Re: Clark on the singularity at T=0

[Brent Meeker]

On 2/8/2025 12:47 AM, Alan Grayson wrote:

I can't recall on which thread I made the argument, and Clark agreed, that if the universe has a finite age, it cannot be infinite in spatial extent. In response, Clark and Brent claimed it could've began as infinite. Isn't there a theorem, which might have been proven by Penrose, that the contracting universe

Only the observable universe, if I recall correctly.

Brent

must converge to a point or zero volume containing all matter and energy? What is the name of that theorem, assuming it exists?  AG --

[Alan Grayson]

On Saturday, February 8, 2025 at 3:26:33 PM UTC-7 Brent Meeker wrote:

On 2/8/2025 12:47 AM, Alan Grayson wrote:

I can't recall on which thread I made the argument, and Clark agreed, that if the universe has a finite age, it cannot be infinite in spatial extent. In response, Clark and Brent claimed it could've began as infinite. Isn't there a theorem, which might have been proven by Penrose, that the contracting universe

Only the observable universe, if I recall correctly.

Applying the Penrose-Hawking Singularity Theorem, running the clock backward implies the universe doesn't converge to a point of zero volume, but to a BH, and that's the whole universe, not just the observable universe. AG

[Jesse Mazer]

On Sun, Feb 9, 2025 at 2:04 AM Alan Grayson <agrays...@gmail.com> wrote:

On Saturday, February 8, 2025 at 3:26:33 PM UTC-7 Brent Meeker wrote:

On 2/8/2025 12:47 AM, Alan Grayson wrote:

I can't recall on which thread I made the argument, and Clark agreed, that if the universe has a finite age, it cannot be infinite in spatial extent. In response, Clark and Brent claimed it could've began as infinite. Isn't there a theorem, which might have been proven by Penrose, that the contracting universe

Only the observable universe, if I recall correctly.

Applying the Penrose-Hawking Singularity Theorem, running the clock backward implies the universe doesn't converge to a point of zero volume, but to a BH, and that's the whole universe, not just the observable universe. AG

The Penrose-Hawking singularity theorems only implies an initial singularity, it doesn't say the universe was a black hole or that the whole universe (not just the observable part) must be finite--a black hole metric is different GR solution than the Friedmann–Lemaître–Robertson–Walker metric for an expanding universe at https://en.wikipedia.org/wiki/Friedmann–Lemaître–Robertson–Walker_metric (sometimes just called the Friedmann-Robertson-Walker metric or FRW). A black hole metric has a radial parameter where curvature gets larger the closer you are to the the black hole, and approaches zero the farther you get (the metric is 'asymptotically flat'), whereas the FLRW is completely uniform in the curvature and density of matter/energy throughout all of space at every moment of the cosmological time parameter. 

Penrose himself refers to the fact that the flat and open versions of the FRW solution imply a spatially infinite universe on pages 323-324 of his book "The Emperor's New Mind":

 

[Alan Grayson]

Firstly, if the age of the universe is finite, it can't expand spatially to infinity regardless of its rate of expansion. So if the universe is spatially infinite, this must have been its initial condition. Secondly, current theory is that the very very early universe was hugely hot, at a much higher temperature than at present. This implies, for me, that it was small, analogous to a highly compressed gas. IMO, it can't be small and hot, and also be spatially infinite. If it's not spatially infinite, it can't be flat. As it contracts, if it forms a singularity with all its mass and energy concentrated in a tiny region, it will presumably form a BH. Planck satelite data allows for a positively and negatively geometry, but the data for flatness is much more persuasive. I therefore believe it is so huge that we cannot distinguish between positively curved and flat. It's likely approximately spherical in shape because the expansion is approximately uniform, that is isotropic, as evidenced by the near uniformity of the Cosmological Red Shift. AG 

 

[Brent Meeker]

On 2/8/2025 11:04 PM, Alan Grayson wrote:

On Saturday, February 8, 2025 at 3:26:33 PM UTC-7 Brent Meeker wrote:

On 2/8/2025 12:47 AM, Alan Grayson wrote:

I can't recall on which thread I made the argument, and Clark agreed, that if the universe has a finite age, it cannot be infinite in spatial extent. In response, Clark and Brent claimed it could've began as infinite. Isn't there a theorem, which might have been proven by Penrose, that the contracting universe

Only the observable universe, if I recall correctly.

Applying the Penrose-Hawking Singularity Theorem, running the clock backward implies the universe doesn't converge to a point of zero volume, but to a BH, and that's the whole universe, not just the observable universe. AG

Anything inside a non-rotating black hole, falls into the singularity, which classically is a point.  But that black hole is a spherically symmetry structure with an event horizon in an infinite asymptotically flat universe.  And that's also what the Penrose singularity theorem applies to, a structure embedded in an otherwise flat universe.  So it doesn't apply to a universe.  Furthermore, Roy Kerr says Penrose's proof makes unjustified assumptions in the case of rotating black holes and is invalid.

Brent

Brent

must converge to a point or zero volume containing all matter and energy? What is the name of that theorem, assuming it exists?  AG --

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[Jesse Mazer]

On Sun, Feb 9, 2025 at 3:57 PM Alan Grayson <agrays...@gmail.com> wrote:

On Sunday, February 9, 2025 at 10:08:36 AM UTC-7 Jesse Mazer wrote:

Firstly, if the age of the universe is finite, it can't expand spatially to infinity regardless of its rate of expansion.

The FLRW metric for a flat or negatively curved universe does not describe a universe that "expands spatially to infinity", it is already infinite at *every* finite time interval after the Big Bang, and there is no size at T=0 because the singularity is more like the edge of spacetime than a part of the spacetime.

 

So if the universe is spatially infinite, this must have been its initial condition. Secondly, current theory is that the very very early universe was hugely hot, at a much higher temperature than at present. This implies, for me, that it was small, analogous to a highly compressed gas. IMO, it can't be small and hot, and also be spatially infinite.

Presumably you can imagine an infinite plane covered with dots that are on average 1 meter apart, and a different infinite plane covered with dots that are on average 1 millimeter apart; this illustrates how the notion of particles having a higher or lower density doesn't depend on there being a finite number of them. And the bottom line is that an infinite space whose density changes with time is a mathematically allowable solution to the Einstein field equations, physicists trust math over personal gut feelings and intuitions.

 

If it's not spatially infinite, it can't be flat. As it contracts, if it forms a singularity with all its mass and energy concentrated in a tiny region, it will presumably form a BH.

Not according to general relativity, no. The classic "Usenet Physics FAQ" at https://math.ucr.edu/home/baez/physics/index.html addresses this point specifically in the question and answer at https://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html where part of the answer is:

>Why did the universe not collapse and form a black hole at the beginning?

>Sometimes people find it hard to understand why the Big Bang is not a black hole.  After all, the density of matter in the first fraction of a second was much higher than that found in any star, and dense matter is supposed to curve spacetime strongly.  At sufficient density there must be matter contained within a region smaller than the Schwarzschild radius for its mass.  Nevertheless, the Big Bang manages to avoid being trapped inside a black hole of its own making and paradoxically the space near the singularity is actually flat rather than curving tightly.  How can this be?

>The short answer is that the Big Bang gets away with it because it is expanding rapidly near the beginning and the rate of expansion is slowing down.  Space can be flat even when spacetime is not.  Spacetime's curvature can come from the temporal parts of the spacetime metric which measures the deceleration of the expansion of the universe.  So the total curvature of spacetime is related to the density of matter, but there is a contribution to curvature from the expansion as well as from any curvature of space.  The Schwarzschild solution of the gravitational equations is static and demonstrates the limits placed on a static spherical body before it must collapse to a black hole.  The Schwarzschild limit does not apply to rapidly expanding matter.

 

Planck data allows for a positively and negatively geometry, but the dats for flatness is more persuasive. I believe is it so huge that we can't distinguish between positively curved and flat. It's likely approximately spherical in shape because the expansion is approximately uniform as evidenced by the near uniformity in outward expansion of the Cosmological Red Shift. AG 

It's certainly possible it is positively curved but so large (much larger than the observable region) that it's indistinguishable from flatness given the precision of our current best measurements. But if you think you can conclude this *must* be the case a priori just given your verbal arguments (arguments which contradict what the GR equations say is a mathematically valid solution), no physicist is going to go along with that.

Jesse

[Alan Grayson]

On Sunday, February 9, 2025 at 2:22:29 PM UTC-7 Jesse Mazer wrote:

On Sun, Feb 9, 2025 at 3:57 PM Alan Grayson <agrays...@gmail.com> wrote:

On Sunday, February 9, 2025 at 10:08:36 AM UTC-7 Jesse Mazer wrote:

On Sun, Feb 9, 2025 at 2:04 AM Alan Grayson <agrays...@gmail.com> wrote:

On Saturday, February 8, 2025 at 3:26:33 PM UTC-7 Brent Meeker wrote:

On 2/8/2025 12:47 AM, Alan Grayson wrote:

I can't recall on which thread I made the argument, and Clark agreed, that if the universe has a finite age, it cannot be infinite in spatial extent. In response, Clark and Brent claimed it could've began as infinite. Isn't there a theorem, which might have been proven by Penrose, that the contracting universe

Only the observable universe, if I recall correctly.

Applying the Penrose-Hawking Singularity Theorem, running the clock backward implies the universe doesn't converge to a point of zero volume, but to a BH, and that's the whole universe, not just the observable universe. AG

The Penrose-Hawking singularity theorems only implies an initial singularity, it doesn't say the universe was a black hole or that the whole universe (not just the observable part) must be finite--a black hole metric is different GR solution than the Friedmann–Lemaître–Robertson–Walker metric for an expanding universe at https://en.wikipedia.org/wiki/Friedmann–Lemaître–Robertson–Walker_metric (sometimes just called the Friedmann-Robertson-Walker metric or FRW). A black hole metric has a radial parameter where curvature gets larger the closer you are to the the black hole, and approaches zero the farther you get (the metric is 'asymptotically flat'), whereas the FLRW is completely uniform in the curvature and density of matter/energy throughout all of space at every moment of the cosmological time parameter. 

Penrose himself refers to the fact that the flat and open versions of the FRW solution imply a spatially infinite universe on pages 323-324 of his book "The Emperor's New Mind":

Firstly, if the age of the universe is finite, it can't expand spatially to infinity regardless of its rate of expansion.

The FLRW metric for a flat or negatively curved universe does not describe a universe that "expands spatially to infinity", it is already infinite at *every* finite time interval after the Big Bang, and there is no size at T=0 because the singularity is more like the edge of spacetime than a part of the spacetime.

That's my claim to some extent, that it must begin as infinite, if it has finite age and is NOW infinite in spatial extent. But beginning as infinite implies some problems which should be discussed. And maybe FLRW shouldn't assume it's flat. AG

 

So if the universe is spatially infinite, this must have been its initial condition. Secondly, current theory is that the very very early universe was hugely hot, at a much higher temperature than at present. This implies, for me, that it was small, analogous to a highly compressed gas. IMO, it can't be small and hot, and also be spatially infinite.

Presumably you can imagine an infinite plane covered with dots that are on average 1 meter apart, and a different infinite plane covered with dots that are on average 1 millimeter apart; this illustrates how the notion of particles having a higher or lower density doesn't depend on there being a finite number of them. And the bottom line is that an infinite space whose density changes with time is a mathematically allowable solution to the Einstein field equations, physicists trust math over personal gut feelings and intuitions.

Many, if not most of the major advances in physics have been the result of personal gut feelings and intuitions. I think it was Feynman who offered the insight that most advances in physics were based in guesses. Yes guesses. Shall I trust physicists such a Carroll who knows GR intimately and yet has evolved into a MW clown? AG

 

If it's not spatially infinite, it can't be flat. As it contracts, if it forms a singularity with all its mass and energy concentrated in a tiny region, it will presumably form a BH.

Not according to general relativity, no. The classic "Usenet Physics FAQ" at https://math.ucr.edu/home/baez/physics/index.html addresses this point specifically in the question and answer at https://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html where part of the answer is:

>Why did the universe not collapse and form a black hole at the beginning?

>Sometimes people find it hard to understand why the Big Bang is not a black hole.  After all, the density of matter in the first fraction of a second was much higher than that found in any star, and dense matter is supposed to curve spacetime strongly.  At sufficient density there must be matter contained within a region smaller than the Schwarzschild radius for its mass.  Nevertheless, the Big Bang manages to avoid being trapped inside a black hole of its own making and paradoxically the space near the singularity is actually flat rather than curving tightly.  How can this be?

>The short answer is that the Big Bang gets away with it because it is expanding rapidly near the beginning and the rate of expansion is slowing down.  Space can be flat even when spacetime is not.  Spacetime's curvature can come from the temporal parts of the spacetime metric which measures the deceleration of the expansion of the universe.  So the total curvature of spacetime is related to the density of matter, but there is a contribution to curvature from the expansion as well as from any curvature of space.  The Schwarzschild solution of the gravitational equations is static and demonstrates the limits placed on a static spherical body before it must collapse to a black hole.  The Schwarzschild limit does not apply to rapidly expanding matter.

 

Planck data allows for a positively and negatively geometry, but the dats for flatness is more persuasive. I believe is it so huge that we can't distinguish between positively curved and flat. It's likely approximately spherical in shape because the expansion is approximately uniform as evidenced by the near uniformity in outward expansion of the Cosmological Red Shift. AG 

It's certainly possible it is positively curved but so large (much larger than the observable region) that it's indistinguishable from flatness given the precision of our current best measurements. But if you think you can conclude this *must* be the case a priori just given your verbal arguments (arguments which contradict what the GR equations say is a mathematically valid solution), no physicist is going to go along with that.

Did I ever say anything "must" be the case? I don't think a spherical universe, finite in spatial extend and expanding, contradicts GR equations. AG 

Jesse

[Jesse Mazer]

On Sun, Feb 9, 2025 at 7:05 PM Alan Grayson <agrays...@gmail.com> wrote:

On Sunday, February 9, 2025 at 2:22:29 PM UTC-7 Jesse Mazer wrote:

On Sun, Feb 9, 2025 at 3:57 PM Alan Grayson <agrays...@gmail.com> wrote:

On Sunday, February 9, 2025 at 10:08:36 AM UTC-7 Jesse Mazer wrote:

On Sun, Feb 9, 2025 at 2:04 AM Alan Grayson <agrays...@gmail.com> wrote:

On Saturday, February 8, 2025 at 3:26:33 PM UTC-7 Brent Meeker wrote:

On 2/8/2025 12:47 AM, Alan Grayson wrote:

I can't recall on which thread I made the argument, and Clark agreed, that if the universe has a finite age, it cannot be infinite in spatial extent. In response, Clark and Brent claimed it could've began as infinite. Isn't there a theorem, which might have been proven by Penrose, that the contracting universe

Only the observable universe, if I recall correctly.

Applying the Penrose-Hawking Singularity Theorem, running the clock backward implies the universe doesn't converge to a point of zero volume, but to a BH, and that's the whole universe, not just the observable universe. AG

The Penrose-Hawking singularity theorems only implies an initial singularity, it doesn't say the universe was a black hole or that the whole universe (not just the observable part) must be finite--a black hole metric is different GR solution than the Friedmann–Lemaître–Robertson–Walker metric for an expanding universe at https://en.wikipedia.org/wiki/Friedmann–Lemaître–Robertson–Walker_metric (sometimes just called the Friedmann-Robertson-Walker metric or FRW). A black hole metric has a radial parameter where curvature gets larger the closer you are to the the black hole, and approaches zero the farther you get (the metric is 'asymptotically flat'), whereas the FLRW is completely uniform in the curvature and density of matter/energy throughout all of space at every moment of the cosmological time parameter. 

Penrose himself refers to the fact that the flat and open versions of the FRW solution imply a spatially infinite universe on pages 323-324 of his book "The Emperor's New Mind":

Firstly, if the age of the universe is finite, it can't expand spatially to infinity regardless of its rate of expansion.

The FLRW metric for a flat or negatively curved universe does not describe a universe that "expands spatially to infinity", it is already infinite at *every* finite time interval after the Big Bang, and there is no size at T=0 because the singularity is more like the edge of spacetime than a part of the spacetime.

That's my claim to some extent, that it must begin as infinite, if it has finite age and is NOW infinite in spatial extent. But beginning as infinite implies some problems which should be discussed. And maybe FLRW shouldn't assume it's flat. AG

FLRW is a family of solutions to the GR equations, you get different individual solutions by varying a "density parameter" in the equations. There is a single value of this parameter, the "critical density", that results in a spatially flat universe, but you can get solutions corresponding to closed/finite universes by picking a value that's smaller.

 

 

So if the universe is spatially infinite, this must have been its initial condition. Secondly, current theory is that the very very early universe was hugely hot, at a much higher temperature than at present. This implies, for me, that it was small, analogous to a highly compressed gas. IMO, it can't be small and hot, and also be spatially infinite.

Presumably you can imagine an infinite plane covered with dots that are on average 1 meter apart, and a different infinite plane covered with dots that are on average 1 millimeter apart; this illustrates how the notion of particles having a higher or lower density doesn't depend on there being a finite number of them. And the bottom line is that an infinite space whose density changes with time is a mathematically allowable solution to the Einstein field equations, physicists trust math over personal gut feelings and intuitions.

Many, if not most of the major advances in physics have been the result of personal gut feelings and intuitions. I think it was Feynman who offered the insight that most advances in physics were based in guesses. Yes guesses. Shall I trust physicists such a Carroll who knows GR intimately and yet has evolved into a MW clown? AG

Yes, but Feynman was talking more about guesses about the mathematical structure of a new theory. He has an essay in chapter 2 of his book The Character of Physical Law where he talks about the history of attempts to find more intuitive mechanical pictures to explain "how gravity works" beyond the abstract equations, and basically concludes these kinds of attempts are fruitless. For example on p. 39 he discusses the flaws in LeSage's "pushing gravity" picture at https://en.wikipedia.org/wiki/Le_Sage%27s_theory_of_gravitation and says:

>So that is the end of that theory. 'Well,' you say, 'it was a good one, and I got rid of the mathematics for a while. Maybe I could invent a better one.' Maybe you can, because nobody knows the ultimate. But up to today, from the time of Newton, no one has invented another theoretical description of the mathematical machinery behind this law which does not either say the same thing over again, or make the mathematics harder, or predict some wrong phenomena. So there is no model of the theory of gravity today, other than the mathematical form.

>If this were the only law of this character it would be interesting and rather annoying. But what turns out to be true is that the more we investigate, the more laws we find, and the deeper we penetrate nature, the more this disease persists. Every one of our laws is a purely mathematical statement in rather complex and abstruse mathematics.

And on p. 57 he writes:

>The next question is whether, when trying to guess a new law, we should use seat-of-the-pants feeling and philosophical principles — ‘I don’t like the minimum principle’, or ‘I do like the minimum principle’, ‘I don’t like action at a distance’, or ‘I do like action at a distance’. To what extent do models help? It is interesting that very often models do help, and most physics teachers try to teach how to use models and to get a good physical feel for how things are going to work out. But it always turns out that the greatest discoveries abstract away from the model and the model never does any good. Maxwell’s discovery of electrodynamics was first made with a lot of imaginary wheels and idlers in space. But when you get rid of all the idlers and things in space the thing is O.K. Dirac discovered the correct laws for relativity quantum mechanics simply by guessing the equation. The method of guessing the equation seems to be a pretty effective way of guessing new laws. This shows again that mathematics is a deep way of expressing nature, and any attempt to express nature in philosophical principles, or in seat-of-the-pants mechanical feelings, is not an efficient way.

I suspect you are also doing the opposite of what Feynman recommends when you dismiss advocates of the MWI like Carroll as "clowns" -- you seem to dismiss it based on physical or philosophical intuitions that lead you to judge that the picture of a vast number of decoherent histories is absurd, and aren't just thinking in terms of criteria like mathematical elegance/simplicity which is why its advocates tend to favor it.

 

 

If it's not spatially infinite, it can't be flat. As it contracts, if it forms a singularity with all its mass and energy concentrated in a tiny region, it will presumably form a BH.

Not according to general relativity, no. The classic "Usenet Physics FAQ" at https://math.ucr.edu/home/baez/physics/index.html addresses this point specifically in the question and answer at https://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html where part of the answer is:

>Why did the universe not collapse and form a black hole at the beginning?

>Sometimes people find it hard to understand why the Big Bang is not a black hole.  After all, the density of matter in the first fraction of a second was much higher than that found in any star, and dense matter is supposed to curve spacetime strongly.  At sufficient density there must be matter contained within a region smaller than the Schwarzschild radius for its mass.  Nevertheless, the Big Bang manages to avoid being trapped inside a black hole of its own making and paradoxically the space near the singularity is actually flat rather than curving tightly.  How can this be?

>The short answer is that the Big Bang gets away with it because it is expanding rapidly near the beginning and the rate of expansion is slowing down.  Space can be flat even when spacetime is not.  Spacetime's curvature can come from the temporal parts of the spacetime metric which measures the deceleration of the expansion of the universe.  So the total curvature of spacetime is related to the density of matter, but there is a contribution to curvature from the expansion as well as from any curvature of space.  The Schwarzschild solution of the gravitational equations is static and demonstrates the limits placed on a static spherical body before it must collapse to a black hole.  The Schwarzschild limit does not apply to rapidly expanding matter.

 

Planck data allows for a positively and negatively geometry, but the dats for flatness is more persuasive. I believe is it so huge that we can't distinguish between positively curved and flat. It's likely approximately spherical in shape because the expansion is approximately uniform as evidenced by the near uniformity in outward expansion of the Cosmological Red Shift. AG 

It's certainly possible it is positively curved but so large (much larger than the observable region) that it's indistinguishable from flatness given the precision of our current best measurements. But if you think you can conclude this *must* be the case a priori just given your verbal arguments (arguments which contradict what the GR equations say is a mathematically valid solution), no physicist is going to go along with that.

Did I ever say anything "must" be the case? I don't think a spherical universe, finite in spatial extend and expanding, contradicts GR equations. AG 

Well, you said in the original post your view was that "if the universe has a finite age, it cannot be infinite in spatial extent" -- I would normally take "cannot be infinite" as synonymous with "must be finite", but maybe you didn't mean it that strongly, and were just expressing an intuition? In the post I first responded to it also seemed like you were trying to use the Hawking-Penrose theorems to show the finiteness of the universe, those theorems are supposed to apply to any spacetime satisfying the GR equations whatsoever, so if the theorems implied finiteness that would imply the universe "must" be finite in the context of GR (leaving aside the issue that GR will likely turn out to only be an approximation to a future theory of quantum gravity), but since Penrose considers infinite universes to be a viable possibility that presumably isn't the case.

Jesse

[Alan Grayson]

Feynman isn't ruling intuition out. He's just saying it's not efficient. About how the Universe exits from an initial BH singularity, I really don't trust our knowledge of the physics of the interior of BH's. Do you? AG 

I suspect you are also doing the opposite of what Feynman recommends when you dismiss advocates of the MWI like Carroll as "clowns" -- you seem to dismiss it based on physical or philosophical intuitions that lead you to judge that the picture of a vast number of decoherent histories is absurd, and aren't just thinking in terms of criteria like mathematical elegance/simplicity which is why its advocates tend to favor it. 

 

If it's not spatially infinite, it can't be flat. As it contracts, if it forms a singularity with all its mass and energy concentrated in a tiny region, it will presumably form a BH.

Not according to general relativity, no. The classic "Usenet Physics FAQ" at https://math.ucr.edu/home/baez/physics/index.html addresses this point specifically in the question and answer at https://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html where part of the answer is:

>Why did the universe not collapse and form a black hole at the beginning?

>Sometimes people find it hard to understand why the Big Bang is not a black hole.  After all, the density of matter in the first fraction of a second was much higher than that found in any star, and dense matter is supposed to curve spacetime strongly.  At sufficient density there must be matter contained within a region smaller than the Schwarzschild radius for its mass.  Nevertheless, the Big Bang manages to avoid being trapped inside a black hole of its own making and paradoxically the space near the singularity is actually flat rather than curving tightly.  How can this be?

>The short answer is that the Big Bang gets away with it because it is expanding rapidly near the beginning and the rate of expansion is slowing down.  Space can be flat even when spacetime is not.  Spacetime's curvature can come from the temporal parts of the spacetime metric which measures the deceleration of the expansion of the universe.  So the total curvature of spacetime is related to the density of matter, but there is a contribution to curvature from the expansion as well as from any curvature of space.  The Schwarzschild solution of the gravitational equations is static and demonstrates the limits placed on a static spherical body before it must collapse to a black hole.  The Schwarzschild limit does not apply to rapidly expanding matter.

 

Planck data allows for a positively and negatively geometry, but the dats for flatness is more persuasive. I believe is it so huge that we can't distinguish between positively curved and flat. It's likely approximately spherical in shape because the expansion is approximately uniform as evidenced by the near uniformity in outward expansion of the Cosmological Red Shift. AG 

It's certainly possible it is positively curved but so large (much larger than the observable region) that it's indistinguishable from flatness given the precision of our current best measurements. But if you think you can conclude this *must* be the case a priori just given your verbal arguments (arguments which contradict what the GR equations say is a mathematically valid solution), no physicist is going to go along with that.

Did I ever say anything "must" be the case? I don't think a spherical universe, finite in spatial extend and expanding, contradicts GR equations. AG 

Well, you said in the original post your view was that "if the universe has a finite age, it cannot be infinite in spatial extent" -- I would normally take "cannot be infinite" as synonymous with "must be finite", but maybe you didn't mean it that strongly, and were just expressing an intuition? In the post I first responded to it also seemed like you were trying to use the Hawking-Penrose theorems to show the finiteness of the universe, those theorems are supposed to apply to any spacetime satisfying the GR equations whatsoever, so if the theorems implied finiteness that would imply the universe "must" be finite in the context of GR (leaving aside the issue that GR will likely turn out to only be an approximation to a future theory of quantum gravity), but since Penrose considers infinite universes to be a viable possibility that presumably isn't the case.

I would say the finiteness of the age of the universe does imply that IF if it is spatially infinite, that infinity must, yes must, originate at its creation. AG 

Jesse

[Alan Grayson]

It's not elegant, but ugly, extremely ugly IMO. How many worlds have you created while responding to my post? Did you take into account that every time you moved your finger in any direction, according to the MWI a countably infinite set of worlds came into existence because of that ONE FINGER? What about your other fingers? Did you wiggle your toes? Give me a break. I view the MWI as not simply wrong, but symptomatic of a mental illness. AG

[Alan Grayson]

On Monday, February 10, 2025 at 6:15:14 PM UTC-7 Alan Grayson wrote:

The universe isn't flat, since flat implies spatially infinite, and that can only be the case at the time of the BB due to its finite age. But spatially infinite at that time contradicts its assumed super-high temperature. So, IMO, cosmologists don't realize that flat geometry and super-high temperature at the time of the BB are incompatible. AG

Jesse

[Alan Grayson]

Jesse; when you have a good estimate of the number of other worlds you were responsible for creating while answering my post here, you might change your mind about the soundness / sanity of the MWI. AG