How big is our Galaxy.

Cavediver hasn't commented on the relativistic versus Doppler issue yet, but this seems inconsistent with other things he has said. I thought he was saying that GR considerations are inevitable once you have to take the expansion of space into account, and that therefore this isn't the kind of comparison that you can make. But the way you've expressed this makes it sound like a perfectly valid comparison.You can even plug in numbers and consider a galaxy retreating from us at .99c, comparing the case where it is most of the way across the visible universe versus just across the room. The Lorentz number for .99c is .14, so a galaxy retreating from us from across the room would have its clock ticking only 14 seconds for every 100 of our own.This would be the only effect we would see if the galaxy were flying by us rather than away from us. If it were only flying by then it's the amount of slowdown we would observe when the galaxy made it's closest approach, i.e., had ceased moving closer to us and had just begun moving away.But since it's retreating from us there is also a sizable Doppler effect. For every tick of our clock the light from this galaxy has an additional .99 light seconds to travel. So if the first tick of its clock occurred at our time 0 seconds, then the second tick of its clock would occur at our time 7.09 seconds (1/.14+), but it would take an additional .99 seconds to reach us, so we wouldn't observe the second tick until 7.09+.99 = 8.08 seconds.I feel like I'm in the middle of a mine field, so rather than take the next step to consider the case where the galaxy is on the other side of the universe I'll just stop here and see how much I've got right so far.--Percy

This is from the Wikipedia entry for the Cosmic Distance LadderSince there are both Doppler and relativistic contributions, it seems like making this calculation of distance wouldn't be possible unless they could make some assumption about one of these two variables. Aren't they assuming that the relativistic contribution is 0 or near 0? Or is the Wikipedia explanation too oversimplified?--Percy

But this brings us right back to where this part of the discussion started. I said that the clocks in distant galaxies proceded at the same rate as our own, minus Doppler effects. And now you're saying that at great distance there are only Doppler effects, not relativistic effects. But Cavediver says GR effects mean you can't reach such conclusions.Something doesn't add up or is just beyond my ken.Regarding the details of your justification, they appear insufficient. At some point a mathematical determination based on other factors (the cosmic step ladder again) has to be performed to separate Doppler from relativistic effects, otherwise it isn't possible to know the expansion rate of space. Sylas mentioned supernova curves and such, probably standard candle type stuff based on the type of supernova. This is a different interpretation of my example than I intended. I wasn't considering a long distance trip, only making a single observation of somebody approaching at a relativistic speed. Nonetheless, I doubt there would be much difficulty navigating between galaxies, GR or not, because the expansion of space between us is small, and we know the distance and the relative speeds of the galaxies, which aren't relativistic.Thinking about my example more, when I look through my telescope and see someone approaching from Andromeda at relativistic speeds, do I have enough information to separate the Doppler from the relativistic? I might, but I'm not sure. I can measure the amount of blue shift, and I can see the degree to which his clocks have slowed, and since relativistic SR effects are always in one direction while Doppler in this case is in the opposite direction, perhaps this is sufficient. And in that case I'll be able to calculate his relative velocity without GR, something Cavediver says I can't do. You can find any number of sources stating that Andromeda and the Milky Way are on a collision course, so obviously we have no problem calculating Andomeda's current velocity, and I wonder to what degree GR was required to calculate it.I guess what I'm rebelling against is Cavediver's claim that to me sounds like, "We can't know nothing." I know he's qualified that with "it all depends how accurate you want to be," but I'm only interested in understanding the general principles and having a good idea of how these things work. If SR is insufficient for some work, I bet it is just fine for most work. This seems analogous to Newton's laws of motion which, while inaccurate, are nonetheless incredibly useful most of the time.Let me try to put this another way. I appreciate all efforts to correct my understanding. But I'm not going to replace an understanding that makes sense to me with an understanding that doesn't make sense to me, no matter how much people tell me I'm wrong. I hear the message that I'm wrong, but I haven't heard an explanation that makes sense yet.--PercyThis message has been edited by Percy, 01-18-2006 03:11 PM

Hi Iblis,The confusion is easily resolved. It does sound like we agree, but I thought Cavediver said this was wrong, and earlier I thought you agreed with him. You're right that I expressed it incorrectly if I seemed to be implying there are no Doppler effects affecting observation of clocks. We were talking relativity, and my attempted point in the post you're thinking of was that distant galaxies are not moving rapidly through space relative to us, and so the relativistic effects that affect clocks are tiny. This doesn't sound right to me. I'm not saying it's wrong, but I want to understand how this is true. That's why I began trying to demonstrate this with some simple math for a nearby retreating galaxy in Message 99. If someone wants to say they agree with the math so far, then I'll next try to do the same thing for a galaxy far, far away. Oh, as a practical matter you could be right once acceleration and deceleration are included. I just want to be sure we're in agreement from an SR perspective. I believe it's possible to calculate a velocity vector using only SR and the mass of the galaxies that would intercept where the Andromeda galaxy will be some day. True, this couldn't actually be used since you somehow have to accelerate to that velocity, thereby introducing GR and throwing everything off, but since I'm not conversant with the GR considerations it's as close an approach to the problem as I can do right now.--Percy

I've never thought of the rubber band model as a real rubber band, but as an infinitely stretchable rubber band. And it's not really a model, just an analogy to make clear the distinction between motion *through* space versus expansion *of* space. It isn't intended as an analogy to or model of relativity. But this is only a thought experiment. If it helps, replace galaxy with the object of your choice. The goal is to understand how relativity works, and considering only real world situations is limiting. Einstein imagined himself traveling on a light beam. Why would you object to considering an object across the room traveling at near light speed so as to remove the expansion of space as a significant consideration?Remember those math problems in grade school that went like this: "A locomotive leaves the station and travels 30 mph for 20 minutes and 50 mph for 30 minutes. How far has it traveled?" If you were like me you raised your hand and said, "But teacher, the locomotive couldn't instantaneously accelerate to 30 mph, and later instantaneously accelerate to 50 mph." True, but beside the point. It's the grade school equivalent of a thought experiment. Ignore the acceleration, just do the problem, the teacher would say, shaking her head. Jason in Foxtrot comes to mind. The furthest objects cannot have infinite red shift because Doppler effects can increase wavelength by only a factor of 2 in the limit as retreating velocity approaches c. It is the tinyness of Doppler effects as compared to relativistic effects that leads me to usually not make explicit reference to them in these discussions. I'm not trying to ignore them, but they're horribly mundane compared to the complexity of SR, GR and the expansion of space. There are no weird twin paradoxes posed by Doppler effects. No clock is actually affected by Doppler effects, only the time of our observation of those clocks because of the increasing distance light must travel. I appreciate the effort, but you've gone way too basic on me. I apologize for leaving the impression I'm ignorant of all this, but it's an excellent presentation and I'm sure many lurkers will find it useful. If it were a model it might be fair to pose these kinds of questions, but it's only an analogy.I'm not sure of your position on my retreating object example. Do you accept the time of 8.08 seconds that I calculated for the time we observe it takes the object's clock to tick one second when the object is retreating at .99c with our observations beginning when the object is across the room?--PercyThis message has been edited by Percy, 01-19-2006 04:19 PMThis message has been edited by Percy, 01-19-2006 04:21 PM

Don't use relativistic to mean SR effects? So even though SR is short for Special Relativity, you're saying its effects shouldn't be described as relativistic. I know you qualified that to the cosmological context, but still.I appreciate that it's difficult to find sufficient time to explain complex and easily misunderstood topics, and I appreciate that you're making the effort, but you haven't given me much to go on. I suppose I could memorize what you're saying so I could parrot it back, but my goal is understanding, not mimicry. Perhaps you could point me to a readily available layperson's book that has a chapter describing what you're trying to explain to me.--Percy

Hi Cavediver,I went back to this message after reading your clarification about use of the word "relativistic" and I think I understand this part now: I already knew about z, but I had never tried to look at it as evidence for the expansion of space. If you take the Hubble constant as 71 km/s/Mpc and you multiply it by the distance to the edge of the observable universe, about 4200 Mpc, you get the speed of light. This says that the furthest reaches of the observable universe, those that are very close to the big bang, are receding from us at nearly the speed of light.But how do we know it is this distant space (and the objects it contains) that is receding, and that it's not just a case of the objects themselves receding through a space which is not expanding? There apparently is this Ives/Stilwell experiment that verifies this is the proper way of viewing things, but I found the math too challenging to figure out why.But while looking into this I did discover that there is a different version of the Doppler effect equation that is used for electromagnetic radiation, and it includes the Lorentz transformation. In other words, it was invalid for me to apply sound-style Doppler to light. And the relativistic Doppler equation appears to take into account both relativity effects and longitudinal motion effects. I can see that for transverse motion the equation reduces to the Lorentz factor. So both longitudinal and transverse components of motion are accounted for in a single equation. See Relativistic Doppler effect - Wikipedia for the equation I'm looking at. It's the first one.I recall complaining at one point in my earlier discussion with Sylas that what science writers for the layperson level consider sufficiently detailed seems to have increased in the 20 years since I last looked at relativity. Ways of saying things that no one would have batted an eyelash at 20 years ago are now considered either wrong or inaccurate or misleading, and I've been making bad interpolations while trying to fill in the blanks.A fundamental question that I should have been asking 20 years ago: Why did Einstein (and before him Lorentz) "know" the Lorentz transformation was required for electromagnetic radiation?Iblis, thanks for your posts, I'll catch up with them when I can. Ultimately I'd like to understand how we know space is expanding and how to properly interpret observations made within an expanding space, but I think I'm further from the goal than I originally thought.--Percy

These pages were also referenced in the previous discussion with Sylas. Working my way through, I have a question on page 1, http://www.astro.ucla.edu/~wright/cosmo_01.htm: v=cz means that for values of z greater than 1, v is greater than c. So two things. I don't see how he concludes v=cz from the simplified relativistic Doppler effect equation. Does his "..." somehow account for that? If so, how? And anyway, such a conclusion seems to contradict the equation, since you can rework the equation to solve for v/c, and if, for example, you plug in z=6, you get v/c=49/51. For increasing values of z, v/c only gets closer and closer to 1. It never exceeds 1. v never exceeds c.--Percy

If we're talking about this equation: Then I can do everything you suggest except the Taylor expansion. Let me try reading on and see if I understand anyway.--Percy

From http://www.astro.ucla.edu/~wright/cosmo_02.htm: I think this is an important part of what I'm trying to figure out. How did we come to know this? It looks like the discussion that follows says that we know this because the relativistic Doppler shift law doesn't provide a model that matches the data from cosmological distances. We have to use the "now" distances, which greatly complicates things.I think Iblis said some things earlier that might help, I'll go back and review those.--Percy

I'm going to have to bow out of this discussion. Thanks, Cavediver and Iblis, for your help. I'll return to trying to better understand GR when I have more time.--Percy