How big is our Galaxy.

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

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?

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.

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.

Thanks, I get it now! We agree in our method for imagining or modeling the universe, but this model is technically false. It's still a good model, at least as good as the stretched rubber-band model which is very widely used to help us visualize the effect. The thing our rubber-band would need next to more closely correspond to the reality would be a telegraph line from one end to the other that slowed down the "apparent" speed of the messages so we observed them as being very slow at great distances. But the model would still be inadequate, one of the reasons it would be inadequate is because it can be say only 6 feet long and we can watch both ends at the same time.I went ahead and read your galaxy-across-the-room bit over again and tried to take it very seriously this time, and I'm ready to poke at it a little now I think But, there aren't any galaxies across the room from us who retreat that fast! I'm not being flippant, I'm saying that local bodies traveling at such great speeds in relation to us are very very rare. The most common thing along these lines would be some quantum physics particles that we can manage to observe for only brief moments. Now if there were such a body, say a great big rock that happened to wander through near-earth orbit at this kind of velocity, our observation of it would be just as you describe. In fact, depending on when we noticed it, by which I mean once it was in fact retreating, we might end up thinking it was much further away than it actually was. But, as we observed it again and again over time our error would become apparent I think.What we see in terms of expansion behaves differently than this. We can look at objects close enough to estimate a distance for them using parallax and whatnot heading up your Cosmic Distance Ladder. And as we do this we can observe that objects at a great enough estimated distance have more red-shift than we would expect, as if they were moving away from us. Furthermore, other objects at about the same estimated distance have the same degree of red-shift! In any direction! Furthermore, the very farthest distances we can observe (on our radio) have essentially infinite red-shift. That last bit of signal has been perpetuated eternally at us and so on as I ranted about enough already, it's a signal artifact.Now from a ballistical viewpoint that means the farther stuff is away from us the faster it is moving in the opposite direction. Consistently! It would be a very remarkable coincidence if we were really the center of the universe wouldn't it? Whereas Einstein's General Relativity, which explains a lot of other things like the fact that gravity isn't instantaneous but instead propagates toward us at or below c like any other phenomenon, also allows for space to be expanding in some uniform manner that would describe the consistency we see in red-shift at distances.Here's how it works. First imagine space as a grid of points. Start by imagining it as a grid of equidistant points, like the vertices of the lines on graph paper. This is the geometry of Special Relativity, it accounts for gravity by basically allowing it to be magic. That is, bodies exert an unexplainable attractive force based on proximity, space itself is flat. Perfectly good for what at that point were greater distances than anyone except science-fiction authors had ever imagined us going anyway, basically a curiousity, a snotty modern-math attempt to improve on Galileo.But, it produced some theoretically observable paradoxes, it didn't cover all the facts, it relied on Newton to be right while also implying he was wrong, it needed improvement. This led to General Relativity, which has the same principles of motion as Special Relativity but accounts for gravity in another way than simple "black magic". The way it does this is by dropping the "equidistant" rule for the points, allowing space to be "curved".Mass in this model is not just something that has to be accelerated using force like the ballistic model of Special Relativity, it is also a contracting of space, a progressive movement-closer-together of the points on our grid. Objects moving through the grid near more massive objects find themselves closer to the object than they would otherwise expect not because of some "attractive force" but because the deck is stacked against them moving away and for them moving toward.The reason that acceleration is the same as gravity is because moving through space at an increasing speed, normal space without much gravity, relatively equidistant points as it were, is the same phenomenon as simply existing or moving at what should be a steady speed where the space itself is contracted. Both phenomena, geometrically, consist of hitting the points faster and faster. From a practical viewpoint, trying to make a distinction between the two is implying that we don't fall at a geometric rate but rather at a steady rate, we know this is false. Or implying that what gravity does to us isn't faster and faster motion in the same way that acceleration is.With me so far? Now, as it turns out, just as Mass is (among other things) a contraction of space, so in the same way Universe is (among other things) an expansion of space. Just as gravity causes us to hit the earth much faster than we might think we would if we had launched ourselves towards it at 5 feet per second and expected inertia to keep us going at that speed, so also expansion causes us to get to Andromeda (or better yet some distant quasar) much more slowly than we would expect to.Here now, this is the gold. I'm going to resort back to our old models, we have two guys coming right up on the opposite ends of some rubber-band being stretched. Let's say it's 500 miles long at this point. They are walking along at 5 miles an hour. The stretching is such though that their "apparent" speed in relation to one another is say 100 miles an hour at this point. They have a 500 mile long rope with a noose on either end, around their necks. Their heads shoot off at what speed?If their relative motion isn't real, it's only ten miles an hour. But their relative motion is real, their heads shoot off at 110 miles per hour. No doubt about it. So, if their relative motion is real, the time-dilation we observe is also real, relative to us. The reason the paradox it produces (each clock moving much more slowly than the other) isn't a problem is because it isn't really observable, only calculable. (We can't observe from both ends at the same time, the observer at either end never actually sees a paradox, only the math sees it.)* credit to Lorentz, Hubble, Hawking and everyone else whose name should have come up in this already-way-too-long explanation* and edited to correct blatant brain-fartsThis message has been edited by Iblis, 01-19-2006 12:39 AM

No no please I am the one who may be ignorant of these most basic ideas, in collecting my thoughts I found it necessary to talk through the whole thing completely and show my work so that people smarter than me can correct if needed and so that I can refer back to it later for the real statements I am trying to make. The only part of the post specifically pointed at you (as something you need to understand and don't seem to) is the rubber-band / tandem-gallows bit at the end, indicated as such with the introductory "Here now, this is the gold ... "I was so brain-burned at the end of my little exposition that I was only able to get to this one part of the idea thereafter, and even so and even with rigorous editing I still screwed it up. For example the "they" in "their relative speeds" should be the ends of the rubber-band, not the guys, or else the head-popping-off speed should be that speed 100 mph.Also, we will need a magic rope It has to be infinitely strong, massless, dragless, cut through necks like water but remain attached to heads somehow, and any number of other unrealistic properties. You get this though already I know, you recognize that the rubber-band has magic properties, my rope just needs totally different magic properties. The train moving at 30 mph and then suddenly 50 mph, these kind of unreal properties aren't a problem with your thought-experimenting, that's fine.Here's the problem though, whatever analogy we use to make you see it, the motion is still real, the sudden stop is still real. Let's say an orbiting satellite shoots down a weight on the end of a long cable at 5 mph and lets it fall freely until it gets to the end of the cable. Will the stress of the stop and its effect on the satellite, weight and cable be consistent with 5 mph, or will it be consistent with say 5 mph plus 32 feet per second squared times the length of time needed to get to the end of the cable? If the "apparent" speed / acceleration produced by gravity is real, then the speed / acceleration produced by expansion is equally real. Why wouldn't it be? Here is where we seriously seriously disagree, and where I am the one trying to agree with GR. The time-dilation created by what we are splitting off as merely "doppler effects" is just as real, relative to the observer, as the time-dilation created by what we are accepting as genuine "relativistic effects". The "space as a series of non-equidistant points" routine is supposed to make sure this is clear, obviously it hasn't.The reason we would like to believe that the time-dilation described as doppler effect is somehow less real than the time-dilation caused by other relative-speed effects is that it cancels out when we turn around and come back. But this is wrong, gravitational effects also cancel out when we turn around and come back (all the energy magically gained by falling must be "put back" when rising.) Yet the motion, speed, and potential impact force involved in gravitation are definitely real aren't they?Once you recognize that there's no such "real" difference in what you are calling doppler and what you are calling relativistic in terms of the (relative) time-dilation they produce, something interesting becomes apparent about our grid of points. Objects travelling away from us undergo slightly more time-dilation than objects traveling past us and even more than that compared to objects travelling toward us. At very great distances, which in our expanding universe also means very great speeds, this part of the time-dilation is the vast majority of the effect.An object travelling through space is a contraction of space ahead of the object and an expansion of space behind it. The one doesn't "cause" the other either, as if it were motion that were warping space; they are two different methods of describing the same geometrical function. The space is only warped relative to the object and observer though, the part we are calling "doppler effect" is due to the observed light coming from the moving object and the part we are calling "relativistic effect" is due to the final measurement after the two-way trip has been made and the doppler dilation / compression has canceled itself out, leaving only the Lorentzian transformation math to be accounted for.A distant object being "expanded" away from us has that same expansion of points behind it, therefore again the relativistic effect is the same as normal motion. The place where it differs is on the other side of the object from us, which is also expanding rather than contracting as it would if the motion were what you are thinking of as "real motion" through space. The local effect there is thus different, but not the relative effect here. Here's my real problem, I know I don't really understand Lorentz and Poincare. I would prefer for the time-dilation to make sense to me, i e if I am trveling at 150,000 kps (.5c) and yet light still seems to be traveling at c (300,000 kps) then in order for me to observe it that way my time should be slowed down to only .5 of its original rate. If I am travelling at .75c and yet light still is going c (relative to me) then my experience of time should only be .25 of what it was. Do you see my logic?But I am wrong, wrong, wrong; and I do not know how to imagine it in such a way that I make the correct deductions. All I can do is look at the table and say Well what you are saying seems to match what I am reading on the table. I will be happy to agree with your math though if I can count on you not to intentionally deceive me, if that helps. Yes I did that, I shot a big rock through near-earth orbit and conceded if we did see such a thing the effect would be just as you described. Assuming that we could still see the same rock across the universe where everything is traveling an "extra" .99c away from us, the fact that it was also still traveling .99c relative to all that local stuff would not, so far as I can tell, have a very large effect on our observations. Maybe you can improve my understanding of this?My math may be afu again, would the total speed relative to us be something like .9999c at this point? How large a difference does that make (from .99c) in the Lorentz transformation? If it's a great difference then I guess it would be observable even at that great distance. From a practical point of view though, the vast majority of local objects are moving at less than .1c relative to each other, and that little margin definitely won't make any difference moved across the universe when added to the .99c relative to us caused by the expansion. And much less using Lorentz's real math than the simple symmetry that I would like for it to be, in the real world .1c has almost no effect in terms of time-dilation instead of the .9 I would like to imagine it as.Is any of this helping? I noticed that you spoke of relativistic effects as if they were actually doing something to the local clocks, they aren't really though. The local clock continues to tell time second by second in a way that looks fine locally. No one in the spaceship feels any time-distortion, a one-minute egg still takes 60 ticks to cook. It isn't affecting the home observer's clock either, how could it? There's no magic action-at-a-distance. What the relative motion is doing is distorting the spacetime between the two clocks. And that's the same thing that expansion is doing, the same thing that gravity is doing, the same thing that acceleration is doing. In every case some points are (relatively) closer together and some points correspondingly farther apart. Thanks Mr. McFall, I hadn't thought of it but entropy (propagation of energy) opens up another source of examples of why General Relativity is the best approximation of what mass/energy and space/time are really doing. I will ponder for a bit and see if I can mine some of these for helpful thoughts.To start with we must go ahead and distinguish between normal acceleration, caused by the necessarily uneven application of force and resulting in relative compression / dilation of spacetime, and gravitation caused by compression / dilation and resulting in the relatively even attainment of force or acceleration.What this has to do with entropy, which is probably so simple it isn't one of the things you were thinking of at all, is that if gravity were a force it would act unevenly, resulting in a "feeling" of acceleration like that we get when firing a rocket or riding in Einstein's elevator (rather than fee-fall that is). This force would eventually have to run out, entropize into nothing, whereas we can expect gravitation to continue as long as the mass continues to exist and distort the space in the same way.Someone has just pointed out to me though that the continued expansion of space will necessarily decrease the space-distorting effect of mass over time, just not at anything like the rate that normal entropy would disperse a real force. So I guess I'm back to the drawing board until I have clearer ideas. In the meantime I'm reading your Goethe vs Newton link, this stuff is fascinating. Thanks again!(Oh, if you get the chance, I would be honored to hear your thoughts on my previous post "When Worlds Collapse" Message 98 )

I'm, not sure how to read this. I get the twins paradox, it isn't really a paradox it's just a weird effect. The twin who travels ages much more slowly than the one who stays at home, eventually returns to earth and marries his own great-great-great-granddaughter. No problem. Near-light travel slows relative aging, all good. Not what I'm complaining about, no no. Here's what I'm complaining about Zigfax lives say 5 billion light years north of us, Bemfu lives say 5 billon light years south of us. They don't travel at all, relative to their own planets, they stay right where they are. They are of near-immortal races, aware of one another somehow, and beam clock-images back and forth as well as analyses of their respective clock-images and conclusions about them. We are in the middle and eavesdrop on their conversation.From Zigfax's point of view, Bemfu ages much more slowly because he is the one travelling away at near-light speeds (thanks to expansion). From Bemfu's point of view Zigfax is the one travelling at near-light speeds and therefore aging much more slowly. We in the middle observe them both as aging a bit more slowly than us, at least as of 5 billion years ago when the latest message was sent from either. We also observe their conclusions about each other, which provide the paradox.Our "doppler vs relativistic" distinction allows us to rest comfortably knowing their math isn't real. It's just "doppler effect" and really they age at the same speed. GR says no, there's no difference, they really do age each slower than the other. Another couple billion light years in each direction, they age not at all relative to one another, or even (as calculated but never observed) in reverse from one another. Yet each one continues aging normally on his own planet where he is.That's a real paradox, just not an observable one.

Thanks again, I've been having a lot of fun following your clues around I don't know that that's perfectly true, the idea that if gravity is energy it must therefore necessarily dissipate is already a good strong indicator that our formulations about it necessarily require a different view, GR being the best approximation of that different view produced so far; and I'm sure that's only the tip of the iceberg! I do understand your reluctance to step too far outside your field though, I just want to encourage you to continue commenting where you see us touching on aspects relevant to your expertise.For example This is shockingly relevant to our discussion of gravity, especially here at this forum. Let me plug in something about Benard cells so our readers can follow the conversation better Rayleigh—Bnard convection - WikipediaThis shows how self-organizing systems can be seen to develop naturally and asymmetrically (either handedness though) as a direct results of what are intrinsic properties of gravitation. The narrow separation of the planes and the need for the lower plane to grow warmer over time, that is the gravitational distortion of entropy toward the source of gravitation, show that gravity as an energy trap is an essential factor in the development of life "as we know it".Pseudo-panspermia (stellar genesis) might provide the complex chemicals, but in order for them to grow into cells with molecules of a particular handedness and begin the long journey towards greater and greater complexity it seems almost mandatory for them to be at the bottom of a gravity well and thereby attain to variant fluid levels and uneven entropy. The very phrase "uneven entropy" is almost a preliminary definition of life in and of itself.

Oh haha, no sir, but as I am looking for models and factoids to help demonstrate why GR is relevant even in the purely ballistical situations SR and Newton were made for I found this insight useful. I am not really up to the task of trying to (effectively) disagree with cavediver yet, even if I had found a reason to, I am still trying to visualize all the implications of simply understanding his argument.I do see your point though as to how shifting the discussion towards the biological implications pushes us even further away from the original topic than Percy has been so kind as to let us stray thus far, your intention not to distract us from the educational process we are still striving through is admirable. And I respect your desire not to distract yourself also, I guess I will just be stuck trying to glean enlightenment from your arguments in other threads where I may have more work to do to find an inroad toward that first glimmer, that's all.As a side comment regarding your potential disagreements with Behe, you do realize the man is a kook right? I mean don't get me wrong, I'm a kook, you're a bit of a kook yourself, but Behe is a whole different scale of kook from us. We may be experimenting from time to time in believing things that may appear to have been demonstrated untrue, as part of what your Goethe links characterized as "exploratory experimentation", but when we discover we have gone wrong we switch off to different tacks. Behe seriously seems to me to be banging his head against the same wall year after year for no good reason other than an obsession with his own fixed ideas. The only value I see coming out of that is a comprehensive list of reasons why he is wrong, surely he should let someone else bear the burden of producing such a list just for his own sanity's sake.

Ok here is where I see the problem, we less-experienced physics fans are going to have trouble reconciling this statement with this one It seems like we are wrong no matter what we try to believe, do you see that?Now based on the more recent statement and all our careful disclaimers about "relative to the observer", I will venture to guess that we are right in imagining that our clocks are going at the same speed, but for the wrong reasons?Considering that when I talk out the points of space and so on you seem to approve my logic, I may not be as wrong as when we try to juice up the rubber-band model.But when I do imagine it in terms of contraction and expansion of the points, I end up thinking time slows down for the distant galaxies for the same reason it slows down for the astronaut who wanders too near a black hole (disregarding the way his feet get ripped off by the gravity differential of course.)That is to say, it proceeds normally for him but slows down relative to us. But when he wanders away again, this has been a real effect, he is much younger than us. This doesn't seem to correspond to what happens with the distant galaxies the way I would like it to, if our clocks are actually proceeding at the same rate due to our common state of being at rest in respect to our individual comoving frames.From this viewpoint I feel Percy would be right in trying to emphasize that the "doppler effect" relativity is not the same as the "actually moving through space" relativity, in that the one doesn't really affect our relative aging and the other does. In other words, contrary to what I have been trying to think, there is a real solid difference between the time-dilation effects of contraction of space like black holes versus expansion of space like the Hubble-Einstein universe.Why would that be?* No rush, whenever you get the chance, thanks for all your help thus far; thanks also Percy for all your input, I think I have gotten a couple of times smarter just trying to research your pointy questions (though not smart enough to understand Lorentz yet lol)

Thanks cavediver, you cleared up the whole confusion in one fell swoop.This puts an end to all my "calculable-but-never-observable" language of course, seeing as how the doppler portion is all about observation there isn't any point where things that cross horizons then experience a reversed duration in any sense at all, relative or otherwise.The time-dilation we see with things moving away has no real relation of any kind to the time-dilation actually experienced in things moving in any direction, they are just confounded together because people want to think that what we observe bears some relation to what actually happens.The triplets paradox doesn't mean anything at all because we have no reason to assume that we can take what we observe, subtract the distance, and call that the time of the event at all in such a case. The aging that is observed differently by the two inertial frames is just a difference in observation, not in the actual procession of time for the observed object. The third "twin" is really experiencing more time-dilation than people traveling slower than him and less than people traveling faster than him, regardless of direction.Thanks for all your assistance!

I hope you don't mind if I try to answer based on cavediver's demonstration of distinguishing out the different effects. If he corrects me I will get to learn something else so I would really appreciate it Let's call the effect of acceleration through spacetime in respect to the observer's inertial frame the genuine time-dilation. This works rather like traveling northwesterly at a set speed, the more north you go the less west you go. Terrible analogy I know, but it helps visualize the whole four-dimensional thing better for me at least, the more northward I go the less futureward I go. The opposite effect will be deceleration, this stops but does not reverse the effects of the genuine time-dilation.Distinct from that we have the doppler effect caused by traveling away from the observer, let's call this red-shift. The opposite effect will be blue-shift, this will reverse the effect of the red-shift.A third effect to consider is the signal-delay, this is the one we mostly already understand. An object at rest (in respect to our inertial frame) at a distance 10 light years away will have its messages delayed by 10 years. Good so far?Now let's try it out in practice. You hop in a spaceship and accelerate in such a way as to make a trip to the Centauri system 3ish light years away, traveling most of the trip at near-light speeds. Your acceleration causes you and your clock to experience a genuine time-dilation, it only takes you say 6 months of your personal time to get there. I am watching your signals back here on earth in mission-control, I see not only this genuine time-dilation but also another additional amount of clock-slowing which is illusory, caused by the red-shift. It also takes me longer and longer to receive your signals. At this point if I try to judge your "now" without the information needed to account for all the effects separately I will come to some very bad conclusions.When you get to whichever of the Centauris, say 3 light years away, you decelerate into a normal orbit. At this point you are to all intents and purposes at rest again in respect to our original inertial frame. The red-shift decreases to normal, you keep the effect of the genuine time-dilation you have already experienced and stopped experiencing, and your messages are delayed by 3 years. At this point if I watch your clock it is ticking normally, but 3 years behind because of the signal delay and another 2.5 years behind because of the genuine time-dilation. I have a reasonably good chance of judging your "now" because I can subtract the 3 years representing your distance and the 2.5 years left over from the 6 months you log as experiencing during the trip.You complete your brief mission, turn around and accelerate back. Again you experience genuine time-dilation due to your acceleration. But because you are moving towards me this time the primary effect I see is the blue-shift, this makes it look to me like your clock is running much faster, even though the genuine time-dilation is actually making it run somewhat slower. Also, there is less and less signal delay. Again I will have a bit of trouble judging your "now" under these circumstances, though slightly less trouble as time goes by rather than more and more because we are reducing rather than increasing the distortion of observation this time.When you get back you decelerate, again stopping but not reversing the genuine time-dilation. The blue-shift cancels out the red-shift completely, the signal delay has been reduced to nothing much and then nothing at all as we meet. The only remaining effect is the genuine time-dilation you experienced as a result of your acceleration. For me it has been 6 years, for you 1 year. There's no coincidence, the illusions and delays have canceled out and what is left is the actual difference between our experience of time, the classic twins problem.* have I got it yet? I should probably add a few days or months in to account for the fact that we can't quite travel at lightspeed, but I don't know how much extra to add to make the 6 months realistic so I have shamelessly glossed over that part of the problem This message has been edited by Iblis, 01-26-2006 06:52 PM

Oh fine, I'm leaving it because it doesn't affect the principle and as a permanent record of what a big dope I am then It can be an as-yet-undiscovered white dwarf only barely in that system to be named Big Dope Centauri, exactly 3 light years away and so on I'm more concerned about the fact that in my scenario the home observer sees the 3 year journey out, experienced by the astronaut as 6 months, as taking up the full 6 years. The clock ticks are normal during the mission, which has to take only an hour or so in order to keep my arithmetic pretty straight. Then the home observer sees the entire 3 year journey back crammed into another hour or so, or whatever the gap in my math is, by the blue-shift, though the astronaut experiences it as the same 6 months it took to get there in the first place.Even assuming this is correct I probably ought to have conjured up a better example that isn't so freaking unbelievable

Yes, an isosceles trapezoid is what you are imagining. (In gringo, in anglo it would be a trapezium.) Keeping in mind how little time I allowed for the actual scoring of the Big Dope, what you will imagine is just short of a triangle.A good example of an isosceles trapezoid is the face of the Pyramid on the Great Seal, the Eye not being considered as part of the structure. Isosceles Trapezoid -- from Wolfram MathWorldAnd yes, the longer the route through spacetime (i e the more of it is space) the less of it is time. We need relatively great spatial distances in conjunction with short periods of time in order for the difference to have much significance though. (More on that part in a bit I expect)

Depends how he measures and what he sets his standards at. No, he never thinks he is traveling faster than any actual light, that's the rough part for me, I will try to wrap my mind around it in a minute.But first, let's say he considers c to be 186000ish miles per second. If he has a "speedometer" display that uses some accurate method to measure the distance he has traveled, continuously corrected parallax or somesuch, and then divides it by his proper time, he certainly thinks he is traveling at 6c just as you described. He could have another speedometer that calculated "real time" using every fact at his disposal, that might show his real speed.It's when we get to "the speed of light" part that it gets tricky and my maths start to fail me. He continues to observe or measure light as traveling at 186,000ish miles per second no matter how fast he goes, just as if he were standing still. If it were as simple as I would like, that would mean he now measures it as traveling at 7c. That would only be the light traveling in the same direction as him though, the light traveling in the opposite direction as him would be going at 5c by the same logic. And sideways? Geez, it would vary accordingly.And as I have mentioned before this logic is wrong Wrong WRONG. According to what I understand, it never varies, neither forward or backwards nor sideways, the speed of the actual light is always measured the same, the actual variance is the doppler stuff we have been yammering about, the stretching of the wavelengths, this is how light deals with its own "proper time", by keeping it at 0 no matter what.How the heck do I visualize that?* yeah side note, I'm glad you mentioned the "warp speed" thing, Roddenberry actually consulted with various popular science types while planning the original Trek. He wanted things to look and sound "realistic" even when we got around to actually traveling in space on a grander scale.This is why, for example, the Enterprise looks the way it does. When he asked about potential "artificial gravity" strategies, of course they only had the 2, normal acceleration and centrifugal force (circular acceleration). They showed him drawings of the usual stuff, a big space station shaped like a wheel and a big continuous-drive fusion system shaped like one pipe for the passengers with some other pipes for the engines. Stick 'em together and write NCC-1701 across the bow, there we are.Anyway the cubic measurement we call "warp speed" now was offered up as what might be a convenient way to measure apparent average speed when crossing various distances at 1g of continuous acceleration, it's the kind of thing we would want because it wouldn't go off the scale as quickly as some sort of distance/time measurement like "miles per hour" or "light years per year". Some of the early versions of the pilot script still had this logic in it, but it was a bit too abstruse for the Desilu and Paramount writers to pay it much mind.Still when you watch the scene in "The Menagerie" where the supposed settler is talking with Pike about his "Time Warp" drive, or when you look at the background history where Zefram Cochrane is said to have first tested his invention by achieving some minor fraction on a trip past Pluto before venturing off to Promixa or Alpha, remember that these ideas were born out of the perfectly-realistic engineering implications inherent in a 1g continuous-acceleration system.