# An infinitely old universe

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## Main Question or Discussion Point

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.

## Answers and Replies

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Nereid
Staff Emeritus
Gold Member
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
Gold Member
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
Gold Member
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.
You will see exactly what we see now. We live in a universe that is infinite, both temporally and spacially.

SpaceTiger
Staff Emeritus
Gold Member
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.....
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
Gold Member
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.
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
Staff Emeritus
Gold Member
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.
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
Homework Helper
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!
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
Gold Member
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.
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
Staff Emeritus
Gold Member
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.
That wasn't my criticism of logarithmic time, that was my refutation of your statement:

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.
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
Gold Member
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.
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 [gµν] of conformally equivalent Lorentz metrics gµν 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.

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

Garth
Gold Member
Chronos said:
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

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

Garth
Gold Member
Chronos said:
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 : PT ~ 10-43 secs.
Size of universe ~ 3. 1017 x 3. 1010 cms = 1028 cms. : PL ~ 10-33 cms.
Mass of universe ~ 1022 x 2.1033 gms. ~ 1055 gms : PM ~ 10-5 gms.

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SpaceTiger
Staff Emeritus
Gold Member
Garth said:
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:

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.
would not be true in general.

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pervect
Staff Emeritus
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.

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SpaceTiger
Staff Emeritus
Gold Member
pervect said:
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.

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.

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pervect
Staff Emeritus
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.
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
Staff Emeritus
Orion1 said:

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

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

Gold Member
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.

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Garth
Gold Member
SpaceTiger said:
Garth said:
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.
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, in the more general case your conclusion
SpaceTiger said:
$$t_{CMB}\propto \int_0^t\frac{d\tau}{\tau^{2/3}}\propto t^{1/3}$$
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:
SpaceTiger said:
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,
$$t'_{CMB} = a_0\nu_0 \int_0^{t'}\frac{d\tau}{a}$$
SpaceTiger said:
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.

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