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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