edearl said:
I fear that I may have inadvertently proposed a personal hypothesis,...
I would say don't worry! I'm not a moderator of course and it's just my opinion but I think you raise quite legitimate questions (given where you are coming from). Obviously ytivarG is just a bit of fun.
Nice name for it actually.
One point is that in the largescale pattern of expansion of distances
nobody gets anywhere so it is not like ordinary motion. Nobody approaches a destination. Everybody thinks they are sitting still, and just getting farther from everywhere.
The 1915 Einstein equation is both our law of geometry (how geometry evolves and interacts with matter) and our law of gravity. We have no right to expect that distances won't change or that geometry will always be flat the way Euclid told us. The 1915 equation keeps passing all the tests that have been devised, with exquisite accuracy. So what can we do?
Certain things that were true in a fixed foursquare Euclid-style geometry turn out to be only very nearly true. Because nature's real geometry is not perfectly flat fixed and non-expanding---only very nearly so.
Newton's laws of motion and the intuition that goes with them turn out to be useful in our local neighborhood---even within our own group of galaxies---where flat geometry is an excellent approximation, but become less applicable at wider scale.
So you need to be somewhat cautious about applying a Newtonian intuition to this larger world beyond our local group of a dozen or so galaxies. It will be NEARLY right a lot of the time but there will be slight discrepancies.
So at very large scale global energy is not welldefined and a good old law like conservation of energy can't be applied, at least without some technical caveats. There are FAQ entries about this kind of thing, I believe. And you ask "if a distant galaxy is receding at an increasing rate, where is it getting the required influx of kinetic energy?" But the galaxy is not going anywhere. The distance to it is simply increasing. Recession is not like ordinary motion. Distances can increase at rates exceeding c. And indeed the distances to most of the galaxies we can see with a telescope like the Hubble ARE increasing at rates >c. I don't know any simple way to associate a kinetic energy with that.
The nice thing is that these effects are very slight percentagewise. The current rate of expansion of distance is only about 1/140 percent per million years. That is tiny! In a million years the distance between two stationary observers only increases by 1/140 of one percent. The acceleration rate is even more negligible, percentagewise. I forget what it is except that it comes out to be a ridiculously small number. These things only matter when you look at the world at very very large scale.
So we can safely continue to rely on our good old Newtonian laws for most practical purposes, conservation of energy included!
Check out the FAQ, they may do a better job with this.
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the really interesting question you raise is about
why the 1915 equation naturally has a second constant lambda in it.
That article by Bianchi and Rovelli has a discussion of this. It turns out that Einstein already in 1916 noticed that a lambda term naturally belonged in the equation
because it was allowed by the ruling symmetry of the theory which he called "general covariance". At that point he had not conceived of a need for the lambda term, so he only mentioned it in a footnote.
Later there was all that blunder-fuss about it. Misusing the lambda term in a blind attempt to force the model to be static. Who says geniuses are always wise? But that was LATER. The first thing he does is point out that the lambda term naturally appears in the theory because it is allowed by symmetry. This is pretty esoteric but I'll venture a comment or two.
Symmetry is a sweet and subtle feature of modern theory. In the 20th century they discovered that you can derive physics equations from symmetries. It is viewed as the cool way to do it. In the Beginning was the Symmetry, that the system or the socalled "Lagrangian" describing it is supposed to satisfy and you include every term that you can without spoiling the symmetry.
I think Tom Stoer had a very down-to-earth description of why the lambda term naturally appears in the Einstein equation. It could have been in the "Why all these prejudices against a constant" thread. You might have a look at that. Tom, or someone, remarked that it was analogous to what you do in First Year Calculus when you learn to do integrals. The answer is not right unless you introduce a constant of integration. Because, in the most general form,
it belongs.
Sorry if this is too esoteric but I can't do better at the moment. Given how A.E. conceived the theory, in its most general and elegant form it must contain TWO constants of nature, namely Newton G and this other Einstein one called λ. Rather than merely having G, like the earlier 1687 law of gravity.
And the amusing bit is that the effect of this constant (just an A.E. footnote in 1916) was only noticed in 1998 by people comparing distances and redshifts of supernovae. Nature keeps reminding us that we are, after all, just a type of monkey.
We don't know everything yet.
In Loop gravity the lambda arises from the use of a new kind of symmetry called a "quantum group". Loop is an attempt to make the classic 1915-1916 theory of geometry/gravity emerge from some deeper description. Which will allow geometry to be uncertain, as all good quantum creatures are. But the Loop description, from which the classic one arises, is as yet just a guess (one of several that the monkeys are working on.)
We don't know the fundamental descriptors (the deeper "degrees of freedom") that describe geometry in conjunction with matter. When we have a better idea we may see how both Newton G and λ emerge from a deeper symmetry.
In any case I think "dark energy" is just a myth or fairy tale. It may turn out to have been quite misleading to speak of lambda as an energy. So far all we know is that it is simply a constant, like Newton G, which occurs in the contemporary law of gravity.
If you want the Bianchi Rovelli paper (which is quite readable) just google "constant prejudices".
Let's not dwell on that. I'm just back from getting temporarily banned for my political opinions. Anyway, thanks for the feedback.
