Dear John:
First of all, thanks very much for reading my essay! I appreciate your comment, and think I can help with some things. I'm not too bothered by your saying that you agree with Israel about expansion, because there are a few things that you seem to misunderstand about how cosmic expansion is thought to work, which I think I can explain, hoping you might like it better in a different light. From what you've written, I think you're actually interested in understanding this (which I think you shoud, because in any case I am a firm believer that you can't criticise what you don't understand), so I'm happy to try to explain. Here are my comments:---
"If expansion is balanced by gravity, then why would the universe as a whole continue to expand? Consider it in terms of the rubber sheet analogy of gravity. Flat space is treated as a rubber sheet, which is deformed by the weight of gravity. If expansion balances this effect, leaving an overall flat space, then the compression of gravity is perfectly matched by expansion in the areas not so compressed. When you consider that light from distant sources most effectively travels through the areas not occupied by gravity and mass, then it would be most affected by this opposite effect of gravity/expansion. If fact, Einstein first proposed the cosmological constant as a balance to the compression of gravity. Thus as light passes through this expanded area, it is first redshifted, then the further it travels, the more the effect is compounded, thus redshift is proportional to distance." Yes, it is understood that in dense regions, galaxies and clusters of galaxies hold together without being ripped apart by the Hubble flow; e.g., the expansion of space in the absence of gravitational attraction does not imply that your body should be expanding as well. Then, it's as you've said, the cosmological redshift as light travels through expanding space is supposed to be far far greater than any gravitational red/blueshift near the observer/source. Galaxies are modeled as points in expanding space in the standard model. Every galaxy stays at the same coordinates while the space between them all expands. Think about Eddington's example of desks separating, which I quoted above to Peter on Aug. 30, 2012 @ 23:29. It's a good one. The desks each stay bound, as they are, but the space between them grows.
"Eventually it is so shifted as to appear traveling/receding faster than light and this creates a horizon line, beyond which light is no longer visible." This is incorrect. Cosmological redshift is not Doppler redshift. The latter occurs as the result of an emitting body's motion *through* space, while the former is supposed to be a consequence of the expansion of space itself. In fact, we do observe a lot of objects with redshift greater than 1. If the redshift were to result from the Doppler effect, then it could not exceed 1. But the cosmological redshift is due to cosmic expansion, which causes light to continually lose energy as it travels through space, so that light from very distant sources can be redshifted to greater than 1. The particle horizon, on the other hand, is due to the finite speed of light through space, which means that in a universe of finite age, we can only see so far.
"But radiation will still travel over this horizon line and that would explain both Olber's paradox and CMBR." The distance to the particle horizon increases as time passes and light from more distant objects will have time to finally reach us. The physical distance to the particle horizon obviously increases, since light can have travelled a greater distance with each passing second; but even the coordinate distance to the particle horizon in the standard model is monotonically increasing. What this means is that despite the fact that the desks are separating from each other through the expansion of space, we'll always be able to see more distant desks than we were the previous moment. In the standard model, the coordinate distance to the particle horizon asymptotically approaches a finite value. This means there is a most distant desk, currently at a finite distance from us, which is the furthest desk we'll ever be able to see, because it will take the light it emitted just after the big bang an infinite amount of time to get to us due to the expansion of space. Although this proven in standard undergraduate textbooks, it's a concept that takes some time to grasp, and even some very reputed physicists, such as Lawrence Krauss and Abraham Loeb have misunderstood it. I pointed this out to Abraham Loeb on his site, and quoted a Scientific American article written by Krauss and Scherrer that has the physics all wrong. I recommend reading my posts there and having a look at the Sci Am article. Olbers' paradox is resolved both because the Universe has only a finite age and because light can only ever travel a finite distance through expanding space, so that we don't need to worry about problems that would arise if light would now be coming to us from infinite distances. It's a dead issue in modern cosmology. This is only tangentially related to the CMBR.
"In fact ever more distant galaxies are constantly being discovered, that push the limits of how galaxies can form within the time constraint of BBT to the very limits of what is plausible. Currently what appear to be significant galaxy structures have been found out to 13 billion lightyears(1, 2, 3, 4, 5,), which means they would have to form in about 700 million years. Given our own galaxy takes 225 million years to make just one rotation, this seems to be a theoretical stretch." I think structure formation simulations do a decent job of modelling what we observe, but there's still a lot of work being done that I've not had any part in. With regard to the comment about galaxies found at 13 billion light years from us, I see a major issue that's related to something else you've said below this. Article 1 describes these galaxies as lying 13 billion lightyears from Earth, which is not right and entirely misleading. 13 billion lightyears is not the present distance, nor any significant past distance to these galaxies. It is the distance that the light from the galaxies travelled *through continually expanding space* en route to us; the light travel distance. When the light we're seeing was emitted, the galaxies were much closer to us than 13 billion lightyears, and they are currently much farther from us than 13 billion lightyears.
"While you point out to Israel that redshift is due to cosmic expansion and not doppler effect, it should be noted that a constant speed of light is still being assumed. According to theory, two galaxies x lightyears apart, will grow to 2x lightyears apart, as the universe doubles in size(if such a concept is applicable), eventually they will disappear altogether [this last part is wrong, as I've said above in the discussion about Krauss et al.---but let's continue:---]. This naturally assumes a constant speed of light over increasing distance. So I am really confused! Cosmology argues space is expanding, because light from distant galaxies is redshifted proportional to distance, yet then assumes this expansion can be calibrated in constant units of lightspeed!!!!? So which is it? Does space expand, or is there a stable measure of space, according to C?" The constant speed of light through space has little to do with the cosmic expansion of space, except that according to relativity theory light moves through expanding space at a constant speed. In fact, the latter is what usually causes this confusion that you seem to be having. I've written about this in this reply already, but I'll try to explain better. Light is supposed to move through space at a constant finite rate. A lightyear is the distance that light travels in a year. Therefore, when we look at something that's supposed to be X lightyears distant, it's understood that we're seeing it as it existed that many years ago. But there is a complication because of the fact that space itself is actually supposed to expand. When we see a value reported stating that we've observed an object that's so many lightyears distant, that value has been taken from the redshift measurement of the object, which tells us how many years ago the light we're currently observing was emitted, according to the standard model. The object is not actually X light years distant. X light years is the distance that light travelled en route to us, and since space was expanding the entire time that light was travelling, the distance X doesn't actually pertain to any physical distance that happened at any one time. If you draw a line on an elastic at a constant speed while also stretching the elastic, the length of the line you measure on the elastic when it's fully stretched is not the distance that your pen travelled. If you let the elastic go back to its natural length, the length of the ink line that you traced on it is also not the distance that the pen travelled. That distance is an integrated distance that has to do with both the speed of the pen and the rate at which you stretch the elastic. So, coming around to your question, does it still make sense to describe the speed of light through space as a constant? Of course it does. No matter what's going on with the elastic, it still may be a physical law that the rate at which you draw lines on it has to be a constant value. The confusion arises because the physical description combines two effects, and particularly because the propagation of light occurs at a finite rate. If light travelled at infinite speed, it would be simple. We could talk about instantaneous distances travelled. We could say that 13 billion years ago we observed galaxy A which was at a distance X_a, and now we see that it's at a larger distance X'_a, because the space in between us and A has expanded. For some reason, reporters still want to say things like, we've observed a galaxy that lies 13 billion lightyears away, even though that's not true. The light travelled 13 billion lightyears at a finite speed through expanding space. To finally answer the last question: space expands, and there is a stable speed limit, which is the rate that light travels *through* space *in* time. Although space expands, this rate can be constant, like the above rate of the pen.
"I have to say about the only response anyone has made to this, other than to ignore it entirely, was Lawrence Crowell, explaining the C is measured locally, not galactically. To which I asked why then do we use lightyears as the measure of cosmic distance. No response to that." I hope this now makes sense. Please feel free to pick my brain if something still isn't making sense.
"I've been wondering if gravity is not so much a property of mass, but an effect of energy condensing into mass and creating a vacuum. (Nature abhors a vacuum.) M=e/c2. Gravity waves would then be the radiation shed by fusion. That would explain why no dark matter is observed, but there is an abundance of cosmic rays in and around galaxies." I don't think there's any dark matter, and I do actually think m=sqrt{1-v^2/c^2}E/c^2 is more appropriate.
Regarding that article, I looked at it last time you linked it for me. I meant to respond, but was really busy for a couple of days and then you and Israel had moved on so far... Sorry. I'm going to read it now if I can, but I've got two four-year-old boys in the house right now who frequently demand my attention. Please feel free to comment and ask more questions, though. I hope you found my anwers helpful.
Best regards,
Daryl
