I appreciate your explanation and taking the time to write it. From your explanation it sounds as if the shape of the universe is still under debate, and not surprisingly so.
When I ask the question, "What shape is the universe", such a question ultimately requires one to define the universe itself before assigning a shape to it. Unfortunately we lack all of the details to accurately define the term universe for the sole fact that the universe itself is composed of everything from the smallest of small and the largest of large - both of which we currently have no complete understanding of.
I do not mean to appear bearing on undermining an explanation - good explanations are food for thought. :) I'm really just caught up in the reasoning involved with this theory of the shape of the universe - on a couple of different levels.
My first hurdle comes down to the presumption that the universe actually has a shape that differs from the observations our modern telescopes provide to our eyes. I understand the concept surrounding these visual observations regarding the distance - time connection. I understand the correlation between distance and redshift, and its nearly symmetric occurence in all directions from our vantage point.
Then things start to get odd from there, even if an accelerated expansion of the universe itself isn't odd enough. :) - I understand comoving distance vs. proper distance, in their absolute definitions. But there's a debacle even with those terms, of which ties into this whole question of the shape of the universe. The debacle is the simple fact that these two terms are defining the same "thing" but doing so with contrasting explanations. Ask the simple question when you look at a star, "How far away is it?" Using comoving distance you'll get one answer and using proper distance you'll get a different result. Using these two explanations will reveal that the star is actually two stars and they are at different distances from each other.
Call me a simple man and explain how one can come to two different mathematically derived solutions in which both are true and have two different results. This simple man suggests that either one or both are incorrect. The star we are looking at is actually "x" miles away from us at that very instant the answer is requested, right? You wouldn't expect to get an answer in the form of a question about how you want to calculate distance, would you? Perhaps a question of miles or Km at best, but I would expect that anyone carrying such a conversation would automatically use the units of measurement the speaker beleives is the most understood unit for the person they are answering. I digress.
My argument on this aspect is simple - the star is "x" miles/Km away, not "x" and "y" at the same time. The only reason anyone could possibly come up with two different distances is if one or both reasonings they used to determine it were flawed. In fact, as a simple man, if anyone were to give me two different values I would disregard both figures and find another source for my answer.
Does this whole comoving distance and proper distance argument underpin the argument of the shape of the universe? Seems to me the only difference between the two comes down to whether or not you believe space itself is expanding isotropically or if things are just moving apart from each other with some type of force that pushes everything apart equally in all directions. It may sound the same to put it that way, but they are two different versions of an explanation trying to explain the observation - they differ solely by the definition of space.
In the former explanation space itself is the "thing" presumed to be expanding. In the latter, there is a force being exerted upon the objects we can see that is causing them all to accelerate away from each other. Dark energy and expanding space are in direct competition with each other as the explanation for our observations and the difference between the two, within the context of the OP, is how distance is calculated. If space is expanding then its expansion has to be taken into account in the determination of distances - the expansion of space itself is what makes objects appear to move apart.
Comoving or proper, there's no certainty. It all depends on what the observer believes is the construct of the universe, and that certainly is up for debate. :)
Going back to the OP and your reply, I do understand the analogies you used to show how variations in measurements could occur. On the same token, to embrace those explanations requires one to make exceptions to well cured definitions. For example - parallel lines. Parallel lines aren't parallel if they intersect at any point - that is the absolute definition of parallel lines. If you have two lines that are parallel over some given interval then so be it. But any two lines that intersect are not parallel, right? OR, are they only non-parallel at the point in which they intersect? Or, just for argument's sake, could I have to parallel lines that intersect because the space between them is curved?
Not trying to sound like a smarty-pants. I'm simply begging someone to tell me what I need to use as reference for these questions. I can use my imagination and see what changes. I just need to know what stays still.
I made my OP a few days ago with a lot less reading on comoving and proper distance theories. It wasn't until this evening that through my effort to reply I found an entirely unexpected approach to my original question - of which has brought a feel of enlightenment, although I can't say I know any more about the structure of the universe now as opposed to before. :) I guess I'm just saying that I've enjoyed the exchange.
Look forward to your reply!
