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Howcome the universe is larger than it's old?

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FunFunkyFritz
Ok, i must admit that i've never quite understood this, so maybe someone could explain this to me?

Statement 1: If two light beams are traveling in opposite directions (at light speed), the speed of one beam relative to the other is still the speed of light. I don't have a quote of this, but it is common knowledge.

Statement 2:
http://en.wikipedia.org/wiki/Universe wrote:
However, the observable universe, consisting of all locations that could have affected us since the Big Bang given the finite speed of light, is certainly finite. The edge of the cosmic light horizon is 13.7 billion light years (4.19 Gpc) distant. The present distance (comoving distance) to the edge of the observable universe is larger, due to the ever increasing rate at which the universe has been expanding; it is estimated to be about 78 billion light years


If i combine these two statements i feel like i end up in a paradox. How could the universe outgrow its own "cosmic light horizon"?
Doesn't that imply speeds faster than light?
But at the same time i feel that it must be correct, because otherwice the Universe would be brighter than the Sun.

Ok, i know there are at least two other threads regarding the size of universe. But i'm only interested in why the above statements seems to clash.

/Was probably sleeping during that class
Bikerman
FunFunkyFritz wrote:

If i combine these two statements i feel like i end up in a paradox. How could the universe outgrow its own "cosmic light horizon"?
Doesn't that imply speeds faster than light?
But at the same time i feel that it must be correct, because otherwice the Universe would be brighter than the Sun.

Ok, i know there are at least two other threads regarding the size of universe. But i'm only interested in why the above statements seems to clash.

/Was probably sleeping during that class


Let me try to clarify. The basic difference is down to a phenomenon called 'expansion'. This is not the basic 'flying apart' of the universe after the BB and should not be confused with it. Expansion is a specific phenomenon which is thought to occur in deep space (it only happens when other forces - specifically gravity - are too weak to stop it). Basically the notion is that space itself is expanding. Sounds simple ? OK, imagine it this way. Distant galaxies are, in a real sense, not moving with respect to each other, instead the space between them is 'stretching'.
What is the difference and why does it matter ?
Well....a simple thought experiment might help. Imagine stretching a tape measure out to a distant galaxy. If it is flying away under normal conditions then you would need to keep letting out more tape, yes ?
Under expansion, however, the tape would remain fixed in 'length' and you would not need to let out any more. When you reeled it back in, however, you would find it was much longer than before because it, in common with the empty space it occupied, had 'expanded' or stretched.
That is the basic concept simply put.
Because of expansion (which is not, by the way, limited to c - the speed of light - as a maximum for the simple reason that c only limits objects within spacetime, not spacetime itself), the universe has got bigger than it would by simply flying apart. The normal flying apart is extent is called the light horizon, wheras expansion means that the actual universe extend well beyond this.

I hope this helps....

Chris
FunFunkyFritz
Thanks, that was an exellent answer.

Just one more question. Are there any proof that gravity actually apply to, or at least affects, the 'expansion'?

IMHO it seems like the expansion is something entirely different than the normal gravitational tug of war between particles. It's, if i understand you correctly, spacetime itself that is expanding. How could gravity affect that?
Bikerman
FunFunkyFritz wrote:
Thanks, that was an exellent answer.

Just one more question. Are there any proof that gravity actually apply to, or at least affects, the 'expansion'?

IMHO it seems like the expansion is something entirely different than the normal gravitational tug of war between particles. It's, if i understand you correctly, spacetime itself that is expanding. How could gravity affect that?


According to relativity, the affect of mass on spacetime is clear - it distorts it proportionally to the amount of mass. That is the relativistic definition of gravity - a distortion of spacetime produced by mass.
As to the expansive force -there is still debate about the exact nature of this force. Some think it is the 'cosmological constant' that Einstein introduced to relativity to make the sums work (and later described as his biggest ever mistake, ironically) and is an inherent property of empty spacetime.
The fact that expansion is actually happening is evidenced by red-shift data. Far galaxies are red-shifted in a way different to normal 'doppler' redshift. As photons move through spacetime, they are expanded with the surrounding spacetime and become 'longer' - equivalent to lowering the frequency.
Wavelegth is lowered in normal doppler shift, of course, but in that case the shift is produced by the relative difference in speed between observer and object. There is also a 'relativistic' redshift produced by the gravitation affect as photons move out of a gravity field (the resultant loss of energy produces the relativistic red shift).
Cosmological redshift is different, since it is produced by the photon itself expanding as it moves through space and is not dependant on relative velocities, or gravitational fields.

Hope this helps

Chris
ClanDestine
Wow, that is some interesting stuff there. Thanks for the answers given Bikerman. You really cleared that up for me too, hehe.
uunter
Quote:
The fact that expansion is actually happening is evidenced by red-shift data. Far galaxies are red-shifted in a way different to normal 'doppler' redshift. As photons move through spacetime, they are expanded with the surrounding spacetime and become 'longer' - equivalent to lowering the frequency.


I'm a physics student, but I haven't taken GR yet. I'm curious--I understand the difference in the cause of redshift between Hubble expansion and spacetime expansion, as you explain it, but how is this difference observable? All we can tell about a photon is its energy.
Bikerman
uunter wrote:
Quote:
The fact that expansion is actually happening is evidenced by red-shift data. Far galaxies are red-shifted in a way different to normal 'doppler' redshift. As photons move through spacetime, they are expanded with the surrounding spacetime and become 'longer' - equivalent to lowering the frequency.


I'm a physics student, but I haven't taken GR yet. I'm curious--I understand the difference in the cause of redshift between Hubble expansion and spacetime expansion, as you explain it, but how is this difference observable? All we can tell about a photon is its energy.


Again I have to say I'm not an expert so don't tell your lecturers that some guy gave you the absolute answers or I might have angry physics lecturers chasing me...I'll try, however, to address this as best I can...
As you say the only data received is the wavelength (energy is another way of putting it, which I don't like, but, hey, I'm not a physicist so what trhe hell).
What scientists therefore have to do is work out some more data indirectly. The clever and vital bit is the use of spectrum absorbtion (and emission) data. The characteristic absorbtion frequencies for various elements are well known and understood. The same is true for various Star types. When observing light from a distant source the astronomer will look for absorbtion lines, using standard 'look-up' tables of reference data.
This diagram from Wikki should help illustrate...


Now the astronomer can use the reference absorbtion lines to calculate the shift. I should add that sometimes emission lines can be used either instead of or in addition to absorbtion. I presume you are famiar with em spectrum absorbtion and emission ? If not then for shame young man!!

Now each type of shift is calculated differently. At this point I have to elaborate slightly and introduce the entire range of red shift (I did not want to confuse the issue earlier by doing this but you did ask...)

1. Doppler redshift - obvious and easy..the light equivalent of the police siren passing the observer. Calculated by the formula :


2. The above is not really good enough for a physicist as you will accept. We don't want any nasty 'nearly equal to' signs. You should already know why it is not exactly an equal sign if you have done any SR. It uses Galilean transformation which is innacurate for anything travelling at near-light speeds. Therefore the proper Lorentzian transformation (which factors in the affect of dilation as prescribed by Special Relativity) should be used. You probably know it but here it is :-


If you are not familiar with the above then the Lambda sign is the 'Lorentz factor' and you will meet this soon.

3. Cosmological red shift is calculated using the 'scale factor' (a) which is derived from the current cosmological model and is given the formulation :

Unlike relativistic shift, this is scale dependant - ie it changes with distance, since the photon is 'stretched' more as it traverses more spacetime. The 'stretch' is preceived, of course, as a wavelength change but since it is scale dependant it will proeduce a scale dependant shift and this, of course, is what Hubble found when he turned his telescopes to distant galaxies outside the local group.

4. Finally we have to mention the influence of General Relativity.
Point 2 only calculated the dilation effect (ie Special relativity and the effect of velocity). GR states that gravitation also produces a time dilation effect. (This means, of course, that if you climb a mountyain you are in a different frame of reference in relativity and your time is slightly slower than when you were at sea level).
The gravitational dilation also affects the photon and the shift is given using GR as follows :


Now you have a complete set of the shift calculations used.

When single source shift is measured by observers it is found that z is pretty constant. When distant observations are taken there is obviously not a single source so assumptions have to be made and a technique called 'photometric redshift K correction' is used which produces a fairly high error range.

Now at that point you know as much as I do and I have to plead ignorance and refer you to a proper physicist for any elaboration/extension.
I'm quite exhausted now Smile I hope this was useful to you - at least it made me revise my notes a bit which was useful...

Regards
Chris

Postscript comment:
I'm not exactly sure how 'fair use' guidelines apply when you are posting a link directly into the message so I have assumed the diagram from wikki would be no problem. If this is thought to be problematic then please let me know - I'm a YaBB user normally and our boards don't allow direct links so I'm not sure of netiquette - I would normally post a hyperlink which is oviously fine, but the diagram in the posting is better for keeping a point going than flicking around windows or tabs. Especially when I've got a bunch of notes on my knee trying to check I got the GR formula right Smile
uunter
Wow--thanks.

I need a little clarification, though. I know you said to ask elsewhere for elaboration, so don't answer this if you don't want to, but hopefully it will require only a brief response. First, z is, I assume, the factor by which the photons wavelength increases. Is that correct? Then, tell me if I've understood this all correctly:

I know all about SR, so obviously #2 is just a modification of #1, making it more accurate. But then the Cosmological Red Shift discussed in #3 is a separate effect, due to the actual stretching of space you explained in earlier posts, and so the total redshift from the effects of #2 and #3 combined would be the two z-factors multiplied, no? And then I'm a little unclear on #4; is this another separate effect to be multiplied in, or another correction to #2? I would assume the former, since it doesn't contain any velocity information, but I know nothing of GR, so I wanted to make sure. I won't ask for the derivation to the GR dilation equation, 'cause I'm sure it takes up pages in some big textbook.

This leaves me with two questions: first, what are the cosmological scale factors a_now and a_then? Or at least, what are the now and then referring to? Second, I still don't understand how one can differentiate among the differing effects. In each equation, z can vary continuously from zero to infinity, so if we observe a z-factor of, say, five, from a particular galaxy, how do we know how much of each effect contributed?

The semester starts in a few weeks, so I'll soon have profs I can bug about this, if you don't want to type out another response.
Bikerman
Quote:

Wow--thanks.

I need a little clarification, though. I know you said to ask elsewhere for elaboration, so don't answer this if you don't want to, but hopefully it will require only a brief response. First, z is, I assume, the factor by which the photons wavelength increases. Is that correct? Then, tell me if I've understood this all correctly:{/quote]

Yep - so far so good.
Quote:

I know all about SR, so obviously #2 is just a modification of #1, making it more accurate. But then the Cosmological Red Shift discussed in #3 is a separate effect, due to the actual stretching of space you explained in earlier posts, and so the total redshift from the effects of #2 and #3 combined would be the two z-factors multiplied, no?

No. The red-shift is often a combination but, unfortunately, it is not a simple relationship. If we consider galaxies in the local group, for example, the cosmological shift is negligable because the gravitational fields (even at galactic distances) are enough to cancel expansion and therefore there is no cosmological factor to be considered. Only at deep space distances (beyond the few tens of light years comprising our Local Group) does expansion kick-in and, therefore, cosmological red shift occur.
Quote:
And then I'm a little unclear on #4; is this another separate effect to be multiplied in, or another correction to #2? I would assume the former, since it doesn't contain any velocity information, but I know nothing of GR, so I wanted to make sure. I won't ask for the derivation to the GR dilation equation, 'cause I'm sure it takes up pages in some big textbook.

Yes this is an entirely new type of red shift. You will meet it in GR later but as a quick summary for you:-
GR specifies that gravitation is equivalent to velocity. This means that gravity produces time dilation in exactly the same way as velocity does. The equivalence principle in GR states that 'all accelerated reference frames possess a gravitational field.' Now, according to General Relativity, inertial mass and gravitational mass are the same. Th GR expression of this is
To*sqrt(1-(2GM/Rc^2))=Tr
(To - Time measured at the object, G - gravitational constant, M - mass, R - distance, Tr - time at observer)
Quote:

This leaves me with two questions: first, what are the cosmological scale factors a_now and a_then? Or at least, what are the now and then referring to? Second, I still don't understand how one can differentiate among the differing effects. In each equation, z can vary continuously from zero to infinity, so if we observe a z-factor of, say, five, from a particular galaxy, how do we know how much of each effect contributed?


OK - scale factor. The distance between any pair of comoving objects grows by a factor (1+H*dt) (H - Hubble constant) in the time period dt.
From this we can wriite the distance to any co-moving observer as follows:
DG(t) = a(t)*DG(to)
DG(to) is the distance (Dnow) to galaxy G(now), and here is the scale factor - a(t) which is a universal scale factor that applies to all comoving objects. How do we get it ? H (Hubble constant) is the ratio of speed to scale factor.
OK - there is another equation for spacetime used called the Robertson-Walker metric of space-time (ds). This is expressed as :



By substitution and other tricks you can calculate a(t)....have a bash later if you fancy a challenge.
Also related to this :
Now, consider an object at distance : D(t) = a(t)xDo with respect to us. Consider this to be the universe and consider it a sphere.
Gravitational acceleration of a sphere of radius D(t) is g = -G*M/D(t)^2
This allows us to compute the dynamics of the universe as a whole.
The mass of the universe is M = 4*pi*D(t)3*p(t)/3 where
(p = rho = density of matter which is only dependant on t).
If you want to continue this what you can now do it consider the case where v <= escape velocity (ie a big crunch will ensue) and work out what that means for rho (p) . In short we can calculate what density of matter will cause the universe to keep expanding. Consider where v = escape velocity.



This gives us the critical mass needed to stop infinite expansion of the Universe.....good eh ?

Cheers
Chris

Correction to the above....I just notices that I stated that GR says Gravity is equivalent to velocity. Sorry...that should read acceleration, not velocity.

C.
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