z = 1.65 then it can today send us a message which we will eventually receive.

If the redshift is any greater, it is too late for them to hail us. Unless they already have of course.

This is just a thought experiment, the business about galaxies sending messages. Nobody I know expects this to happen. It is a way of illustrating the limits on causal connectedness.

 

[Chalnoth]

I had not seen that simple synopsis before...that makes it unambiguous...

Just please bear in mind that how far we can observe at some point in the future depends critically upon the future fate of the universe, which we don't yet know. So it's worth bearing in mind that if the dark energy is something substantially different from a cosmological constant, then the distance we can see may be very different indeed.

 

[Chalnoth]

If the redshift is any greater, it is too late for them to hail us. Unless they already have of course.

Well, we are and will continue to receive light from these objects. It's just that the light they're emitting today won't ever reach us: this means that if we watched these objects for infinity, we would see them age more and more slowly as they are accelerated away by the expansion, reaching an asymptotic age that depends upon when they crossed our horizon. Of course, the galaxy will continue to do stuff, it's just that the information of what that galaxy is doing will never reach us.

 

[Chronos]

Correct, we will still 'see' them forever. Albeit, they may eventually 'freeze' due to time dilation.

 

[Chalnoth]

Correct, we will still 'see' them forever. Albeit, they may eventually 'freeze' due to time dilation.

Well, more precisely they will asymptitically approach being 'frozen', which we will see as them being infinitely redshifted. Exact same principle as something falling into a black hole.

 

[sylas]

Correct, we will still 'see' them forever. Albeit, they may eventually 'freeze' due to time dilation.

Just to clarify... they don't "freeze" in the sense of something happening to them; the effect is symmetric. Observers on those galaxies would long since have seen the Milky Way "frozen" at a point in our distant past. When we see a distant galaxy approaching this horizon, we have long since crossed the corresponding horizon in the view of observers in that galaxy.

 

[Chalnoth]

Just to clarify... they don't "freeze" in the sense of something happening to them; the effect is symmetric. Observers on those galaxies would long since have seen the Milky Way "frozen" at a point in our distant past. When we see a distant galaxy approaching this horizon, we have long since crossed the corresponding horizon in the view of observers in that galaxy.

Another good point.

 

[DaveC426913]

Correct me if I'm wrong, but the visual effect of frozen in time will not actually come to pass. While true in principle, what will really happen is that the galaxies will get dimmer and dimmer as fewer and fewer photons reach us.

It is tantamount to watching an astronaut fall into a black hole. In principle, he'll freeze in time but what's really happening is we're seeing all the photons from that last moment before he falls past the EH. They are limited.

So it is with the receding galaxies. The flow of photons will ebb even as the image of the galaxy slows. Eventually, it wil be down to one photon every time unit, etc.

 

[sylas]

Correct me if I'm wrong, but the visual effect of frozen in time will not actually come to pass. While true in principle, what will really happen is that the galaxies will get dimmer and dimmer as fewer and fewer photons reach us.

It is tantamount to watching an astronaut fall into a black hole. In principle, he'll freeze in time but what's really happening is we're seeing all the photons from that last moment before he falls past the EH. They are limited.

So it is with the receding galaxies. The flow of photons will ebb even as the image of the galaxy slows. Eventually, it wil be down to one photon every time unit, etc.

That is correct. And one other thing... there will be a finite number of photons arriving at our world line from that galaxy, and hence there will be a last photon. The last photons will be redshifted to absurdly long wavelengths, and hence invisible to any practical detector.

Cheers -- sylas

 

[Chalnoth]

Correct me if I'm wrong, but the visual effect of frozen in time will not actually come to pass. While true in principle, what will really happen is that the galaxies will get dimmer and dimmer as fewer and fewer photons reach us.

Well, part of that is because the photons that were emitted at a high rate will reach us at a low rate. Part of it is because the photons emitted at higher wavelengths will reach us at much lower wavelengths. The redshift, after all, is a visual effect of time dilation (in part). As time approaches infinity, the redshift will approach infinity, at which point these galaxies will effectively look 'frozen', though that also means we won't see any more photons from them.

 

[camilus]

Ok great. Let's talk about a finite universe for a moment. Suppose the universe is finite, what shape do you think it has? What global geometry in specific?

 

[Chalnoth]

Ok great. Let's talk about a finite universe for a moment. Suppose the universe is finite, what shape do you think it has? What global geometry in specific?

Er, nobody knows?

 

[camilus]

Of course, but let's atleast speculate.

Most people agree that the local geometry is flat (Euclidean), but I am more interested in the global geometry, the geometric shape of the universe as a whole.

To me, spherical makes the most sense but a lot of people argue for a hyperbolic structure. What arguments are there for hyperbolic? And then I'll share mine for a universe with Ω > 1.

 

[Chronos]

Just to clarify... they don't "freeze" in the sense of something happening to them; the effect is symmetric. Observers on those galaxies would long since have seen the Milky Way "frozen" at a point in our distant past. When we see a distant galaxy approaching this horizon, we have long since crossed the corresponding horizon in the view of observers in that galaxy.

Agreed. We already see all that is possible to perceive.

 

[Chalnoth]

Of course, but let's atleast speculate.

The problem is that there are no even remotely compelling arguments that say much of anything about the overall shape of the universe. Some people may "like" one shape or another, but that just means they like that shape. It has no bearing whatsoever on whether or not it's true.

So the only reasonable statement one can make right now is that we just don't know.

 

[sylas]

Agreed. We already see all that is possible to perceive.

I'm glad you agree, but I don't understand the second sentence. It doesn't make sense; of course there are things in the universe that will be perceived and haven't been perceived yet.

So if you mean that we "already" see everything which can be seen so far, then this appears to be a tautology, and not relevant to the existence or otherwise of event horizons, which is what I was addressing. And if you mean that we "already" see everything that we can hope to perceive in the universe, then that is false.

Note that there is a real substantive difference between, say, a critical density universe and a universe with a cosmological constant. In the first case, there is no event horizon, everything in the universe is in principle able to be seen, if we wait long enough. In the second, there is an event horizon, and there are regions of spacetime that can never be seen. The difference is a real difference, not resolve with philosophical argument but with empirical investigation of whether expansion of the universe admits an event horizon or not.

Cheers -- sylas

 

[Chronos]

We 'see' the CMB, but, will never see beyond it. We will, of course, see more events unfold in the universe as their photons reach us, but, those photons will always be in the CMB foreground. I fail to see how this is relevant to any horizon or density issues. The CMB is our observational horizon [at present] IMO.

 

[sylas]

We 'see' the CMB, but, will never see beyond it. We will, of course, see more events unfold in the universe as their photons reach us, but, those photons will always be in the CMB foreground. I fail to see how this is relevant to any horizon or density issues.

As time passes we see further and further reaches of the surface of last scattering. There is no event horizon here, so its got nothing much to do with the preceding discussion of what is seen when a distant galaxy crosses an event horizon.

 

[Chronos]

For clarity, no galaxy ever crosses our observational 'horizon'. At worst, they 'freeze' against the CMB as they approach infinite time dilation - agreed?

 

[sylas]

For clarity, no galaxy ever crosses our observational 'horizon'. At worst, they 'freeze' against the CMB as they approach infinite time dilation - agreed?

This is analogous to the common problem people have with objects falling into a black hole. We never see an object falling into a black hole... we see it redshifted to infinity. It is, however, incorrect to say that no object crosses the horizon.

Distant galaxies DO cross the event horizon, or our observational horizon, just as we have already crossed the event horizon for those distant galaxies (presuming the FRW model with dark energy and dark matter). You already agreed with this! We merely don't see this occurring for other galaxies.

Cheers -- sylas

 

[Chalnoth]

We 'see' the CMB, but, will never see beyond it. We will, of course, see more events unfold in the universe as their photons reach us, but, those photons will always be in the CMB foreground. I fail to see how this is relevant to any horizon or density issues. The CMB is our observational horizon [at present] IMO.

With photons. With other particles, we might be able to 'see' quite a bit further back in time (and thus further). For example, if we could directly detect the cosmic neutrino background, that would lead a fair amount further back in time. Or, if we could directly detect the cosmic gravity wave background, that would go even further back.

 

[sylas]

With photons. With other particles, we might be able to 'see' quite a bit further back in time (and thus further). For example, if we could directly detect the cosmic neutrino background, that would lead a fair amount further back in time. Or, if we could directly detect the cosmic gravity wave background, that would go even further back.

Yes... this is one of the reasons I really hope LISA gets the nod for NASA projects!

 

[Chalnoth]

Yes... this is one of the reasons I really hope LISA gets the nod for NASA projects!

Yup. But it's worth noting that even without directly detecting these gravity waves, they do leave a polarization signal on the CMB that we can detect indirectly. It's very difficult to measure this polarization signal, but we're working on it.

Planck, by the way, probably won't be sensitive enough to detect the gravity wave signature in the CMB.

 

[Chronos]

A neutrino telescope might allow us to peer beyond the EM veil of ignorance. That would be fascinating. I agree Planck may not be sensitive enough to detect gravity waves, but, should resolve a number of other interesting debates in cosmology.