Is the Universe Infinitely Old and What Would We Expect to See?

[Chronos]

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.

 

[Nereid]

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!

 

[Garth]

As we are talking about infinity then it really does depend on how we measure time.

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...

Garth

 

[turbo]

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.

 

[SpaceTiger]

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...

There's nothing physically meaningful about that. I can define a different logarithmic scale, setting t=0 to be five minutes ago, and say that an infinite amount of logarithmic time has passed in the last five minutes. This is basically just a variant on Zeno's paradox. 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]

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.

That depends on what physical process you are using to measure time with.

If your clock 'ticking' is an vibrating atom then there have been a finite number of ticks since the BB - about 14 Gyrs of them.

If your clock 'ticking' is the inverse frequency of a CMB photon then there have been an infinite number of ticks since the BB.

Garth

 

[SpaceTiger]

If your clock 'ticking' is the inverse frequency of a CMB photon then there have been an infinite number of ticks since the BB.

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. You're not wrong that, if we defined time logarithmically from the moment of the big bang, there is an infinite age to the universe. What I'm saying is that this definition of time has no correspondence to what we normally understand to be the "age" of something. This understanding is intimately connected to your first example, the ticking of the atomic clock.

 

[Alkatran]

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!

What if it was a steady-state universe? (The sky would be filled with blinding light if I remember correctly..)

 

[-Job-]

Supposing gravity wins and everything gets back together, are we assuming space gets compressed as well? Will gravity pull back space itself? What are the properties of this compressed space? Is it occupiable by matter?
If space can become compressed under the effect of gravity then are we able to identify "compressed space" around massive objects?
Or is it that even though matter turns around and gets back together, space does not recede but stays where it is.

 

[Garth]

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.

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

 

[SpaceTiger]

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.

That wasn't my criticism of logarithmic time, that was my refutation of your statement:

If your clock 'ticking' is the inverse frequency of a CMB photon then there have been an infinite number of ticks since the BB.

Presumably, you were trying to justify your choice of logarithmic scale with an actual physical process, but I was pointing out that your justification only worked back to z~1100. Aside from that, it's only one physical process and I don't see how it's justified to define time in that way.

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.

 

[Garth]

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.

ST - the question is: "How do we measure anything?"

We have to adopt a convention - define a method of measurement in which a particular unit is constant when we conceptually transport it across space and time to make a comparison. In order to identify such a convention we need a conservation principle - something that does not change under translations of boost or position across the changing gravitational and therefore curvature fields of the universe.

In GR that conservation principle is that of energy-momentum encapsulated in Einstein's Equivalence Principle. The unit that does not change is the 'rest' mass of an atom. Therefore we can use its size - a steel rule - to measure space and its 'vibrations' to measure time - an atomic clock.

However Weyl’s hypothesis¹ was that a true infinitesimal geometry should recognize only a principle for transferring the magnitude of a vector to an infinitesimally close point, and not throughout the space-time manifold as in GR. This led to the concept that the space-time manifold M is equipped with a class [g_µν] of conformally equivalent Lorentz metrics g_µν and not a unique metric as in GR.

This hypothesis is the basis of conformal gravity theories.

Conformal transformations preserve angles - and hence the WMAP data set is consistent with conformally flat geometries as well as just flat ones - but they do not preserve particle masses. Hence the opportunity exists to define other ways of measuring space and time.

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.

Is this conformal frame physically significant and what is the conservation principle it depends on? Well not only is the measurement of photons a physical activity - it is the only activity at present we are engaged in when observing the distant universe! (Cosmic rays excepted) The conservation principle is that of the conservation of energy rather than energy-momentum. Yes you do need a special - even preferred - frame of reference to define that energy, it is the Machian CoM frame indentified to be the isotropic frame of the CMB.

Garth

Notes:
¹ Weyl, H.: 1918, ‘Gravitation und Electriticitat’ Sitzungsberichte der Preussichen Akad. d. Wissenschaften,
English translation, 1923, in: The Principle of Relativity, Dover Publications.
²A photon selected (at the peak intensity) from the CMB radiation bath, either before or after the universe became transparent at the Surface of Last Scattering.

 

[Chronos]

I fundamentally object to any 'How do we measure anything?' proposition. That begs for an absolute reference frame, in my mind.

 

[Garth]

I fundamentally object to any 'How do we measure anything?' proposition. That begs for an absolute reference frame, in my mind.

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.

We define a standard unit and then compare it with the object under observation. When that object is at the far side of the universe the comparison itself may be problematic!

Garth

 

[Chronos]

Are not 'measurements' a relational concept? How do you set the bar before there was a bar?

 

[Garth]

Are not 'measurements' a relational concept? How do you set the bar before there was a bar?

That is what I am saying.

Henry VIII defined a 'foot' to be the length of his own foot - or so folklore has it - we do the same with the metre, kilogramme and second, however Planck units do provide what appears to be an 'absolute' set of measurements. They also link together the cosmological and quantum worlds.

The universe is therefore ~ 10⁶⁰ Planck units age, size and mass! (OOM of course) (Using atomic clocks, steel rulers and atomic masses to make the measurement)

Garth

NB - Age of the universe ~ 3. 10¹⁷ seconds : P_T ~ 10^-43 secs.
Size of universe ~ 3. 10¹⁷ x 3. 10¹⁰ cms = 10²⁸ cms. : P_L ~ 10^-33 cms.
Mass of universe ~ 10²² x 2.10³³ gms. ~ 10⁵⁵ gms : P_M ~ 10^-5 gms.

 

[SpaceTiger]

The question is: "Are these conformal 'frames of measurement' physically significant?

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.

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.

Let's explore this claim in a bit more detail.

If the frequency of the CMB photons, $\nu$, 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:

$$t_{CMB}\equiv N_{tick} = \int_0^t\nu d\tau$$

where the proper time, $\tau$, 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), but in standard cosmology, the frequency redshifts:

$$\nu = \nu_0 (1+z) = \nu_0\frac{a_0}{a}$$

Here, a is the scale factor and the variables with "0" subscripts are just their current values. Plugging this into the earlier equation, we get:

$$t_{CMB}\propto \int_0^t\frac{d\tau}{a}$$

This is, not surprisingly, just the definition of conformal time commonly used in cosmology. However, the conformal time is not generically divergent in standard cosmological models. For example, take the flat, matter-dominated universe:

$$\int_0^t\frac{d\tau}{\tau^{2/3}}\propto t^{1/3}$$

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. I can't speak for any of the alternative gravity models, but this statement:

If your clock 'ticking' is the inverse frequency of a CMB photon then there have been an infinite number of ticks since the BB.

would not be true in general.

 

[pervect]

Diverging cosmological time is associated with the broad class of "coasting" models where a(t) $\propto$ t however, as the intergal becomes

$$\int_0^t \frac{d\tau}{\tau} \propto ln(\tau)}$$

which diverges.

These models are not currently standard, but they have an appealing simplicity and from what I've read, fit observational data very well with fewer "free" parameters than the current standard model with a cosmological constant. Unfortunately they do appear to require revising Einstein's field equations. Which is where Garth's SCC theory enters.

 

[SpaceTiger]

Diverging cosmological time is associated with the broad class of "coasting" models where a(t) $\propto$ however, as the intergal becomes

$$\int_0^t \frac{d\tau}{\tau} \propto ln(\tau)}$$

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.

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]

My understanding is that the absolute 'Universal Clock' on the universe is the 'Hubble Time' which is derived from the 'Hubble Constant':

$$T_u = \frac{1}{H_{\circ}}$$

Therefore, a Universe that that is 'infinitely old' would also be 'infinitely vast' and also 'infinitesimaly cold' (near absolute zero), a Cryoverse.

The 'Hubble Constant' in an infinitely old Cryoverse would be nearly infinitesimal and therefore would not be observable.

An infinitely old 'Cryoverse' would be a vast cold expanse that is not observable, not even to itself.

 

[pervect]

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.

That's a very good point. Standard cosmological models use Einstien's field equations to model the scale factor a(t) during the early history of the universe, and predict (with the possible exception of inflation) both a finte elapsed time and a finite number of vibrations of the microwave bacground, at least up to the inflationary era. It's only freely coasting cosmologies that have the features that Garth is talking about AFAIK.

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.

 

[pervect]

My understanding is that the absolute 'Universal Clock' on the universe is the 'Hubble Time' which is derived from the 'Hubble Constant':

And you believe this because?

I.e. do you have a reference for this "absolute Universal Clock" statement?.

 

[SpaceTiger]

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.

Yeah, that's pretty much what I was trying to sum up (along with what you said in your previous post) in this paragraph:

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.

I suppose that was a rather terse way of saying it, but the basic idea is that I agree with you.

 

[Chronos]

So the long and the short of it sums up like this, in my mind: there is no 'absolute clock'. These kinds of arguments are unproductive and distracting. While it's great fun to force the envelope past the the first Planck tick of the clock, it's all guess work.

 

[Garth]

The question is: "Are these conformal 'frames of measurement' physically significant?

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.

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.
All we can do is deduce a measurement made by observing photons (and eventually gravitational waves) from these regions. Therefore a frame of measurement based on the photons/gravitons used to make the observation may indeed be an alternative and physically significant frame of measurement.

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, in the more general case your conclusion

$$t_{CMB}\propto \int_0^t\frac{d\tau}{\tau^{2/3}}\propto t^{1/3}$$

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!
The corrected general case is as follows:

If the frequency of the CMB photons, $\nu$, 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:
$$t_{CMB}\equiv N_{tick} = \int_0^t\nu d\tau$$
where the proper time, $\tau$, 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),

concur, this would give the 'atomic' age useful here for comparison - and we have
$$t_{atom}\equiv N_{tick(clock)} = \int_0^t\nu d\tau = \nu_0t_0$$

but in standard cosmology, the frequency redshifts:
$$\nu = \nu_0 (1+z) = \nu_0\frac{a_0}{a}$$
Here, a is the scale factor and the variables with "0" subscripts are just their current values.

Concur

Plugging this into the earlier equation, we get:
$$t_{CMB}\propto \int_0^t\frac{d\tau}{a}$$
This is, not surprisingly, just the definition of conformal time commonly used in cosmology.

It may indeed be, but here we have to keep in the all the factors to maintain correct dimensionality,
$$t'_{CMB} = a_0\nu_0 \int_0^{t'}\frac{d\tau}{a}$$

However, the conformal time is not generically divergent in standard cosmological models.

Agreed for the general case, which in the E-deS, flat, matter-dominated universe becomes, when we remember that

$$a=a(t)=a_0(\frac{t}{t_0})^{2/3}$$

so we have,

$$t'_{CMB} = a_0\nu_0\int_0^{t'}\frac{d\tau}{a_0(\frac{\tau}{t_0})^{2/3}}=3\nu_0t_0(\frac{t'}{t_0})^{1/3}$$

Now setting $$t'=t_0$$ to obtain the present age of the universe, we have

$$t_{CMB} = 3\nu_0t_0=3t_{atom}$$

i.e. 3 x the present 'atomic' age derived above.

In general if $$a(t) = a_0(\frac{t}{t_0})^n$$

then $$t_{CMB} = \frac{1}{1-n}\nu_0t_0=\frac{1}{1-n}t_{atom}$$

which diverges as n -> 1 for the linearly expanding model.

Garth

As a footnote, both the two conformal frames of SCC are physically meaningful as they measure the universe using atoms and photons (carefully defined) respectively as the units of physical measurement. In the Einstein frame the universe is finite expanding linearly from a BB and in the Jordan frame it is static and eternal.

 

[SpaceTiger]

I was indeed thinking of the linearly expanding universe, in the more general case your conclusion:

$$t_{CMB} \propto \int_0^t\frac{d\tau}{\tau^{2/3}}\propto t^{1/3}$$

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!

There is nothing wrong with that equation...in fact, it appears in your calculation:

$$t'_{CMB} = a_0\nu_0\int_0^{t'}\frac{d\tau}{a_0(\frac{\tau}{t_0})^{2/3}}=3\nu_0t_0(\frac{t'}{t_0})^{1/3}$$

All you've done is substitute in the appropriate proportionality constants and redefined the variables. Although I see nothing wrong with what you've done, you'll see that your conclusion is exactly the same -- it will only diverge if the scale factor has a linear (or steeper) dependence -- yet you've done more work!

 

[Garth]

If
$$a(t) = a_0(\frac{t}{t_0})^n$$ then

$$t_{CMB}\propto \int_0^t\frac{d\tau}{\tau^{2/3}}\propto t^{1/3}$$

is the relationship between
t_CMB and t_atomic as t_atomic varies with n = 2/3.

Using the present 'tick' of both an atomic and photon clock to be 1 second, i.e. $$\nu = 1 sec^{-1}$$ and if we take the present age to be 10¹⁸ secs. i.e. 10¹⁸ 'atomic ticks'.

Your formula would suggest the conformal time, i.e. the number of 'vibrations' of the CMB photon would only be 10⁶ even though they are blue shifted under time reversal and therefore there should be more 'photon ticks' than 'atomic' ones!

We want to know the relationship at fixed t_atomic as n varies,
it is $$t_{CMB} = \frac{1}{1-n}t_{atom}$$ or in your E-deS case

$$t_{CMB} = 3t_{atom} = 3.10^{18}$$

or three times the number of 'atomic ticks' in the above case as expected.

I hope this helps.

Garth

 

[SpaceTiger]

If
$$a(t) = a_0(\frac{t}{t_0})^n$$ then
$$t_{CMB}\propto \int_0^t\frac{d\tau}{\tau^{2/3}}\propto t^{1/3}$$
is the relationship between
t_CMB and t_atomic as t_atomic varies with n = 2/3.

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.

In particular, if the integral returns some function, f(t), we need only look at:

$$f(t)|_{t=0}$$

which clearly diverges if f(t) is a power law with index $n-1<0$.

Your final expression is not incorrect, but it is also not in contradiction with mine if the variables are interpreted correctly. Considering the number of different "times" that went into this calculation, I'm not surprised that there was some confusion over definitions. Are all of the variables in my calculation clear now, or are there others about which I should be more explicit?

 

[Garth]

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.

The important question is does this time parameter "t" have physical significance; that is, does it relate to some clock usable in physical experiments?

Have we not agreed that in the time coordinate t system the 'tick' of an atomic clock, when the frequency $$\nu$$ is constant is given by,

$$t_{atom}\equiv N_{tick(clock)} = \int_0^{t_0}\nu d\tau = \nu_0t_0$$
this coordinate time "t" is atomic time?

However, other forms of coordinate time can be anything we want them to be through conformal transformations - that is why it is important to connect any particular definition of time with a physical process to ensure that it is physically significant.

When investigating the physical significance of other, possibly divergent, time scales it is important to relate and compare them with the atomic standard.
We can define two physically significant times as follows:

Sample two photons, one emitted by a caesium atom the other sampled from the CMB radiation.

The first, an "atomic" second, is defined as the duration of exactly 9.19263177x10⁹ periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

The second, a "photonic" second, is defined as the duration of exactly 1.604x10¹¹ periods of the radiation corresponding to the peak of the CMB black body spectrum.

Both systems of time measurement are physically significant and agree with each other in the present time, although they will diverge from each other at other times.

When compared to the atomic standard, the "photonic" clock in the linearly expanding model, extrapolated back to the earliest moments of the BB, diverges to (-) inifinity as atomic time t->0.

Thus in this model we can recover "an infinitely old universe" within an apparently finite (as measured by an "atomic" clock) BB paradigm.

Furthermore, if ephemeris time is that measured in the "photonic" system, as it is in SCC, then the Pioneer spacecraft will appear to have an anomalous sunwards acceleration of cH or 6.69×10⁻⁸ cm.sec^-2; such an acceleration a_P = (8.74±1.33)×10⁻⁸ cm.sec^-2 is actually observed. (Allowing for drag and radiation non-inertial forces and uncertainty in H.)

Garth

 

[SpaceTiger]

The important question is does this time parameter "t" have physical significance; that is, does it relate to some clock usable in physical experiments?

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:

If your clock 'ticking' is the inverse frequency of a CMB photon then there have been an infinite number of ticks since the BB.

Given that no mainstream cosmologist actually believes the linearly expanding model, this claim is deceptive, to say the least.

Have we not agreed that in the time coordinate t system the 'tick' of an atomic clock, when the frequency $$\nu$$ is constant is given by,
$$t_{atom}\equiv N_{tick(clock)} = \int_0^t\nu d\tau = \nu_0t_0$$
so that this coordinate time "t" is atomic time?

On this point, you are correct. As suggested by your equation, the upper limit on that integral should have been $t_0$, not t.

 

[Garth]

As suggested by your equation, the upper limit on that integral should have been $t_0$, not t.

ST thank you - typo noted.

But I found your reply inconsistent - for if we have agreed that "t", coordinate time, is that recorded by atomic clocks then surely it does have physical significance?

Garth

 

[SpaceTiger]

But I found your reply inconsistent - for if "t", coordinate time, is that recorded by atomic clocks then surely it does have physical significance?

The parameter, "t", only appears in proportionalities, implying that it could be given an arbitrary normalization. A given one of these normalizations could be said to be physically significant, but the parameter itself only reflects a scaling.

 

[Garth]

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:

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

Given that no mainstream cosmologist actually believes the linearly expanding model, this claim is deceptive, to say the least.

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?

Garth

 

[SpaceTiger]

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?

There's nothing in mainstream theory that says the universe can't evolve to infinite age. Furthermore, I wasn't criticizing your reference to linearly coasting or SCC, I was criticizing your tacit assumption that the universe was governed by it.

 

[Garth]

There's nothing in mainstream theory that says the universe can't evolve to infinite age.

I must have got the wrong impression, when the OP 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.

I assumed he meant the age into the past was infinite!

Furthermore, I wasn't criticizing your reference to linearly coasting or SCC,

Yes, but I should have made that clearer earlier - thank you for correcting me.

I was criticizing your tacit assumption that the universe was governed by it.

We wait and see!

Garth