The Cosmological Constant (CC)

[Alan Grayson]

Einstein claimed that when his GR field equations predicted an explanding universe when he believed in the Steady State theory, he added the CC to GR to make it consistent with his belief. But I recall a remark by Vic Stenger that the constant could have arisen naturally as the constant in an indefinite integral. Is there any substance to Stenger's claim? That is, in the opaque process of creating the GR field equations, do INDEFINITE integrals play a role? AG.

[Alan Grayson]

On Sunday, February 2, 2025 at 1:42:06 AM UTC-7 Alan Grayson wrote:

Einstein claimed that when his GR field equations predicted an explanding universe when he believed in the Steady State theory, he added the CC to GR to make it consistent with his belief. But I recall a remark by Vic Stenger that the constant could have arisen naturally as the constant in an indefinite integral. Is there any substance to Stenger's claim? That is, in the opaque process of creating the GR field equations, do INDEFINITE integrals play a role? AG.

 Related question; while it's generally claimed that the GR field equations predict an expanding universe, do they also predict a contracting universe? AG

[John Clark]

On Sun, Feb 2, 2025 at 3:47 AM Alan Grayson <agrays...@gmail.com> wrote:

> Einstein claimed that when his GR field equations predicted an explanding universe when he believed in the Steady State theory, he added the CC to GR to make it consistent with his belief. But I recall a remark by Vic Stenger that the constant could have arisen naturally as the constant in an indefinite integral. Is there any substance to Stenger's claim? 

General Relativity remains consistent if the value of the cosmological constant is zero, but it is also consistent if it is non zero; however if it's zero then the universe would have to be either expanding or contracting, and if we take thermodynamics into consideration we would have to conclude that it is expanding not contracting. At the time astronomers thought the universe was stable and Einstein thought that making the cosmological constant nonzero would make it so, but it turned out that wouldn't work very well, the universe would only be semi-stable like a pencil balancing on its point, the slightest perturbation would make it fall in one direction or another.

That's why Einstein thought that sticking in the cosmological constant into his beautiful equations was the greatest blunder of his life; if he had just believed what his equations were telling him he could have predicted that the universe was expanding 10 years before astronomer Edwin Hubble discovered that it was. 

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

4vu

[Brent Meeker]

On 2/2/2025 12:42 AM, Alan Grayson wrote:

Einstein claimed that when his GR field equations predicted an explanding universe when he believed in the Steady State theory, he added the CC to GR to make it consistent with his belief.

That's not quite accurate.  He saw that solutions to the GR equations for a universe contained an undetermined constant, the Cosmological Constant.  So he sought to determine it from the observed data.  He consulted the best astronomers of his time and they assured him that the universe consisted of Milky Way and a some scattered nebula and it was unchanging.  So he set the CC value to make the universe in equilibrium.  As soon as he published this, it was pointed out to him that this would be an unstable equilibrium and was not consistent with the observed existence of the universe. About the same time Hubble published his discovery that the universe was expanding and Einstein called the CC, "My greatest blunder."  If not for the astronomers he might have predicted the expansion of the universe before Hubble observed it.  What a coup that would have been.

But I recall a remark by Vic Stenger that the constant could have arisen naturally as the constant in an indefinite integral. Is there any substance to Stenger's claim?

Sure.  But the value of the constant can't be derived from the equation.  Like any constant of integration it has to be determined by something else, usually boundary conditions.

Brent

That is, in the opaque process of creating the GR field equations, do INDEFINITE integrals play a role? AG. --

[Alan Grayson]

On Sunday, February 2, 2025 at 3:24:53 PM UTC-7 Brent Meeker wrote:

On 2/2/2025 12:42 AM, Alan Grayson wrote:

Einstein claimed that when his GR field equations predicted an explanding universe when he believed in the Steady State theory, he added the CC to GR to make it consistent with his belief.

That's not quite accurate.  He saw that solutions to the GR equations for a universe contained an undetermined constant, the Cosmological Constant.  So he sought to determine it from the observed data.  He consulted the best astronomers of his time and they assured him that the universe consisted of Milky Way and a some scattered nebula and it was unchanging.  So he set the CC value to make the universe in equilibrium. 

 

What value would that be; CC=0? AG

 

As soon as he published this, it was pointed out to him that this would be an unstable equilibrium and was not consistent with the observed existence of the universe.

 

Are you saying he was told by astromers that the universe is in stable equilibrium? Do you have a reference which shows why, presumably with CC=0, the equilibrium would be unstable? AG

 

About the same time Hubble published his discovery that the universe was expanding and Einstein called the CC, "My greatest blunder."  If not for the astronomers he might have predicted the expansion of the universe before Hubble observed it.  What a coup that would have been.

What value for CC would he have needed to predict an expanding universe? Was this the value he originally set CC to? AG 

[John Clark]

On Sun, Mar 9, 2025 at 10:39 AM Alan Grayson <agrays...@gmail.com> wrote:

What value for CC would he have needed to predict an expanding universe? Was this the value he originally set CC to?

The Cosmological Constant is the energy density of empty space, when Einstein first published the General Theory Of Relativity in 1915 he assumed that the CC was zero because he knew that if it was anything other than zero the universe would have to be either expanding or contracting (it would have to be expanding if you take the second law of thermodynamics into consideration) and all his astronomer friends told him that the universe with static, so he changed his field equations to make it non zero even though he thought it made his equation less beautiful. This turned out to be, in Einstein's own words, his "greatest blunder" because it wouldn't have made the universe stable, only metastable, and more importantly the 1915 astronomers were wrong, the universe is NOT static. Einstein had everything he needed to predict an expanding universe 10 years before Edwin Hubble discovered that fact with his telescope, but he trusted astronomers more than he trusted his equation.  

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

3sp

[Brent Meeker]

On 3/9/2025 7:38 AM, Alan Grayson wrote:

On Sunday, February 2, 2025 at 3:24:53 PM UTC-7 Brent Meeker wrote:

On 2/2/2025 12:42 AM, Alan Grayson wrote:

Einstein claimed that when his GR field equations predicted an explanding universe when he believed in the Steady State theory, he added the CC to GR to make it consistent with his belief.

That's not quite accurate.  He saw that solutions to the GR equations for a universe contained an undetermined constant, the Cosmological Constant.  So he sought to determine it from the observed data.  He consulted the best astronomers of his time and they assured him that the universe consisted of Milky Way and a some scattered nebula and it was unchanging.  So he set the CC value to make the universe in equilibrium. 

 

What value would that be; CC=0? AG

No it would be positive. 

 

As soon as he published this, it was pointed out to him that this would be an unstable equilibrium and was not consistent with the observed existence of the universe.

 

Are you saying he was told by astromers that the universe is in stable equilibrium? Do you have a reference which shows why, presumably with CC=0, the equilibrium would be unstable? AG

Why would you need a reference.  Think for yourself.  If you have a constant repulsive force balancing an inverse square attractive force...

 

About the same time Hubble published his discovery that the universe was expanding and Einstein called the CC, "My greatest blunder."  If not for the astronomers he might have predicted the expansion of the universe before Hubble observed it.  What a coup that would have been.

What value for CC would he have needed to predict an expanding universe? Was this the value he originally set CC to? AG

None. CC=0  It was just expanding due to the initial motion of bodies.

Brent

But I recall a remark by Vic Stenger that the constant could have arisen naturally as the constant in an indefinite integral. Is there any substance to Stenger's claim?

Sure.  But the value of the constant can't be derived from the equation.  Like any constant of integration it has to be determined by something else, usually boundary conditions.

Brent

That is, in the opaque process of creating the GR field equations, do INDEFINITE integrals play a role? AG. --

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[Alan Grayson]

On Sunday, March 9, 2025 at 2:54:12 PM UTC-6 Brent Meeker wrote:

On 3/9/2025 7:38 AM, Alan Grayson wrote:

On Sunday, February 2, 2025 at 3:24:53 PM UTC-7 Brent Meeker wrote:

On 2/2/2025 12:42 AM, Alan Grayson wrote:

Einstein claimed that when his GR field equations predicted an explanding universe when he believed in the Steady State theory, he added the CC to GR to make it consistent with his belief.

That's not quite accurate.  He saw that solutions to the GR equations for a universe contained an undetermined constant, the Cosmological Constant.  So he sought to determine it from the observed data.  He consulted the best astronomers of his time and they assured him that the universe consisted of Milky Way and a some scattered nebula and it was unchanging.  So he set the CC value to make the universe in equilibrium. 

 

What value would that be; CC=0? AG

No it would be positive. 

 

As soon as he published this, it was pointed out to him that this would be an unstable equilibrium and was not consistent with the observed existence of the universe.

 

Are you saying he was told by astromers that the universe is in stable equilibrium? Do you have a reference which shows why, presumably with CC=0, the equilibrium would be unstable? AG

Why would you need a reference.  Think for yourself.  If you have a constant repulsive force balancing an inverse square attractive force...

I don't think you understand my question. Without a CC, or equivalently setting it to zero, don't we get a universe which is in UNSTABLE equilibrium, like balancing a pencil of its writing tip, so the universe expands or contracts in a very short time interval? Isn't this the issue Einstein faced? If so, why would he choose a positive CC? AG 

About the same time Hubble published his discovery that the universe was expanding and Einstein called the CC, "My greatest blunder."  If not for the astronomers he might have predicted the expansion of the universe before Hubble observed it.  What a coup that would have been.

What value for CC would he have needed to predict an expanding universe? Was this the value he originally set CC to? AG

None. CC=0  It was just expanding due to the initial motion of bodies.

So what about the claim of UNSTABLE equilibrium if CC=0? AG

[John Clark]

On Mon, Mar 10, 2025 at 2:14 AM Alan Grayson <agrays...@gmail.com> wrote:

> Without a CC, or equivalently setting it to zero, don't we get a universe which is in UNSTABLE equilibrium, like balancing a pencil of its writing tip, 

No. Einstein knew if the cosmological constant was zero then the universe would keep expanding forever and no small change, or even a supernova, could alter that situation, certainly a butterfly in Paraguay flapping its wings couldn't. So things would not be static but they would be in a state of stable equilibrium. However if the cosmological constant was not zero, as Einstein's reluctantly revised and less beautiful equations said, then the universe could be static but the equilibrium would be unstable (although that instability was not discovered until 13 years later by Arthur Eddington), if that butterfly flaps its wings too much then the universe will either start to expand or contract. 

So Einstein was trying to fix a problem that didn't exist, and even if it had existed it was a very poor way of fixing it, so it's no wonder that Einstein called it his "greatest blunder". Fortunately as soon as Hubble discovered that the universe was expanding Einstein immediately dropped the CC idea and he went back to his original beautiful equations.   

 > so the universe expands or contracts in a very short time interval?

Forever is not a very short time interval.  

 

 > why would he choose a positive CC? AG 

The short answer is because Einstein was desperate. He knew that however beautiful a theory is, if it conflicts with observation then it's wrong, and in 1915 he thought General Relativity did conflict with observations, so he reluctantly tacked on another term even though he thought it made the equation less beautiful. But it turned out the 1915 observations were wrong, not the theory.

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

tge

[Alan Grayson]

Which observations were wrong? Weren't they measureing the advancement of Mercury's perihelion, not the expansion of the universe? AG

tge

[John Clark]

On Mon, Mar 10, 2025 at 8:43 AM Alan Grayson <agrays...@gmail.com> wrote:

> Which observations were wrong?

In 1914 astronomers thought the universe was static, and the stars in the Milky Way were not getting further apart, and in 1914 astronomers thought the Milky Way was the entire universe. But the 1914 astronomers were wrong   

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

fla

[Alan Grayson]

Someone here, I think it was YOU, who claimed Einstein's field equation without the CC implied unstable equilibrium. Did that result only apply with his attempt to predict a static universe with a positive CC? AG 

fla

[John Clark]

On Mon, Mar 10, 2025 at 9:33 AM Alan Grayson <agrays...@gmail.com> wrote:

> Someone here, I think it was YOU, who claimed Einstein's field equation without the CC implied unstable equilibrium.

Static versus dynamic, and stable versus unstable, and stable versus metastable, are three different things. 

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

t3r

[Alan Grayson]

This isn't remotely helpful. You said the universe was predicted to be in unstable equilibrium, like a pencil balanced on its point. Was that AFTER Einstein added the CC? AG 

[Brent Meeker]

On 3/9/2025 11:14 PM, Alan Grayson wrote:

I don't think you understand my question. Without a CC, or equivalently setting it to zero, don't we get a universe which is in UNSTABLE equilibrium, like balancing a pencil of its writing tip, so the universe expands or contracts in a very short time interval? Isn't this the issue Einstein faced? If so, why would he choose a positive CC? AG 

No, Einstein's model with the CC=0 was static.  The model when I was in grad school was an expanding universe with the CC=0 but the expansion kinetic energy was just balanced by the negative gravitational potential, so the universe would expand forever but slowing asymptotically toward static.

Brent

[Alan Grayson]

Now I am totally confused. If E's model was static with CC=0, it agreed with what astronomers thought in 1915, so why would he add a positive CC, tantamount to a repulsive force as you earlier claimed, to counteract what he then thought was a false prediction of GR of an expanding universe? Does anyone have a coherent answer to what's going on with the CC? AG 

[Brent Meeker]

On 3/10/2025 11:04 PM, Alan Grayson wrote:

On Monday, March 10, 2025 at 11:15:07 PM UTC-6 Brent Meeker wrote:

On 3/9/2025 11:14 PM, Alan Grayson wrote:

I don't think you understand my question. Without a CC, or equivalently setting it to zero, don't we get a universe which is in UNSTABLE equilibrium, like balancing a pencil of its writing tip, so the universe expands or contracts in a very short time interval? Isn't this the issue Einstein faced? If so, why would he choose a positive CC? AG 

No, Einstein's model with the CC=0 was static.  The model when I was in grad school was an expanding universe with the CC=0 but the expansion kinetic energy was just balanced by the negative gravitational potential, so the universe would expand forever but slowing asymptotically toward static.

Brent

Now I am totally confused. If E's model was static with CC=0,

Sorry, I miswrote.  I intended to say Einstein had to make the CC>0 in order to balance the gravitational attraction.

Brent

it agreed with what astronomers thought in 1915, so why would he add a positive CC, tantamount to a repulsive force as you earlier claimed, to counteract what he then thought was a false prediction of GR of an expanding universe? Does anyone have a coherent answer to what's going on with the CC? AG 

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[Alan Grayson]

On Tuesday, March 11, 2025 at 12:33:36 AM UTC-6 Brent Meeker wrote:

On 3/10/2025 11:04 PM, Alan Grayson wrote:

On Monday, March 10, 2025 at 11:15:07 PM UTC-6 Brent Meeker wrote:

On 3/9/2025 11:14 PM, Alan Grayson wrote:

I don't think you understand my question. Without a CC, or equivalently setting it to zero, don't we get a universe which is in UNSTABLE equilibrium, like balancing a pencil of its writing tip, so the universe expands or contracts in a very short time interval? Isn't this the issue Einstein faced? If so, why would he choose a positive CC? AG 

No, Einstein's model with the CC=0 was static.  The model when I was in grad school was an expanding universe with the CC=0 but the expansion kinetic energy was just balanced by the negative gravitational potential, so the universe would expand forever but slowing asymptotically toward static.

Brent

Now I am totally confused. If E's model was static with CC=0,

Sorry, I miswrote.  I intended to say Einstein had to make the CC>0 in order to balance the gravitational attraction.

Brent

OK. Does setting CC>0 result in unstable equilibrium as I think Clark claimed, and discovered by Arthur Eddington?  IOW, will the universe suddenly contract if it is expanding? AG

[Alan Grayson]

On Tuesday, March 11, 2025 at 12:48:31 AM UTC-6 Alan Grayson wrote:

On Tuesday, March 11, 2025 at 12:33:36 AM UTC-6 Brent Meeker wrote:

On 3/10/2025 11:04 PM, Alan Grayson wrote:

    On Monday, March 10, 2025 at 11:15:07 PM UTC-6 Brent Meeker wrote:

          On 3/9/2025 11:14 PM, Alan Grayson wrote:

I don't think you understand my question. Without a CC, or equivalently setting it to zero, don't we get a universe which is in UNSTABLE equilibrium, like balancing a pencil of its writing tip, so the universe expands or contracts in a very short time interval? Isn't this the issue Einstein faced? If so, why would he choose a positive CC? AG 

No, Einstein's model with the CC=0 was static.  The model when I was in grad school was an expanding universe with the CC=0 but the expansion kinetic energy was just balanced by the negative gravitational potential, so the universe would expand forever but slowing asymptotically toward static.

Brent

Now I am totally confused. If E's model was static with CC=0,

Sorry, I miswrote.  I intended to say Einstein had to make the CC>0 in order to balance the gravitational attraction.

Brent

OK. Does setting CC>0 result in unstable equilibrium as I think Clark claimed, and discovered by Arthur Eddington?  IOW, will the universe suddenly contract if it is expanding? AG

Maybe Clark meant that setting CC>0 results in a static universe, which is in unstable equilibrium, meaning that it will suddenly expand or contract? AG 

[Brent Meeker]

On 3/10/2025 11:48 PM, Alan Grayson wrote:

On Tuesday, March 11, 2025 at 12:33:36 AM UTC-6 Brent Meeker wrote:

On 3/10/2025 11:04 PM, Alan Grayson wrote:

On Monday, March 10, 2025 at 11:15:07 PM UTC-6 Brent Meeker wrote:

On 3/9/2025 11:14 PM, Alan Grayson wrote:

I don't think you understand my question. Without a CC, or equivalently setting it to zero, don't we get a universe which is in UNSTABLE equilibrium, like balancing a pencil of its writing tip, so the universe expands or contracts in a very short time interval? Isn't this the issue Einstein faced? If so, why would he choose a positive CC? AG 

No, Einstein's model with the CC=0 was static.  The model when I was in grad school was an expanding universe with the CC=0 but the expansion kinetic energy was just balanced by the negative gravitational potential, so the universe would expand forever but slowing asymptotically toward static.

Brent

Now I am totally confused. If E's model was static with CC=0,

Sorry, I miswrote.  I intended to say Einstein had to make the CC>0 in order to balance the gravitational attraction.

Brent

OK. Does setting CC>0 result in unstable equilibrium as I think Clark claimed, and discovered by Arthur Eddington?  IOW, will the universe suddenly contract if it is expanding? AG

No, it's unstable as a static universe, which was the general opinion of astronomers at the time.  The Milky Way was the only known galaxy.  The other smudges in the night sky were "nebula".  So Einstein calculated a value for the CC that would just balance the gravitational attraction of the Milky Way, to explain why it hadn't collapsed.  But this produced an unstable equilbrium.  It was about 10yrs later that Hubble discovered the universe was much bigger than just the Milky Way and it was expanding.

Brent

it agreed with what astronomers thought in 1915, so why would he add a positive CC, tantamount to a repulsive force as you earlier claimed, to counteract what he then thought was a false prediction of GR of an expanding universe? Does anyone have a coherent answer to what's going on with the CC? AG 

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[Alan Grayson]

On Tuesday, March 11, 2025 at 1:41:29 PM UTC-6 Brent Meeker wrote:

On 3/10/2025 11:48 PM, Alan Grayson wrote:

On Tuesday, March 11, 2025 at 12:33:36 AM UTC-6 Brent Meeker wrote:

On 3/10/2025 11:04 PM, Alan Grayson wrote:

On Monday, March 10, 2025 at 11:15:07 PM UTC-6 Brent Meeker wrote:

On 3/9/2025 11:14 PM, Alan Grayson wrote:

I don't think you understand my question. Without a CC, or equivalently setting it to zero, don't we get a universe which is in UNSTABLE equilibrium, like balancing a pencil of its writing tip, so the universe expands or contracts in a very short time interval? Isn't this the issue Einstein faced? If so, why would he choose a positive CC? AG 

No, Einstein's model with the CC=0 was static.  The model when I was in grad school was an expanding universe with the CC=0 but the expansion kinetic energy was just balanced by the negative gravitational potential, so the universe would expand forever but slowing asymptotically toward static.

Brent

Now I am totally confused. If E's model was static with CC=0,

Sorry, I miswrote.  I intended to say Einstein had to make the CC>0 in order to balance the gravitational attraction.

Brent

OK. Does setting CC>0 result in unstable equilibrium as I think Clark claimed, and discovered by Arthur Eddington?  IOW, will the universe suddenly contract if it is expanding? AG

No, it's unstable as a static universe, which was the general opinion of astronomers at the time.  The Milky Way was the only known galaxy.  The other smudges in the night sky were "nebula".  So Einstein calculated a value for the CC that would just balance the gravitational attraction of the Milky Way, to explain why it hadn't collapsed.  But this produced an unstable equilbrium.  It was about 10yrs later that Hubble discovered the universe was much bigger than just the Milky Way and it was expanding.

Brent

It was Arthur Eddington in 1930 who showed that a static universe with CC>0, would be in unstable equilibrium. AG 

[Alan Grayson]

On Tuesday, March 11, 2025 at 10:26:37 PM UTC-6 Alan Grayson wrote:

On Tuesday, March 11, 2025 at 1:41:29 PM UTC-6 Brent Meeker wrote:

On 3/10/2025 11:48 PM, Alan Grayson wrote:

On Tuesday, March 11, 2025 at 12:33:36 AM UTC-6 Brent Meeker wrote:

On 3/10/2025 11:04 PM, Alan Grayson wrote:

On Monday, March 10, 2025 at 11:15:07 PM UTC-6 Brent Meeker wrote:

On 3/9/2025 11:14 PM, Alan Grayson wrote:

I don't think you understand my question. Without a CC, or equivalently setting it to zero, don't we get a universe which is in UNSTABLE equilibrium, like balancing a pencil of its writing tip, so the universe expands or contracts in a very short time interval? Isn't this the issue Einstein faced? If so, why would he choose a positive CC? AG 

No, Einstein's model with the CC=0 was static.  The model when I was in grad school was an expanding universe with the CC=0 but the expansion kinetic energy was just balanced by the negative gravitational potential, so the universe would expand forever but slowing asymptotically toward static.

Brent

Now I am totally confused. If E's model was static with CC=0,

Sorry, I miswrote.  I intended to say Einstein had to make the CC>0 in order to balance the gravitational attraction.

Brent

OK. Does setting CC>0 result in unstable equilibrium as I think Clark claimed, and discovered by Arthur Eddington?  IOW, will the universe suddenly contract if it is expanding? AG

No, it's unstable as a static universe, which was the general opinion of astronomers at the time.  The Milky Way was the only known galaxy.  The other smudges in the night sky were "nebula".  So Einstein calculated a value for the CC that would just balance the gravitational attraction of the Milky Way, to explain why it hadn't collapsed.  But this produced an unstable equilbrium.  It was about 10yrs later that Hubble discovered the universe was much bigger than just the Milky Way and it was expanding.

Brent

It was Arthur Eddington in 1930 who showed that a static universe with CC>0, would be in unstable equilibrium. AG 

After Einstein removed the CC from his field equations in recognizing that the universe is expanding, did he reintroduce it when realizing that empty space is non-existent, that it has energy? When did he do that, and was it in reaction to the quantization of the EM field and its zero point energy? AG 

[Brent Meeker]

On 3/11/2025 9:26 PM, Alan Grayson wrote:

On Tuesday, March 11, 2025 at 1:41:29 PM UTC-6 Brent Meeker wrote:

On 3/10/2025 11:48 PM, Alan Grayson wrote:

On Tuesday, March 11, 2025 at 12:33:36 AM UTC-6 Brent Meeker wrote:

On 3/10/2025 11:04 PM, Alan Grayson wrote:

On Monday, March 10, 2025 at 11:15:07 PM UTC-6 Brent Meeker wrote:

On 3/9/2025 11:14 PM, Alan Grayson wrote:

I don't think you understand my question. Without a CC, or equivalently setting it to zero, don't we get a universe which is in UNSTABLE equilibrium, like balancing a pencil of its writing tip, so the universe expands or contracts in a very short time interval? Isn't this the issue Einstein faced? If so, why would he choose a positive CC? AG 

No, Einstein's model with the CC=0 was static.  The model when I was in grad school was an expanding universe with the CC=0 but the expansion kinetic energy was just balanced by the negative gravitational potential, so the universe would expand forever but slowing asymptotically toward static.

Brent

Now I am totally confused. If E's model was static with CC=0,

Sorry, I miswrote.  I intended to say Einstein had to make the CC>0 in order to balance the gravitational attraction.

Brent

OK. Does setting CC>0 result in unstable equilibrium as I think Clark claimed, and discovered by Arthur Eddington?  IOW, will the universe suddenly contract if it is expanding? AG

No, it's unstable as a static universe, which was the general opinion of astronomers at the time.  The Milky Way was the only known galaxy.  The other smudges in the night sky were "nebula".  So Einstein calculated a value for the CC that would just balance the gravitational attraction of the Milky Way, to explain why it hadn't collapsed.  But this produced an unstable equilbrium.  It was about 10yrs later that Hubble discovered the universe was much bigger than just the Milky Way and it was expanding.

Brent

It was Arthur Eddington in 1930 who showed that a static universe with CC>0, would be in unstable equilibrium. AG

He may have shown it, but I don't believe he was the first.  Friedmann, in 1922, already showed that the universe must either expand or collapse, that it has no steady state with or without a CC. 

Brent

[Brent Meeker]

On 3/11/2025 9:40 PM, Alan Grayson wrote:

On Tuesday, March 11, 2025 at 10:26:37 PM UTC-6 Alan Grayson wrote:

On Tuesday, March 11, 2025 at 1:41:29 PM UTC-6 Brent Meeker wrote:

On 3/10/2025 11:48 PM, Alan Grayson wrote:

On Tuesday, March 11, 2025 at 12:33:36 AM UTC-6 Brent Meeker wrote:

On 3/10/2025 11:04 PM, Alan Grayson wrote:

On Monday, March 10, 2025 at 11:15:07 PM UTC-6 Brent Meeker wrote:

On 3/9/2025 11:14 PM, Alan Grayson wrote:

I don't think you understand my question. Without a CC, or equivalently setting it to zero, don't we get a universe which is in UNSTABLE equilibrium, like balancing a pencil of its writing tip, so the universe expands or contracts in a very short time interval? Isn't this the issue Einstein faced? If so, why would he choose a positive CC? AG 

No, Einstein's model with the CC=0 was static.  The model when I was in grad school was an expanding universe with the CC=0 but the expansion kinetic energy was just balanced by the negative gravitational potential, so the universe would expand forever but slowing asymptotically toward static.

Brent

Now I am totally confused. If E's model was static with CC=0,

Sorry, I miswrote.  I intended to say Einstein had to make the CC>0 in order to balance the gravitational attraction.

Brent

OK. Does setting CC>0 result in unstable equilibrium as I think Clark claimed, and discovered by Arthur Eddington?  IOW, will the universe suddenly contract if it is expanding? AG

No, it's unstable as a static universe, which was the general opinion of astronomers at the time.  The Milky Way was the only known galaxy.  The other smudges in the night sky were "nebula".  So Einstein calculated a value for the CC that would just balance the gravitational attraction of the Milky Way, to explain why it hadn't collapsed.  But this produced an unstable equilbrium.  It was about 10yrs later that Hubble discovered the universe was much bigger than just the Milky Way and it was expanding.

Brent

It was Arthur Eddington in 1930 who showed that a static universe with CC>0, would be in unstable equilibrium. AG 

After Einstein removed the CC from his field equations in recognizing that the universe is expanding, did he reintroduce it when realizing that empty space is non-existent, that it has energy? When did he do that, and was it in reaction to the quantization of the EM field and its zero point energy? AG

He never "realized empty space has energy", that's just one way of looking at the acceleration of expansion which wasn't discovered till the 1990's.  When did he do what?...that thing he didn't do in response to the thing he never knew about?  Einstein never believed in zero point energy.   It always comes out infinite unless you impose an arbitrary cutoff.

Brent

[Alan Grayson]

I don't think that's right. I recall recently reading, possibly on this list, words by Einstein that empty space doesn't exist. AG 

[Alan Grayson]

I was thinking about this:

There is no such thing as an empty space, i.e. a space without field. Space-time does not claim existence on its own, but only as a structural quality of the field.
- Albert Einstein, Relativity The Special and General Theories, 15th edition, Appendix 5 (Note there are numerous editions available online. Appendix 5 only appears in the 15th edition of 1952, a few years before Einstein's death.)

AG

[Alan Grayson]

On Sunday, February 2, 2025 at 3:24:53 PM UTC-7 Brent Meeker wrote:

On 2/2/2025 12:42 AM, Alan Grayson wrote:

Einstein claimed that when his GR field equations predicted an explanding universe when he believed in the Steady State theory, he added the CC to GR to make it consistent with his belief.

That's not quite accurate.  He saw that solutions to the GR equations for a universe contained an undetermined constant, the Cosmological Constant.  So he sought to determine it from the observed data.  He consulted the best astronomers of his time and they assured him that the universe consisted of Milky Way and a some scattered nebula and it was unchanging.  So he set the CC value to make the universe in equilibrium. 

Google says the following: The cosmological constant, often associated with dark energy, represents a positive force that drives the accelerated expansion of the universe, acting as a repulsive force against gravity. 

If the GR field equations imply an expanding universe without a CC, how can an accelerated

expansion using the CC result in a steady state universe, the one E believed to be the case?

Wasn't the insertion of the CC supposed to force the field equations to imply a steady state

universe? How can it do that if the expansion rate is accelerated? AG

[Brent Meeker]

On 3/30/2025 9:04 PM, Alan Grayson wrote:

On Sunday, February 2, 2025 at 3:24:53 PM UTC-7 Brent Meeker wrote:

On 2/2/2025 12:42 AM, Alan Grayson wrote:

Einstein claimed that when his GR field equations predicted an explanding universe when he believed in the Steady State theory, he added the CC to GR to make it consistent with his belief.

That's not quite accurate.  He saw that solutions to the GR equations for a universe contained an undetermined constant, the Cosmological Constant.  So he sought to determine it from the observed data.  He consulted the best astronomers of his time and they assured him that the universe consisted of Milky Way and a some scattered nebula and it was unchanging.  So he set the CC value to make the universe in equilibrium. 

Google says the following: The cosmological constant, often associated with dark energy, represents a positive force that drives the accelerated expansion of the universe, acting as a repulsive force against gravity. 

If the GR field equations imply an expanding universe without a CC,

They don't.  You need boundary conditions, not just equations to imply anything.

how can an accelerated

expansion using the CC result in a steady state universe, the one E believed to be the case?

Wasn't the insertion of the CC supposed to force the field equations to imply a steady state

No, they permitted a steady state solution.

Brent

universe? How can it do that if the expansion rate is accelerated? AG

 

As soon as he published this, it was pointed out to him that this would be an unstable equilibrium and was not consistent with the observed existence of the universe. About the same time Hubble published his discovery that the universe was expanding and Einstein called the CC, "My greatest blunder."  If not for the astronomers he might have predicted the expansion of the universe before Hubble observed it.  What a coup that would have been.

But I recall a remark by Vic Stenger that the constant could have arisen naturally as the constant in an indefinite integral. Is there any substance to Stenger's claim?

Sure.  But the value of the constant can't be derived from the equation.  Like any constant of integration it has to be determined by something else, usually boundary conditions.

Brent

That is, in the opaque process of creating the GR field equations, do INDEFINITE integrals play a role? AG. --

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[Alan Grayson]

On Sunday, March 30, 2025 at 11:27:14 PM UTC-6 Brent Meeker wrote:

On 3/30/2025 9:04 PM, Alan Grayson wrote:

On Sunday, February 2, 2025 at 3:24:53 PM UTC-7 Brent Meeker wrote:

On 2/2/2025 12:42 AM, Alan Grayson wrote:

Einstein claimed that when his GR field equations predicted an explanding universe when he believed in the Steady State theory, he added the CC to GR to make it consistent with his belief.

That's not quite accurate.  He saw that solutions to the GR equations for a universe contained an undetermined constant, the Cosmological Constant.  So he sought to determine it from the observed data.  He consulted the best astronomers of his time and they assured him that the universe consisted of Milky Way and a some scattered nebula and it was unchanging.  So he set the CC value to make the universe in equilibrium. 

Google says the following: The cosmological constant, often associated with dark energy, represents a positive force that drives the accelerated expansion of the universe, acting as a repulsive force against gravity. 

If the GR field equations imply an expanding universe without a CC,

They don't.  You need boundary conditions, not just equations to imply anything.

how can an accelerated

expansion using the CC result in a steady state universe, the one E believed to be the case?

Wasn't the insertion of the CC supposed to force the field equations to imply a steady state

No, they permitted a steady state solution.

Brent

But for Einstein to get his equations to permit a steady state solution, wouldn't his CC have to augment 

gravitational attraction, and thus be negative, but after it was discovered that the universe's expansion

was accelerating, the sign of the CC was changed to positive? AG 

[John Clark]

On Mon, Mar 31, 2025 at 3:23 AM Alan Grayson <agrays...@gmail.com> wrote:

> For Einstein to get his equations to permit a steady state solution, wouldn't his CC have to augment gravitational attraction, and thus be negative, but after it was discovered that the universe's expansion was accelerating, the sign of the CC was changed to positive? AG

The Cosmological Constant would've been a property of space that gave it a constant negative pressure, and that would have been a sort of anti-gravity. If the negative pressure had been just strong enough to exactly counteract gravity and no stronger or weaker then it would have permitted a static universe, although it would have been unstable, the slightest nudge would have caused the universe to either collapse or expand forever. However Einstein didn't realize that at the time, if he had I don't believe he would've ever proposed it. As soon as astronomers discovered that the universe was expanding Einstein quickly abandon the entire Cosmological Constant idea.

When in the late 1990s astronomers discovered that the universe was accelerating the cosmological constant hypothesis came back big-time because it could explain why the universe is accelerating (if it had just the right value) and quantum mechanics provides an easy way to explain how empty space could produce negative pressure. But they were problems, the amount of negative pressure that quantum mechanics says empty space should have is too large, 10^120 times too large. And very recently the evidence started to mount that the rate of acceleration of the universe is decreasing, and that doesn't fit the cosmological constant model because a property inherent to space itself, wouldn't be expected to change its strength with time. To put it in technical language, the cosmological constant died because the universe behaved like a jerk (d³x(t)/dt³). 

So if those recent astronomical observations turn out to be correct then dark energy must be dynamic. One possibility is Quintessence, a fifth fundamental force that produces negative pressure by way of a scalar field, that is to say a field gives every point in space an intensity but not a direction and that can change with time.  Another idea is that dark energy (whatever that is) might decay into dark matter (whatever that is); this could explain why dark matter and dark energy are of the same order of magnitude today when there is no reason to believe that they should be anywhere close.    

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

awc

[Alan Grayson]

Thanks for that data dump. When E was contemplating the CC, he knew that gravity was attractive and NOT the cause of the expansion implied for some values of the CC. Why then would he think that by assuming a repulsive CC which eliminated gravity, would imply a steady-state universe? AG

awc

[Brent Meeker]

On 3/31/2025 3:25 PM, Alan Grayson wrote:

Thanks for that data dump. When E was contemplating the CC, he knew that gravity was attractive and NOT the cause of the expansion implied for some values of the CC. Why then would he think that by assuming a repulsive CC which eliminated gravity, would imply a steady-state universe? AG

THINK, AG!  When Einstein wrote is first cosmology paper base on GR, he thought the universe was (1) Small: consisting of only the Milky Way and some "nebula" and (2) Static: having always existed just as seen at the time.  The way to fit this with his GR models was to assume the CC had exactly the value needed to counter the gravitational attraction so that the universe could be infinitely old in this same state. 

When Hubble discovered the universe was expanding then the universe was finitely old and was dynamic.  If the matter of the universe started off as from explosion the matter could be just coasting outward and no CC was needed.  The universe was expanding due to an initial impetus and coasting with just enough energy to asymptotically approach zero expansion rate at infinite time.  The LambdaCDM model with CC=0 seemed to fit the data up until about 1990.

The Einstein's GR equations for these two scenarios were exactly the same.  Only the boundary conditions were different.

Brent

[Alan Grayson]

On Monday, March 31, 2025 at 6:07:49 PM UTC-6 Brent Meeker wrote:

On 3/31/2025 3:25 PM, Alan Grayson wrote:

Thanks for that data dump. When E was contemplating the CC, he knew that gravity was attractive and NOT the cause of the expansion implied for some values of the CC. Why then would he think that by assuming a repulsive CC which eliminated gravity, would imply a steady-state universe? AG

THINK, AG!  When Einstein wrote is first cosmology paper base on GR, he thought the universe was (1) Small: consisting of only the Milky Way and some "nebula"

No shit. Is that what E thought? I never heard that before! AG

and (2) Static: having always existed just as seen at the time. 

No shit2. AG

 

The way to fit this with his GR models was to assume the CC had exactly the value needed to counter the gravitational attraction so that the universe could be infinitely old in this same state. 

The only person here who isn't THINKING clearly is YOU! If gravity isn't causing the expansion when presumably the CC is set to zero, why would eliminating it with some appropriate value of the CC, result in a steady-state universe? IOW, gravity is irrelevant to why the universe is expanding, and E knew this. So why would eliminating gravity have any effect on causing a static universe, the one E believed existed before Hubble proved otherwise? AG 

When Hubble discovered the universe was expanding then the universe was finitely old and was dynamic.  If the matter of the universe started off as from explosion the matter could be just coasting outward and no CC was needed.  The universe was expanding due to an initial impetus and coasting with just enough energy to asymptotically approach zero expansion rate at infinite time.  The LambdaCDM model with CC=0 seemed to fit the data up until about 1990.

Indeed. I know this story. AG 

The Einstein's GR equations for these two scenarios were exactly the same.  Only the boundary conditions were different.

Which two scenarios are you referring to? AG 

Brent

[John Clark]

On Mon, Mar 31, 2025 at 11:49 PM Alan Grayson <agrays...@gmail.com> wrote:

On Monday, March 31, 2025 at 6:07:49 PM UTC-6 Brent Meeker wrote:

>> THINK, AG!  When Einstein wrote is first cosmology paper base on GR, he thought the universe was (1) Small: consisting of only the Milky Way and some "nebula"

> No shit. Is that what E thought?

Yes because Einstein was not an astronomer but he knew that's what nearly every astronomer on the planet thought in 1915, although a small minority were starting to have suspicions that a few of those "nebula" were a little more distant than originally thought.  

 

> I never heard that before! AG

So you have learned something new. Congratulations. 

>> The way to fit this with his GR models was to assume the CC had exactly the value needed to counter the gravitational attraction so that the universe could be infinitely old in this same state. 

>The only person here who isn't THINKING clearly is YOU!

The pattern is always the same, you politely ask a question and when a person answers it you get angry and insulting, especially if the answer is correct.  

 

>If gravity isn't causing the expansion

Nobody ever thought gravity was causing the universe to expand, certainly not Einstein. In General Relativity the cosmological constant is NOT gravity, it's more like anti-gravity, and if it's set too low the universe will collapse to an infinitely small point, if it's set too high the universe will expand forever, if it's set even higher it will accelerate forever, and if it's set exactly precisely right then the universe will be static but, as was discovered later, it would be an unstable state.  

> when presumably the CC is set to zero, why would eliminating it with some appropriate value of the CC, result in a steady-state universe?

 

Huh? What does the pronoun "it" in the above refer to? "it" can't be the cosmological constant because if the CC is already set to zero then you can't eliminate "it" and "it" can't be gravity because NOBODY would be stupid enough to eliminate gravity.

 

>  gravity is irrelevant to why the universe is expanding, and E knew this. So why would eliminating gravity [...]

I stand corrected.  

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

i7z

[Alan Grayson]

On Tuesday, April 1, 2025 at 5:32:42 AM UTC-6 John Clark wrote:

On Mon, Mar 31, 2025 at 11:49 PM Alan Grayson <agrays...@gmail.com> wrote:

On Monday, March 31, 2025 at 6:07:49 PM UTC-6 Brent Meeker wrote:

>> THINK, AG!  When Einstein wrote is first cosmology paper base on GR, he thought the universe was (1) Small: consisting of only the Milky Way and some "nebula"

> No shit. Is that what E thought?

Yes because Einstein was not an astronomer but he knew that's what nearly every astronomer on the planet thought in 1915, although a small minority were starting to have suspicions that a few of those "nebula" were a little more distant than originally thought.  

 

> I never heard that before! AG

So you have learned something new. Congratulations. 

My sarcasim went over your head, way over! AG 

>> The way to fit this with his GR models was to assume the CC had exactly the value needed to counter the gravitational attraction so that the universe could be infinitely old in this same state. 

>The only person here who isn't THINKING clearly is YOU!

The pattern is always the same, you politely ask a question and when a person answers it you get angry and insulting, especially if the answer is correct.  

Dumb and dumber! The answer wasn't complete, and Brent was being insulting instead of making the effort to understand my question. You, as well. It seems to me the geniuses here don't understand my question. AG

 

>If gravity isn't causing the expansion

Nobody ever thought gravity was causing the universe to expand, certainly not Einstein. In General Relativity the cosmological constant is NOT gravity, it's more like anti-gravity,

The CC probably has nothing to do with gravity. AG

 

and if it's set too low the universe will collapse to an infinitely small point, if it's set too high the universe will expand forever, if it's set even higher it will accelerate forever, and if it's set exactly precisely right then the universe will be static but, as was discovered later, it would be an unstable state.  

I don't disagree! Now see if you can answer my question, that the CC has nothing to do with gravity, which just slows the rate of expansion, as the situation seemed prior to 1990. AG 

> when presumably the CC is set to zero, why would eliminating it with some appropriate value of the CC, result in a steady-state universe?

 

Huh? What does the pronoun "it" in the above refer to?

Gravity. AG 

"it" can't be the cosmological constant because if the CC is already set to zero then you can't eliminate "it" and "it" can't be gravity because NOBODY would be stupid enough to eliminate gravity.

Then why characterize the CC as being anti-gravity? AG 

 

>  gravity is irrelevant to why the universe is expanding, and E knew this. So why would eliminating gravity [...]

I stand corrected.  

So now you understand my question? AG 

[John Clark]

On Tue, Apr 1, 2025 at 8:26 AM Alan Grayson <agrays...@gmail.com> wrote:

>>I stand corrected.  

> So now you understand my question? AG 

To quote you "My sarcasim went over your head, way over! AG"

 

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

2qu

i7z

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[Alan Grayson]

On Tuesday, April 1, 2025 at 6:47:27 AM UTC-6 John Clark wrote:

On Tue, Apr 1, 2025 at 8:26 AM Alan Grayson <agrays...@gmail.com> wrote:

>>I stand corrected.  

> So now you understand my question? AG 

To quote you "My sarcasim went over your head, way over! AG"

I don't get your riddle. FWIW, it's spelled SARCASM. AG 

[John Clark]

On Tue, Apr 1, 2025 at 9:27 AM Alan Grayson <agrays...@gmail.com> wrote:

On Tuesday, April 1, 2025 at 6:47:27 AM UTC-6 John Clark wrote:

On Tue, Apr 1, 2025 at 8:26 AM Alan Grayson <agrays...@gmail.com> wrote:

>>I stand corrected.  

> So now you understand my question? AG 

To quote you "My sarcasim went over your head, way over! AG"

I don't get your riddle. FWIW, it's spelled SARCASM. AG 

Then why did YOU spell it "sarcasim"? 

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

eb8

[Alan Grayson]

On Tuesday, April 1, 2025 at 7:35:16 AM UTC-6 John Clark wrote:

On Tue, Apr 1, 2025 at 9:27 AM Alan Grayson <agrays...@gmail.com> wrote:

On Tuesday, April 1, 2025 at 6:47:27 AM UTC-6 John Clark wrote:

On Tue, Apr 1, 2025 at 8:26 AM Alan Grayson <agrays...@gmail.com> wrote:

>>I stand corrected.  

> So now you understand my question? AG 

To quote you "My sarcasim went over your head, way over! AG"

I don't get your riddle. FWIW, it's spelled SARCASM. AG 

Then why did YOU spell it "sarcasim"? 

Is this what concerns you? I momentarily forgot how it's spelled. AG 

[Brent Meeker]

On 3/31/2025 8:49 PM, Alan Grayson wrote:

On Monday, March 31, 2025 at 6:07:49 PM UTC-6 Brent Meeker wrote:

On 3/31/2025 3:25 PM, Alan Grayson wrote:

Thanks for that data dump. When E was contemplating the CC, he knew that gravity was attractive and NOT the cause of the expansion implied for some values of the CC. Why then would he think that by assuming a repulsive CC which eliminated gravity, would imply a steady-state universe? AG

THINK, AG!  When Einstein wrote is first cosmology paper base on GR, he thought the universe was (1) Small: consisting of only the Milky Way and some "nebula"

No shit. Is that what E thought? I never heard that before! AG

It wasn't that he made it up.  He asked astronomers and that was the consensus at the time.

and (2) Static: having always existed just as seen at the time. 

No shit2. AG

 

The way to fit this with his GR models was to assume the CC had exactly the value needed to counter the gravitational attraction so that the universe could be infinitely old in this same state. 

The only person here who isn't THINKING clearly is YOU! If gravity isn't causing the expansion when presumably the CC is set to zero,

Gravity is always attractive, i.e. toward contraction.  The CC is also a force and can be positive or negative.  Both gravity and the CC are forces not velocities and not displacements.  So any value of CC is consistent with contraction or expansion.

Brent

why would eliminating it with some appropriate value of the CC, result in a steady-state universe? IOW, gravity is irrelevant to why the universe is expanding, and E knew this. So why would eliminating gravity have any effect on causing a static universe, the one E believed existed before Hubble proved otherwise? AG 

When Hubble discovered the universe was expanding then the universe was finitely old and was dynamic.  If the matter of the universe started off as from explosion the matter could be just coasting outward and no CC was needed.  The universe was expanding due to an initial impetus and coasting with just enough energy to asymptotically approach zero expansion rate at infinite time.  The LambdaCDM model with CC=0 seemed to fit the data up until about 1990.

Indeed. I know this story. AG 

The Einstein's GR equations for these two scenarios were exactly the same.  Only the boundary conditions were different.

Which two scenarios are you referring to? AG 

Brent

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[Brent Meeker]

On 4/1/2025 6:27 AM, Alan Grayson wrote:

On Tuesday, April 1, 2025 at 6:47:27 AM UTC-6 John Clark wrote:

On Tue, Apr 1, 2025 at 8:26 AM Alan Grayson <agrays...@gmail.com> wrote:

>>I stand corrected.  

> So now you understand my question? AG 

To quote you "My sarcasim went over your head, way over! AG"

I don't get your riddle. FWIW, it's spelled SARCASM. AG \

It's an accurate quote.

Brent

[Alan Grayson]

You really need to stop playing juvenile games. Of course he quoted me correctly, and I explained the spelling error. AG 

[Brent Meeker]

If you don't want to play, don't post.

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[Alan Grayson]

On Tuesday, April 1, 2025 at 4:23:51 PM UTC-6 Brent Meeker wrote:

On 4/1/2025 2:17 PM, Alan Grayson wrote:

On Tuesday, April 1, 2025 at 2:48:03 PM UTC-6 Brent Meeker wrote:

On 4/1/2025 6:27 AM, Alan Grayson wrote:

On Tuesday, April 1, 2025 at 6:47:27 AM UTC-6 John Clark wrote:

On Tue, Apr 1, 2025 at 8:26 AM Alan Grayson <agrays...@gmail.com> wrote:

>>I stand corrected.  

> So now you understand my question? AG 

To quote you "My sarcasim went over your head, way over! AG"

I don't get your riddle. FWIW, it's spelled SARCASM. AG \

It's an accurate quote.

Brent

You really need to stop playing juvenile games. Of course he quoted me correctly, and I explained the spelling error. AG

If you don't want to play, don't post.

It was apparent you responded without carefully reading the relevant posts. This isn't playing fairly. AG 

[Alan Grayson]

On Tuesday, April 1, 2025 at 1:09:46 PM UTC-6 Brent Meeker wrote:

On 3/31/2025 8:49 PM, Alan Grayson wrote:

On Monday, March 31, 2025 at 6:07:49 PM UTC-6 Brent Meeker wrote:

On 3/31/2025 3:25 PM, Alan Grayson wrote:

Thanks for that data dump. When E was contemplating the CC, he knew that gravity was attractive and NOT the cause of the expansion implied for some values of the CC. Why then would he think that by assuming a repulsive CC which eliminated gravity, would imply a steady-state universe? AG

THINK, AG!  When Einstein wrote is first cosmology paper base on GR, he thought the universe was (1) Small: consisting of only the Milky Way and some "nebula"

No shit. Is that what E thought? I never heard that before! AG

It wasn't that he made it up.  He asked astronomers and that was the consensus at the time.

and (2) Static: having always existed just as seen at the time. 

No shit2. AG

 

The way to fit this with his GR models was to assume the CC had exactly the value needed to counter the gravitational attraction so that the universe could be infinitely old in this same state. 

The only person here who isn't THINKING clearly is YOU! If gravity isn't causing the expansion when presumably the CC is set to zero,

Gravity is always attractive, i.e. toward contraction.  The CC is also a force and can be positive or negative.  Both gravity and the CC are forces not velocities and not displacements.  So any value of CC is consistent with contraction or expansion.

Brent

So when E had his happiest thought, that gravity wasn't a force, he was hallucinating? Do the astronauts in free fall feel a force of gravity? AG 

[Alan Grayson]

If the universe has no boundary, then one cannot determine what the CC could be, since such a calculation requires a boundary. And if different assumed values of the CC give different evolutions of the universe, I don't see that the CC has any relationship to gravity. AG 

[John Clark]

On Wed, Apr 2, 2025 at 6:36 AM Alan Grayson <agrays...@gmail.com> wrote:

> If the universe has no boundary, then one cannot determine what the CC could be, since such a calculation requires a boundary.

No, it doesn't.  

> I don't see that the CC has any relationship to gravity. AG 

Sorry to hear that, I guess you'll have to study physics and cosmology more deeply. 

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

hts

[Alan Grayson]

On Wednesday, April 2, 2025 at 5:21:27 AM UTC-6 John Clark wrote:

On Wed, Apr 2, 2025 at 6:36 AM Alan Grayson <agrays...@gmail.com> wrote:

> If the universe has no boundary, then one cannot determine what the CC could be, since such a calculation requires a boundary.

No, it doesn't.  

Brent implies otherwise. Are you saying you can get a definite solution from a set of differential equations without a boundary condition? AG 

> I don't see that the CC has any relationship to gravity. AG 

Sorry to hear that, I guess you'll have to study physics and cosmology more deeply.  

That's a reply from someone who insists on being a prick. Choose an evolution of the universe you prefer, and you can find a CC that does that for you. AG 

[Alan Grayson]

I think I get it. You're learned about physics and cosmology and I'm a know-nothing schmuck who asks stupid questions. OR, maybe you're a pretentious fool who thinks he knows much more than he really knows? If you're so learned about these arcane subjects, then maybe you can shed some light on my question, assuming you in fact understand it. Firstly, gravity isn't causing the universe to expand. At most, it's causing the rate of expansion to decrease, at least that was the understanding until around 1990. So, if Einstein determined a value of the CC which caused the expansion to cease, resulting in a steady state universe, why would anyone associate that value of the CC as having anything to do with ANTI-GRAVITY? Remember, GRAVITY, WHICH IS ATTRACTIVE, CANNOT BE THE CAUSE OF THE EXPANSION, SO ANY CC WHICH CEASES THE EXPANSION, HAS NOTHING TO DO WITH GRAVITY! AG

[Alan Grayson]

On Tuesday, April 1, 2025 at 1:09:46 PM UTC-6 Brent Meeker wrote:

On 3/31/2025 8:49 PM, Alan Grayson wrote:

         On Monday, March 31, 2025 at 6:07:49 PM UTC-6 Brent Meeker wrote:

                On 3/31/2025 3:25 PM, Alan Grayson wrote:

Thanks for that data dump. When E was contemplating the CC, he knew that gravity was attractive and NOT the cause of the expansion implied for some values of the CC. Why then would he think that by assuming a repulsive CC which eliminated gravity, would imply a steady-state universe? AG

THINK, AG!  When Einstein wrote is first cosmology paper base on GR, he thought the universe was (1) Small: consisting of only the Milky Way and some "nebula"

No shit. Is that what E thought? I never heard that before! AG

It wasn't that he made it up.  He asked astronomers and that was the consensus at the time.

and (2) Static: having always existed just as seen at the time. 

No shit2. AG 

The way to fit this with his GR models was to assume the CC had exactly the value needed to counter the gravitational attraction so that the universe could be infinitely old in this same state. 

The only person here who isn't THINKING clearly is YOU! If gravity isn't causing the expansion when presumably the CC is set to zero,

Gravity is always attractive, i.e. toward contraction.  The CC is also a force and can be positive or negative.  Both gravity and the CC are forces not velocities and not displacements.  So any value of CC is consistent with contraction or expansion.

Brent

If you claim gravity is a force, then you're affirming revisionist history, since E's happiest thought was that it isn't (a force). AG 

[Alan Grayson]

The point I was trying to make, might have been too suble for you to grasp. so you, JC, defaulted to insults. Einstein initially set the CC to zero, and when it was determined that his field equations predicted an expanding universe, he reset it to a positive value, presumably to make gravity stronger so the effect of the positive CC and gravity would produce a static universe. In this situation, the CC would augment the attractive force of gravity. Later, when E was convinced that the universe is expanding, he reset the CC back to zero. In 1990, when it was discovered that the rate of expansion was in fact increasing, the CC was re-introduced in his field equations, this time to oppose the attractive force of gravity, using "dark matter" as a placeholder for the cause of the increase in the rate of expansion. So, it is natural to imagine the CC as related to gravity, and to think of it as a force, notwithstanding the revisionist concept of a force in GR, when E's happiest thought was to realize that gravity isn't a force. In any event, the point in my preceding post is that the cause of the expansion of the universe seems totally unrelated to gravity -- I've never seen any argument affirming that gravity IS related to the expansion, other than slowing its rate -- so anything beyond gravity that effects the expansion might be independent of gravity. Finally, it would be nice if one could speculate here without being the subject of a pissing contest. AG

[Brent Meeker]

On 4/9/2025 4:42 PM, Alan Grayson wrote:

On Thursday, April 3, 2025 at 12:48:49 AM UTC-6 Alan Grayson wrote:

On Wednesday, April 2, 2025 at 6:03:49 AM UTC-6 Alan Grayson wrote:

On Wednesday, April 2, 2025 at 5:21:27 AM UTC-6 John Clark wrote:

On Wed, Apr 2, 2025 at 6:36 AM Alan Grayson <agrays...@gmail.com> wrote:

> If the universe has no boundary, then one cannot determine what the CC could be, since such a calculation requires a boundary.

No, it doesn't.  

Brent implies otherwise. Are you saying you can get a definite solution from a set of differential equations without a boundary condition? AG

The boundary condition for the universe is its present state and it's not finite.

Brent

> I don't see that the CC has any relationship to gravity. AG 

Sorry to hear that, I guess you'll have to study physics and cosmology more deeply.  

That's a reply from someone who insists on being a prick. Choose an evolution of the universe you prefer, and you can find a CC that does that for you. AG 

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

I think I get it. You're learned about physics and cosmology and I'm a know-nothing schmuck who asks stupid questions. OR, maybe you're a pretentious fool who thinks he knows much more than he really knows? If you're so learned about these arcane subjects, then maybe you can shed some light on my question, assuming you in fact understand it. Firstly, gravity isn't causing the universe to expand. At most, it's causing the rate of expansion to decrease, at least that was the understanding until around 1990. So, if Einstein determined a value of the CC which caused the expansion to cease, resulting in a steady state universe, why would anyone associate that value of the CC as having anything to do with ANTI-GRAVITY? Remember, GRAVITY, WHICH IS ATTRACTIVE, CANNOT BE THE CAUSE OF THE EXPANSION, SO ANY CC WHICH CEASES THE EXPANSION, HAS NOTHING TO DO WITH GRAVITY! AG

The point I was trying to make, might have been too suble for you to grasp. so you, JC, defaulted to insults. Einstein initially set the CC to zero, and when it was determined that his field equations predicted an expanding universe, he reset it to a positive value, presumably to make gravity stronger so the effect of the positive CC and gravity would produce a static universe. In this situation, the CC would augment the attractive force of gravity. Later, when E was convinced that the universe is expanding, he reset the CC back to zero. In 1990, when it was discovered that the rate of expansion was in fact increasing, the CC was re-introduced in his field equations, this time to oppose the attractive force of gravity, using "dark matter" as a placeholder for the cause of the increase in the rate of expansion. So, it is natural to imagine the CC as related to gravity, and to think of it as a force, notwithstanding the revisionist concept of a force in GR, when E's happiest thought was to realize that gravity isn't a force. In any event, the point in my preceding post is that the cause of the expansion of the universe seems totally unrelated to gravity -- I've never seen any argument affirming that gravity IS related to the expansion, other than slowing its rate -- so anything beyond gravity that effects the expansion might be independent of gravity. Finally, it would be nice if one could speculate here without being the subject of a pissing contest. AG

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[John Clark]

On Wed, Apr 9, 2025 at 7:42 PM Alan Grayson <agrays...@gmail.com> wrote:

> Einstein initially set the CC to zero, and when it was determined that his field equations predicted an expanding universe, he reset it to a positive value, presumably to make gravity stronger so the effect of the positive CC and gravity would produce a static universe. In this situation, the CC would augment the attractive force of gravity.

In 1915 when Einstein originally published his field equation for general relativity the left-hand part of the equation is a 4D tensor that described the curvature of spacetime, and the curvature of space time is what we experience as gravity.  The right hand side of the equation is a tensor that specifies the distribution of all forms of energy and momentum in a given region of spacetime. Later when Einstein added a cosmological constant he put it on the left-hand side of the equation, the geometry part. He thought that additional term spoiled the mathematical beauty of his original equation but he thought he had no choice because all his astronomer friends insisted that the universe was stable. When astronomers changed their mind about that Einstein immediately dropped the entire cosmological constant idea. 

Much later in the late 1990s astronomers discovered that the universe is accelerating and the cosmological constant idea came back, but this time they put it on the other side of the equation and gave it a minus sign. Doing this is mathematically equivalent but it has a very different physical interpretation, now it's not a modification of spacetime geometry, instead it's a form of energy intrinsic to the vacuum, because of that negative sign its pressure is negative and equal to the energy density.  

 > I've never seen any argument affirming that gravity IS related to the expansion, other than slowing its rate 

I think what you really want to know is why negative pressure produces a repulsive effect. The acceleration of the universe’s expansion is described by:

-a [(-4πG/3)(ρ+3P)] 

where ρ is the energy density, P is the pressure, G is Newton's gravitational constant, and a is just a scale factor. The 3 is in there because there are three spatial dimensions, so pressure contributes to the push or pull of gravity depending on if the pressure is positive or negative. 

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

nae 

[Alan Grayson]

On Wednesday, April 9, 2025 at 6:14:52 PM UTC-6 Brent Meeker wrote:

On 4/9/2025 4:42 PM, Alan Grayson wrote:

On Thursday, April 3, 2025 at 12:48:49 AM UTC-6 Alan Grayson wrote:

On Wednesday, April 2, 2025 at 6:03:49 AM UTC-6 Alan Grayson wrote:

On Wednesday, April 2, 2025 at 5:21:27 AM UTC-6 John Clark wrote:

On Wed, Apr 2, 2025 at 6:36 AM Alan Grayson <agrays...@gmail.com> wrote:

> If the universe has no boundary, then one cannot determine what the CC could be, since such a calculation requires a boundary.

No, it doesn't.  

Brent implies otherwise. Are you saying you can get a definite solution from a set of differential equations without a boundary condition? AG

The boundary condition for the universe is its present state and it's not finite.

Brent

How do you know that? ISTM, you're speculating and misrepresenting your speculation for knowledge. Data from the Planck spacecraft isn't conclusive. AG 

[Brent Meeker]

On 4/10/2025 6:20 AM, John Clark wrote:

On Wed, Apr 9, 2025 at 7:42 PM Alan Grayson <agrays...@gmail.com> wrote:

> Einstein initially set the CC to zero, and when it was determined that his field equations predicted an expanding universe, he reset it to a positive value, presumably to make gravity stronger so the effect of the positive CC and gravity would produce a static universe. In this situation, the CC would augment the attractive force of gravity.

In 1915 when Einstein originally published his field equation for general relativity the left-hand part of the equation is a 4D tensor that described the curvature of spacetime, and the curvature of space time is what we experience as gravity.  The right hand side of the equation is a tensor that specifies the distribution of all forms of energy and momentum in a given region of spacetime. Later when Einstein added a cosmological constant he put it on the left-hand side of the equation, the geometry part. He thought that additional term spoiled the mathematical beauty of his original equation but he thought he had no choice because all his astronomer friends insisted that the universe was stable. When astronomers changed their mind about that Einstein immediately dropped the entire cosmological constant idea.

That's not quite right.  His astronomer friends told him the universe was static, not stable though that would be implied.  So Einstein put in a non-zero CC to make the universe (which was just the Milky Way and a few nebula) static.  As soon as he published this, it was pointed out to him that while static, his solution was unstable.  If they had told him it was stable, he probably would have checked for stability and not embarrassed himself with "My greatest error".

He set the CC=0 when Hubble showed the universe was expanding, something consistent both with an old universe and no CC.

Brent

Much later in the late 1990s astronomers discovered that the universe is accelerating and the cosmological constant idea came back, but this time they put it on the other side of the equation and gave it a minus sign. Doing this is mathematically equivalent but it has a very different physical interpretation, now it's not a modification of spacetime geometry, instead it's a form of energy intrinsic to the vacuum, because of that negative sign its pressure is negative and equal to the energy density.  

 > I've never seen any argument affirming that gravity IS related to the expansion, other than slowing its rate 

I think what you really want to know is why negative pressure produces a repulsive effect. The acceleration of the universe’s expansion is described by:

-a [(-4πG/3)(ρ+3P)] 

where ρ is the energy density, P is the pressure, G is Newton's gravitational constant, and a is just a scale factor. The 3 is in there because there are three spatial dimensions, so pressure contributes to the push or pull of gravity depending on if the pressure is positive or negative. 

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

nae 

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[Brent Meeker]

On 4/10/2025 6:56 AM, Alan Grayson wrote:

On Wednesday, April 9, 2025 at 6:14:52 PM UTC-6 Brent Meeker wrote:

On 4/9/2025 4:42 PM, Alan Grayson wrote:

On Thursday, April 3, 2025 at 12:48:49 AM UTC-6 Alan Grayson wrote:

On Wednesday, April 2, 2025 at 6:03:49 AM UTC-6 Alan Grayson wrote:

On Wednesday, April 2, 2025 at 5:21:27 AM UTC-6 John Clark wrote:

On Wed, Apr 2, 2025 at 6:36 AM Alan Grayson <agrays...@gmail.com> wrote:

> If the universe has no boundary, then one cannot determine what the CC could be, since such a calculation requires a boundary.

No, it doesn't.  

Brent implies otherwise. Are you saying you can get a definite solution from a set of differential equations without a boundary condition? AG

The boundary condition for the universe is its present state and it's not finite.

Brent

How do you know that? ISTM, you're speculating and misrepresenting your speculation for knowledge. Data from the Planck spacecraft isn't conclusive. AG

Read any text, or Vic's "Comprehensible Universe".  It you're going to choose a boundary condition for the universe what would you pick besides the one state you know?

Brent

[Alan Grayson]

We don't KNOW that the universe is infinite in spatial extent! This is true regardless of what one chooses as its boundary condition. AG 

[Brent Meeker]

Did you miss the word "choose"?  Do you have an alternative in mind?  Do you know what the equation is?

Brent

[Alan Grayson]

What's an equation? I have no idea what it means or is. Please stop you're BS. You claimed the universe is infinite in spatial extent. YOUR WORDS! You don't know what the fuck you are claiming. AG 

[Alan Grayson]

[John Clark]

On Thu, Apr 10, 2025 at 9:53 PM Brent Meeker <meeke...@gmail.com> wrote:

>> In 1915 when Einstein originally published his field equation for general relativity the left-hand part of the equation is a 4D tensor that described the curvature of spacetime, and the curvature of space time is what we experience as gravity.  The right hand side of the equation is a tensor that specifies the distribution of all forms of energy and momentum in a given region of spacetime. Later when Einstein added a cosmological constant he put it on the left-hand side of the equation, the geometry part. He thought that additional term spoiled the mathematical beauty of his original equation but he thought he had no choice because all his astronomer friends insisted that the universe was stable. When astronomers changed their mind about that Einstein immediately dropped the entire cosmological constant idea.

> That's not quite right.  His astronomer friends told him the universe was static, not stable though that would be implied. 

You're right, "static" would have been a better word because observational astronomers can tell you if the universe was static or not (and when they got enough observations eventually they got it right) but only theory can tell you if it's stable or not. 

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

yvv

nae 

[Brent Meeker]

On 4/10/2025 9:42 PM, Alan Grayson wrote:

On Thursday, April 10, 2025 at 9:43:20 PM UTC-6 Brent Meeker wrote:

On 4/10/2025 8:34 PM, Alan Grayson wrote:

The boundary condition for the universe is its present state and it's not finite.

Brent

How do you know that? ISTM, you're speculating and misrepresenting your speculation for knowledge. Data from the Planck spacecraft isn't conclusive. AG

Read any text, or Vic's "Comprehensible Universe".  It you're going to choose a boundary condition for the universe what would you pick besides the one state you know?

Brent

We don't KNOW that the universe is infinite in spatial extent! This is true regardless of what one chooses as its boundary condition. AG

Did you miss the word "choose"?  Do you have an alternative in mind?  Do you know what the equation is?

Brent

What's an equation? I have no idea what it means or is.

Look up FLRW cosmology or read Vic's Comprehensible Cosmos chapter on cosmology.

Please stop you're BS. You claimed the universe is infinite in spatial extent. YOUR WORDS! You don't know what the fuck you are claiming. AG

And you don't know what the fuck you're talking about.  I notice you write "YOUR WORDS!"  but you didn't actually quote me. 

The FLRW equation for the universe only has a scale factor which is set to 1 at the present so depending on the other parameters it describes a universe that expands indefinitely or that collapses in the future.  The scale factor going to zero in the past (or future) means that the part of the universe we know was then infinitely dense.  All the stuff we can see was packed into a zero size. 

Whether the universe is spatially infinite is a slightly different question.  It's an extrapolation from the part we can see to assume it's homogeneous and isotropic on a large scale. The CMB is at 2.73degK and varies by only 0.0001degK across the sky.  If we make that extrapolation, as is commonly done, the universe is infinite.  Without some such extrapolation beyond what we can see we can't write down any solution of Einstein's equations and we can't do cosmology.

Brent

The boundary condition for the universe is its present state and it's not finite.

Brent

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[Alan Grayson]

On Friday, April 11, 2025 at 2:14:37 PM UTC-6 Brent Meeker wrote:

On 4/10/2025 9:42 PM, Alan Grayson wrote:

On Thursday, April 10, 2025 at 9:43:20 PM UTC-6 Brent Meeker wrote:

On 4/10/2025 8:34 PM, Alan Grayson wrote:

The boundary condition for the universe is its present state and it's not finite.

Brent

How do you know that? ISTM, you're speculating and misrepresenting your speculation for knowledge. Data from the Planck spacecraft isn't conclusive. AG

Read any text, or Vic's "Comprehensible Universe".  It you're going to choose a boundary condition for the universe what would you pick besides the one state you know?

Brent

We don't KNOW that the universe is infinite in spatial extent! This is true regardless of what one chooses as its boundary condition. AG

Did you miss the word "choose"?  Do you have an alternative in mind?  Do you know what the equation is?

Brent

What's an equation? I have no idea what it means or is.

Look up FLRW cosmology or read Vic's Comprehensible Cosmos chapter on cosmology.

Please stop you're BS. You claimed the universe is infinite in spatial extent. YOUR WORDS! You don't know what the fuck you are claiming. AG

And you don't know what the fuck you're talking about.  I notice you write "YOUR WORDS!"  but you didn't actually quote me. 

I certainly did quote you. You need to scroll down a bit to see it. AG 

[Alan Grayson]

When Einstein included the CC to make the universe steady state, this CC would have augmented the attractive force of gravity, which apparently wasn't strong enough to reduce the expansion implied by his field equations to zero. Is this augmentation of gravity what you, JC, called negative pressure? AG

[Alan Grayson]

On Friday, April 18, 2025 at 6:38:32 PM UTC-6 Alan Grayson wrote:

When Einstein included the CC to make the universe steady state, this CC would have augmented the attractive force of gravity, which apparently wasn't strong enough to reduce the expansion implied by his field equations to zero. Is this augmentation of gravity what you, JC, called negative pressure? AG

What is the theoretical cause of negative pressure, and how can it exist in a universe without a boundary? TY, AG