Posted: Mar 25, 2017 2:34 pm
Are you blind, the explanation is clearly indicated, right where I said "...or I'm full of shit"
Also, the previous phrase "Or maybe I'm saying it wrong". In other words, I don't understand this enough to explain what I'm thinking, and what I'm thinking is likely to be wrong, I have read about 1/3 [3 pages] of the paper right after that post, then had other stuff to do, am going to get back to soon. I can tell I'm not going to understand a lot of what is said, but there is one bit that says a lot that I did not have a clue about: Also, some concepts I have little to no understanding of are rife, e.g., the very crucial to this whole issue, "comoving", which I vaguely understand, I think it is basically the relative velocities of objects if you 'take out' the expansion, and 'Minkowski space', locally Minkowskian', etc which I have little understanding of. And don't really know what they mean by a "locally comoving family of observers".In the curved spacetime of general relativity, there is no unique way to compare vectors at widely separated spacetime points, and hence the notion of the relative velocity of a distant galaxy is almost meaningless.
Another bit I'm struggling with, which doesn't bode well for me understanding the paper at all, is this:
An expanding universe with density Ω = 0 (often known as the Milne model ) is merely the flat Minkowski spacetime of special relativity expressed in nonstandard coordinates. In an Ω = 0 universe there are no gravitational effects at all, so any observed redshift, even of a very distant galaxy, must be a Doppler shift.
This implies that the expansion is not a gravitational effect, but I don't understand why, in the absence of gravitational effects, the conclusion is that the redshift must then be doppler. I'm missing the crucial severing of expansion and wavelength and how gravity is needed to get the photon to shift frequency, or stretch, or whatever it's doing. There's another thing that brought me up short as to what I had understood [should say 'thought I understood'], it's this:
A student presented with the stretching-of-space description of the redshift cannot be faulted for concluding,
incorrectly, that hydrogen atoms, the Solar System, and the Milky Way Galaxy must all constantly “resist the
temptation” to expand along with the universe. One way to see that this belief is in error is to consider the problem
sometimes known as the “tethered galaxy problem,” in which a galaxy is tethered to the Milky Way, forcing
the distance between the two to remain constant. When the tether is cut, does the galaxy join up with the Hubble
flow and start to recede due to the expansion of the universe? The intuition that says that objects suffer from a
temptation to be swept up in the expansion of the universe will lead to an affirmative answer, but the truth is the
reverse: unless there is a large cosmological constant and the galaxy’s distance is comparable to the Hubble length,
the galaxy falls toward us. Similarly, it is commonly believed that the Solar System has a very slight tendency to
expand due to the Hubble expansion (although this tendency is generally thought to be negligible in practice). Again,
explicit calculation shows this belief not to be correct. The tendency to expand due to the stretching of space is
nonexistent, not merely negligible.
If I could grasp this, then I think i'd understand the issue. I don't get how you show '"The tendency to expand due to the stretching of space is nonexistent, not merely negligible." Obviously, it's in the maths, but I'm not into the maths enough, so it's looking like this will for now be opaque to me. One of the 'if I won the lottery' type fantasies I've entertained frequently is to find a physics grad student I could hire, like on a retainer, so he would be on call when I needed something like this explained. He'd have to be quite patient, and tolerant to idiocy, but since so many of them tend to having little money, it might not be too hard to find one.
I had to reread the 3 pages to make this post, got small blip of an increased understanding, not significant, too much time spent on this topic.
Now, to actually address your question
, my remarks come from a too simple understanding of the issue, it relies on the naive view that the first quoted text above demolishes. The 'categorical difference' relied on there being something real in the question of relative velocity of two widely separated observers. I thought if you had two observers who were close enough to determine they had zero relative velocity wrt each other 13 billion years ago, and that neither accelerated for 13 billion years, then after 13 billion years of expansion, they should still have zero relative velocity, but this seems to not make sense in GR terms. 13 proves unlucky, and I hope I can stop the blood oozing out of both ears now. Unless someone steps in with a virtuoso explanation that is simple enough to grasp by my obtuse brain but complete enough to convey the physics involved, I'm afraid the issue will remain fairley opaque to me. I'll finish the paper, maybe something will spark off some comprehension, but I doubt it. It doesn't help that I've lost the focus I had way back in my college days and forgotten too much of the math.