Hartle, Gravity: An Introduction to Einstein's General Relativity 1st Edition, 2002

[Alan Grayson]

On page 21 Hartle asserts that at the BB, "the whole of the observable universe today was compressed to the smallest possible volume." He's considered authoritative on General Relativity. I wonder; why do some experts think the universe decreases in volume as we go back in time, but others, such as Penrose (according to Quentin), believe in an always infinite universe where the average distance between galaxies decreases as we back in time? AG

[Brent Meeker]

I think all cosmologist, like Hartle, recognize that the observable universe was much smaller in the past.  Which is perfectly compatible with the universe be spacially flat and infinite.

Brent

On 2/25/2025 2:40 AM, Alan Grayson wrote:

On page 21 Hartle asserts that at the BB, "the whole of the observable universe today was compressed to the smallest possible volume." He's considered authoritative on General Relativity. I wonder; why do some experts think the universe decreases in volume as we go back in time, but others, such as Penrose (according to Quentin), believe in an always infinite universe where the average distance between galaxies decreases as we back in time? AG

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[Alan Grayson]

On Tuesday, February 25, 2025 at 12:46:46 PM UTC-7 Brent Meeker wrote:

I think all cosmologist, like Hartle, recognize that the observable universe was much smaller in the past.  Which is perfectly compatible with the universe be spacially flat and infinite.

Brent

I fully anticipated that response. But why would the observable universe behave radically different from the entire principle, particularly in light of the Cosmological Principle? AG

[Brent Meeker]

On 2/25/2025 3:48 PM, Alan Grayson wrote:

On Tuesday, February 25, 2025 at 12:46:46 PM UTC-7 Brent Meeker wrote:

I think all cosmologist, like Hartle, recognize that the observable universe was much smaller in the past.  Which is perfectly compatible with the universe be spacially flat and infinite.

Brent

I fully anticipated that response. But why would the observable universe behave radically different from the entire principle, particularly in light of the Cosmological Principle? AG

It's not radically different.  It's different in exactly the way that finite subsets of infinite sets behave.

Brent

[Alan Grayson]

But if the observable universe contracts to zero volume, the entire universe has a singularity, which is inherently contradictory. So, the model is, to say the least, inconsistent. AG 

[Brent Meeker]

It's not contradictory or inconsistent, it's unphysical, i.e. it can't be physically realized; which just means the theory of general relativity doesn't work there.  This is not a surprise since GR is not a quantum theory and if you're concerned with a subatomic scale region you'll probably need a quantum theory.

Brent

[Alan Grayson]

My conjecture is that there's a fifth force, repulsive in Nature, that prevents the mass of a high mass collapsing star to reach zero volume. AG 

[Alan Grayson]

I don't imagine a quantum theory. More important, I can't grasp the idea of the observable universe contracting to zero or near zero volume as we go backward in time, while the unobservable universe remains infinite in spatial extent. Can you grasp it? Can you explain it? AG 

[Quentin Anciaux]

As I've explained already, it's not that the volume goes to zero, but density that goes to infinity, everywhere, there is no valid notion of volume in an infinite universe. 

Quentin 

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[Alan Grayson]

On Wednesday, February 26, 2025 at 3:33:55 AM UTC-7 Quentin Anciaux wrote:

Le mer. 26 févr. 2025, 10:24, Alan Grayson <agrays...@gmail.com> a écrit :

On Wednesday, February 26, 2025 at 1:22:21 AM UTC-7 Alan Grayson wrote:

On Tuesday, February 25, 2025 at 10:07:41 PM UTC-7 Brent Meeker wrote:

On 2/25/2025 7:59 PM, Alan Grayson wrote:

      On Tuesday, February 25, 2025 at 6:40:35 PM UTC-7 Brent Meeker wrote:

On 2/25/2025 3:48 PM, Alan Grayson wrote:

On Tuesday, February 25, 2025 at 12:46:46 PM UTC-7 Brent Meeker wrote:

I think all cosmologist, like Hartle, recognize that the observable universe was much smaller in the past.  Which is perfectly compatible with the universe be spacially flat and infinite.

Brent

I fully anticipated that response. But why would the observable universe behave radically different from the entire principle, particularly in light of the Cosmological Principle? AG

It's not radically different.  It's different in exactly the way that finite subsets of infinite sets behave.

Brent

But if the observable universe contracts to zero volume, the entire universe has a singularity, which is inherently contradictory. So, the model is, to say the least, inconsistent. AG

It's not contradictory or inconsistent, it's unphysical, i.e. it can't be physically realized; which just means the theory of general relativity doesn't work there.  This is not a surprise since GR is not a quantum theory and if you're concerned with a subatomic scale region you'll probably need a quantum theory.

Brent

My conjecture is that there's a fifth force, repulsive in Nature, that prevents the mass of a high mass collapsing star to reach zero volume. AG 

I don't imagine a quantum theory. More important, I can't grasp the idea of the observable universe contracting to zero or near zero volume as we go backward in time, while the unobservable universe remains infinite in spatial extent. Can you grasp it? Can you explain it? AG 

As I've explained already, it's not that the volume goes to zero, but density that goes to infinity, everywhere, there is no valid notion of volume in an infinite universe. 

Quentin 

Density can't diverge unless volume goes to zero. FWIW, Brent thinks the observable universe shrinks to zero or near zero as we go backward in time, while the unobservable part remains infinite. AG 

[Quentin Anciaux]

AG, your statement "density can't diverge unless volume goes to zero" assumes a finite volume, which doesn’t apply in an infinite universe. In an infinite universe, density can increase indefinitely everywhere without requiring a total volume to shrink.

Brent is correct that the observable universe (the region we can see) shrinks as we go back in time, but that doesn’t mean the entire universe (including the unobservable part) does the same. The observable universe is just a region within an infinite space, and as we go back in time, the light cone that defines what we can observe gets smaller.

If the entire universe is infinite, its total volume remains infinite at all times—but its density can still increase without bound. There’s no contradiction.

Quentin 

To view this discussion visit https://groups.google.com/d/msgid/everything-list/75204ad8-707f-4c12-a5b0-fb86d41df833n%40googlegroups.com.

[Alan Grayson]

On Wednesday, February 26, 2025 at 3:51:50 AM UTC-7 Quentin Anciaux wrote:

AG, your statement "density can't diverge unless volume goes to zero" assumes a finite volume, which doesn’t apply in an infinite universe. In an infinite universe, density can increase indefinitely everywhere without requiring a total volume to shrink.

I was explicit, that the observable universe shrinks, but according to you and Brent the unobservable part remains infinite. I can't imagine such a dichotomy. AG 

Brent is correct that the observable universe (the region we can see) shrinks as we go back in time, but that doesn’t mean the entire universe (including the unobservable part) does the same.

Why not? Is that just your opinion, or something demonstrable? AG 

The observable universe is just a region within an infinite space, and as we go back in time, the light cone that defines what we can observe gets smaller.

If the entire universe is infinite, its total volume remains infinite at all times

OK. AG

 

—but its density can still increase without bound.

Density of what region? AG 

There’s no contradiction.

The contradiction is the dichotomy between the behavior of the two regions. AG 

[Quentin Anciaux]

AG, the key point is that the observable universe is just a finite portion of an infinite whole. As we go back in time, the observable region contracts because the horizon of what we can see shrinks, but the entire universe remains infinite.

Why does the unobservable part remain infinite? Because spatial infinity doesn’t depend on what we can observe. If the universe was infinite at one moment, it stays infinite—shrinking only applies to what is within our causal past, not the entire space.

The density increases everywhere, meaning in any finite region—including our observable universe—matter gets packed into a smaller space. But an infinite universe still has no overall “volume”, so it never “shrinks,” only becomes denser.

The dichotomy isn’t a contradiction, it’s a consequence of causal horizons—our observable universe is just a window into an infinite cosmos.

Quentin 

To view this discussion visit https://groups.google.com/d/msgid/everything-list/bce2fa4e-3a25-4257-944c-da1be1eba1b3n%40googlegroups.com.

[Alan Grayson]

On Wednesday, February 26, 2025 at 4:29:13 AM UTC-7 Quentin Anciaux wrote:

AG, the key point is that the observable universe is just a finite portion of an infinite whole. As we go back in time, the observable region contracts because the horizon of what we can see shrinks, but the entire universe remains infinite.

Why does the unobservable part remain infinite? Because spatial infinity doesn’t depend on what we can observe. If the universe was infinite at one moment, it stays infinite—shrinking only applies to what is within our causal past, not the entire space.

The density increases everywhere, meaning in any finite region—including our observable universe—matter gets packed into a smaller space. But an infinite universe still has no overall “volume”, so it never “shrinks,” only becomes denser.

The dichotomy isn’t a contradiction, it’s a consequence of causal horizons—our observable universe is just a window into an infinite cosmos.

And you know that how? How did you conclude it's infinite, other than having an opinion? AG 

[Quentin Anciaux]

AG, the question isn’t whether I conclude the universe is infinite—it’s whether the cosmological models allow for an infinite universe and what their implications are.

We don’t know if the universe is infinite or finite. Observations are consistent with both possibilities. If it is infinite, then it has always been infinite, and the observable region shrinking as we go back in time is just a consequence of our causal horizon contracting, not the entire universe shrinking. If it is finite, then its total volume could decrease over time.

This isn’t about opinion, it’s about following the logical consequences of each assumption. If you’re struggling with that distinction, that’s on you.

To view this discussion visit https://groups.google.com/d/msgid/everything-list/0f5daf8f-5658-41c6-850c-5a214eba601cn%40googlegroups.com.

[Alan Grayson]

On Wednesday, February 26, 2025 at 4:44:05 AM UTC-7 Quentin Anciaux wrote:

AG, the question isn’t whether I conclude the universe is infinite—it’s whether the cosmological models allow for an infinite universe and what their implications are.

We don’t know if the universe is infinite or finite.

OK, but in the post I responded to, you categorically stated that the universe is infinite, and that's on you! AG 

[John Clark]

On Tue, Feb 25, 2025 at 6:48 PM Alan Grayson <agrays...@gmail.com> wrote:

On Tuesday, February 25, 2025 at 12:46:46 PM UTC-7 Brent Meeker wrote:

>>I think all cosmologist, like Hartle, recognize that the observable universe was much smaller in the past.  Which is perfectly compatible with the universe be spacially flat and infinite.

> I fully anticipated that response. But why would the observable universe behave radically different from the entire principle, particularly in light of the Cosmological Principle? AG

Because infinite things (like the entire universe) have fundamentally different properties than finite things (like the observable universe). For example, a proper subset of the infinite set of all the integers (the even integers for example) can be placed in a one to one correspondence with the entire set of integers. You can't do that if the set of integers is finite.  

John K Clark    See what's on my new list at  Extropolis

eda

[Alan Grayson]

On Wednesday, February 26, 2025 at 5:52:15 AM UTC-7 John Clark wrote:

On Tue, Feb 25, 2025 at 6:48 PM Alan Grayson <agrays...@gmail.com> wrote:

On Tuesday, February 25, 2025 at 12:46:46 PM UTC-7 Brent Meeker wrote:

>>I think all cosmologist, like Hartle, recognize that the observable universe was much smaller in the past.  Which is perfectly compatible with the universe be spacially flat and infinite.

> I fully anticipated that response. But why would the observable universe behave radically different from the entire principle, particularly in light of the Cosmological Principle? AG

Because infinite things (like the entire universe)

BS. You affirm categorically what you don't really know! AG

 

have fundamentally different properties than finite things (like the observable universe). For example, a proper subset of the infinite set of all the integers (the even integers for example) can be placed in a one to one correspondence with the entire set of integers. You can't do that if the set of integers is finite.  

Now tell me something I don't know. BTW, the CC claims the properties of the universe are the same everywhere, but in the unobservable region the expansion is faster than light speed, which is why we can't observe it. So one could say the CC is violated. AG 

[John Clark]

On Wed, Feb 26, 2025 at 8:08 AM Alan Grayson <agrays...@gmail.com> wrote:

>  BTW, the CC

IHA.

 John K Clark    See what's on my new list at  Extropolis

eex

[Quentin Anciaux]

Le mer. 26 févr. 2025, 12:02, Alan Grayson <agrays...@gmail.com> a écrit :

On Wednesday, February 26, 2025 at 4:44:05 AM UTC-7 Quentin Anciaux wrote:

AG, the question isn’t whether I conclude the universe is infinite—it’s whether the cosmological models allow for an infinite universe and what their implications are.

We don’t know if the universe is infinite or finite.

OK, but in the post I responded to, you categorically stated that the universe is infinite, and that's on you! AG 

I did not and never have. You're so entrenched in your own prejudices that you forget to read.

Quentin 

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[Alan Grayson]

On Wednesday, February 26, 2025 at 6:30:06 AM UTC-7 Quentin Anciaux wrote:

Le mer. 26 févr. 2025, 12:02, Alan Grayson <agrays...@gmail.com> a écrit :

On Wednesday, February 26, 2025 at 4:44:05 AM UTC-7 Quentin Anciaux wrote:

AG, the question isn’t whether I conclude the universe is infinite—it’s whether the cosmological models allow for an infinite universe and what their implications are.

We don’t know if the universe is infinite or finite.

OK, but in the post I responded to, you categorically stated that the universe is infinite, and that's on you! AG 

I did not and never have. You're so entrenched in your own prejudices that you forget to read.

Really? Here are YOUR words.  "AG, the key point is that the observable universe is just a finite portion of an infinite whole. As we go back in time, the observable region contracts because the horizon of what we can see shrinks, but the entire universe remains infinite."  Later, you took a more objective view. AG

[Quentin Anciaux]

AG, you’re cherry-picking while ignoring the full context. My statement was a conditional explanation, not a categorical claim. Here’s what I actually said:

"If the universe was infinite at one moment, it stays infinite—shrinking only applies to what is within our causal past, not the entire space."

And earlier:

"We don’t know if the universe is infinite or finite. Observations are consistent with both possibilities."

I was explaining the logical consequences of an infinite universe—not asserting that the universe is infinite. Your failure to distinguish between an explanation and a claim is your problem, not mine.

Quentin 

To view this discussion visit https://groups.google.com/d/msgid/everything-list/536d62ff-ee43-4d47-a7bf-1ccbcdf840cen%40googlegroups.com.

[Alan Grayson]

On Wednesday, February 26, 2025 at 6:13:40 AM UTC-7 John Clark wrote:

On Wed, Feb 26, 2025 at 8:08 AM Alan Grayson <agrays...@gmail.com> wrote:

>  BTW, the CC

IHA.

Google, if you know how. AG 

[Brent Meeker]

But the reason GR predicts a singularity is that all forces contribute to mass-energy density and the higher the density the higher the curvature (that's Einstein's equations).  So adding a repulsive force just makes the singularity more certain; still with the caveat that this is a classical equation.

Brent

[Brent Meeker]

Yes and yes.  If the universe is infinite then the ratio of its size to that of any finite subset is infinite, no matter how large or small the subset is.  Imagine the infinite set of the integers.  Consider the finite subset {0,1,2,3,4,5,6,7,8,9,10,...,1e12}.  It's size is obviously 1e12.  Now shrink the universe by striking every tenth number. Your subset is now {0,1,2,3,4,5,6,7,8,9,11,...,1e12-1} and it's size is 1e12-1.  But the universe is still infinite.

Brent

[Alan Grayson]

Brentc

I know enough about set theory to have easily generated what you write above. But math isn't physics. If the finite observable universe converges to a singularity, we have a hypothetical universe which is not physically possible, whether finite or infinite. So I am not sure how we can distingush between an infinite and finite universe. Set theory does not help. AG 

[Alan Grayson]

If we assume an infinite universe and run the clock backward, is it reasonable to conclude that the singularity we imagine forming in the observable region, is identically the same singularity for the entire universe? Secondly, why do we imagine the hypothetical singularlty indicates the GR fails in this situation? After all, if the expanding universe is determined by measurements, and the average distances between galaxies decreases as the clock runs backward is also determined by measurements, what has this to do with GR, since it's all measurement determined? TY, AG 

[Alan Grayson]

On Wednesday, February 26, 2025 at 6:49:39 AM UTC-7 Quentin Anciaux wrote:

AG, you’re cherry-picking while ignoring the full context. My statement was a conditional explanation, not a categorical claim. Here’s what I actually said:

"If the universe was infinite at one moment, it stays infinite—shrinking only applies to what is within our causal past, not the entire space."

And earlier:

"We don’t know if the universe is infinite or finite. Observations are consistent with both possibilities."

I was explaining the logical consequences of an infinite universe—not asserting that the universe is infinite. Your failure to distinguish between an explanation and a claim is your problem, not mine.

Quentin 

I would have written it differently. To avoid confusion, I would have begun each statement with the phrase,  "When modelling the universe as infinite (finite), the following is the case, ... . "   Not worth arguing about. AG

[John Clark]

On Wed, Feb 26, 2025 at 11:41 PM Alan Grayson <agrays...@gmail.com> wrote:

> math isn't physics.

Agreed.  

 > If the finite observable universe converges to a singularity, we have a hypothetical universe which is not physically possible, 

 "Converges to a singularity" means that things become so small that all our known laws of physics stop working and new laws of an unknown nature take over, therefore at that point it is a little cavalier to decree what is and is not physically possible.  

>  I am not sure how we can distingush between an infinite and finite universe. 

I'm not sure we will ever know the answer to the infinite versus finite question, in fact I rather doubt we will; but we will be able to prove that the entire universe is much much larger than the observable universe.   

John K Clark    See what's on my new list at  Extropolis

5g8

[John Clark]

On Thu, Feb 27, 2025 at 2:39 AM Alan Grayson <agrays...@gmail.com> wrote:

> why do we imagine the hypothetical singularlty indicates the GR fails in this situation?

Because when space-time becomes infinitely curved General Relativity starts giving nonsense answers, like things having infinite energy and infinite momentum and infinite density and infinite temperature etc. Everybody agrees that new laws of physics must take over at that point, but nobody agrees on what those new laws are.  

John K Clark    See what's on my new list at  Extropolis

rsa

[Brent Meeker]

On 2/26/2025 8:41 PM, Alan Grayson wrote:

Yes and yes.  If the universe is infinite then the ratio of its size to that of any finite subset is infinite, no matter how large or small the subset is.  Imagine the infinite set of the integers.  Consider the finite subset {0,1,2,3,4,5,6,7,8,9,10,...,1e12}.  It's size is obviously 1e12.  Now shrink the universe by striking every tenth number. Your subset is now {0,1,2,3,4,5,6,7,8,9,11,...,1e12-1} and it's size is 1e12-1.  But the universe is still infinite.

Brentc

I know enough about set theory to have easily generated what you write above. But math isn't physics. If the finite observable universe converges to a singularity, we have a hypothetical universe which is not physically possible, whether finite or infinite. So I am not sure how we can distingush between an infinite and finite universe. Set theory does not help. AG 

If you can grasp that, why can't you grasp Cantor's theory of infinite sets.  I and others have said over and over that the singularity is a prediction of GR which assumes spacetime is a continuum.  Quantum mechanics almost certainly modifies the physics short of infinite density.

Brent

[Brent Meeker]

On 2/26/2025 11:39 PM, Alan Grayson wrote:

If we assume an infinite universe and run the clock backward, is it reasonable to conclude that the singularity we imagine forming in the observable region,

The singularity is not IN the observable region, it is the limiting origin of the observable region.

is identically the same singularity for the entire universe? Secondly, why do we imagine the hypothetical singularlty indicates the GR fails in this situation? After all, if the expanding universe is determined by measurements, and the average distances between galaxies decreases as the clock runs backward is also determined by measurements, what has this to do with GR, since it's all measurement determined? TY, AG

You can't be so dense as to not know the difference between a measurement and an extrapolation.

Brent

[Alan Grayson]

Cantor's theory of infinite sets is now referred to as Naive Set Theory, ever since 1901 when Russell published his paradox. It is replaced by ZFC set theory. I just meant that one doesn't need GR to predict a singularity for a contracting universe. AG 

[Alan Grayson]

I'm just saying that measurements suggest a singularity without applying GR. The reason the unobservable region is unobservable is because expansion in that region is faster than light speed. So if we run the clock backward, won't that region collapse faster than light speed, with the result that the entire universe converges to a single singularity? AG 

[Brent Meeker]

It depends I suppose on what "run the clock backwards" means.  It's unphysical to have spheres of outgoing radiation contract backward to a point as in playing a video backwards.  But if that's what you mean then yes the entire universe becomes infinitely dense, a singularity...but not a point, it's still infinite.

Brent

[John Clark]

On Wed, Feb 26, 2025 at 3:24 PM Brent Meeker <meeke...@gmail.com> wrote:

> the reason GR predicts a singularity is that all forces contribute to mass-energy density and the higher the density the higher the curvature (that's Einstein's equations). 

In Newtonian gravity only mass creates gravitational fields but in General Relativity, because E=MC^2, energy also makes a contribution, but that's not all, it makes a difference what sort of energy it is. Both positive pressure and negative pressure (tension) are forms of energy, but they have opposite effects on the gravitational field. Positive pressure increases spacetime curvature and makes gravitational attraction stronger than what you would expect from mass/energy density alone, while negative pressure does the opposite. Negative pressure causes spacetime curvature to be smaller than what you would expect and causes a sort of anti-gravity effect.

The ACTIVE gravitational mass/energy density is proportional to the gravitational mass density PLUS 3p/c^2. So if the pressure is sufficiently negative then things will start to expand, not contract; and that's why many people think Dark Energy is some sort of negative pressure and is a fundamental property of space.

John K Clark    See what's on my new list at  Extropolis

ica

[Brent Meeker]

On 2/28/2025 10:42 PM, Alan Grayson wrote:

So, as we go backward in time, the observable universe seems to converge to a point, while the rate of expansion of the unobservable universe increases since the rate of expansion in earlier times was greater than it is at present? In this scenario, how could the unobservable univese reach an ultra high temperature as we approach the BB? AG 

The matter in it becomes more dense.  That's the opposite of expansion.

Brent

[Quentin Anciaux]

On the 26th and in other replies I did say:

As I've explained already, it's not that the volume goes to zero, but density that goes to infinity, everywhere, there is no valid notion of volume in an infinite universe. 

What is difficult to understand? 

Quentin 

Le sam. 1 mars 2025, 06:42, Alan Grayson <agrays...@gmail.com> a écrit :

So, as we go backward in time, the observable universe seems to converge to a point, while the rate of expansion of the unobservable universe increases since the rate of expansion in earlier times was greater than it is at present? In this scenario, how could the unobservable univese reach an ultra high temperature as we approach the BB? AG  

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[Alan Grayson]

On Saturday, March 1, 2025 at 4:02:15 PM UTC-7 Quentin Anciaux wrote:

On the 26th and in other replies I did say:

As I've explained already, it's not that the volume goes to zero, but density that goes to infinity, everywhere, there is no valid notion of volume in an infinite universe. 

What is difficult to understand? 

Quentin 

I deleted that post. You must have replied to your email list.  But you misconstrued the question posed. As the density goes to infinity, the rate of expansion keeps increasing (but not to infinity), so how do the competing rates result in an ultra high temperature? I suppose it's because the first is unbounded and latter bounded. AG

[Quentin Anciaux]

AG, temperature follows density. As density increases indefinitely, so does temperature. Expansion rate doesn’t need to be infinite, compression alone drives temperatures to extreme levels.

Quentin 

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