Flat geometry vs Super-High Temperature at the Big Bang

[Alan Grayson]

If the age of the universe is finite, which is generally believed, then no matter how fast it expands, it can never become spatially infinite, So, IF it is spatially infinite, this must have been its initial condition at or around he time of the Big Bang (BB). But this contradicts the assumption that it was at a super high temperature at or around the time of the BB. IOW, if we run the clock backward, the universe seems to get incredibly small, and for this reason incredibly hot, roughly analogous to a highly compressed gas. Therefore, it cannot have a flat global geometry, since such a geometry is infinite in spatial extent. QED. AG

 

[Quentin Anciaux]

Le mer. 12 févr. 2025, 09:55, Alan Grayson <agrays...@gmail.com> a écrit :

If the age of the universe is finite, which is generally believed, then no matter how fast it expands, it can never become spatially infinite, So, IF it is spatially infinite, this must have been its initial condition at or around he time of the Big Bang (BB). But this contradicts the assumption that it was at a super high temperature at or around the time of the BB.

AG, your assumption that a finite-age universe must be spatially finite is flawed. If the universe is infinite now, it was infinite at the Big Bang, just in a much hotter and denser state everywhere. The Big Bang wasn’t an explosion from a point but a transition from an extremely dense, uniform state, which applies whether the universe is finite or infinite.

Eternal inflation suggests the universe was already infinite before the Hot Big Bang phase. The observable universe was once small and dense, but the entire universe could have been infinite at all times. Spatial flatness doesn’t imply finiteness—flat, infinite universes expanding from a dense state are fully consistent with general relativity.

There’s no contradiction between a spatially infinite universe and high density at early times. The problem isn’t with cosmology—it’s with your mistaken assumption that high density requires finiteness.

Quentin 

IOW, if we run the clock backward, the universe seems to get incredibly small, and for this reason incredibly hot, roughly analogous to a highly compressed gas. Therefore, it cannot have a flat global geometry, since such a geometry is infinite in spatial extent. QED. AG

 

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[Alan Grayson]

On Wednesday, February 12, 2025 at 2:09:58 AM UTC-7 Quentin Anciaux wrote:

Le mer. 12 févr. 2025, 09:55, Alan Grayson <agrays...@gmail.com> a écrit :

If the age of the universe is finite, which is generally believed, then no matter how fast it expands, it can never become spatially infinite, So, IF it is spatially infinite, this must have been its initial condition at or around he time of the Big Bang (BB). But this contradicts the assumption that it was at a super high temperature at or around the time of the BB.

AG, your assumption that a finite-age universe must be spatially finite is flawed. If the universe is infinite now, it was infinite at the Big Bang,

That's what I wrote. AG 

just in a much hotter and denser state everywhere. The Big Bang wasn’t an explosion from a point

I didn't assume that. What it actually is, or was, we don't know. But at that time it was hugely denser and hotter than at present. AG

 

but a transition from an extremely dense, uniform state, which applies whether the universe is finite or infinite.

Eternal inflation suggests the universe was already infinite before the Hot Big Bang phase.

Sure, provided eternal inflation is occurring, but it's speculative, as is my conclusion. Most cosmologists believe it was smaller in the past than at present, as implied by present day expanson run in reverse. AG 

 

The observable universe was once small and dense, but the entire universe could have been infinite at all times.

Yes, COULD HAVE BEEN. I assumed, for the sake of argument, that it COULD NOT HAVE BECOME INFINITE IN FINITE TIME,  and THEN inferred what that implied; namely, that it became infinite at the time of the BB. Also, if you believe in the Cosmological Principle, if the observable universe was finite, then so was the entire universe.AG 

Spatial flatness doesn’t imply finiteness

I didn't assume it does. In fact, I assumed the reverse, as do cosmologists. I don't object to your criticisms, but you seem to be reading me with a jaundiced eye. AG

 

—flat, infinite universes expanding from a dense state are fully consistent with general relativity.

Does my conjecture conflict with GR, or is it also consistent? AG 

There’s no contradiction between a spatially infinite universe and high density at early times. The problem isn’t with cosmology—it’s with your mistaken assumption that high density requires finiteness.

My assumption isn't necessarily mistaken. Rather, it's another possibility. AG 

[Quentin Anciaux]

Le mer. 12 févr. 2025, 17:55, Alan Grayson <agrays...@gmail.com> a écrit :

On Wednesday, February 12, 2025 at 2:09:58 AM UTC-7 Quentin Anciaux wrote:

Le mer. 12 févr. 2025, 09:55, Alan Grayson <agrays...@gmail.com> a écrit :

If the age of the universe is finite, which is generally believed, then no matter how fast it expands, it can never become spatially infinite, So, IF it is spatially infinite, this must have been its initial condition at or around he time of the Big Bang (BB). But this contradicts the assumption that it was at a super high temperature at or around the time of the BB.

AG, your assumption that a finite-age universe must be spatially finite is flawed. If the universe is infinite now, it was infinite at the Big Bang,

That's what I wrote. AG 

just in a much hotter and denser state everywhere. The Big Bang wasn’t an explosion from a point

I didn't assume that. What it actually is, or was, we don't know. But at that time it was hugely denser and hotter than at present. AG

No, you initially framed it as a contradiction—"If it’s infinite now, it must have been infinite at the Big Bang, but that contradicts the high temperature assumption." That’s what was wrong. There’s no contradiction between an infinite universe and high density. If you now accept that, great, but don’t pretend that was your original point.

Yet, your reasoning implicitly relies on treating the universe as if it "shrinks" to a single location when run backward. A spatially infinite universe was never "smaller" in an absolute sense—just denser everywhere.

 

but a transition from an extremely dense, uniform state, which applies whether the universe is finite or infinite.

Eternal inflation suggests the universe was already infinite before the Hot Big Bang phase.

Sure, provided eternal inflation is occurring, but it's speculative, as is my conclusion. Most cosmologists believe it was smaller in the past than at present, as implied by present day expanson run in reverse. AG 

No, they believe the observable universe was smaller. That doesn’t mean the entire universe was ever finite.

 

The observable universe was once small and dense, but the entire universe could have been infinite at all times.

Yes, COULD HAVE BEEN. I assumed, for the sake of argument, that it COULD NOT HAVE BECOME INFINITE IN FINITE TIME,  and THEN inferred what that implied; namely, that it became infinite at the time of the BB. Also, if you believe in the Cosmological Principle, if the observable universe was finite, then so was the entire universe.AG 

Spatial flatness doesn’t imply finiteness

I didn't assume it does. In fact, I assumed the reverse, as do cosmologists. I don't object to your criticisms, but you seem to be reading me with a jaundiced eye. AG

 

—flat, infinite universes expanding from a dense state are fully consistent with general relativity.

Does my conjecture conflict with GR, or is it also consistent? AG 

Yes, if you’re implying an infinite universe can’t be dense at early times or that it had to "become" infinite

There’s no contradiction between a spatially infinite universe and high density at early times. The problem isn’t with cosmology—it’s with your mistaken assumption that high density requires finiteness.

My assumption isn't necessarily mistaken. Rather, it's another possibility. AG 

No, it’s mistaken. Assuming high density requires finiteness is a misunderstanding of both GR and cosmology.

Quentin 

Quentin 

IOW, if we run the clock backward, the universe seems to get incredibly small, and for this reason incredibly hot, roughly analogous to a highly compressed gas. Therefore, it cannot have a flat global geometry, since such a geometry is infinite in spatial extent. QED. AG

 

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[Alan Grayson]

On Wednesday, February 12, 2025 at 10:10:40 AM UTC-7 Quentin Anciaux wrote:

Le mer. 12 févr. 2025, 17:55, Alan Grayson <agrays...@gmail.com> a écrit :

On Wednesday, February 12, 2025 at 2:09:58 AM UTC-7 Quentin Anciaux wrote:

Le mer. 12 févr. 2025, 09:55, Alan Grayson <agrays...@gmail.com> a écrit :

If the age of the universe is finite, which is generally believed, then no matter how fast it expands, it can never become spatially infinite, So, IF it is spatially infinite, this must have been its initial condition at or around he time of the Big Bang (BB). But this contradicts the assumption that it was at a super high temperature at or around the time of the BB.

AG, your assumption that a finite-age universe must be spatially finite is flawed. If the universe is infinite now, it was infinite at the Big Bang,

That's what I wrote. AG 

just in a much hotter and denser state everywhere. The Big Bang wasn’t an explosion from a point

I didn't assume that. What it actually is, or was, we don't know. But at that time it was hugely denser and hotter than at present. AG

No, you initially framed it as a contradiction—"If it’s infinite now, it must have been infinite at the Big Bang, but that contradicts the high temperature assumption." That’s what was wrong. There’s no contradiction between an infinite universe and high density. If you now accept that, great, but don’t pretend that was your original point.

I assumed that if the universe were infinite, it couldn't have become so in finite time, so IF infinite that must have been its initial condition. I later added, in summary, or that's what I meant to do, that this is contradictory to a super high temperature at the time of the BB. You claim this is inconsistent with GR. Can you prove that? AG

Yet, your reasoning implicitly relies on treating the universe as if it "shrinks" to a single location when run backward. A spatially infinite universe was never "smaller" in an absolute sense—just denser everywhere.

Well, that's what all the diagrams of the evolution of the universe show, that it becomes smaller as we go back in time, begins as a point, and what I've heard or read what some cosmologists claim. AG 

 

but a transition from an extremely dense, uniform state, which applies whether the universe is finite or infinite.

Eternal inflation suggests the universe was already infinite before the Hot Big Bang phase.

Sure, provided eternal inflation is occurring, but it's speculative, as is my conclusion. Most cosmologists believe it was smaller in the past than at present, as implied by present day expanson run in reverse. AG 

No, they believe the observable universe was smaller.

Why just the observable region? AG

 

That doesn’t mean the entire universe was ever finite.

 

The observable universe was once small and dense, but the entire universe could have been infinite at all times.

Yes, COULD HAVE BEEN. I assumed, for the sake of argument, that it COULD NOT HAVE BECOME INFINITE IN FINITE TIME,  and THEN inferred what that implied; namely, that it became infinite at the time of the BB. Also, if you believe in the Cosmological Principle, if the observable universe was finite, then so was the entire universe.AG 

Spatial flatness doesn’t imply finiteness

I didn't assume it does. In fact, I assumed the reverse, as do cosmologists. I don't object to your criticisms, but you seem to be reading me with a jaundiced eye. AG

 

—flat, infinite universes expanding from a dense state are fully consistent with general relativity.

Does my conjecture conflict with GR, or is it also consistent? AG 

Yes, if you’re implying an infinite universe can’t be dense at early times or that it had to "become" infinite

I am assuming it couldn't become infinite in finite time, so, IF it is infinite now, it had to BE infinite at the time of the BB. AG 

There’s no contradiction between a spatially infinite universe and high density at early times. The problem isn’t with cosmology—it’s with your mistaken assumption that high density requires finiteness.

My assumption isn't necessarily mistaken. Rather, it's another possibility. AG 

No, it’s mistaken. Assuming high density requires finiteness is a misunderstanding of both GR and cosmology.

You claim it's not even a possibility. Why not? AG 

[Quentin Anciaux]

AG, your reasoning is flawed because it assumes a contradiction where none exists. An infinite universe doesn’t have to "become" infinite—it can be infinite at all times, just evolving in density and scale factor. High temperature and density at the Big Bang don’t require finiteness; they describe local conditions, not global topology.

Cosmological diagrams showing a "point" origin are simplifications based on the observable universe, not statements about the entire cosmos. The observable universe was smaller, but an infinite universe was never "shrinking" in the way you imply—just getting denser everywhere.

You ask why it’s not even a possibility that finiteness is required for high density. The answer is that GR and the FLRW metric allow for infinite spatial extent at all times, even under extreme density conditions. There’s no physical principle preventing this, so the burden is on you to show why infinity at high density would be impossible.

Quentin 

To view this discussion visit https://groups.google.com/d/msgid/everything-list/3d88ac70-0c72-41c3-8df7-2a5a52fcc1cdn%40googlegroups.com.

[Alan Grayson]

On Wednesday, February 12, 2025 at 11:49:23 AM UTC-7 Quentin Anciaux wrote:

AG, your reasoning is flawed because it assumes a contradiction where none exists. An infinite universe doesn’t have to "become" infinite—it can be infinite at all times, just evolving in density and scale factor. High temperature and density at the Big Bang don’t require finiteness; they describe local conditions, not global topology.

Cosmological diagrams showing a "point" origin are simplifications based on the observable universe, not statements about the entire cosmos. The observable universe was smaller, but an infinite universe was never "shrinking" in the way you imply—just getting denser everywhere.

But this contradicts the Cosmological Principle (which might be wrong). AG 

You ask why it’s not even a possibility that finiteness is required for high density. The answer is that GR and the FLRW metric allow for infinite spatial extent at all times, even under extreme density conditions. There’s no physical principle preventing this, so the burden is on you to show why infinity at high density would be impossible.

Although I posed it as impossible, but that's probably going too far. I think It's possible that the entire universe is getting smaller as we go back in time, and this accounts for its super high temperature at or near the BB. AG 

[Quentin Anciaux]

AG, you're backpedaling again. You originally claimed that an infinite universe contradicts high temperature at the Big Bang, now you're just saying it's "possible" the universe was finite. Fine, but that’s not what’s debated—the issue is whether an infinite universe must be contradictory to high density, and it isn’t.

The Cosmological Principle states that the universe is homogeneous and isotropic on large scales. This applies whether the universe is finite or infinite. Nothing about it requires the universe to be finite. If the universe was spatially infinite at the Big Bang, it was just an infinite, uniformly dense, hot state. The fact that the observable universe shrinks as we go back in time doesn’t mean the entire universe had to be finite.

If you’re now saying finiteness is just "possible" rather than required, then you’re conceding that your original contradiction doesn’t hold. So what’s left of your argument?

Quentin 

To view this discussion visit https://groups.google.com/d/msgid/everything-list/feb74974-a36e-4270-8825-61fcb5f5cf38n%40googlegroups.com.

[Alan Grayson]

On Wednesday, February 12, 2025 at 12:08:13 PM UTC-7 Quentin Anciaux wrote:

AG, you're backpedaling again. You originally claimed that an infinite universe contradicts high temperature at the Big Bang, now you're just saying it's "possible" the universe was finite. Fine, but that’s not what’s debated—the issue is whether an infinite universe must be contradictory to high density, and it isn’t.

Please cease with accusations. I just see that stating a contradiction is too strong, and I believe it is possible that the high temperature implies very small volume.  You're relying on a metric which allows your pov, but that's just one metric. It doesn't prove that I am mistaken, or some experts who claim the size of the universe decreases as we go backward in time.. AG

The Cosmological Principle states that the universe is homogeneous and isotropic on large scales.

And that it's the same everywhere. AG

 

This applies whether the universe is finite or infinite. Nothing about it requires the universe to be finite.

It does, if the universe's observable region is finite, then the entire universe is finite. AG

  

If the universe was spatially infinite at the Big Bang, it was just an infinite, uniformly dense, hot state. The fact that the observable universe shrinks as we go back in time doesn’t mean the entire universe had to be finite.

I am just claiming it could be finite, and that would explain its high temperature at or near the BB. The alternative is difficult to give credence to --- that it's infinite and expanding, and remains infinite as we go backward in time. AG 

If you’re now saying finiteness is just "possible" rather than required, then you’re conceding that your original contradiction doesn’t hold. So what’s left of your argument?

What's left is that you can't categorically rely on one metric to assert with finality what the physical reality might be. Apriori, hugely high early temperature is consistent with very small volume. AG 

[Brent Meeker]

On 2/12/2025 12:55 AM, Alan Grayson wrote:

If the age of the universe is finite, which is generally believed, then no matter how fast it expands, it can never become spatially infinite, So, IF it is spatially infinite, this must have been its initial condition at or around he time of the Big Bang (BB). But this contradicts the assumption that it was at a super high temperature at or around the time of the BB.

No it doesn't.  I can be infinite and high temperature.  What gave you idea it couldn't?

IOW, if we run the clock backward, the universe seems to get incredibly small,

If the universe is infinite, then it is only the Observable Universe that gets incredibly small.

Brent

[Quentin Anciaux]

AG, you're shifting from claiming a contradiction to merely suggesting a possibility, which is a step forward, but your reasoning is still flawed.

The Cosmological Principle states that the universe is homogeneous and isotropic on large scales, but that does not mean "if the observable universe is finite, then the entire universe is finite." That’s a categorical error. The observable universe is just the portion of the universe we can see due to the finite speed of light. Its size has no bearing on whether the universe as a whole is finite or infinite.

Your assumption that high temperature implies a very small global volume is only valid if the universe was already finite. If the universe is infinite now, it was infinite at the Big Bang, just in a state of uniform extreme density. An infinite universe can still be compressed arbitrarily while remaining infinite—density increases, but spatial extent doesn’t shrink to a finite size.

You say I "rely on one metric," but the FLRW metric isn't just a convenient choice—it’s what general relativity and observational data support. If you want to claim the universe was finite, you need a model that explains why it would have a global boundary while still obeying large-scale homogeneity. So far, all you’ve done is assert that finiteness is "possible" without providing a physical reason why it would be preferred.

Quentin 

To view this discussion visit https://groups.google.com/d/msgid/everything-list/cd6fd141-fd52-4e74-980d-73f0f1613457n%40googlegroups.com.

[Alan Grayson]

On Wednesday, February 12, 2025 at 12:36:38 PM UTC-7 Brent Meeker wrote:

On 2/12/2025 12:55 AM, Alan Grayson wrote:

If the age of the universe is finite, which is generally believed, then no matter how fast it expands, it can never become spatially infinite, So, IF it is spatially infinite, this must have been its initial condition at or around he time of the Big Bang (BB). But this contradicts the assumption that it was at a super high temperature at or around the time of the BB.

No it doesn't.  I can be infinite and high temperature.  What gave you idea it couldn't?

The temperature behavior of gases at low volume, and the Cosmological Principle. AG

[Alan Grayson]

On Wednesday, February 12, 2025 at 12:49:19 PM UTC-7 Quentin Anciaux wrote:

AG, you're shifting from claiming a contradiction to merely suggesting a possibility, which is a step forward, but your reasoning is still flawed.

The Cosmological Principle states that the universe is homogeneous and isotropic on large scales, but that does not mean "if the observable universe is finite, then the entire universe is finite." That’s a categorical error. The observable universe is just the portion of the universe we can see due to the finite speed of light. Its size has no bearing on whether the universe as a whole is finite or infinite.

Your assumption that high temperature implies a very small global volume is only valid if the universe was already finite. If the universe is infinite now, it was infinite at the Big Bang, just in a state of uniform extreme density. An infinite universe can still be compressed arbitrarily while remaining infinite—density increases, but spatial extent doesn’t shrink to a finite size.

You say I "rely on one metric," but the FLRW metric isn't just a convenient choice—it’s what general relativity and observational data support. If you want to claim the universe was finite, you need a model that explains why it would have a global boundary while still obeying large-scale homogeneity.

 

I postulated a slightly positively curved spherically shaped univere with no boundary, AG

[Quentin Anciaux]

AG, if you’re postulating a closed universe, that’s entirely different from claiming an infinite universe contradicts high temperature at the Big Bang. It just means you're favoring a specific topology.

The problem is that your argument keeps shifting. Initially, you argued that an infinite universe contradicts high temperature at the Big Bang to saying a finite, positively curved universe is a possible model—which is trivially true but irrelevant to your claim.

If your point is just "a finite universe is possible," sure, but if you're still trying to argue that an infinite universe is incompatible with high density at early times, you haven't demonstrated that at all.

Quentin 

To view this discussion visit https://groups.google.com/d/msgid/everything-list/3ff6a35f-022a-4864-afc4-bbfdf09749den%40googlegroups.com.

[Alan Grayson]

On Wednesday, February 12, 2025 at 1:12:13 PM UTC-7 Quentin Anciaux wrote:

AG, if you’re postulating a closed universe, that’s entirely different from claiming an infinite universe contradicts high temperature at the Big Bang. It just means you're favoring a specific topology.

The problem is that your argument keeps shifting. Initially, you argued that an infinite universe contradicts high temperature at the Big Bang to saying a finite, positively curved universe is a possible model—which is trivially true but irrelevant to your claim.

Can't I make more than one claim without being accused of "shifting"? I concluded that a flat geometry is infinite, so it can't be the case IF our universe is finite; that is, If it's finite, it can't be flat. In such case, it's very likely slightly positively curved and spherical, thus closed and finite. I am virtually certain that some cosmologists claim the entire universe actually decreased in volume as we run the clock backward. I'll try to name names if I can. BTW, I'm not making a category error when applying the Cosmological Principle. It says what you said it says, but there's more to it than that. Being the same everywhere in terms of distribution of matter is just one example of sameness. Finite or infinite everywhere is another example of sameness. AG

If your point is just "a finite universe is possible," sure, but if you're still trying to argue that an infinite universe is incompatible with high density at early times, you haven't demonstrated that at all.

I'm arguing that super high temperature is ALSO compatible with very low volume. So, I would think some "expert" would have made the effort to prove this contradicts GR, instead of relying solely on showing that a small volume is actually not compatible with GR. AG 

Quentin 

[Alan Grayson]

On Wednesday, February 12, 2025 at 1:48:06 PM UTC-7 Alan Grayson wrote:

On Wednesday, February 12, 2025 at 1:12:13 PM UTC-7 Quentin Anciaux wrote:

AG, if you’re postulating a closed universe, that’s entirely different from claiming an infinite universe contradicts high temperature at the Big Bang. It just means you're favoring a specific topology.

The problem is that your argument keeps shifting. Initially, you argued that an infinite universe contradicts high temperature at the Big Bang to saying a finite, positively curved universe is a possible model—which is trivially true but irrelevant to your claim.

Can't I make more than one claim without being accused of "shifting"? I concluded that a flat geometry is infinite, so it can't be the case IF our universe is finite; that is, If it's finite, it can't be flat. In such case, it's very likely slightly positively curved and spherical, thus closed and finite. I am virtually certain that some cosmologists claim the entire universe actually decreased in volume as we run the clock backward. I'll try to name names if I can. BTW, I'm not making a category error when applying the Cosmological Principle. It says what you said it says, but there's more to it than that. Being the same everywhere in terms of distribution of matter is just one example of sameness. Finite or infinite everywhere is another example of sameness. AG

If your point is just "a finite universe is possible," sure, but if you're still trying to argue that an infinite universe is incompatible with high density at early times, you haven't demonstrated that at all.

CORRECTION: I'm arguing that super high temperature is ALSO compatible with very low volume. So, I would think some "expert" would have made the effort to prove this contradicts GR, instead of just claiming, as you do, that a small volume is actually not compatible with GR without proving it. AG 

Quentin 

[Quentin Anciaux]

AG, you can make multiple claims, but when you start with "an infinite universe contradicts high temperature at the Big Bang" and then pivot to "a finite universe is possible," it is shifting the argument. If your real point was just that a finite universe is possible, we could have skipped all the contradictions that weren’t actually contradictions.

You're correct that a finite universe can't be spatially flat—a positively curved, closed universe would be finite. That’s basic topology, and it’s a valid possibility. But whether the universe is finite or infinite is still an open question in cosmology, and current observations suggest it’s either infinite or so large that any curvature is undetectable.

As for your claim that some cosmologists say the entire universe decreased in volume as we go backward, that only applies to finite universes. An infinite universe doesn’t have a meaningful "volume" in the same way—only the density increases. If you find specific names making this claim, make sure they’re talking about the global universe, not just the observable one.

Your argument about high temperature being "ALSO compatible with very low volume" is trivial—it’s true for finite universes. But you started by arguing that an infinite universe was somehow incompatible with high density, which is false. GR allows both scenarios. You haven’t shown any physical reason why an infinite, high-density early universe would be impossible. You’re just asserting that a small volume would be possible, which no one is disputing.

Quentin 

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[Quentin Anciaux]

AG, no one is claiming that a small volume is incompatible with GR. A finite, positively curved universe would have had a smaller volume in the past, and that’s completely consistent with GR. No contradiction there.

What was incorrect in your earlier argument was implying that an infinite universe couldn’t have been in a high-density state at early times. That’s what doesn’t follow. GR allows an infinite universe to remain infinite while its density increases as you go back in time, no need for a global volume to "shrink."

If your point is just that a finite universe with high temperature is also possible, then there’s nothing to argue about. But if you’re still implying that only a finite universe makes sense with high temperature, then yes, that contradicts GR and modern cosmology. If you think an expert has proven otherwise, find the argument, because right now, you’re just asserting it without backing it up.

Quentin 

Quentin 

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[Brent Meeker]

On 2/12/2025 11:04 AM, Alan Grayson wrote:

On Wednesday, February 12, 2025 at 11:49:23 AM UTC-7 Quentin Anciaux wrote:

AG, your reasoning is flawed because it assumes a contradiction where none exists. An infinite universe doesn’t have to "become" infinite—it can be infinite at all times, just evolving in density and scale factor. High temperature and density at the Big Bang don’t require finiteness; they describe local conditions, not global topology.

Cosmological diagrams showing a "point" origin are simplifications based on the observable universe, not statements about the entire cosmos. The observable universe was smaller, but an infinite universe was never "shrinking" in the way you imply—just getting denser everywhere.

But this contradicts the Cosmological Principle (which might be wrong). AG

No it doesn't.  Every finite subset of the infinite universe originated in a point (at least in the classical analysis).
Brent

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[Alan Grayson]

On Wednesday, February 12, 2025 at 2:17:30 PM UTC-7 Quentin Anciaux wrote:

AG, you can make multiple claims, but when you start with "an infinite universe contradicts high temperature at the Big Bang" and then pivot to "a finite universe is possible," it is shifting the argument. If your real point was just that a finite universe is possible, we could have skipped all the contradictions that weren’t actually contradictions.

You're correct that a finite universe can't be spatially flat—a positively curved, closed universe would be finite. That’s basic topology, and it’s a valid possibility. But whether the universe is finite or infinite is still an open question in cosmology, and current observations suggest it’s either infinite or so large that any curvature is undetectable.

As for your claim that some cosmologists say the entire universe decreased in volume as we go backward, that only applies to finite universes. An infinite universe doesn’t have a meaningful "volume" in the same way—only the density increases. If you find specific names making this claim, make sure they’re talking about the global universe, not just the observable one.

Your argument about high temperature being "ALSO compatible with very low volume" is trivial—it’s true for finite universes. But you started by arguing that an infinite universe was somehow incompatible with high density, which is false. GR allows both scenarios. You haven’t shown any physical reason why an infinite, high-density early universe would be impossible. You’re just asserting that a small volume would be possible, which no one is disputing.

So we're on the same page. But what I am claiming is plausible and possible, and my initial comment was too extreme, so I corrected it. But it's certainly not trivial. Calling it trivial shows your bias, which you essentially presented as a certainty, AG

[Alan Grayson]

On Wednesday, February 12, 2025 at 2:26:02 PM UTC-7 Brent Meeker wrote:

On 2/12/2025 11:04 AM, Alan Grayson wrote:

On Wednesday, February 12, 2025 at 11:49:23 AM UTC-7 Quentin Anciaux wrote:

AG, your reasoning is flawed because it assumes a contradiction where none exists. An infinite universe doesn’t have to "become" infinite—it can be infinite at all times, just evolving in density and scale factor. High temperature and density at the Big Bang don’t require finiteness; they describe local conditions, not global topology.

Cosmological diagrams showing a "point" origin are simplifications based on the observable universe, not statements about the entire cosmos. The observable universe was smaller, but an infinite universe was never "shrinking" in the way you imply—just getting denser everywhere.

But this contradicts the Cosmological Principle (which might be wrong). AG

No it doesn't.  Every finite subset of the infinite universe originated in a point (at least in the classical analysis).
Brent

So, every finite subset of an infinite universe originated in a point, but the entire universe didn't? I can't agree with that. AG 

[Quentin Anciaux]

Le mer. 12 févr. 2025, 22:30, Alan Grayson <agrays...@gmail.com> a écrit :

On Wednesday, February 12, 2025 at 2:17:30 PM UTC-7 Quentin Anciaux wrote:

AG, you can make multiple claims, but when you start with "an infinite universe contradicts high temperature at the Big Bang" and then pivot to "a finite universe is possible," it is shifting the argument. If your real point was just that a finite universe is possible, we could have skipped all the contradictions that weren’t actually contradictions.

You're correct that a finite universe can't be spatially flat—a positively curved, closed universe would be finite. That’s basic topology, and it’s a valid possibility. But whether the universe is finite or infinite is still an open question in cosmology, and current observations suggest it’s either infinite or so large that any curvature is undetectable.

As for your claim that some cosmologists say the entire universe decreased in volume as we go backward, that only applies to finite universes. An infinite universe doesn’t have a meaningful "volume" in the same way—only the density increases. If you find specific names making this claim, make sure they’re talking about the global universe, not just the observable one.

Your argument about high temperature being "ALSO compatible with very low volume" is trivial—it’s true for finite universes. But you started by arguing that an infinite universe was somehow incompatible with high density, which is false. GR allows both scenarios. You haven’t shown any physical reason why an infinite, high-density early universe would be impossible. You’re just asserting that a small volume would be possible, which no one is disputing.

So we're on the same page. But what I am claiming is plausible and possible, and my initial comment was too extreme, so I corrected it. But it's certainly not trivial. Calling it trivial shows your bias, which you essentially presented as a certainty, AG

AG, if your point is simply that a finite universe shrinking in volume as we go backward in time is possible, then sure, that’s a valid scenario within GR. But that was never in question—cosmologists already consider positively curved, closed universes as a possibility.

What was in question was your earlier claim that an infinite universe contradicts high temperature at the Big Bang, which was incorrect. That’s why your shift to simply defending the plausibility of a finite universe seems like a retreat rather than an actual defense of your original argument.

Calling it trivial isn’t bias—it’s just stating that this is a well-known, uncontroversial fact. The debate was never about whether a finite universe was possible; it was about whether an infinite one was impossible under high density, which you originally suggested. If you’re now just saying a finite universe is a possibility, then there’s no actual argument left.

Quentin 

Quentin 

Le mer. 12 févr. 2025, 21:48, Alan Grayson <agrays...@gmail.com> a écrit :

On Wednesday, February 12, 2025 at 1:12:13 PM UTC-7 Quentin Anciaux wrote:

AG, if you’re postulating a closed universe, that’s entirely different from claiming an infinite universe contradicts high temperature at the Big Bang. It just means you're favoring a specific topology.

The problem is that your argument keeps shifting. Initially, you argued that an infinite universe contradicts high temperature at the Big Bang to saying a finite, positively curved universe is a possible model—which is trivially true but irrelevant to your claim.

Can't I make more than one claim without being accused of "shifting"? I concluded that a flat geometry is infinite, so it can't be the case IF our universe is finite; that is, If it's finite, it can't be flat. In such case, it's very likely slightly positively curved and spherical, thus closed and finite. I am virtually certain that some cosmologists claim the entire universe actually decreased in volume as we run the clock backward. I'll try to name names if I can. BTW, I'm not making a category error when applying the Cosmological Principle. It says what you said it says, but there's more to it than that. Being the same everywhere in terms of distribution of matter is just one example of sameness. Finite or infinite everywhere is another example of sameness. AG

If your point is just "a finite universe is possible," sure, but if you're still trying to argue that an infinite universe is incompatible with high density at early times, you haven't demonstrated that at all.

I'm arguing that super high temperature is ALSO compatible with very low volume. So, I would think some "expert" would have made the effort to prove this contradicts GR, instead of relying solely on showing that a small volume is actually not compatible with GR. AG 

Quentin 

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[Alan Grayson]

On Wednesday, February 12, 2025 at 2:43:01 PM UTC-7 Quentin Anciaux wrote:

Le mer. 12 févr. 2025, 22:30, Alan Grayson <agrays...@gmail.com> a écrit :

On Wednesday, February 12, 2025 at 2:17:30 PM UTC-7 Quentin Anciaux wrote:

AG, you can make multiple claims, but when you start with "an infinite universe contradicts high temperature at the Big Bang" and then pivot to "a finite universe is possible," it is shifting the argument. If your real point was just that a finite universe is possible, we could have skipped all the contradictions that weren’t actually contradictions.

You're correct that a finite universe can't be spatially flat—a positively curved, closed universe would be finite. That’s basic topology, and it’s a valid possibility. But whether the universe is finite or infinite is still an open question in cosmology, and current observations suggest it’s either infinite or so large that any curvature is undetectable.

As for your claim that some cosmologists say the entire universe decreased in volume as we go backward, that only applies to finite universes. An infinite universe doesn’t have a meaningful "volume" in the same way—only the density increases. If you find specific names making this claim, make sure they’re talking about the global universe, not just the observable one.

Your argument about high temperature being "ALSO compatible with very low volume" is trivial—it’s true for finite universes. But you started by arguing that an infinite universe was somehow incompatible with high density, which is false. GR allows both scenarios. You haven’t shown any physical reason why an infinite, high-density early universe would be impossible. You’re just asserting that a small volume would be possible, which no one is disputing.

So we're on the same page. But what I am claiming is plausible and possible, and my initial comment was too extreme, so I corrected it. But it's certainly not trivial. Calling it trivial shows your bias, which you essentially presented as a certainty, AG

AG, if your point is simply that a finite universe shrinking in volume as we go backward in time is possible, then sure, that’s a valid scenario within GR. But that was never in question—cosmologists already consider positively curved, closed universes as a possibility.

What was in question was your earlier claim that an infinite universe contradicts high temperature at the Big Bang, which was incorrect.

It's not incorrect; just not generally accepted at this time. AG

 

That’s why your shift to simply defending the plausibility of a finite universe seems like a retreat rather than an actual defense of your original argument.

You have an agenda to prove me wrong. I changed my position in response to your comments. Maybe you'd prefer that I stubbornly insist on a contradiction. I believe that a super high temperature is more plausible due to spatial contraction, than simply due to infinite space in the context of shortening distances between galaxies. AG 

Calling it trivial isn’t bias—it’s just stating that this is a well-known, uncontroversial fact.

It is a bias IMO. You've fallen in love with your theory because that's the prevailing opinion based on measurements of a flat universe. You can't seem to imagine a universe finite but so large that the distinction between flat and slightly spherical is a reasonable position. AG

 

The debate was never about whether a finite universe was possible;

At first you seemed to suggest it was not possible, if not expressly than implicitly, then you were clearer, so that was useful information, causing me to change my mind. But apparently you insist on being right, so you refuse to allow that. AG

it was about whether an infinite one was impossible under high density, which you originally suggested. If you’re now just saying a finite universe is a possibility, then there’s no actual argument left.

I think it's not just possible but likely because if it started out infinite in spatial extent, IOW from Nothing to instantaneously infinite, that would be a type of singularity which seems impossible and to be avoided in any physical theory. Now that's my opinion, and last I heard I allowed to have it. AG 

Quentin 

[Alan Grayson]

On Wednesday, February 12, 2025 at 2:26:02 PM UTC-7 Brent Meeker wrote:

On 2/12/2025 11:04 AM, Alan Grayson wrote:

On Wednesday, February 12, 2025 at 11:49:23 AM UTC-7 Quentin Anciaux wrote:

AG, your reasoning is flawed because it assumes a contradiction where none exists. An infinite universe doesn’t have to "become" infinite—it can be infinite at all times, just evolving in density and scale factor. High temperature and density at the Big Bang don’t require finiteness; they describe local conditions, not global topology.

Cosmological diagrams showing a "point" origin are simplifications based on the observable universe, not statements about the entire cosmos. The observable universe was smaller, but an infinite universe was never "shrinking" in the way you imply—just getting denser everywhere.

But this contradicts the Cosmological Principle (which might be wrong). AG

No it doesn't.  Every finite subset of the infinite universe originated in a point (at least in the classical analysis).
Brent

Do you have a reference for this, like a theorem which proves the claim? TY, AG

[Quentin Anciaux]

AG, you’re trying to rewrite your position while accusing me of having an agenda. You initially claimed an infinite universe contradicts high temperature at the Big Bang. That’s not "just not generally accepted"—it’s wrong. An infinite universe can still be extremely hot and dense everywhere.

Now you’re arguing that a finite universe is more plausible. That’s a completely different claim. Changing your position is fine, but pretending you didn’t is dishonest. If you had simply said, "I think a finite universe is more likely," we wouldn’t have been debating this at all.

Your claim that a finite universe is being dismissed due to "bias" is nonsense. The best measurements suggest the universe is extremely close to flat, which implies either an infinite universe or one so large that its curvature is undetectable. No one is ignoring evidence—cosmologists follow the data.

Your argument about "from nothing to infinite" being a singularity is based on a misunderstanding. If the universe is infinite now, it was infinite at the Big Bang, just in a much hotter and denser state. There’s no "instantaneously infinite" transition. That only seems strange if you assume an origin point, which an infinite universe doesn’t have.

You’re allowed to have an opinion, but you originally presented your claim as a contradiction. Now that it’s been shown not to be one, you’re reframing it as just a personal belief. If you’re now simply saying "I think a finite universe is more likely," fine. But don’t pretend that was your argument from the start.

Quentin 

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[Alan Grayson]

On Wednesday, February 12, 2025 at 11:50:09 PM UTC-7 Quentin Anciaux wrote:

AG, you’re trying to rewrite your position while accusing me of having an agenda. You initially claimed an infinite universe contradicts high temperature at the Big Bang. That’s not "just not generally accepted"—it’s wrong. An infinite universe can still be extremely hot and dense everywhere.

Now you’re arguing that a finite universe is more plausible. That’s a completely different claim. Changing your position is fine, but pretending you didn’t is dishonest.  If you had simply said, "I think a finite universe is more likely," we wouldn’t have been debating this at all.

You're really are an incorrigible asshole. I explicitly stated that I changed my position, in response to your replies! No dishonesty except in your perverted imagination. I told you the truth, but you refuse to accept it. The truth is that your replies showed me that my original claim about a contradiction was too extreme, so I consciously changed my position. That's really all there is to it, but because of your agenda, you just can't accept it and continue with your baseless, juvenile accusations. AG

Your claim that a finite universe is being dismissed due to "bias" is nonsense. The best measurements suggest the universe is extremely close to flat, which implies either an infinite universe or one so large that its curvature is undetectable. No one is ignoring evidence—cosmologists follow the data.

Your argument about "from nothing to infinite" being a singularity is based on a misunderstanding. If the universe is infinite now, it was infinite at the Big Bang, just in a much hotter and denser state. There’s no "instantaneously infinite" transition. That only seems strange if you assume an origin point, which an infinite universe doesn’t have.

IMO, Brent's post implies that an infinite universe began at a point. If so, it would have to begin as instantaneously infinite, a singularity of sorts which I reject. You behave as IF you know something about the time the universe came into existence. I think you give yourself way too much credit. AG 

You’re allowed to have an opinion, but you originally presented your claim as a contradiction. Now that it’s been shown not to be one, you’re reframing it as just a personal belief. If you’re now simply saying "I think a finite universe is more likely," fine. But don’t pretend that was your argument from the start.

 

Fact is I'm not pretending anything. It's just something in your sick and aggresive mentality. AG 

[Quentin Anciaux]

AG, you’re lashing out because you got called out. You claim you changed your position, yet you keep twisting the conversation to make it seem like your original argument was reasonable all along. That’s the issue, not whether you’re "allowed" to change your mind.

Brent’s post doesn’t imply an infinite universe "began at a point" because an infinite universe doesn’t have a single origin point, it was always infinite, just in a hotter, denser state. The idea that it must have started as "instantaneously infinite" is your own misunderstanding, not a flaw in the model.

You accuse others of having an agenda, playing the victim each time, yet you’re the one constantly using insults,  you’re the one shifting from argument to argument, looking for something to cling to. If you reject an infinite universe on personal grounds, just say so. But stop acting like it’s some deep physical contradiction when it’s just your own discomfort with the idea.

Quentin 

To view this discussion visit https://groups.google.com/d/msgid/everything-list/a2c479c5-2d20-47b2-ae71-7877ff2c5b04n%40googlegroups.com.

[Alan Grayson]

On Thursday, February 13, 2025 at 1:06:31 AM UTC-7 Quentin Anciaux wrote:

AG, you’re lashing out because you got called out. You claim you changed your position, yet you keep twisting the conversation to make it seem like your original argument was reasonable all along. That’s the issue, not whether you’re "allowed" to change your mind.

Brent’s post doesn’t imply an infinite universe "began at a point" because an infinite universe doesn’t have a single origin point, it was always infinite, just in a hotter, denser state. The idea that it must have started as "instantaneously infinite" is your own misunderstanding, not a flaw in the model.

You accuse others of having an agenda, playing the victim each time, yet you’re the one constantly using insults,  you’re the one shifting from argument to argument, looking for something to cling to. If you reject an infinite universe on personal grounds, just say so. But stop acting like it’s some deep physical contradiction when it’s just your own discomfort with the idea.

Quentin 

I was certainly correct on at least one point; you're an incurable, incorrigible asshole, who just can't understand that I changed my opinion, and stated that I did so because of your comments. It's like you can't take YES for an answer. It's useless to try to have a mature discussion with someone like you. AG

[Quentin Anciaux]

Le jeu. 13 févr. 2025, 09:25, Alan Grayson <agrays...@gmail.com> a écrit :

On Thursday, February 13, 2025 at 1:06:31 AM UTC-7 Quentin Anciaux wrote:

AG, you’re lashing out because you got called out. You claim you changed your position, yet you keep twisting the conversation to make it seem like your original argument was reasonable all along. That’s the issue, not whether you’re "allowed" to change your mind.

Brent’s post doesn’t imply an infinite universe "began at a point" because an infinite universe doesn’t have a single origin point, it was always infinite, just in a hotter, denser state. The idea that it must have started as "instantaneously infinite" is your own misunderstanding, not a flaw in the model.

You accuse others of having an agenda, playing the victim each time, yet you’re the one constantly using insults,  you’re the one shifting from argument to argument, looking for something to cling to. If you reject an infinite universe on personal grounds, just say so. But stop acting like it’s some deep physical contradiction when it’s just your own discomfort with the idea.

Quentin 

I was certainly correct on at least one point; you're an incurable, incorrigible asshole, who just can't understand that I changed my opinion, and stated that I did so because of your comments. It's like you can't take YES for an answer. It's useless to try to have a mature discussion with someone like you. AG

AG, you’re just deflecting with insults because you don’t like being called out. Changing your opinion is fine, but pretending your original argument was reasonable all along isn’t. You keep shifting positions while acting like you were always on solid ground. If you actually changed your mind, then stop trying to justify your earlier mistake and move on.

Quentin 

To view this discussion visit https://groups.google.com/d/msgid/everything-list/ee92ce41-7625-45a0-a1ae-0a42a6059121n%40googlegroups.com.

[Alan Grayson]

On Thursday, February 13, 2025 at 1:29:01 AM UTC-7 Quentin Anciaux wrote:

Le jeu. 13 févr. 2025, 09:25, Alan Grayson <agrays...@gmail.com> a écrit :

On Thursday, February 13, 2025 at 1:06:31 AM UTC-7 Quentin Anciaux wrote:

AG, you’re lashing out because you got called out. You claim you changed your position, yet you keep twisting the conversation to make it seem like your original argument was reasonable all along. That’s the issue, not whether you’re "allowed" to change your mind.

Brent’s post doesn’t imply an infinite universe "began at a point" because an infinite universe doesn’t have a single origin point, it was always infinite, just in a hotter, denser state. The idea that it must have started as "instantaneously infinite" is your own misunderstanding, not a flaw in the model.

You accuse others of having an agenda, playing the victim each time, yet you’re the one constantly using insults,  you’re the one shifting from argument to argument, looking for something to cling to. If you reject an infinite universe on personal grounds, just say so. But stop acting like it’s some deep physical contradiction when it’s just your own discomfort with the idea.

Quentin 

I was certainly correct on at least one point; you're an incurable, incorrigible asshole, who just can't understand that I changed my opinion, and stated that I did so because of your comments. It's like you can't take YES for an answer. It's useless to try to have a mature discussion with someone like you. AG

AG, you’re just deflecting with insults because you don’t like being called out. Changing your opinion is fine, but pretending your original argument was reasonable all along isn’t. You keep shifting positions while acting like you were always on solid ground. If you actually changed your mind, then stop trying to justify your earlier mistake and move on.

Quentin 

You're hopelessly confused. I changed my mind due to your comments. Later, I explained why I prefer my model to yours, and it involved what I conceive as a singularity added to the BB, of a universe coming into being with spatial infinity. That's all there is to. I just told you why I prefer my model to yours. I never pretended my original model was reasonable all along. I am allowed to have certain preferences. I can't waste more time responding to your juvenile, hostile accusations, so you can have the last word. AG 

[Quentin Anciaux]

AG, you’re spinning in circles. You changed your mind, fine, but you’re still trying to justify your original reasoning instead of just admitting it was flawed. Your so-called "singularity" argument is just your own discomfort with an infinite universe, not an actual contradiction. If you prefer a finite model, that’s your choice, but stop pretending it’s based on some deep physical insight.

Quentin 

To view this discussion visit https://groups.google.com/d/msgid/everything-list/9217c461-81d2-4943-b156-5081e6e05d27n%40googlegroups.com.

[Alan Grayson]

If there are two finite subsets of an infinite universe, is it conceivable that if one contains the other, can their union originate at the same point? AG 

[Alan Grayson]

On Wednesday, February 12, 2025 at 12:36:38 PM UTC-7 Brent Meeker wrote:

On 2/12/2025 12:55 AM, Alan Grayson wrote:

If the age of the universe is finite, which is generally believed, then no matter how fast it expands, it can never become spatially infinite, So, IF it is spatially infinite, this must have been its initial condition at or around he time of the Big Bang (BB). But this contradicts the assumption that it was at a super high temperature at or around the time of the BB.

No it doesn't.  I can be infinite and high temperature.  What gave you idea it couldn't?

IOW, if we run the clock backward, the universe seems to get incredibly small,

If the universe is infinite, then it is only the Observable Universe that gets incredibly small.

Is there any principle you are aware of, which prevents an infinite universe from becoming incredible small? 

[Alan Grayson]

On Friday, February 14, 2025 at 2:15:31 AM UTC-7 Alan Grayson wrote:

On Wednesday, February 12, 2025 at 11:09:34 PM UTC-7 Alan Grayson wrote:

On Wednesday, February 12, 2025 at 2:26:02 PM UTC-7 Brent Meeker wrote:

On 2/12/2025 11:04 AM, Alan Grayson wrote:

On Wednesday, February 12, 2025 at 11:49:23 AM UTC-7 Quentin Anciaux wrote:

AG, your reasoning is flawed because it assumes a contradiction where none exists. An infinite universe doesn’t have to "become" infinite—it can be infinite at all times, just evolving in density and scale factor. High temperature and density at the Big Bang don’t require finiteness; they describe local conditions, not global topology.

Cosmological diagrams showing a "point" origin are simplifications based on the observable universe, not statements about the entire cosmos. The observable universe was smaller, but an infinite universe was never "shrinking" in the way you imply—just getting denser everywhere.

But this contradicts the Cosmological Principle (which might be wrong). AG

No it doesn't.  Every finite subset of the infinite universe originated in a point (at least in the classical analysis).
Brent

Do you have a reference for this, like a theorem which proves the claim? Given two finite subsets of an infinite universe where one fully contains the other, can their union originate at the same point? AG

[Brent Meeker]

Sure.  Any subset of finite set is finite and so must originate from a point (in an FLRW model).

Brent

[Alan Grayson]

I was referring to the situation where one could keep containing the initial finite set, say the observable universe, and keep enlarging it by containing it in another finite set, but still having the SAME original point. Anyway, what I have real trouble conceptualizing is how a universe can emerge, or come into being, as infinite in spatial extent. It seems like a singularity of sorts, where there's an instantaneous expansion to infinity. AG 

[Brent Meeker]

On 2/14/2025 3:23 PM, Alan Grayson wrote:

On Wednesday, February 12, 2025 at 12:36:38 PM UTC-7 Brent Meeker wrote:

On 2/12/2025 12:55 AM, Alan Grayson wrote:

If the age of the universe is finite, which is generally believed, then no matter how fast it expands, it can never become spatially infinite, So, IF it is spatially infinite, this must have been its initial condition at or around he time of the Big Bang (BB). But this contradicts the assumption that it was at a super high temperature at or around the time of the BB.

No it doesn't.  I can be infinite and high temperature.  What gave you idea it couldn't?

IOW, if we run the clock backward, the universe seems to get incredibly small,

If the universe is infinite, then it is only the Observable Universe that gets incredibly small.

Is there any principle you are aware of, which prevents an infinite universe from becoming incredible small?

It would have to undergo an infinite change in size in a finite time, which would require infinite relative velocities.

Brent

[Alan Grayson]

I can't imagine a universe starting as infinite in spatial extent -- can you? -- which is why I imagine it finite in the beginning, and because of its finite age, it can never become infinite in spatial extent.  AG

[Brent Meeker]

As well as I can imagine any infinite thing.  Imagination can be trained.  My supervising professor, Englebert Schucking, could visualize four dimensional objects and draw their projection on the blackboard.  If you can't do that, you just have to suppress some dimensions; then in the (t,r) plane there's an infinite line, the t-axis, and to the right of this line is the (t,r) plane and in that plane everything is moving apart.  Just look at Ned Wright's cosmology tutorial:

https://www.astro.ucla.edu/~wright/cosmolog.htm

Brent

[Alan Grayson]

The problem is this; how does one imagine a universe which suddenly comes into being, initially resumably with zero spatial extent, and when it does, it's infinite in spatial extent? IMO, this would be a singularity implying infinite spatial expansion instantaneously. I have no alternative but to reject this model for a finite one, starting small and hot, and expanding, since I have no idea what it means to begin infinitely. I am open to suggestions. AG

BTW, since a finite volume such as the observable universe, can originate from a point, those pictorial models of the evolution of the universe, starting from a point, aka the BB,  are apparently accurate in their descriptions. That is, they're not necessarily simplifications of the evolution. AG

[Alan Grayson]

On Saturday, February 15, 2025 at 1:56:14 PM UTC-7 Brent Meeker wrote:

On 2/14/2025 11:36 PM, Alan Grayson wrote:

On Friday, February 14, 2025 at 11:06:42 PM UTC-7 Brent Meeker wrote:

On 2/14/2025 3:23 PM, Alan Grayson wrote:

On Wednesday, February 12, 2025 at 12:36:38 PM UTC-7 Brent Meeker wrote:

On 2/12/2025 12:55 AM, Alan Grayson wrote:

If the age of the universe is finite, which is generally believed, then no matter how fast it expands, it can never become spatially infinite, So, IF it is spatially infinite, this must have been its initial condition at or around he time of the Big Bang (BB). But this contradicts the assumption that it was at a super high temperature at or around the time of the BB.

No it doesn't.  I can be infinite and high temperature.  What gave you idea it couldn't?

IOW, if we run the clock backward, the universe seems to get incredibly small,

If the universe is infinite, then it is only the Observable Universe that gets incredibly small.

Is there any principle you are aware of, which prevents an infinite universe from becoming incredible small?

It would have to undergo an infinite change in size in a finite time, which would require infinite relative velocities.

Brent

I can't imagine a universe starting as infinite in spatial extent -- can you? --

As well as I can imagine any infinite thing.

But you can! For any real number x, and any integer N, imagine X + N, as N as N increases without limit. AG

[Brent Meeker]

On 2/15/2025 7:03 PM, Alan Grayson wrote:

On Saturday, February 15, 2025 at 1:56:14 PM UTC-7 Brent Meeker wrote:

On 2/14/2025 11:36 PM, Alan Grayson wrote:

On Friday, February 14, 2025 at 11:06:42 PM UTC-7 Brent Meeker wrote:

On 2/14/2025 3:23 PM, Alan Grayson wrote:

On Wednesday, February 12, 2025 at 12:36:38 PM UTC-7 Brent Meeker wrote:

On 2/12/2025 12:55 AM, Alan Grayson wrote:

If the age of the universe is finite, which is generally believed, then no matter how fast it expands, it can never become spatially infinite, So, IF it is spatially infinite, this must have been its initial condition at or around he time of the Big Bang (BB). But this contradicts the assumption that it was at a super high temperature at or around the time of the BB.

No it doesn't.  I can be infinite and high temperature.  What gave you idea it couldn't?

IOW, if we run the clock backward, the universe seems to get incredibly small,

If the universe is infinite, then it is only the Observable Universe that gets incredibly small.

Is there any principle you are aware of, which prevents an infinite universe from becoming incredible small?

It would have to undergo an infinite change in size in a finite time, which would require infinite relative velocities.

Brent

I can't imagine a universe starting as infinite in spatial extent -- can you? --

As well as I can imagine any infinite thing.  Imagination can be trained.  My supervising professor, Englebert Schucking, could visualize four dimensional objects and draw their projection on the blackboard.  If you can't do that, you just have to suppress some dimensions; then in the (t,r) plane there's an infinite line, the t-axis, and to the right of this line is the (t,r) plane and in that plane everything is moving apart.  Just look at Ned Wright's cosmology tutorial:

https://www.astro.ucla.edu/~wright/cosmolog.htm

Brent

The problem is this; how does one imagine a universe which suddenly comes into being, initially resumably with zero spatial extent, and when it does, it's infinite in spatial extent? IMO, this would be a singularity implying infinite spatial expansion instantaneously. I have no alternative but to reject this model for a finite one, starting small and hot, and expanding, since I have no idea what it means to begin infinitely. I am open to suggestions. AG

Expand your imagination.  Remember "infinite" just means without bound.  You don't  have to imagine the whole infinite line, just imagine a line without imagining it's ends.

BTW, since a finite volume such as the observable universe, can originate from a point, those pictorial models of the evolution of the universe, starting from a point, aka the BB,  are apparently accurate in their descriptions. That is, they're not necessarily simplifications of the evolution. AG

Probably they are since they don't take account of quantum mechanics; but we don't know exactly how they are wrong.

Brent

[Alan Grayson]

On Saturday, February 15, 2025 at 9:11:22 PM UTC-7 Brent Meeker wrote:

On 2/15/2025 7:03 PM, Alan Grayson wrote:

On Saturday, February 15, 2025 at 1:56:14 PM UTC-7 Brent Meeker wrote:

On 2/14/2025 11:36 PM, Alan Grayson wrote:

On Friday, February 14, 2025 at 11:06:42 PM UTC-7 Brent Meeker wrote:

On 2/14/2025 3:23 PM, Alan Grayson wrote:

On Wednesday, February 12, 2025 at 12:36:38 PM UTC-7 Brent Meeker wrote:

On 2/12/2025 12:55 AM, Alan Grayson wrote:

If the age of the universe is finite, which is generally believed, then no matter how fast it expands, it can never become spatially infinite, So, IF it is spatially infinite, this must have been its initial condition at or around he time of the Big Bang (BB). But this contradicts the assumption that it was at a super high temperature at or around the time of the BB.

No it doesn't.  I can be infinite and high temperature.  What gave you idea it couldn't?

IOW, if we run the clock backward, the universe seems to get incredibly small,

If the universe is infinite, then it is only the Observable Universe that gets incredibly small.

Is there any principle you are aware of, which prevents an infinite universe from becoming incredible small?

It would have to undergo an infinite change in size in a finite time, which would require infinite relative velocities.

Brent

I can't imagine a universe starting as infinite in spatial extent -- can you? --

As well as I can imagine any infinite thing.  Imagination can be trained.  My supervising professor, Englebert Schucking, could visualize four dimensional objects and draw their projection on the blackboard.  If you can't do that, you just have to suppress some dimensions; then in the (t,r) plane there's an infinite line, the t-axis, and to the right of this line is the (t,r) plane and in that plane everything is moving apart.  Just look at Ned Wright's cosmology tutorial:

https://www.astro.ucla.edu/~wright/cosmolog.htm

Brent

The problem is this; how does one imagine a universe which suddenly comes into being, initially resumably with zero spatial extent, and when it does, it's infinite in spatial extent? IMO, this would be a singularity implying infinite spatial expansion instantaneously. I have no alternative but to reject this model for a finite one, starting small and hot, and expanding, since I have no idea what it means to begin infinitely. I am open to suggestions. AG

Expand your imagination.  Remember "infinite" just means without bound.  You don't  have to imagine the whole infinite line, just imagine a line without imagining it's ends.

Not saying I believe it, but the best bet at this point in time, is that the universe began as a quantum fluctuation, thus small, very small! AG

[Alan Grayson]

Consider this: For Nothing to become Something and also be infinite in spatial extent, that Something must have that infinity as its initial condition, given that it now has a finite age. But transforming from Nothing to Something and having that infinity as its initial condition as infinite in spatial extent, is, if you think about, not remotely intelligible. For this reason, I conclude it can't have this infinity as its initial condition and can't be flat, which implies this infinity. AG 

[Quentin Anciaux]

AG, your argument assumes a false dichotomy between "nothing" and "something" while making unjustified claims about infinity. If the universe is infinite now, it was infinite at the Big Bang, there’s no "transition" from finite to infinite. Your assertion that this is "not remotely intelligible" is just an appeal to personal incredulity, not an actual argument.

Quentin 

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[Alan Grayson]

On Sunday, February 16, 2025 at 1:57:39 AM UTC-7 Quentin Anciaux wrote:

AG wrote > Consider this: For Nothing to become Something and also be infinite in spatial extent, that Something must have that infinity as its initial condition, given that it now has a finite age. But transforming from Nothing to Something and having that infinity as its initial condition as infinite in spatial extent, is, if you think about, not remotely intelligible. For this reason, I conclude it can't have this infinity as its initial condition and can't be flat, which implies this infinity. AG 

Quentin replied> AG, your argument assumes a false dichotomy between "nothing" and "something" while making unjustified claims about infinity. If the universe is infinite now, it was infinite at the Big Bang, there’s no "transition" from finite to infinite. Your assertion that this is "not remotely intelligible" is just an appeal to personal incredulity, not an actual argument. 

You need to factor in the finite age of the universe, which shows that if it is infinite now, that must have been its initial condition, and then continue the analysis from the creation event. Much more important, you're certainly entitled to your opinion, but saying that I am assuming a false dichotomy isn't true just because you believe it's true. AG 

[Quentin Anciaux]

AG, the finite age of the universe doesn’t create the problem you think it does. If the universe is infinite now, it was infinite at the Big Bang. There was no "transition" from finite to infinite, just a change in density and scale factor. This follows directly from the FLRW metric, which allows an infinite universe to evolve from an extremely dense state.

Your claim that this transformation is "not remotely intelligible" is just an argument from personal incredulity. You haven't provided any actual contradiction, just a statement that you find it hard to grasp. That’s not physics, that’s just a preference.

Flatness implies infinite extent only in the absence of curvature, but small positive curvature would still be consistent with observations. 

I have no preference for either a finite or infinite universe. The question of whether the universe is finite or infinite remains unresolved, and neither possibility can be dismissed outright.

Quentin 

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[Alan Grayson]

On Sunday, February 16, 2025 at 2:26:37 AM UTC-7 Quentin Anciaux wrote:

AG, the finite age of the universe doesn’t create the problem you think it does. If the universe is infinite now, it was infinite at the Big Bang. There was no "transition" from finite to infinite, just a change in density and scale factor.

 

That's your opinion. AG 

This follows directly from the FLRW metric, which allows an infinite universe to evolve from an extremely dense state.

That's one metric, not necessarily the whole story. Your model assumes the universe "began" as infinite. But couldn't it have started as Nothingness? You dismiss that possibility, which is your OPINION! AG 

Your claim that this transformation is "not remotely intelligible" is just an argument from personal incredulity. You haven't provided any actual contradiction, just a statement that you find it hard to grasp. That’s not physics, that’s just a preference.

I am entitled to my opinion, and you are entitled to yours. Your opinion is to start the universe with some non-zero density and then apply the FLRW metric. My opinion is that it started as a singularity with zero volume and then hugely expanded. Where the matter and energy came from I have no idea. That's the best argument for your model. AG 

Flatness implies infinite extent only in the absence of curvature, but small positive curvature would still be consistent with observations. 

We agree on that! AG 

I have no preference for either a finite or infinite universe. The question of whether the universe is finite or infinite remains unresolved, and neither possibility can be dismissed outright.

I dismiss that our bubble is infinite, not that that from which it emerged is finite. IOW, my opinion is that the sub-stratum from which it emerged is infinite, but of course this is just my guess. AG

[Quentin Anciaux]

AG, you keep framing this as a matter of "opinion," but the issue isn’t what either of us prefers, it’s what the mathematics of cosmology allows. The FLRW metric isn’t just "one model"; it’s the framework derived from GR that describes how a universe evolves given its initial conditions. If the universe is infinite now, it was infinite at the Big Bang, there’s no logical contradiction in that.

Starting from "nothingness" isn’t something GR addresses; that’s a separate issue in quantum cosmology. You act as if rejecting a universe "starting from nothing" is just a personal stance, but the physics we have today describes a high-density early state, not a spontaneous emergence from absolute nothing. That’s not opinion, that’s what current models describe.

Your "singularity with zero volume" interpretation is fine, but it’s not the only possibility. Whether the universe was initially finite or infinite remains open, but your argument that an infinite universe must have "transitioned" from nothing to infinite is flawed. If you’re now saying the substratum from which the universe emerged is infinite, then you’ve already accepted an infinite framework, it just shifts the question one level back.

Quentin 

To view this discussion visit https://groups.google.com/d/msgid/everything-list/de06d36e-2b40-429a-ac0f-ed02db2603f5n%40googlegroups.com.

[Alan Grayson]

On Sunday, February 16, 2025 at 3:18:58 AM UTC-7 Quentin Anciaux wrote:

AG, you keep framing this as a matter of "opinion," but the issue isn’t what either of us prefers, it’s what the mathematics of cosmology allows. The FLRW metric isn’t just "one model"; it’s the framework derived from GR that describes how a universe evolves given its initial conditions. If the universe is infinite now, it was infinite at the Big Bang, there’s no logical contradiction in that.

That wasn't my claim. I claimed it couldn't become infinite if its age is finite. So if it's now infinite, that must have been its initial condition. AG 

 

Starting from "nothingness" isn’t something GR addresses; that’s a separate issue in quantum cosmology. You act as if rejecting a universe "starting from nothing" is just a personal stance,

You rejected that pov. I asserted it as true, or at least plausible. AG

 

but the physics we have today describes a high-density early state, not a spontaneous emergence from absolute nothing. That’s not opinion, that’s what current models describe.

I never disputed that pov. Our theories begin slightly AFTER the BB. AG

Your "singularity with zero volume" interpretation is fine, but it’s not the only possibility. Whether the universe was initially finite or infinite remains open, but your argument that an infinite universe must have "transitioned" from nothing to infinite is flawed.

Why flawed? You seem OK with articulating an opinion, but only if the opinion is yours. AG

 

If you’re now saying the substratum from which the universe emerged is infinite, then you’ve already accepted an infinite framework, it just shifts the question one level back.

I am stating what I believe is likely true, which of course I cannot prove. Nothing wrong with going back beyond current theories. AG 

[Alan Grayson]

On Sunday, February 16, 2025 at 3:38:12 AM UTC-7 Alan Grayson wrote:

On Sunday, February 16, 2025 at 3:18:58 AM UTC-7 Quentin Anciaux wrote:

AG, you keep framing this as a matter of "opinion," but the issue isn’t what either of us prefers, it’s what the mathematics of cosmology allows. The FLRW metric isn’t just "one model"; it’s the framework derived from GR that describes how a universe evolves given its initial conditions. If the universe is infinite now, it was infinite at the Big Bang, there’s no logical contradiction in that.

That wasn't my claim. I claimed it couldn't become infinite if its age is finite. So if it's now infinite, that must have been its initial condition. AG 

 

Starting from "nothingness" isn’t something GR addresses; that’s a separate issue in quantum cosmology. You act as if rejecting a universe "starting from nothing" is just a personal stance,

You rejected that pov. I asserted it as true, or at least plausible. AG

 

but the physics we have today describes a high-density early state, not a spontaneous emergence from absolute nothing. That’s not opinion, that’s what current models describe.

I never disputed that pov. Our theories begin slightly AFTER the BB. AG

Your "singularity with zero volume" interpretation is fine, but it’s not the only possibility. Whether the universe was initially finite or infinite remains open, but your argument that an infinite universe must have "transitioned" from nothing to infinite is flawed.

Why flawed? You seem OK with articulating an opinion, but only if the opinion is yours. AG

FWIW, I can imagine Something emerging from Nothing, say a quantum fluctuation, but NOT Something that is initially infinite in spatial extent. AG 

[Alan Grayson]

On Sunday, February 16, 2025 at 1:57:39 AM UTC-7 Quentin Anciaux wrote:

AG, your argument assumes a false dichotomy between "nothing" and "something"

Why a false dichotomy? No transition from finite to infinite if it was alway infinite, but was it? AG

[Liz R]

Apparently the simplest model of the universe is one that is infinite at all times (according to Max Tegmark) - the "concordance" model? There is no reason an infinite universe couldn't have undergone scale expansion, an (in this case, presumably uncountably) infinite thing remains infinite no matter how much you expand it. Whether the universe is a continuum is key to this, so it depends on an as-yet unknown TOE. If spacetime is quantised - in some sense - then whether it could be infinite, and whether it could expand, might still be up for grabs.

Note that a quantised spacetime would presumably only contain a finite number of possible states inside any volume (e.g. our cosmological horizon) and hemce an infinite universe would eventually repeat itself across sufficiently large distances. Again quoting Max Tegmark, this would occur for our Hubble sphere at something like a distance of 10^10^37 metres (from memory - the actual figures don't really matter much for any practical purpose, just note that they make a googol look ultramicroscopic). Assuming that repeated identical quantum states are indistinguishable, an infinite quantised universe would in fact be "piecewise finite" on Vast scales - repeating arbitrarily large identical volumes would be not just indistinguishable in principle but actually identical. So on this basis, the universe would be a sort of Library of Babel in which all possible quantum states exist (including "Harry Potter" and "White Rabbit" universes) - but since the number of possible states is finite for a given volume, it would eventually run out of combinations and repeat itself. Quite what this would look like on "hyperastronomical scales" I leave to the mathematicians.

By the way the Cosmological Principle is an observation / assumption, not an actual principle based on any physical laws.

[Alan Grayson]

On Monday, February 17, 2025 at 12:49:27 PM UTC-7 Liz R wrote:

Apparently the simplest model of the universe is one that is infinite at all times (according to Max Tegmark) - the "concordance" model? There is no reason an infinite universe couldn't have undergone scale expansion, an (in this case, presumably uncountably) infinite thing remains infinite no matter how much you expand it. Whether the universe is a continuum is key to this, so it depends on an as-yet unknown TOE. If spacetime is quantised - in some sense - then whether it could be infinite, and whether it could expand, might still be up for grabs.

Note that a quantised spacetime would presumably only contain a finite number of possible states inside any volume (e.g. our cosmological horizon) and hemce an infinite universe would eventually repeat itself across sufficiently large distances. Again quoting Max Tegmark, this would occur for our Hubble sphere at something like a distance of 10^10^37 metres (from memory - the actual figures don't really matter much for any practical purpose, just note that they make a googol look ultramicroscopic). Assuming that repeated identical quantum states are indistinguishable, an infinite quantised universe would in fact be "piecewise finite" on Vast scales - repeating arbitrarily large identical volumes would be not just indistinguishable in principle but actually identical. So on this basis, the universe would be a sort of Library of Babel in which all possible quantum states exist (including "Harry Potter" and "White Rabbit" universes) - but since the number of possible states is finite for a given volume, it would eventually run out of combinations and repeat itself. Quite what this would look like on "hyperastronomical scales" I leave to the mathematicians.

FWIW, our best current measurements fail to show any quantization of spacetime. This was discussed here by Lawrence Crowell a long time ago, and I don't recall the level of fineness of these results. AG 

 

By the way the Cosmological Principle is an observation / assumption, not an actual principle based on any physical laws.

Not exactly. Physical observation do play a significant role in generating principles. Faraday's observations of the behavior of magnetic fields comes to mind, and the MM experiment, which Einstein was aware of, which showed the velocity of light is independent of an observer's motion. In the case of the CC, we have ambiguous results. The CMBR suggests the universe was very close to homogeneous and isoptropic when its age was about 380,000 years old, but measurements much later in time show it's actually lumpy, with ultra long filaments containing galaxies, separated by huge voids. I'd go with the later, showing that the CC is false. AG 

[Brent Meeker]

On 2/17/2025 5:08 PM, Alan Grayson wrote:

On Monday, February 17, 2025 at 12:49:27 PM UTC-7 Liz R wrote:

Apparently the simplest model of the universe is one that is infinite at all times (according to Max Tegmark) - the "concordance" model? There is no reason an infinite universe couldn't have undergone scale expansion, an (in this case, presumably uncountably) infinite thing remains infinite no matter how much you expand it. Whether the universe is a continuum is key to this, so it depends on an as-yet unknown TOE. If spacetime is quantised - in some sense - then whether it could be infinite, and whether it could expand, might still be up for grabs.

Note that a quantised spacetime would presumably only contain a finite number of possible states inside any volume (e.g. our cosmological horizon) and hemce an infinite universe would eventually repeat itself across sufficiently large distances. Again quoting Max Tegmark, this would occur for our Hubble sphere at something like a distance of 10^10^37 metres (from memory - the actual figures don't really matter much for any practical purpose, just note that they make a googol look ultramicroscopic). Assuming that repeated identical quantum states are indistinguishable, an infinite quantised universe would in fact be "piecewise finite" on Vast scales - repeating arbitrarily large identical volumes would be not just indistinguishable in principle but actually identical. So on this basis, the universe would be a sort of Library of Babel in which all possible quantum states exist (including "Harry Potter" and "White Rabbit" universes) - but since the number of possible states is finite for a given volume, it would eventually run out of combinations and repeat itself. Quite what this would look like on "hyperastronomical scales" I leave to the mathematicians.

FWIW, our best current measurements fail to show any quantization of spacetime. This was discussed here by Lawrence Crowell a long time ago, and I don't recall the level of fineness of these results. AG

It was a paper I cited years ago that noted there was no dispersion of gamma rays from very distant galaxies which ruled out on discrete structure to space down to less than the Planck scale.  Here's a more recent paper: https://physics.aps.org/articles/v17/s99

Brent

To view this discussion visit https://groups.google.com/d/msgid/everything-list/b2d1a9a2-0170-4529-81ee-d2167665a05en%40googlegroups.com.

[Quentin Anciaux]

Missing Bruno here, but in the UDA framework, reality is continuous, emerging from the infinite computations that pass through your current state.

Quentin 

To view this discussion visit https://groups.google.com/d/msgid/everything-list/8467b426-aae9-4700-be09-b226e387b375%40gmail.com.

[Alan Grayson]

On Tuesday, February 18, 2025 at 3:42:56 PM UTC-7 Brent Meeker wrote:

On 2/17/2025 5:08 PM, Alan Grayson wrote:

On Monday, February 17, 2025 at 12:49:27 PM UTC-7 Liz R wrote:

Apparently the simplest model of the universe is one that is infinite at all times (according to Max Tegmark) - the "concordance" model? There is no reason an infinite universe couldn't have undergone scale expansion, an (in this case, presumably uncountably) infinite thing remains infinite no matter how much you expand it. Whether the universe is a continuum is key to this, so it depends on an as-yet unknown TOE. If spacetime is quantised - in some sense - then whether it could be infinite, and whether it could expand, might still be up for grabs.

Note that a quantised spacetime would presumably only contain a finite number of possible states inside any volume (e.g. our cosmological horizon) and hemce an infinite universe would eventually repeat itself across sufficiently large distances. Again quoting Max Tegmark, this would occur for our Hubble sphere at something like a distance of 10^10^37 metres (from memory - the actual figures don't really matter much for any practical purpose, just note that they make a googol look ultramicroscopic). Assuming that repeated identical quantum states are indistinguishable, an infinite quantised universe would in fact be "piecewise finite" on Vast scales - repeating arbitrarily large identical volumes would be not just indistinguishable in principle but actually identical. So on this basis, the universe would be a sort of Library of Babel in which all possible quantum states exist (including "Harry Potter" and "White Rabbit" universes) - but since the number of possible states is finite for a given volume, it would eventually run out of combinations and repeat itself. Quite what this would look like on "hyperastronomical scales" I leave to the mathematicians.

FWIW, our best current measurements fail to show any quantization of spacetime. This was discussed here by Lawrence Crowell a long time ago, and I don't recall the level of fineness of these results. AG

It was a paper I cited years ago that noted there was no dispersion of gamma rays from very distant galaxies which ruled out on discrete structure to space down to less than the Planck scale.  Here's a more recent paper: https://physics.aps.org/articles/v17/s99

Brent

Do you have any idea how has this result has effected the quest for a quantum theory of gravity? AG