Re: Is the Big Bang Still Happening?
From: Bjoern Feuerbacher (feuerbac_at_thphys.uni-heidelberg.de)
Date: 11/03/04
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Date: Wed, 03 Nov 2004 13:39:03 +0100
Alastair wrote:
> Bjoern Feuerbacher <feuerbac@thphys.uni-heidelberg.de> wrote in message news:<clm3cd$jt7$1@news.urz.uni-heidelberg.de>...
>
> [Just got your reply today... it took a week to show up... snip]
>
>
>>>>>So we agree that the scattering surface is changing over time as it
>>>>>moves away from us.
>>>>
>>>>The region of the universe which we see now as the last scattering
>>>>surface is changing and moving (or better: moved) away from us, yes.
>>>
>>>So the region "inside" (where we are) is growing.
>>
>>Sorry, it is not clear to me what you mean by "the region inside".
Care to explain?
>>>Not just because the
>>>scattering surface is a static region
>>
>>What do you mean by "static region"?
Care to explain?
>>>that recedes from us, but also because it cools.
>>
>>You seem to confuse some things here.
>
>
> Like what?
The different effects, i.e. cooling and expansion.
>>>>>Assuming that the surface represents a known temperature of
>>>>>recombination,
>>>>
>>>>The temperature of that region in space goes down, and recombination
>>>>will soon have completed there.
>>>
>>>The physical process of recombination occurs at the same temperature.
>>
>>Same as what?
>
>
> The laws of Physics don't change... so the recombination occurs at (or is
> occurring at) the same temperature every time we look.
The recombination *did* occur. Past tense. It *is* not occuring.
Did you want to say "the temperature we observe as having been present
in the regions of recombination is the same every time we observe it"?
>>>So since the universe cools, then the scattering surface must move
>>>further out from our point of observation.
>>
>>No, you are approaching this in the wrong way. The light emitted by
>>regions further away from us than the region which we now see as
>>the last scattering surface simply took a longer time to reach us.
>>The expansion of the universe has little to do with that argument.
>
>
> But we are observing an *evolving* system.
> As it cools, it moves further out...
> or to put it another way, we can see further (note, you will find we
> already agreed about this).
Yes, I agree with all that. What is your point?
> As for the "expansion", yes it has little to do with the argument, which
> seems to be my point... please try to respond to the question and stop
> trying to change the subject to, "oh... you just don't get it, let me show
> how you got it all wrong".
Err, which question? Do you mean the one where you asked what the
standard BBT says about a changing baryon-photon ratio? I already
answered that.
>>>>Essentially we are seeing *another* last scattering surface every time
>>>>we look - we look at a surface which is further and further away from
>>>>us. The region of space which we saw the last time as the "last
>>>>scattering surface" is a little time later already a region where the
>>>>recombination has completed.
>>>
>>>The region where recombination has completed has thus emitted photons,
>>>adding to the total number of photons in our observable universe.
>>
>>Perhaps you should consider that at the same time, photons are *leaving*
>>our observable universe.
>
>
> ...as well as *entering* our observable universe.
Yes. You already said that above. Your point?
>>The total density of photons in our observable universe would stay constant
>
>
> ...regardless of the expansion, and not...
No, not regardless of the expansion. If there is expansion, the number
density of photons goes down with 1/a^3. It only stays constant if there
is no expansion.
>>if there were no expansion
>
>
> Glad we straightened that out!
>
>
>>and actually
>>goes down with time with 1/a^3 (a is the scale parameter) because
>>of the expansion. It does not increase, as you seem to suggest here.
>
>
> Uh? Do you mean number density within a given fixed volume?
I mean the mean number density within any arbitraryy (sufficiently
large) volume.
> I was talking about the overall universe, in which case, it all depends
> on what you measure relative to a^3 (volume of the universe).
Huh? Sorry, I don't understand what you mean here.
> If the volume of the universe is proportional to a^3,
That makes sense only if the universe is finite. For an infinite
universe, talking about its volume being proportional to a^3 makes no sense.
> then the number density within the universe is constant...
No. Why on earth do you think so?
The *number* of photons obviously stays constant (neglecting
absorption and the like). Hence the number *density* goes down when the
a^3 increases.
> but that is assuming the
> scattering surface is "static" which we seemed to agree it wasn't.
The argumentation above has nothing to do with the question if
the scattering surface is static or not. It is essentially simple
geometry.
>>>>>then the number of photons being released is also increasing
>>>>>over time.
>>>>
>>>>Huh? How on earth did you arrive at this conclusion?
>>>
>>>I arrived at the conclusion following the logic above. Did I miss
>>>something?
>>
>>Yes. See above.
>>
>>And you also apparently made some huge jumps in logic. *I* could
>>understand how you arrived at your conclusion.
>
>
> I'm glad you understand... but did you agree?
Sorry, obvious type - I meant that I could *not* understand your chain
of argumentation.
>>>>>So does this imply that the baryon-photon ratio is also changing
>>>>>over time.
>>>>
>>>>The baryon-photon ratio where?
>
>
> This is a question in which you ask me to clarify whether...
>
>
>>>>The one in that region,
>
>
> One question...
>
>
>>>>or the one observed here in our vicinity?
>
>
> Another question... to which I answer,
>
>
>>>I believe BBT (specifically the cosmological principle) implies that
>>>this doesn't (shouldn't matter). The baryon-photon ratio is
>>>essentially a refection of the matter anti-matter asymmetry during
>>>baryogenesis.
>
>
> Which is an answer to neither question...
>
>
>>Right.
>
>
> So I guess we cleared that up!
Say, do you think this is funny, or are you trolling?
>>Well, the baryon-photon ratio stays essentially the same (neglecting
>>emission and absorption processes and the like), since both the number
>>density of photons and that of the baryons decreases with time with
>>1/a^3.
>
>
> Number density within a fixed volume,
Mean number density within any arbitrary volume, even the whole universe.
> but not mass-energy density
> (where the energy of photons (or any radiation) goes by 1/a^4).
Agreed.
>>>Where this argument is leading us is to whether the mass of our
>>>observable universe increases over time.
>>
>>The density decreases with 1/a^3, but the observable volume increases
>>(the horizon gets greater). I don't know the formula for the horizon by
>>rote, so I don't know if these effects balance each other.
>
>
> It all depends on equation of state etc...
Which is not accurately known.
> but as for number density, it
> doesn't really make any difference.
Well, your question directly above was about the mass of the observable
universe, not about the number density.
>>>If the number of photons
>>>*within* our observable universe increases, then does the number of
>>>baryons also increase.
>>
>>Well, according to my argument directly above, the number of photons and
>>the number of baryons should behave in the same way.
>
>
> Not so much an argument, as an assumption I believe...
This argument is a direct consequence of the Friedmann-Lemaitre
equations. Or, even more direct, a consequence of the conservation
of photon number (neglecting absorption and the like).
>>>Or are you implying that the baryon-photon
>>>ratio changes depending on where or when you look at the universe?
>>
>>In general, no.
>>
>>But obviously it *was* different before the recombination.
>>
>>
>>>Here is a handy formula to calculate the baryon-photon ratio:
>>
>>Where does it come from?
>
>
> So you admit I know something you don't!
I readily admit to not knowing every single formula used somewhere
in cosmology by rote, yes.
> It's not too difficult to derive... can you do it before looking it up?
One probably could derive it by simply using the definitions of
the Omega's. Nevertheless, I still would like to know where you got
it from.
>>>Nb/Ny=(Omega-b*Ey)/(Omega-y*Eb)
>>>
>>>Where: Omega-b is Omega Baryon,
>>
>>Minor quibble: the minus sign is confusing. Better write Omega_b.
>
>
> Noted
>
>
>>>Ey is the energy of a CMB photon = 2.7kT,
>>
>>I assume that k is Boltzmann's constant?
>
>
> Correct (this is an approximation, but a pretty good one)
Probably using Wien's law for the wavelength of maximum emission
of a black body?
>>>where T=2.725,
>>
>>Kelvin.
>
>
> Obviously?
Yes, but nevertheless one should write it.
>>>Omega-y is the ratio of CMB radiation density to the
>>>critical density and Eb=Mb*c^2, where Mb is the mass of a baryon.
>>
>>I agree with your formula.
>
>
> Ok, moving on...
>
>
>>Now you only have to consider that
>>the energy of a photon changes with 1/a,
>
>
> Correct.
>
>
>>Omega_b changes with 1/a^3
>
>
> Wrong.
Oh, sorry, you are right - it is rho_b, not Omega_b, which changes
with 1/a^3. But since we can rewrite your equation above with the rho's
instead of the Omega's, that does not change my argument.
> The typical number often quoted is 0.044. If your statement was correct,
> then at a redshift of 2 (a=1/3) omega_b would be 1.188!
Right.
> Going with the typical Lambda CDM model, omega_b would never be
> more than about 0.16 (the rest CDM and no Lambda).
I wonder how you arrived at this number?
> This is a change
> between now are recombination (a=1/1090) of 6.
>
> Due to this relatively (to a) small change, you can think of omega_b as a
> constant without losing to much meaning here.
I disagree. A change by a factor of 6 is not the same as staying constant.
>>Omega_y with 1/a^4
>
>
> Wrong.
Again, you are right - rho_y, the energy density of radiation, goes with
1/a^4, not Omega_y. But see above - that does not change my
argument.
[snip]
>>and Eb stays constant
>
>
> Correct.
>
>
>>in order to see that Nb/Ny stays constant.
>>
>>
>>>You should be able to see the relationship between the Hubble
>>>parameter and the temperature of the universe in this equation.
>>
>>A rather indirect relation, since the Hubble parameter does not
>>appear directly in the equation. Only in the Omega's - and the
>>dependence of the Omega's on H cancels out!
>
>
> Wrong.
No, right. The dependence of the Omega's on H indeed cancels out.
Omega_b = rho_b / rho_crit
Omega_y = rho_y / rho_crit
Hence in the ratio, rho_crit, the only quantity which depends on
H, cancels out. rho_b and rho_y depend on a, not on H (and please
spare me a quibble that a depends on H and that therefore the rho's also
depend on H!)
> You can rewrite this equation as:
>
> nb/ny=(omega_b.H2/T3).(81.k/80.pi.G.a.Mb)
How did you arrive at this equation? (please no smug answer
like "find it out yourself")
> Where I've used dots to denote multiplication and broken it into two pieces
> (in brackets). The left bracket contains the variables and the right bracket
> contains the constants.
>
> The constants are k as Boltzmann's constant, pi as pi, G as Newtonian
> gravitaion constant, a as radiation constant (not scale parameter) and Mb as
> mass of baryon.
>
> The variables show a relationship between H^2 and T^3, assuming you
> keep omega_b constant (since H^2 and T^3 overwhelm any change).
Even if the changes in H and T are much greater than the change in Omega_b,
I don't think it is a good idea to ignore that change simply.
> Another cool thing about writing it this way is that you can indirectly plug
> in the parameter omega_b.h^2 (after converting h which is H in km/s/Mpsc
> divided by 100).
>
> Give it a try with the WMAP value of omega_b.h^2 and compare it to
> their baryon-photon ratio... it works like a treat!
Nice.
>>>So we
>>>are basically trying yo establish how the temperature of the universe
>>>varies with time,
>>
>>Err, I already told you that calling the temperature of the CMB the
>>"temperature of the universe" makes little sense.
>
>
> I think it makes a lot of sense...
Why? The universe as a whole is not in thermal equilibrium and
hence *has* no defined temperature. Only the CMBR, which is only a
*part* of the universe, is in thermal equilibrium.
> it depends how you look at it guess. If the
> universe was "hot" in the past and then "cools" doesn't it still have a
> temperature?
Peebles obviously talked here rather colloquially about the *mean*
temperature.
> Can't you think of temperature as the energy divided by the
> entropy of the CMB photons which make up 410 per cm^3 here and now?
No. Again, that would be the temperature of the CMBR, not the
temperature of the universe.
[snip]
>>>[Hint: ratio is constant for a dust/matter universe, where w=0]
>>
>>Hint: the ratio is constant for *all* models following the
>>Friedmann-Lemaitre equations.
>>
>>Another hint: w=0 implies that no radiation at all is present.
>>
>>And yet another hint: w does in general not stay constant with time.
>
>
> Wrong.
No, right. Why on earth do you think otherwise?
w is the ratio of pressure and energy density. Since the pressure is
contributed by two sources, radiation and dark energy, and the energy
density is contributed by three sources, radiation, dark energy and
matter, and all these contributions change with time, is is quite
obvious that w can't stay constant!
> Equation of state where w=0 is the only *apparent* situation where
> the baryon-photon ratio stays constant. Please refer to above equation
> is there is any confusion here.
An equation for which you did not explain where it came from.
[snip]
>>>>>>>There is an assumption that the universe is the same age all the
>>>>>>>way across, as if you could step" outside and see the thing as
>>>>>>>if it exists in an external absolute time dimension.
>>>>>>
>>>>>>No, stepping outside is not needed for that. Only co-moving.
>>>>>
>>>>>I'm not sure I understand what you mean,
>>>>
>>>>"co-moving with the cosmological expansion" means "having
>>>>non-changing coordinates" (the coordinates of the RW metric!).
>>
>>Did you get that?
Did you?
[snip]
>>>>>So even though a distant galaxy "recedes" from us, it remains in
>>>>>the same inertial frame (no SR time dilation). This would imply
>>>>>you could connect a rigid rod (let say 100 mega parsecs long)
>>>>>between one galaxy and another. If the rigid rod does not expand
>>>>>with the universe, then if one galaxy is kept fixed at one end
>>>>>of the rod, then the other will be moving at around 7,200 km/s
>>>>>relative to the rod.
>>>>
>>>>Yes, indeed.
>>>
>>>Hold on, this was a trick question.
>>
>>As expected.
>>
>>
>>>Let's try it again with the two co-moving galaxies above:
>>>
>>>If they are co-moving, then they are in the same inertial frame.
>>
>>>However, there is nothing from stopping me from constructing a rigid
>>>rod 3.3Mpc long and move it such that one end is stationary with
>>>respect to one co-moving galaxy. Meanwhile, I can sit on the other end
>>>of the rod and observe the other co-moving galaxy moving past me at
>>>over 237 km/s.
>>
>>>So if we assume the rigid rod is rigid and doesn't change over time,
>>>then I can use it to measure the velocity between two things in the
>>>same inertial frame. Which doesn't make much sense.
>>
>>Well, did you consider that the frame maybe is not inertial?
>
>
> "maybe"? Was that a retorical question? Is it inertial, or isn't it?
Well, the universe is expanding. So one could argue that there
is a constant acceleration. An accelerating frame is not inertial.
> Would you agree or disagree with the following paragraph from page
> 140 of, "The Runaway Universe: The Race to Find the Future of the
> Cosmos", by Donald Goldsmith? (remember this guy is a graduate from
> Harvard, PhD from UC Berkley in Astronomy, teaches this stuff for a
> living, has written over a dozen (award winning) books on the subject.
Is this a book written for laymen? The title seems to suggest that. If
yes, I would not rely on all he says there - in popular science books,
even highly acclaimed scientists often write things which are not
strictly correct, in order to dumb down the stuff for the general public.
> "When astronomers observe a supernova receding from us at 60 percent
> the speed of light, for example, they expect to find that the
> supernova's entire light curve, from the rise to the peak and on
> through slow decline, shows a history that unfolds at only 80 percent
> of the rate that they observe for a nearby supernova with identical
> qualities. As discussed in Chapter 4, each supernova's redshift
> reveals its recession velocity. A redshift of 2, for example,
> corresponds to a recession velocity equal to 60 percent of the speed
> of light. For such a supernova, astronomers expect to observe a light
> curve that embodies the slowing down of time, with the result that the
> supernova's light curve passes through its different stages only 80
> percent as rapidly as the light curve for a nearby supernova with
> identical spectral properties. First analyzed in detail by Gerson
> Goldhaber, a member of the Supernova Cosmology Project, this observed
> slowing down of time in distant, rapidly receding supernova provides
> one of the finest proofs that Einstein's special theory of relativity
> enjoys cosmic validity".
Well, this is a nice example of what I said above. The time dilation
seen in cosmology has little to do with Einstein's Doppler shift formula
from SR! See e.g. here:
<http://www.astronomycafe.net/cosm/expan.html>
and the last paragraph here:
<http://www.astro.ucla.edu/~wright/doppler.htm>
Probably Goldsmith knows that quite well, but considering that this
addresses lay people, chose to not confuse them by bringing up yet
another Doppler shift phenomenon and simply said that this agrees with SR.
>>>>>The implication here is that *everything* expands with the universe.
>>
>>>>Huh? Why on earth do you think that that is implied? That is simply
>>>>wrong. Locally, there is no expansion at all. You might try reading up
>>>>on how one incorporates local Schwarzschild metrics into the RW
>>>>metric.
>>>
>>>So assuming the redshift is really there, and it represents an
>>>"expansion" of the universe, then *everything* expands
>>
>>Non sequitur!!!
>
>
> Ok, I'll let *you* draw the conlusion...
>
> If the "rigid rid" does not expand with the expansion of space, then I can
> use it to measure the "expansion velocity" between one region of the
> universe and another (one co-moving object, relative to another co-moving
> object). I could fix one end to remain stationary relative to one co-moving
> object and use the other end of the rod to "measure" the velocity of the
> other object. This could be done by trasnsmitting a signal between the two
> and reflecting it back.
Well, even if such a measurement were not possible, this would only
prove that the existence of a rigid rod *of a length on which the
cosmological expansion becomes relevant* is not possible, that such
a rod has to expand. It does *not* show that also things with *smaller*
lengths have to expand!
> This "clock" would must measure a SR time dilation
> in the way Goldsmith describes...
Which he describes wrongly. The time dilation in cosmology is *not* the
SR time dilation.
> and as you can probably tell by now, I don't agree here.
Well, I also don't agree, but for different reasons.
> Hence, my contention is that this is not what happens in reality, so I conclude
> that the rod must also "expand".
If it is long enough (and the forces holding it together are not strong
enough), then it will expand. But that does *not* imply that
*everything*, even *smaller* things, *also* expand.
> (I could conclude that the redshift is caused
> by some tired light mechanism, but I think we would both agree that that is
> plain stupid?)
No, not plain stupid. Just not consistent with the evidence.
> So what is your conclusion... is Goldsmith's really correct?
No, he isn't.
Bye,
Bjoern
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