Relativity Question

[CraigS]

Ok all you relativists out thar .. he's a conundrum question I've been trying to wrap my mind around for a while … this has to do with cosmological event/particle horizons ...

Say there are two exo-galaxies out there, galaxy X and galaxy Y, where X is nearer to us than Y. Now with cosmic acceleration, there will be some last photon from either galaxy after which we will see nothing. Now, at the time X sends out its last photon, there will also be a Y photon passing by X. They both travel at the same speed, and thus they both reach us at the same time (Y will be more redshifted than X). We will see both galaxies blink out together, even though Y is further away (and is presumably younger than X).

So if we think of the entire universe consisting of galaxies of different ages, then this would mean that at one instant we will see our entire observable universe …. and in the next instant … all of it blinks out ??

There is some flaw here, but where is it … ??...

Answerers welcome.

Cheers

[SkyViking (Rolf)]

But there won't be a 'last photon' will there?
The cosmological redshift will merely shift and dim the light until the point where we can no longer detect any signal from them, it will just get lost in the CMB eventually. And that will all happen for galaxy Y first.

[Archy (George)]

Originally Posted by CraigS

Ok all you relativists out thar .. … this has to do with cosmological event/particle horizons ...there will be some last photon from either galaxy after which we will see nothing. (Y will be more redshifted than X). There is some flaw here, but where is it … ??...

Answerers welcome.

Cheers

I can understand a redshifted spectrum: how can the "redshift" of a single proton be measured

[renormalised (Carl)]

Originally Posted by Archy

I can understand a redshifted spectrum: how can the "redshift" of a single proton be measured

Photon....not proton. Very easily, with a photomultiplier tube and in exactly the same way as you measure a redshifted spectrum. You look at (or determine via theory) what the original wavelength/frequency of the photon was when it left the source and compare that with what you measured at the photomultiplier.

[CraigS]

Originally Posted by SkyViking

But there won't be a 'last photon' will there?
The cosmological redshift will merely shift and dim the light until the point where we can no longer detect any signal from them, it will just get lost in the CMB eventually. And that will all happen for galaxy Y first.

Thanks Rolf.

For this hypothetical example, I'm trying to ascertain whether or not there is a theoretical limit, so I've kind of assumed the CMB is out of the scope. I think this just makes it a bit less complicated .. (?)

So is what you say then, not just a practical detection issue ?
Ie: build a more powerful detector commensurate with the increase in redshifted wavelength/decrease in power ?

What I'm trying to ascertain is will the accelerated (metric) expansion of space mean that there will be an instant when both photons are simply not able to reach us - ie: we are causally disconnected ?

Cheers

[michaellxv (Michael)]

IFF your original statement is true that would imply we can currently see the entire universe.

A question to help my thinking.
Galaxy X and Y are currently receding from each other at a rate R. Photons can travel between X and Y and they can see each other.
The rate R is increasing and at time T reaches C. At time T a photon can not complete the trip between X and Y. Assuming there were a continuous stream of photons along the path what happens to these photons at time T? Are they all trapped at their point in space at time T? Does this also imply that every point in space along the path is expanding at a rate of C? Does this mean that your original statement is true and all galaxies blink out when all of space is expanding at a rate of C?

Having typed this out it still doesn't sound right but i'll leave it anyway. I think it would contradict all of Hubble's observations.

[SkyViking (Rolf)]

On a second thought, I think that strictly speaking yes there is a 'last photon', but by the time galaxy X emits the last photon that will ever reach us, galaxy Y has already passed beyond the event horizon. So there won't be a Y photon passing by X at the time.

[sjastro]

Originally Posted by CraigS

Ok all you relativists out thar .. he's a conundrum question I've been trying to wrap my mind around for a while … this has to do with cosmological event/particle horizons ...

Say there are two exo-galaxies out there, galaxy X and galaxy Y, where X is nearer to us than Y. Now with cosmic acceleration, there will be some last photon from either galaxy after which we will see nothing. Now, at the time X sends out its last photon, there will also be a Y photon passing by X. They both travel at the same speed, and thus they both reach us at the same time (Y will be more redshifted than X). We will see both galaxies blink out together, even though Y is further away (and is presumably younger than X).

So if we think of the entire universe consisting of galaxies of different ages, then this would mean that at one instant we will see our entire observable universe …. and in the next instant … all of it blinks out ??

There is some flaw here, but where is it … ??...

Answerers welcome.

Cheers

If galaxy X is at the horizon, galaxy Y is already beyond that horizon and hence photons from Y are unobservable as the recession velocity of Y is greater than C.

Despite the fact that galaxy X is accelerating faster than galaxy Y because X is younger than Y, the Hubble "constant" increases with decreasing cosmological time. Since galaxy Y is older than galaxy X, the Hubble "constant" is larger at the time when say galaxy Y is formed. The recession velocity for galaxy Y will always be greater than that of galaxy X.

While this might seem counter intuitive as X is accelerating at a faster rate than Y, it's very easy to explain mathematically.

Since the Universe is expanding metrically, the scale of the Universe increases with time.
Suppose R(t) is the scale of the Universe at some time t, then dR/dt is the rate of change of the scale R(t). dR/dt is the acceleration of the Universe.
Hubble's "constant" H is simply (dR/dt)/R(t).

Since galaxy Y is formed before galaxy X, the scale R(t) is less than at the time of the formation of galaxy X. Since you are dividing by a smaller number, the Hubble "constant" is greater at the time of formation of galaxy Y despite dR/dt being greater at the time of formation of galaxy X.

Hence the Hubble "constant" and therefore the recession velocity of galaxy Y will always be greater than galaxy X.

Regards

Steven

[CraigS]

Thanks Steven (and all - much appreciated);

I suspected the answer was in the formal definition of the acceleration/Hubble "Constant".

However, I'm still a bit perplexed because that photon that was emitted by Y, and was adjacent to galaxy X just before X made it to lightspeed, should still arrive at Earth at the same instant as X's last photon (??)

We loose sight of both at the same instant (??) Even though we'd lost sight of Y before X ??

(Sorry if I'm being slow on the uptake here .. there is more than one frame of reference involved in this ..)

Cheers

[Robh (Rob)]

Hi Craig,

I'm not sure but I suspect that the answer lies in time dilation due to the differences in relative velocity resulting from the accelerated expansion of space. This time dilation can be less for particles arriving from Y to X but much much greater for particles arriving here from X and more from Y.

The images of the galaxies don't actually disappear but are frozen in time as they pass the cosmic event horizon. Any further information (e.g. photons from Y) after it passes the event horizon no longer reaches us.

This is similar to the event horizon of a black hole where the image of an ingoing object is seemingly frozen at the event horizon to a distant observer.

The effect is relative to the different reference frames from which the photons are being observed.

Regards, Rob

[CraigS]

G'Day Rob;
Long time .. no hear .. good to see you back in these parts !

I was having recall about our previous discussions about the similarity of this and BH Event Horizons. I think I recall leaving that discussion with the QM/String Theory view that 'frozen' images break into ever increasing smaller components (vibrating strings) covering the entire EH. At the moment though, I'm trying to get the Relativity perspective embedded in my brain. The relativists seem to always refer to the 'blinking out' phenomenon and I think this is derived from the formal definitions posted by Steven. (I'll have to have more of a think about the ramifications of these).

There's another issue also .. raised by Rolf … the redshift one. In theory, redshift would cause the wavelength to become just about infinite wouldn't it ?

What happens to the energy of the photon if/where this happens ?

Cheers

[Robh (Rob)]

Craig,

The light is not just red-shifted in the visible spectrum. The more distant object will be progressively more red-shifted, which makes it harder to detect in the visible spectrum, then harder to detect in the infrared, microwave and radio spectrums etc. The photons are moving progressively along the spectrum as the object is further away.

That is, the light (photons) do not blink out at the same time for galaxy X as the further galaxy Y. It is a gradual process.

Rob

[CraigS]

Originally Posted by Robh

Craig,

The light is not just red-shifted in the visible spectrum. The more distant object will be progressively more red-shifted, which makes it harder to detect in the visible spectrum, then harder to detect in the infrared, microwave and radio spectrums etc. The photons are moving progressively along the spectrum as the object is further away.

That is, the light (photons) do not blink out at the same time for galaxy X as the further galaxy Y. It is a gradual process.

Rob

In an accelerating universe, there must come a point where the photons can never feasibly make it to Earth, because they are beyond our Cosmo EH. This would be independent of our inability to detect infinitely big redshifts though .. I suppose the question would be … which comes first: the 'blink out', or; the disappearance due to diminished light.

And, if we could build a radio detector big enough, perhaps we could still go on 'seeing' the ever increasingly redshifted photons from Y. If we could tap into the energy of our newly expanded universe, we might have enough energy/power to pump into the detector, too.

(I'm talkin' the extreme limits here, also .. so its another one of 'those' hypotheticals … but the theory must tell us something about the limits and which phenomenon happens first ??)

Cheers
PS: I still can't see why X's and Y's co-incident photons wouldn't arrive simultaneously and then, spectacularly, blink out together .. I tend to agree that the process you mention would be a gradual one and intuitively, I agree with you .. what I'm trying to do is to understand why the logic in my original post is in error … (I'm sure it is .. 'intuitively'.)

[sjastro]

Originally Posted by CraigS

G'Day Rob;
Long time .. no hear .. good to see you back in these parts !

I was having recall about our previous discussions about the similarity of this and BH Event Horizons. I think I recall leaving that discussion with the QM/String Theory view that 'frozen' images break into ever increasing smaller components (vibrating strings) covering the entire EH. At the moment though, I'm trying to get the Relativity perspective embedded in my brain. The relativists seem to always refer to the 'blinking out' phenomenon and I think this is derived from the formal definitions posted by Steven. (I'll have to have more of a think about the ramifications of these).

This is a consequence from the Robertson-Walker metric (http://en.wikipedia.org/wiki/Friedma...3Walker_metric). The event horizon incidentally for a BH is based on a gravitational redshift mechanism, not a cosmological redshift or time dilation mechanism.

There's another issue also .. raised by Rolf … the redshift one. In theory, redshift would cause the wavelength to become just about infinite wouldn't it ?

Cosmologists prefer to define the frequency of light rather than it's wavelength for a very good reason. Frequency has the units of reciprocal time. Cosmological redshift is a result of time dilation as derived from the R-W metric, rather than the wavelength stretching. The stretching of the wavelength implies loss of energy which leads to the tired light hypothesis.

What happens to the energy of the photon if/where this happens ?

Nothing at all happens. The tired light hypothesis is elegantly refuted by our friend Ned Wright.
http://www.astro.ucla.edu/~wright/tiredlit.htm

Regards

Steven

[CraigS]

Ok Steven;

So, I'm on track with this now .. no problems ..

So, I guess, as Rob mentions, the Y photons experience more time dilation when compared with the X photons .. I would expect that this would impact their relative arrival times, perhaps to the extent of Y's photons not arriving at all (unlike as I originally hypothesised ?). If so, then that problem's solved.

The next issue is if nothing at all happens to the photon's energy (ie: it remains constant), then does this also imply that the energy density of the expanding obs. universe has dropped, due to the expansion of our hubble sphere, which has happened as photon Y makes its way (alongside photon X), to our scopes ?

Cheers
PS: Ned says .. 'yes' .. as per observations ! (I just read Ned ..).

[CraigS]

So, photons "blink out", and also diminish from our abilities to detect 'em because of extreme redshifts, eh ?

So, which happens first .. and;
Does this phenomenon define the difference between a merely expanding universe .. and an acceleratingly expanding one ?

Cheers

[Robh (Rob)]

Originally Posted by sjastro

Cosmologists prefer to define the frequency of light rather than it's wavelength for a very good reason. Frequency has the units of reciprocal time. Cosmological redshift is a result of time dilation as derived from the R-W metric, rather than the wavelength stretching. The stretching of the wavelength implies loss of energy which leads to the tired light hypothesis.

Regards

Steven

Thanks Steven, that makes sense.

Regards, Rob

[sjastro]

Originally Posted by CraigS

Ok Steven;

So, I'm on track with this now .. no problems ..

So, I guess, as Rob mentions, the Y photons experience more time dilation when compared with the X photons .. I would expect that this would impact their relative arrival times, perhaps to the extent of Y's photons not arriving at all (unlike as I originally hypothesised ?). If so, then that problem's solved.

The next issue is if nothing at all happens to the photon's energy (ie: it remains constant), then does this also imply that the energy density of the expanding obs. universe has dropped, due to the expansion of our hubble sphere, which has happened as photon Y makes its way (alongside photon X), to our scopes ?

Cheers
PS: Ned says .. 'yes' .. as per observations ! (I just read Ned ..).

I wouldn't want to disagree with Ned.
Imagine if he appeared in Thunderblogs.

[CraigS]

Ok .. done some reading .. from Wiki it defines the Particle Horizon:

The particle horizon is the maximum distance from which particles could have traveled to the observer in the age of the universe.

and then .. it makes the distinction ...

The particle horizon differs from the cosmic event horizon in that the particle horizon represents the largest comoving distance from which light could have reached the observer by a specific time, while the event horizon is the largest comoving distance from which light emitted now can ever reach the observer in the future.

They give two equations for the particle horizon and then the cosmic event horizon.
If you add the particle horizon and cosmological horizon equations together, that should equal where the boundary is at any one time, right ?
Ie:
particle horizon + cosmological horizon = 'the boundary'.

Cheers
PS: Err .. the boundary being the difference between what we can see and what we can't see yet .. but will in the future ..

[renormalised (Carl)]

Originally Posted by sjastro

I wouldn't want to disagree with Ned.
Imagine if he appeared in Thunderblogs.

That would be like the devil turning up in St Peter's wanting an audience with the Pope!!!!