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Assuming the universe is infinitely old, what would, or would you not expect to see? I will start with 'black' galaxies composed of burnt out stars.
You will see exactly what we see now. We live in a universe that is infinite, both temporally and spacially.Chronos said:Assuming the universe is infinitely old, what would, or would you not expect to see? I will start with 'black' galaxies composed of burnt out stars.
Garth said:For example, the standard BB becomes infinitely old if we measure time on a logarithmic scale. Such a scale is physically presented by the frequency (inverse) of the CMB photons...
That depends on what physical process you are using to measure time with.SpaceTiger said:There's nothing physically meaningful about that...If we want to define an absolute age for the universe, it only makes sense to talk in linear units...logarithmic units are better for relative ages.
Garth said:If your clock 'ticking' is the inverse frequency of a CMB photon then there have been an infinite number of ticks since the BB.
Nereid said:You couldn't, wouldn't, {more} see anything!
Either gravity wins (and everything ends up in a humongous SMBH), or it doesn't (and you get an infinitely thin, 0K gas).
IIRC, there was an interesting article in Sky&Telescope some years ago on a similar topic; the authors assumed BH evaporation and protons decay, and ended up with a universe comprised of positronium, with the mean distance between the (bound) electron and positron of several billion ly!
Exactly the same criticism can be used against an atomic clock; how do you define the first nano-second, or whatever, when there were no atoms around to measure it? You have to extrapolate back from the epoch when they do exist.SpaceTiger said:The CMB, as we know it, only goes back to z ~ 1100, so this isn't really true. Prior to that, the photons in the universe were all "young", in the sense that they were recently emitted/scattered by a particle...so you can't use them as a clock, in the usual sense.
Garth said:Exactly the same criticism can be used against an atomic clock; how do you define the first nano-second, or whatever, when there were no atoms around to measure it? You have to extrapolate back from the epoch when they do exist.
Garth said:If your clock 'ticking' is the inverse frequency of a CMB photon then there have been an infinite number of ticks since the BB.
ST - the question is: "How do we measure anything?"SpaceTiger said:When I say that our understanding of time is "intimately connected" to the atomic clock, I don't mean that it's the atoms themselves that are important. Rather, I mean that the "clock" measures the same time that governs aging, brain functions, and other things we associate with the passage of time. A hypothetical clock based on the frequency of the CMB radiation would not be measuring time in this same sense and would therefore be referring to a different concept from what was intended in the thread.
Chronos why on Earth do you say that? Defining how observations are made is fundamental to experimental physics and even more important in astrophysics, where by their very nature such observations are (extremely) remote. It is not a position of 'agnosticism' - we can't know anything - but one of methodology and definition.Chronos said:I fundamentally object to any 'How do we measure anything?' proposition. That begs for an absolute reference frame, in my mind.
That is what I am saying.Chronos said:Are not 'measurements' a relational concept? How do you set the bar before there was a bar?
Garth said:The question is: "Are these conformal 'frames of measurement' physically significant?
I have simply pointed out that if one used the frequency (inverse) of a cosmological photon2 to be the unit of time measurement then the finite aged universe becomes infinite in this conformal frame, because the 'number of beats' of the photon asymptotically approaches infinity as it is infinitely blue shifted when the BB is approached under time reversal.
Garth said:If your clock 'ticking' is the inverse frequency of a CMB photon then there have been an infinite number of ticks since the BB.
pervect said:Diverging cosmological time is associated with the broad class of "coasting" models where a(t) [itex]\propto[/itex] however, as the intergal becomes
[tex]\int_0^t \frac{d\tau}{\tau} \propto ln(\tau)}[/tex]
These models are not currently standard, but they have an appealing simplicity. Unfortunately they do appear to require revising Einstein's field equations. Which is where Garth's SCC theory enters.
SpaceTiger said:Yes, a model like that would have the scale factor decreasing linearly as one approached the Big Bang. I was just making it clear that his statement about the "CMB" time frame was not generically true for the cosmological models being considered.
Orion1 said:
My understanding is that the absolute 'Universal Clock' on the universe is the 'Hubble Time' which is derived from the 'Hubble Constant':
pervect said:I'm not quite sure exactly how to model a(t) during the inflationary era, but my instinct is that it is the behavior of a(t) pre-inflation that's important to the finiteness of the intergal - i.e. the issue is how a(t) approaches zero. This would make the contribution of inflation to the intergal huge, but not necessarily infinite. I could be wrong, however.
SpaceTiger said:In fact, the conformal age of the universe won't diverge unless the scale factor is decreasing linearly with time (or faster) as we approach the big bang in reverse. Since we don't know much of anything about the universe pre-inflation, the age of the universe in these coordinates would seem to be highly uncertain.
We use rigid rulers (constructed, say, of steel) and regular clocks (that count atomic processes) to define a "physically significant" frame of measurement. However, we cannot transport such rulers and clocks out and back to the far end of the universe to make cosmological measurements.SpaceTiger said:That is indeed the question and, to my knowledge, there is absolutely no evidence that they are. Until such evidence arises, there's no reason to view this definition of "time" as anything more than a mathematical convenience.Garth said:The question is: "Are these conformal 'frames of measurement' physically significant?
I was indeed thinking of the linearly expanding universe, in the more general case your conclusionGarth said:If your clock 'ticking' is the inverse frequency of a CMB photon then there have been an infinite number of ticks since the BB.
is obviously not correct as that photon-clock would count a smaller number of 'ticks' than an atomic clock, even though the photons are blue shifted under time reversal!SpaceTiger said:[tex]t_{CMB}\propto \int_0^t\frac{d\tau}{\tau^{2/3}}\propto t^{1/3}[/tex]
concur, this would give the 'atomic' age useful here for comparison - and we haveSpaceTiger said:If the frequency of the CMB photons, [itex]\nu[/itex], were given, then we can calculate the number of times our "clock" would have "ticked" since the beginning. Our new definition of time could then be described in terms of the old one:
[tex]t_{CMB}\equiv N_{tick} = \int_0^t\nu d\tau[/tex]
where the proper time, [itex]\tau[/itex], just becomes a parameter for the cosmological model that is connected to the new definition of time by the frequency of a hypothetical CMB photon. If the frequency were constant, this new definition of time would be measuring the same thing as the old one (that is, it would just be proportional to it),
Concurbut in standard cosmology, the frequency redshifts:
[tex]\nu = \nu_0 (1+z) = \nu_0\frac{a_0}{a}[/tex]
Here, a is the scale factor and the variables with "0" subscripts are just their current values.
It may indeed be, but here we have to keep in the all the factors to maintain correct dimensionality,Plugging this into the earlier equation, we get:
[tex]t_{CMB}\propto \int_0^t\frac{d\tau}{a}[/tex]
This is, not surprisingly, just the definition of conformal time commonly used in cosmology.
Agreed for the general case, which in the E-deS, flat, matter-dominated universe becomes, when we remember thatSpaceTiger said:However, the conformal time is not generically divergent in standard cosmological models.
Garth said:I was indeed thinking of the linearly expanding universe, in the more general case your conclusion:
[tex]t_{CMB} \propto \int_0^t\frac{d\tau}{\tau^{2/3}}\propto t^{1/3}[/tex]
is obviously not correct as that photon-clock would count a smaller number of 'ticks' than an atomic clock, even though the photons are blue shifted under time reversal!
Garth said:[tex]t'_{CMB} = a_0\nu_0\int_0^{t'}\frac{d\tau}{a_0(\frac{\tau}{t_0})^{2/3}}=3\nu_0t_0(\frac{t'}{t_0})^{1/3}[/tex]
Garth said:If
[tex]a(t) = a_0(\frac{t}{t_0})^n[/tex] then
[tex]t_{CMB}\propto \int_0^t\frac{d\tau}{\tau^{2/3}}\propto t^{1/3}[/tex]
is the relationship between
tCMB and tatomic as tatomic varies with n = 2/3.
The important question is does this time parameter "t" have physical significance; that is, does it relate to some clock usable in physical experiments?SpaceTiger said:That's incorrect. That is the relation between the CMB "time" and the time parameter, t. I never went out of my way to relate the CMB time to the atomic time because it was unnecessary for testing the divergence of the various models. Can you see why this is? In fact, "t" is much more convenient for testing the divergence because it is the variable over which the integral is evaluated.
Garth said:The important question is does this time parameter "t" have physical significance; that is, does it relate to some clock usable in physical experiments?
Garth said:If your clock 'ticking' is the inverse frequency of a CMB photon then there have been an infinite number of ticks since the BB.
Have we not agreed that in the time coordinate t system the 'tick' of an atomic clock, when the frequency [tex]\nu[/tex] is constant is given by,
[tex]t_{atom}\equiv N_{tick(clock)} = \int_0^t\nu d\tau = \nu_0t_0 [/tex]
so that this coordinate time "t" is atomic time?
ST thank you - typo noted.SpaceTiger said:As suggested by your equation, the upper limit on that integral should have been [itex]t_0[/itex], not t.
Garth said:But I found your reply inconsistent - for if "t", coordinate time, is that recorded by atomic clocks then surely it does have physical significance?
Just to defend my introduction of the idea here, rather than deliberately "peddlng" SCC, I was responding to the subject of the thread "An Infinitely old Universe", which itself is not mainstream.SpaceTiger said:No Garth, it doesn't. The physically meaningful result, as I said in the original post and have repeated several times in this thread, is that the conformal time to the big bang converges for many reasonably cosmological models. This was in response to your claim:Given that no mainstream cosmologist actually believes the linearly expanding model, this claim is deceptive, to say the least.Garth said:If your clock 'ticking' is the inverse frequency of a CMB photon then there have been an infinite number of ticks since the BB.
.......
I was indeed thinking of the linearly expanding universe
Garth said:Just to defend my introduction of the idea here, rather than deliberately "peddlng" SCC, I was responding to the subject of the thread "An Infinitely old Universe", which itself is not mainstream.
Perhaps there should have been no posts in this thread at all?
I must have got the wrong impression, when the OP saidSpaceTiger said:There's nothing in mainstream theory that says the universe can't evolve to infinite age.
I assumed he meant the age into the past was infinite!Chronos said:Assuming the universe is infinitely old, what would, or would you not expect to see? I will start with 'black' galaxies composed of burnt out stars.
Yes, but I should have made that clearer earlier - thank you for correcting me.Furthermore, I wasn't criticizing your reference to linearly coasting or SCC,
We wait and see!I was criticizing your tacit assumption that the universe was governed by it.