Subject: Einstein's cosmological term and his inappropriate use of Poisson's equation in ruling out an infinite universe.
This letter has been edited.
September 5, 1995
Dear [name withheld],
I wish to note my opinion that you have given too much weight to Silk and Davies’ comments. This is in regard to your parenthetical remark on page 196:
(Some writers have stated or implied that Einstein gratuitously added the cosmic repulsion term to his equations. But experts deny that. Silk has said that Einstein’s equations “in their most general form contain this term,” and Davies has said that Einstein “didn’t conjure up cosmic repulsion in an ad hoc way. He found that his gravitational field equations contained an optional term which gave rise to a force with exactly the desired properties.”)Timothy Ferris writes (Coming Of Age In The Milky Way, 1988), p. 206:Einstein never liked the cosmological constant. He called it “gravely detrimental to the formal beauty of the theory,” pointing out that it was nothing more than a mathematical fiction, without any real physical basis, one that had been introduced solely to [bring] the theory into accord with observational facts. As he wrote in 1917:The quotation Ferris provides us with is from Einstein’s The Principle of Relativity, (1952) p.188. “Cosmological Considerations On The General Theory of Relativity.” (Incidentally, Ferris informs us in the Bibliography that the Dover book is useful but marred by errors in translation.)
[W]e admittedly had to introduce an extension of the field equations of gravitation....That term is necessary only for the purpose of making possible a quasi-static distribution of matter, as required by the fact of the small velocity of the stars.What does it mean when Davies remarks “He [Einstein] found that his gravitational field equations contained an optional my emphasis] term which gave rise to a force with exactly the desired properties.”? It means to me that Davies contradicts himself by saying Einstein “didn’t conjure up cosmic repulsion in an ad hoc way.” Neither does the remark by Silk in any way negate the comments of “some writers” “that Einstein gratuitously added the cosmic repulsion term to his equations.”
If you have any remaining doubt on this question see page 83 of J.D. North’s The Measure Of The Universe: A History of Modern Cosmology (Dover, 1990) where North writes:
As Einstein admitted, the extension of the field equations was “not justified by our actual knowledge of gravitation” but was merely “logically consistent.”And on page 86:By 1919 even Einstein had taken up the cry [in favor of rejecting the cosmological term], holding that the introduction of [cosmological term], was “gravely detrimental to the formal beauty of the theory”. He held this view to the end of his life and always looked with favor upon the Friedmann metric as avoiding this “ad hoc addition” to the field equations.To further verify Einstein’s inclusion of the cosmological term as ad hoc see page 117 in Einstein’s The Meaning of Relativity, fifth edition, (Princeton University Press, 1974 printing). Einstein writes:We must now further satisfy the field equations of gravitation, that is to say the field equations without the “cosmologic member” which has been introduced previously ad hoc...To restate what I’ve said before, the cosmological term was something Einstein introduced, not because general relativity demanded it, but because Einstein believed (mistakenly) that the gravitational potential tends toward a fixed limiting value at infinity. Einstein writes: “It is well known that Newton’s limiting condition of the constant limit for ø at spatial infinity leads to the view that the density of matter becomes zero at infinity.” Or alternatively, if matter continues out to infinity an infinite gravitational force can be expected on each place in the universe as Einstein referred to on pages 105-107 in Relativity The Special and the General Theory (See my reference #7 in my larger BB critique, and page 13.) This belief that the effect of gravity is accumulative on all scales is very much incorrect as I shall explain below.I know of no mathematics or philosophy that is properly applicable in forbidding an infinite universe. In order for Newton-Poisson equation to be properly applicable gravity would have to be accumulative at all scales. It is not. Gravity may have an unlimited reach, but the reach counts for nothing because it is the effect which counts.
The effect of gravity, that which we experience and measure, is negated in many ways, and at many scales. For example, on the inside of a hollow sphere in inertial motion there is no gravitational effect anywhere inside the sphere. And at the center of every massive (solid) body in inertial motion there is also zero gravity. Also, all stars and planets assume a motion that results in nearly no felt gravity on them from the other bodies in their neighborhood (tidal effects are the exception).
It makes no difference how much matter is around you if you are at the center of a mass, such as a planet, star, galaxy or anywhere in an infinite universe, as long as you are freely moving (inertial). The gravitational pull from one direction negates the pull from the opposite direction.
Gravity makes itself felt most at surfaces (away from inertial centers), and when there is uneven distributions in conglomerations of matter. This is true on the largest scales as with galaxies. In a very uniform distribution of galaxies the effect of one galaxy on another is going to be very limited (think in terms of a cloud of dust). The effective distance of the gravitational effect increases only as the scale of clumpiness of matter increases. For example, a distant superclusters gravitational effect on our galaxy would disappear if the space between and around the supercluster and our galaxy were now occupied with the same density of galaxies as that of the supercluster. (Of course, in the latter case there would no longer be a supercluster to have a distinction as such.) The greater the scale of nonuniformity of matter, the greater is the scale at which gravitational effects are manifested, but only up to that scale of nonuniformity. At an even greater scale when nonuniformity becomes uniformity this will be the scale when cosmologically large distance gravitational effects are negated beyond that scale.
With some thought we can see that the effects of gravity are limited in various ways and at various scales. So for some mathematicians to assume that gravity has a continually accumulative effect I can only say that they are mistaken, and that the mathematics that is based on their assumption will of necessity also be mistaken. To only argue that the math is straight forward and proves something is to ignore certain assumptions that underlie the math. This is a problem I’ve seen many times; students of science will do well to learn this lesson.
Yours,
Vincent Sauve
skeptica@pacbell.net