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