Re: The Cosmological constant (was Re: [asa] Predestined Fame:)

From: George Murphy <GMURPHY10@neo.rr.com>
Date: Wed Jul 16 2008 - 08:31:27 EDT

Murray -

I'm glad you pushed me on this & perhaps saved me later embarassment, for looking back at the footnote in Einstein's 1915 paper I see that he didn't say what I remembered him as saying. So my comment about that should be stricken from the record. OTOH it raises the question why at just that point he didn't recognize the possibility of what would come to be called the cosmological term.

For the argument that he made for the left side of the field equations outside a matter distribution was that it be formed from the metric tensor and its first and second derivatives, and be linear in the second derivatives. He then said that the contracted Riemann tensor was the only tensor satisfying that condition. But in reality the metric tensor itself, multiplied by an arbitrary constant (i.e., the cosmological constant) can be added to the Riemann tensor & the conditions will still be satisfied. This continues to be the case when the necessary changes are made to include matter.

It's hard to know why Einstein didn't at least comment on that possibility in 1915. In any case he did realize and exploit it in 1917 when he first dealt with the cosmological problem. There he wanted a static universe 1st because the general belief of astronomers at that time was that the universe was static on a large scale.
But Max Jammer has also argued (in Einstein and Religion) that Einstein's commitment to Spinozistic pantheism may have played a role here. For if the universe and God are different names for the same thing, & if God is immutable, the universe must be immutable. That Einstein may have had extra-scientific motives is suggested by the facts that he was quite slow in accepting both observational and theoretical arguments for a non-static universe.

I think it's pretty well agreed that Einstein did tell Gamow that introducing the cosmological term was his "greatest blunder." One reason for that is that that term does from one standpoint make the field equations more complicated and less "elegant." But Einstein probably also realized that if he hadn't introduced it he might have been forced to realize that the universe wasn't static - that it was either expanding or contracting, & already by the early 20s there were enough galactic spectra to indicate expansion. Thus the expansion of the universe could have been announced as a "fourth test" of general relativity. (Although Newtonian cosmology gives the same result.)
 

Shalom
George
http://web.raex.com/~gmurphy/
----- Original Message -----
From: "Murray Hogg" <muzhogg@netspace.net.au>
To: "ASA" <asa@calvin.edu>
Sent: Tuesday, July 15, 2008 10:25 PM
Subject: The Cosmological constant (was Re: [asa] Predestined Fame:)

> Hi George,
>
> I don't intend to defend a position on which I admit to being rather
> uninformed. So please take the following as a request for increased
> understanding.
>
> My reference is ONLY to Einstein's introduction of the cosmological
> constant in 1917 - a.k.a. "the biggest mistake of my career." -
> regardless of what constructive work it might subsequently do.
>
> So while I acknowledge that it isn't a "fudge-factor" now, it does seem
> to me to have been so at the time Einstein introduced it.
>
> If this is not the case then (first question) what was the point of the
> infamous "biggest mistake" remark? Indeed, to ask a more basic question,
> is this comment correctly ascribed to Einstein in the first place?
>
> And the second question: can you unpack a little the significance of the
> footnote in the earlier paper? Again, if this demonstrates the 1917
> cosmological constant to be a valid inclusion - why did Einstein
> subsequently distance himself from the idea?
>
> Perhaps, were he aware of subsequent developments, Einstein might now
> describe the cosmological constant as the most fortuitous mistake of his
> career?
>
> Blessings,
> Murray Hogg
> Pastor, East Camberwell Baptist Church, Victoria, Australia
> Post-Grad Student (MTh), Australian College of Theology
>
> gmurphy10@neo.rr.com wrote:
>> This has nothing to do with numerology but I have to make my standard defence of the cosmological term. It's true that Einstein introduced it only to get a static universe in his 1917 paper. But in his basic general relativity paper 2 years earlier there is a footnote which in essence recognizes the possibility of including such a term in the field equations. & when he did introduce it he gave another argument for it, viewing it as an averaging of the "Poincare stresses" that were thought to be needed in classical electron theory.
>>
>> If Einstein had not introduced the cosmological term for the reasons he did, someone else would eventually have introduced them for other reasons - of which several can be given. & of course now we know that it provides at least a first approximation to the effects of dark energy.
>>
>> The popular designation of the cosmological constant as the quintessential fudge factor should cease.
>>
>> Shalom,
>> George Murphy
>>
>> ---- Murray Hogg <muzhogg@netspace.net.au> wrote:
>> ...........................
>>> To offer an analogy pertinent to the scientific nature of the list, I
>>> see your approach as working ONLY if you are allowed to get away with a
>>> highly questionable "fudging" of the equations -- a bit like Einstein's
>>> addition of a cosmological constant to "fix" the theory of general
>>> relativity. Such a constant was required by Einstein's need to
>>> demonstrate a point, not because of any truly scientific motive.
>> ...............................
>>
> --
> Murray Hogg
> Pastor, East Camberwell Baptist Church, Victoria, Australia
> Post-Grad Student (MTh), Australian College of Theology
>
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Received on Wed Jul 16 08:35:27 2008

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