How big is our Galaxy.

Okay, but now let's apply a gradualistic argument similar to yours for the atomic clock. Someone is approaching me at high speed from the other side of the room, so we know we're in the same inertial frame. What I observe of him has both a relativistic and a Doppler contribution, and I can clearly make measurements. Now what if he's approaching me from the moon. Same thing, right? Now from Pluto. Same thing, right? Now from Alpha Centauri? Same thing, right? Now from Andromeda? Same thing, right? But as the distance increases, somewhere along the line you're going to claim we're no longer in the same inertial frame. I know we can't fix an exact distance, but can you explain how you know a distance is too far to make inertial frame determinations? And even if we can't do this for great distances for practical reasons, why can't we still do it theoretically for thought experiments?I can tell that this is what Silas was alluding to, and I'm guessing he chose not to address the specifics of my surmise because of the uncertainty.--Percy

If this is going to be GR from the outset, then there are no two distinct frames that are inertial. If curvatures are small compared to the separation of the frames, you may approximate them as inertial, but that is all. In other words, you can play at SR locally, on the understanding that it is an approximation which will break down if you push it hard enough.How far is too far? How far is any first order linear approximation valid? It depends on the accuracy required. Specify an accuracy and I can tell you how far you can stretch the inertial approximation.This message has been edited by cavediver, 01-15-2006 05:56 PM

Let's start with a distance we know darn well is too far and make clear why. Then we can work our way back to locality.An object that we observe as being say slightly less than 13 billion light years away, which was only 2 billion light years away when the light left it, and which is "now" 78 billion light years away. This object, which we observe as it was 13 billion years ago, has since then already passed far beyond the space-moving-at-the-speed-of-light horizon. That is to say, the entirety of its observable future is contained within our calculable past. Nothing that happens "there" "now" can possibly have any effect on us, gravitational, electromagnetic, or otherwise. There is therefore no grounds for conceiving it as having any "inertial" relationship to us whatsoever. Any Special Relativity we try to do with it will therefore be not only prone to immense error, but actually meaningless.Let's drop back to obeservations only 8 billion light years away. This object has also passed over the horizon between "then" and "now" and whatever is going on "there" can longer have any relation to us. I don't know if this remains true regarding 4 billion light years away, I think it still is, but let's say for a moment that it isn't, that that stuff is still capable of having some vague tiny effect on us.Special Relativity still won't work right, anymore than Newtonian physics would! The closer we get though, the better both will work, because they are both approximations of the reality that General Relativity is a better approximation of.In the same room as you the results of General or Special Relativity or Newton and Galileo will all work equally well. In earth's orbit I believe we have done some clock experiments that indicate that Relativity (either approximation) works better than Newton. When we go traveling to other stars we will eventually arrive at points where SR and GR produce slightly different calculations, those are by definition the points where we are going to want to trust GR over SR.In terms of "thought experiments" you can use SR for any distance you like, you will be wrong to the degree that gravitation=acceleration is left out of your accounting, and eventually like Einstein you will have to go to General Relativity to account for the ever-larger errors.

Though I'm replying to your message, Iblis, this is actually a reply to both you and Cavediver.I guess my goal is to understand the general principals, and to be able to have a small library in my mind of "when this, then that" situations. Those with a more informed understanding can look at the layperson approximations and say that they're wrong or inaccurate or misleading or whatever, but that gives the layperson nothing to understand.So while SR is an approximation, it is as far as most laypeople are going to get, but maybe I can go part of the way. Can someone explain why we need to involve GR in a thought experiment not involving mass or acceleration?About my galaxy example, some of my readings have taken care to consider separately the relativistic and Doppler effects. Can someone explain why this isn't correct?--Percy

Yes, I hope to understand this better myself before we are done here.The way I conceive it now, which may be terribly wrong, is that the greater the distance the greater the proportion of doppler effect to special relativity effect. In other words, distant galaxies are not only not moving that much relative to us but the amount that they are moving is a much smaller proportion of the observable relationship than the same amount of motion would be if they were much closer. On the other hand up close the amount of relativity effect is the vast proportion of the time-dilation, very little of it is doppler.See, if the light has to travel a billion light years to get to us, that's a lot of room for the doppler effect to stack up and a very small portion of the sky for relativity effects to be observed in. Vice-versa if the light only has to travel a light-second it doesn't have any room to build up a cumulative doppler effect but plenty of sky to measure relativistic effects in.But keep in mind that I agree with you about the expansion not having local "relativity" effects there in that distant galaxy. From their point of view it is we who are receding at just short of the speed of light. If special relativity were to apply then we would each be aging much slower than the other, and that's clearly nonsense.The way we get around that question up local is to set the inertial frame of reference as the body that is undergoing less physical acceleration. That is, if I accelerate away from you at 1g, I am the one whose aging rate decrease relative to you. It decreases in the same way it would if we added an actual extra g worth of gravity somehow, perhaps by hanging out near a more massive body.The apparent movement caused by the expansion of space is not experienced as acceleration by the person observing it. They feel no extra g's as result of the increasing "movement", quite the opposite they experience the points of space as being farther apart rather than closer together as we do when we accelerate.I will be very happy if someone can correct or improve on this understanding for me

Sorry Percy if I was being unclear. You have a good background in this stuff and it is difficult to judge where your understanding starts to fade. Ok, the difference between SR and GR is quite simple: SR deals with the very special case of completely flat space-time, space-time with no curavture (note that this is very different to a "flat" universe, which has curvature), where as GR deals with the more general case of curved space-time. You do not need mass or acceleration to have curved space-time. An expanding universe is totally in the realm of GR.You may realise that any patch of a curved surface looks flat when viewed from a sufficiently close vanatge point (the Hausdorff property). Thus SR applies locally in the universe, say in your home town. SR also applies locally in a town in a distant galaxy. But SR cannot apply between these two towns. The obvious analogy is to consider 2d Euclidean geometry in a field in your town, and in a field in Sydney. Works fine in both places, but breaks down totally to the point of making no sense what-so-ever in between.In your galaxy example, you cannot apply SR reasoning between the two vantage points. You have to use GR.You want to think of two observers stationary in their respective comoving frames in two widely separated galaxies as being at rest wrt each other from the point of view of SR, but this is simply non-sensical.Just because an observer may be moving at relativistic speed wrt his own comoving frame does not mean that you, in a different comoving frame, will necessarily see an associated time-dilation.

Yes, this is what happens. SR doesn't apply, but this is still what happens. To be otherwise would break the symmetry of the situation.

Would we be inside the event horizon of that black hole? If so, what would we perceive our experience as being?If I'm grasping Hawkings correctly, inside the event horizon our "light cones" would be turned inside out. That is to say our future as calculated (but never observed) by those outside would be fixed and inevitable, i e falling to the center, whereas it would be our (relative) past that could be / could have been anything at all, indeterminate. This is the opposite of duration as we currently think of it, where the past is inevitable and it is the future that is indeterminate.This goes along fairly well with the idea that as matter crosses the event horizon it arrives at the speed of light and ceases aging. On the other side we can calculate (but never observe) it as traveling faster than the speed of light, though not getting anywhere much because it has to travel through space which is more and more super-infinitely compressed. Thus again we would calculate it as aging "backwards" from the way that those inside the event would perceive it.In other words, the inhabitants of the black hole would not experience an endless contraction of space toward, but never arriving at, an infinite density level, with everything being pulled together and objects falling in but never making it out, as we would calculate to be happening from the outside. Because their sense of duration was reversed, they would experience endless expansion from, but never actually starting at, the infinite density and a distant horizon that objects fell out of but never into. Furthermore they would not experience all the suns and so forth as being very close because of the same super-density of space that keeps them from getting anywhere much even though traveling faster than light (from our viewpoint).Is this not identical to what we actually experience? Inflation keeps us from starting at the center, the light horizon keeps us from ever getting back across it, we seem to be falling out of a white hole. If our sense of duration were reversed, as it would be inside a black hole, our current conditions would be exactly what we would expect to see if we were inside a black hole.Where am I going wrong?

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

First of all thanks for emphasizing the fact that what we are calling "Doppler effects" represent movement either towards us (blue-shift, time-compression) or away from us (red-shift, time-dilation) whereas what we are calling "Relativistic effects" represent movement in any direction (time-dilation, apparent red-shiftiness but not really). I know I certainly didn't make that clear before, for anyone who doesn't understand it, whereas you have covered it really really well.That said, here's the heart of it This is what my previous post is trying to emphasize. At any cosmologically significant distance, the "relativistic" contribution to the amount of red-shift we see must be essentially negligible.Why? Because it is red-shift, not blue-shift or shiftiness, and because it is consistent with other objects believed to be near it based on other kinds of geometry; and in particular because, regardless of what the math says about the experience of the observer who is there locally, our own observation is slanted in favor of "almost entirely Doppler" due to the great distances involved in the process of observation.By "cosmologically significant" I mean any distance great enough that the curvature (expansion) of the universe is the larger part of the math. Nope, definitely broke down at this point. If you were to try to navigate from Andromeda using SR, you won't ever make it. It will take you longer to get "here" then you think, and furthermore we won't be "here" when you arrive.I believe there is already a vague margin of this same error involved in navigating from Alpha Centauri, but as you noticed the error and kept correcting based on your real observations and using SR you would eventually be correct enough and local enough to make it here safely. The amount of error involved in traveling from Andromeda will be too great for you to ever correct it this way. It's still nonsense though. I can accept it, I can do math with it, but I can't ever "understand" it. The only thing that makes it even remotely tolerable is that we can't ever meet. If we could somehow "suddenly" meet under these circumstances, we could compare clocks, and one would either be slower than the other or else they would agree. The reason we can't actually meet while the phenomenon is happening is because it requires us to be traveling away from one another, if we turn around and travel towards one another the acceleration involved is going to cancel out any paradox before we arrive at a point where we will be mutually local.

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

Good for you! Way to be! Now if all you are rejecting is my lame analogies and over-simplified models then you are doing fine. But if the "nonsense" you are rejecting is the reality of the math, nonsense like us and distant galaxies observably aging slower each one then the other, then you are going to need some sort of technically-false model to get through your physics day.I'm having trouble at this point understanding where we disagree though. You say distant galaxies aren't actually having strong relativistic effects in relation to us, it's all just doppler. I'm saying that the overwhelming majority of the time-dilation (red-shift) that we observe in distant galaxies is necessarily doppler. Remind me again where you think we disagree?Earlier you indicated you didn't think we actually did observe time-dilation in our view of distant galaxies. I think you had the idea that they pulsed or flickered or whatever at normal speed, only redder. That's dead wrong and you understand that now, you can't help but understand it if you imagine each photon leaving from a distance greater than the previous one.So let's recap again. You and I both choose to imagine that if we could somehow 'port to those distant galaxies we would find them not actually whizzing north (for example) at just under the speed of light, but rather standing still like our own galaxy while the distant galaxies "appeared" to be the ones whizzing away in every direction.Now cavediver, who understands the GR math better than us, says this comparison isn't actually useful for physics. He also says that the time-dilation or red-shift caused by the expansion is the same time-dilation or red-shift caused by acceleration/gravity. Technically this is true in the sense that the compression of space caused by acceleration/gravity is the same kind of geometry (though in reverse) as the decompression of space caused by expansion. In this sense we can think of expansion as a kind of "anti-gravity" or gravity with a reversed duration arrow, hence my "When Worlds Collapse" question above. I could be wrong about this, but I don't think I am. Yes, the amount of curvature at that range is still very small, but with the great distance involved and the extemely-near-light speeds you would have to travel at to confine the length of the trip to your lifetime, that tiny error would put you way WAY off course before you could know it. I'm ready for correction on this one though.I'm going to spend some more time imagining spaceships traveling about in different directions transmitting video of their ship chronometers to one another and see if I can come up with a better model or analogy to describe what we will see than I have so far.

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

quote:

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IblisNow cavediver, who understands the GR math better than us, says this comparison isn't actually useful for physics. He also says that the time-dilation or red-shift caused by the expansion is the same time-dilation or red-shift caused by acceleration/gravity.

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Percy
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.

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When I was a teenager I had THOUGHT (actually) that expansion and acceleration(or gravity) were two different things. This thought caused some confusion for me when thinking about entropy. Figenbaum's sideing with Goethe over Newton
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on the subjective element in color (per)reception AND his clear distinction of Thermodynamics from Dynamics still continued the seperation in mind that might not be justified. Cavediver would be a better physicist than Mitchell who felt that Cornell was not doing what Rockefellar was physically and left Ithaca a week before I could ask him about this. Perhaps it was just my low level of physical intuition that caused that however. This posting sequence appears to be shaping into an interesting thread!!This message has been edited by Brad McFall, 01-18-2006 10:28 PM