How big is our Galaxy.

Hi Percy... first off, thanks for the detail in your post. However... You might say Special Relativistic effects are only caused by relative motion within space... but of course we are talking General Relativity here as we are dealing with a cosmological model. Until you consider GR that is oh, and observation Pulsars and Cepheids are observed in proximities that show virtually no expansion effects. The Virgo Cluster (the furthest Cepheid measurements of which I am aware) is on our doorstep and is still dominated by peculiar motion. The recessional red-shift effect is tiny compared to the many other errors. True, and also from local gravitational effects. One of the big breakthroughs in understanding relativity comes when you realise that these three are all the same thing. So what causes the time dilation between two observers sitting at different heights in a grav well? You would say that there is no motion at all here.What do you think red-shifting is? It is the very time dilation we are discussing whatever the source of the red-shift, be it relativistic motion, cosmological expansion, or gravitational potential. Imagine an atomic clock on a receding galaxy and think of observations of that clock from here... keep thinking... think of the resonant frequency of the clock... keep thinking... think of observations of that resonant frequency... keep thinking... now, do you believe me yet?This is a major observational difference between recessional red-shift and tired-light. Tired-light will have no associated time-dilation. Percy, as a member of the Cambridge Relativity Group I used to help teach Cambridge graduates their GR... it may be a long time ago now but my pride can still only take so much of this Yes, this is quite true. All objects will have peculiar motions wrt their own comoving frame. But this is irrelevent to the point that cosmological expansion produces time dilation.Oh, almost forgot. I did mention that is has been observed didn't I? Well, how about time dilation of Type 1A SN signatures at lowish z. And the initial stuff was all on time dilation of gamma ray burster signatures as a way of proving their cosmological origin.I hope this helps...This message has been edited by cavediver, 01-15-2006 11:14 AM

Thanks, I'll check the reference out a little later. For now, the easiest way to understand all of this is to do as Einstein did and form simple Gedanken experiments. Hopefully my "atomic clock on receding galaxy" should be enough to convince yourself of what is going on.

re-read Sylas's post Message 226 in response to your message Message 225.It could be my reply above re-worded. Scary.So yes, I would say that you have misinterpreted him.

I know, that's how I found it!

quote:

---

Caution... if you speak about what is "seen", then actually you do see the second hand ticking more slowly. Suppose a photon leaves the watch at a certain instant. Another photon leaves when the second hand has ticked off another second. The second photon has further to travel than the first, and so arrives more than a second after the first. You see the clock ticking off seconds more slowly.

---

I "think" I've found the issue... are you concerned that the "time-dilation" of the slow ticking watch is caused by just the obvious point that the photons have further to travel, and so isn't the "true" time-dilation that you are used to in Special Relativity?In relativity, we don't really make any distinction. All sources of time-dilation are down to geometry. Just because the geometry in this cosmological case seems more obvious makes no difference. None of these time-dilations are real as such. However, in each case, if you try to move from your frame to the other frame, you will get a very real time difference (say, respective elapsed times from the Big Bang).This comsological "trivial" time-dilation still gives rise to an infinte red-shift horizon as Iblis was describing.This message has been edited by cavediver, 01-15-2006 12:39 PM

Yes he was, and I'm in complete agreement with doing that. No, absolutely not. Remember, I said

quote:

---

All sources of time-dilation are down to geometry

---

but not down to recessional velocity. I say that the time-dilation of cosmological expansion is most definitely down to expansion of space and "nothing to do with recessional velocity" although I would caveat that by saying again that it is all highly related. Here's your problem. We have no "tremendous relative velocity". This is what Sylas was trying to explain. The two observers are in two different inertial frames. You cannot make these kinds of comparison. The simple world of Special Relativity does not apply. Just because the galaxy is moving rapidly wrt its [abe: remove "inertial", replace with "local comoving"] frame, it doesn't mean that it is wrt ours, whatever that means... you must be psychic This message has been edited by cavediver, 01-16-2006 04:22 AM

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

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.

Percy and Iblis, sorry for not being able to partake in this for these last few days... my workload has been cosnsiderable. I will try and pick this up again over the weekend, but just for now I will make a comment based on Percy: No, no, no. The cosmological doppler IS relativistic. It cannot be otherwise. Please do not use "relativistic" to mean SR effects, especially as there are no SR effects in cosmology, only approximations to SR effects which come from the GR metric... precisely where the cosmological redshift and gravitational redshift originate.The cosmological redshift is not conventional classical doppler. There is no "retreating velocity". You cannot equate the expanding space to a simple effective velocity of recession. The doppler effect of expanding space is anything but mundane! The redshift parameter is unbounded, not bound by 2... which is a good job for all those thousands of z>2 objects we have discovered! The farthest quasars are z>6. Iblis is quite correct in this.Oh, and while i remember: acceleration is prefectly fine in SR. You do not need GR. You only need GR where curvature is involved.This message has been edited by cavediver, 01-19-2006 07:25 PM

Sorry, I should have said "don't use relativistic to mean solely SR effects, to the exclusion of GR". You were splitting the red-shift effect into doppler and relativistic, which undermines the very important fact that the doppler is a very relativistic effect.To produce the red-shift calculations you have to go to the metric. In fact, just about every calculation in GR revolves around the metric. Do you want me to go through some of the maths with you? It's not that hard, though typesetting is a pain... any suggestions for inserting equations on this forum?I don't know of any layman book which will increase your knowledge. I'm afraid it's text book time. Essential Relativity by Rindler is probably my choice for your particular line of questioning. He is less mathematical and heavily into cosmological models.This message has been edited by cavediver, 01-20-2006 04:00 AM

The one who had journied would always measure less time from the big bang than the one who had not. It cannot be otherwise. Geodesics are (perversely) the LONGEST path between two points in space-time. Any deviation (acceleration) from a geodesic will shorten the path and hence less time will have elapsed. It is purely the acceleration that is responsible for the twin's paradox in SR.

No, they perceive each other as aging more slowly. They are actually aging at exactly the same rate, as they are at rest in comoving frames. If you were in one galaxy and travelled to the other, which you had perceived as aging more slowly, by the time you go there it would be YOU that was young, not them! (as a result of your acceleration).This is almost identical to SR. Two observers at some relative velocity will perceive each other as aging more slowly. Both are just perceptions. There can be no true stationary observer in SR (unlike GR, where a stationary observer is one who is stationary wrt the comoving frame) Only when you accelerate sufficiently to make yourself stationary wrt the other observer do you realise that it is YOU that are the one that has aged slowly (as a result of your acceleration).This message has been edited by cavediver, 01-20-2006 07:47 AM

Percy, got to be quick. Check out this link and the following pages. After a quick glance I think they are very good. Especially check out the diagrams on pages 3 and 4. Lorentz postulated the transformations as a way of explaining the null MM experimental results. Einstein noticed that Maxwell's wave equations were Lorentz invariant... which leads to the constancy of c.

Ok, v=cz is only valid for small v wrt c. For larger v, you need the higher order corrections. It's not too hard to get that expansion: square both sides, times top and bottom of rhs by c. Isolate v on lhs and Taylor expand rhs.You are correct, v does not exceed c.

No, it comes directly from GR. Don't forget that the Big Bang model is not empirical, it is a prediction of GR.