jbahr

As I remember, the surface of a 4-dimensional hypersphere is a 3-dimensional sphere (a 3-ball). However, if I'm reading all those noted cosmologists correctly, the universe isn't anything like a sphere. It has neither a center nor an edge, and (as Wright likes to point out repeatedly) it doesn't expand into anything. Regards, J

I just had to think about homologous expansion (meanwhile, I'm reading Wright's tutorials: http://www.astro.ucla.edu/~wright/cosmolog.htm). For an expansion to be homologous, the expansion must "not alter the shape of patterns in the Universe". This leads to a kind of proportionality constraint (see Wright's face stretch in different ways with alternative expansions here: http://www.astro.ucla.edu/~wright/distort.html). So in a simple example, an object A may at some point in time be 1 LY away, and another object B be 2 LY away. After some time, to maintain proportionality we note that object A is now 2 LY away. Every other object (except us) is also twice as far away as it was before, including B. But means that B expanded away from us 2 LY (4 - 2) in the same time that object A expanded away from us 1 LY (2 - 1). Hence, B has to have appeared to always have, during this interval of time, twice the velocity of A. One thing that sort of puzzles me is that you seldom see this expressed in the usual physics units. We have recession velocity as a function of distance, thanks to the Hubbard Parameter. But the first thing a physics guys would ask (I would think) is what are the velocity and acceleration in terms of time. Ignoring gravitational effects and other niggles, if two bodies at time t(0) are relatively close, then we could view the expansion as the acceleration of body B from body A. Knowing the function for velocity, we could integrate from 0 to some arbitrary time t®. That would give us the distance R between the bodies. We also know that V(t®) = R*H. In any event, I don't think I've seen any kind of estimate for the velocity or acceleration in terms of t, unless it related to the 3ct that Wright alludes to here: http://www.astro.ucla.edu/~wright/cosmology_faq.html#DN. Most of the explanations along these lines seem to involved arguments involving successive distances, as if everyone is avoiding calculus.

Well, I'm impatient, so let me wander around my question a bit longer. Suppose there are two objects (galaxies will do), one 10 ly from us and one 20 ly from us. In the absence of non-expansion velocity relative to us, all one would have a redshift and an apparent velocity twice the other. Two things are evident: 1. The apparent velocity of one is twice the other. 2. Light has traveled in the presence of expansion twice as long for the one more distant. So does the redshift have a component that is attributable to the velocity of the galaxy relative to us at the point of light emission PLUS some redshift attributable to universe expansion while it was traveling? Or is the galaxy at rest relative to us, and the reason that the more distant galaxy has twice the redshift is that it's simply traveled in the presence of expansion twice as long? J

I was a physics major 35 years ago (they didn't even know what quasars were and black holes were exotic theories). I've recently been reading my tail off here and 100 other Google hits on cosmology. I've completed a couple of relativity tutorials, and done the math on Hubble's Parameter and topics relating to it. And still ... I must be missing something fundamental. I can't figure out why increasingly distant objects should have increasing redshift (assuming that this is the appearance of receding velocity). In Newtonian terms, this would mean that distant objects have had more time to accelerate, but I'm cool with an isotropic universe, so there are no "distant objects" (or perhaps, better said, I'm just as distant to somebody out there, with identical redshift). I think I'll stop here and ask more dumb questions after a response J

I have been looking for interesting science poetry for a while. Albert Goldbarth often has some interesting work. C. Dale Young and I have both published poems that include a sigma Here's mine, from the Spoon River Poetry Review: Do The Math From its core to its curved cooling griddle, photons take 50,000 years to bang around and spin off progeny of less and less ambition. Poles shift and pop up at the sun’s equator and, every 11 years, sunspots dot the photosphere like someone making dollar pancakes. Back on track, light spends 500 seconds of unperturbed isolation, then slams our little planet. It would, of course, kill us in a minute. Luckily, the troposphere absorbs all but enough to give my second wife a nice even tan and leave with the guy in the Miata. She would chat from the balcony while I computed how much information passed from her mouth to the man with the sports car, roughly -∑ Pm log2 Pm Think of the little m’s as mass, momentum, and my missing heartbeats. She the free radical, and I the banker in a convex mirror. There’s a theorem that shows that some things are unknowable. Thank God Einstein died before we found particles popping out of nowhere. My second wife showed up 20 years later, but that’s another poem, like a proof by induction: Step 1: Verify that the desired result holds for n=1. Step 2: Assume that the desired result holds for n=k. Step 3: Use the assumption from Step 2 to show that the result holds for n=(k+1). Note how desire insinuates itself into the simplest of mathematical methods. Think Albert and his mistresses, Descartes and his need to unknow God (of course he’d been through a war). There’s no science of desire. It’s older than that. I thought I’d be a paleontologist. By the time Alvarez and his son predicted the meteor that annihilated the Yucatan, I was already on to algorithms. They’re like those mail-order plastic mats with footprints and arrows that teach you how to samba. They don’t always work, they’re counting on abandonment. And desire, two apogees of the pendulum. There's one the size of a Kronos yo-yo in the Smithsonian. It's hard to watch it and not wonder how it stays true. Ignoring the spin of the world. Back and forth through the light of the canopy. As if it knows where it’s going and then, just as certain, changes its mind. ~~~ I'm currently struggling with cosmology. I was a physics major a long time ago, but things have gotten a lot more complicated. Thank God for Google. J