Iggy

I don't understand what you're asking with the first thing. To the second, if every galaxy at a certain distance has a peculiar velocity directly away from us then we must live in a very special place in the universe.

I agree, but what you and MD said are not mutually exclusive unless we have acceleration of expansion. I believe MD was pondering otherwise. Indeed. What I said last post about the proper distance to the horizon eventually being constant would be true only if the cosmological constant's equation of state is -1. In that case, everything that is gravitationally bound today will be bound indefinitely. If it is less than that then we all better believe every little thing is going to be ripped to pieces.

Ned wright explains how both descriptions of light amount to the same thing here under "many distances". The condensed version is that the coordinates of special relativity (static space) are not the same as FLRW coordinates (expanding space). Distance and time mean something different under the two different assumptions. Velocity (which is distance divided by time) is naturally going to be different as well. The coordinate system changes, not the reality of the situation being described. You get the same predictions either way. Right. The same explanation would then have to be required of the standard model. Either way the thing that caused the initial expansion isn't know. Yes to the same distance all around. The bolded one is where we're headed. We aren't there yet. The horizon is still receding, it's just that space is receding faster where it is because of acceleration. In the future the hubble parameter should end up being about constant over time which gives a horizon of a constant proper distance. Of course, it depends on what you mean by "horizon" and "distance". The comoving distance to the event horizon shrinks indefinitely. A galaxy that has a comoving distance of 10 billion lightyears today will always have that same distance. That's how the coordinates of standard cosmology work. The coordinate distance to a galaxy that is expanding away from us doesn't increase over time.

I firmly believe there is categorically no difference. Expansion just means outward velocity. Back toward the first second or so of the big bang there was an initial velocity everything got away from everything else. It has never been explained in terms of a cause, but the momentum everything got from that initial burst is what continues to carry everything along inertially today. It isn't nearly as mysterious as everyone makes out. It's just that if you fling two things away from each other, they'll tend to keep moving that way. Gravity affects expansion. It isn't synonymous with it. The observation that Hubble made (v=H*d) is that galaxies twice as far from an observer have twice the velocity. That is true even in a freely coasting universe. A galaxy today that has a certain velocity today would have half the velocity of a different galaxy that is (today) twice as far away. If a specific galaxy always has the same recessional velocity at any point in the future then the rate of expansion is constant and that is freely coasting. It remains that at any point in the future galaxies which are twice as far would still be twice as fast. I would just say that a constant rate of expansion should be considered expansion nonetheless. But, it is always a distinction without a difference even with the more standard models. Are galaxies redshifted from a recessional velocity or because of expansion? It depends on how you look at it. Two ways of saying the same thing. If you assume that space is static then galaxies are moving through space. If you assume that space is expanding then galaxies are static relative to their local space. Different coordinate systems offer different descriptions of the same reality. Are galaxies really moving away from us or is space just expanding? This depends on how you measure things, or your choice of coordinates. In one view, the spatial positions of galaxies are changing, and this causes the redshift. In another view, the galaxies are at fixed coordinates, but the distance between fixed points increases with time, and this causes the redshift. General relativity explains how to transform from one view to the other, and the observable effects like the redshift are the same in both views. Part 3 of the tutorial shows space-time diagrams for the Universe drawn in both ways. In the absence of the cosmological constant, an object released at rest with respect to us does not then fly away from us to join the Hubble flow. Instead, it falls toward us, and then joins the Hubble flow on the other side of the sky, as discussed by Davis, Lineweaver & Webb (2003, AJP, 71, 358). In what are arguably the most reasonable coordinates, the cosmic time t and the distance D(t) measured entirely at the cosmic time t, the acceleration is given by g = -GM(r<D)/D2 where M(r<D) is the mass contained within radius D. This gives g = -(4*pi/3)*G*(rho(t)+3P(t)/c2)*D(t). The 3P/c2 term is a general relativistic correction to the otherwise Newtonian dynamics. Galaxies all move under the influence of this acceleration and their initial position and velocity. In other words, F = ma and gravity provides the force. Nothing extra or weird is needed. Ed Wright cosmology FAQ Agreed 100% I meant only to say that the ant / rope analogy didn't apply to standard cosmology.

It's a freely coasting universe. One where gravity (attractive from matter or repulsive from dark energy) doesn't affect expansion. I did a search and it is correct that such a universe doesn't have an event horizon: It's pretty far from mainstream.

Yeah, I think the black hole is a perfect analogy. Krauss had a good reading on it, I think it might be difficult to say that the last photon reaches us in finite time, just because we could never be sure, no matter how long we waited, that no photon remains. I don't know specifically to what you are referring. You did confuse distance in spacetime with velocity, but that isn't a discussion we should have here. my bold. That analogy works only for a freely coasting universe (one without gravity) where the hubble parameter gets steadily smaller and the scale factor evolves linearly. It does, however, effectively prove that there is no cosmic event horizon at the infinite future of such a universe. Cool

Or in the case of accelerated cosmic expansion, the photons are diluted into the infinite future like Tar says, but they become unobservable because, like Krauss says, the size of telescope needed to detect them is prohibitive. The explanations and diagrams in this paper are superior in every way to the blog I somewhat haphazardly posted yesterday,

Or, at least require a telescope larger than a planet to see. this diagram (and accompanying article) is really fantastic for this thread because it shows the event horizon at the infinite future.

The distance for which you're groping is the 'comoving distance'. What does this mean? Are you saying that the speed of light is constant over cosmic distance when expressed as comoving distance and proper (unscaled) time? That is how I've understood you.

It's like hearing Einstein say "I don't know what weapons will be used in world war three, but in world war four people will use sticks and stones" and thinking "My God, how could Einstein be so arrogant to think he can predict the weapons used in the fourth world war... It contradicts his admission that he can't predict the weapons of the third world war. It's hubris". Or, imagine if I were explaining length contraction and I said "an alien ship approaches earth at some fraction of the speed of light and the alien pilot sees the earth as an oblate spheroid". Your answer might be, "Length contraction, HA! I seriously doubt it. How can you know there are alien civilizations? You can't know how an alien's eyes work or even if they have eyes!" By making an extremely literal reification of a rhetorical example you've missed the point completely.

And after they went ape shit the Supreme Court ruled in 2010 that, of course, the second amendment applies to the states via the 14th amendment like Swansont pointed out.

Are these the remarks from Krauss that you're talking about? If you heard Krauss say that and then you thought "Careful, Krauss, we can't know everything about the universe. Science can be wrong"... that just doesn't make sense. Something seriously doesn't add up. I understand that you don't like the model, but I can think of no more salient example to make the point that you and Krauss both seem to be making. The same model that predicts that there was a big bang also predicts that the evidence for the big bang will disappear in the future. There is no reason to think, in other words, that the universe willingly cooperates with us to answer the questions we have about it. The more we learn the more evident it is that the universe isn't interested in explaining itself to us. You made clear that you don't like the model -- that you'd rather think of the universe as eternal and unchanging. I can only imagine that is the basis of your objection and not really anything to do with the hubris you accuse Krauss of having for using the model as an example. Because, if those are the remarks you're talking about then it is extremely strange to hear them then caution Krauss that we can't know everything about the universe. Extraordinarily strange.

(bolded mine) Yes you do. Taking as granted that C is NOT influenced by the scale factor: how is it possible... The speed of light is locally measured at c and is not locally influenced by a change in scale. Please stop mischaracterizing what I said! If leaving the thread is the only way for you to do that then please leave and don't return.

You're equivocating. I refer you to my previous answer: More equivocation. The velocity of the photon relative to the emitter at the time of emission is the same as the velocity of the photon relative to the observer at the time of observation. That is what I said, and it absolutely does not imply that the velocity of the photon relative to the observer is constant between emission and observation. I suspect you are intentionally missing the distinction.

You can measure a photon's redshift and determine the amount of cosmic expansion to which the photon has been subjected. Measuring its velocity can't tell you that. Let's make this perfectly clear. Bob sends a photon off into the cosmic distance. He notes when it is sent that it has a certain wavelength. Alice, on the other side of the visible universe, receives the photon. She notes its new wavelength. The difference in wavelength is directly related to the change in scale factor of the universe between emission and observation. It depends on that and nothing else. Bob sends a photon off at velocity c. It crosses the universe and Alice receives it measuring its velocity at c. The difference in velocity (there isn't one) has absolutely nothing to do with the scale factor, or how much the scale factor has changed, or how quickly it changed, or any combination of the above.

the wavelength, yes

and it simply does not apply to the invariant sense in which you used it in post 119 that started us off. What you quote agrees that general relativity is not constant in that way. Your statement that the speed of light scales with the cosmological scale factor needs corrected because it is demonstrably false. They are precisely not constant in that way. It needs to be admitted. You missed entirely what I was saying which reinforces my fears that we have no common ground on which to talk

You didn't answer this question. I have no idea why you think it would imply that so it is difficult to answer. "constant velocity" means constant relative to any observer. It doesn't mean constant relative to a local penny. Pennies, like galaxies and the people in them, don't expand. The grid on the rubber sheet, like intergalactic distance, does expand. Light acts like a bug that is capable of crossing a penny in one second. That is how fast its feet will carry it. Set the bug on the rubber sheet and let it go. Stretch the sheet. The bug will cross its local penny in one second, but the distance between the bug and a distant penny will change by much more than the width of a penny in one second. You can if the model decelerated. I'll quote wikipedia for all the good it'll do: For the first few billion years the universe had decelerating expansion. This allowed events on galaxies with superluminal recession at the time of emission to eventually be seen by us. We are seeing such events now. The base of knowledge necessary to understand this, and / or the level of communication needed to successfully communicate it are prohibitive. I don't think, in other words, it does us any good to keep discussing it. The simpler point is that you asserted that c is constant in relativity. That is easily refuted and itself shows a profound lack of knowledge.

Either we're both talking past one another or you're mimicking me. Either way, I'll try harder to successfully communicate. No. C can be (and is) variable with respect to the the global expanding coordinate system while superluminal sources are observed due to deceleration. How do you maintain saying this when you must have looked it up by now and found out it is false? Look at the formula for distance as a function of scale factor if you have to. It isn't constant... and of course it isn't constant. If the speed of light were constant relative to an expanding coordinate system then it wouldn't be constant in flat static pace lie Minkowski spaceime -- but it is. Not only does everyone maintain that c has no universal consistency in relativity, your own logic tells you as much. Why can't you accept it and accept your mistake ? God knows we've all had t0 d0 it

I don't follow. The speed of light is locally c, but is not necessarily c in an expanding metric. That is not the main property (or any property) of c. c is not constant in an expanding metric. c is not constant in relativity. It is not constant relative to a nearby observer whom is accelerating, a metric that is expanding, or any observer in a gravitational field. The best way to understand this is to glue pennies on a rubber sheet. The distance between pennies increases as you expand the sheet, but the photon always moves as if to cross a local penny in one second. The speed of a photon relative to one penny is not the same as the speed relative to another penny. Not constant, in other words. Constant is the opposite of relative. If the distance traveled per time relative to one thing is different from the distance traveled per time relative to another thing then it is not constant.

You are right to say so. I've seen you accept an error when it is validly pointed out to you, so I do sincerely apologize for saying what I said. My last post was sloppily (very sloppily) submitted in a rush basically while walking in the door from an overindulged party. That is correct. [edit, I mean to say: "the thing you quoted is not wrong"]

The speed of light is constant (constant mean that it don't change over time) with respect to the pennies [and you can't imagine how confirmed such a basic fact is because not the expanding metric. The exact thing you said about relativity and about your expectation of a misinterpreted constant c were exactly wrong. Cant you just move on? You clearly can't make,

c is constant in special relativity and not constant in general relativity (general relativity is the more general case of relativity... the complete theory). Expanding cosmic models are solutions of general relativity because one thing that makes special relativity special is that it can't handle expanding metrics like your analogy. By the way... galaxies don't expand compared to expanding space. If the speed of light were constant compared to an expanding metric like you say then it would be variable compared to observers that don't expand in galaxies that don't expand like pennies glued on the rubber sheet.

The size of the telescope needed to make the observation is the limiting factor. That's why Krauss added the qualifier about the size of the telescope in his remarks. It is even less simple. The scale factor grows (even if the universe is always expanding at a constant rate) over time. If the scale factor is one today (it usually is set that way) then the scale factor will be two when the distance between things doubles (from what they are today). Not at all. Imagine gluing pennies to a rubber sheet. As you stretch the sheet the thing that remains constant is the speed of the photon relative to the size of a penny. If you draw a grid on a rubber sheet, and stretch it, the speed of the photon relative to the grid is not constant. Your conclusion is true that photons are currently arriving here in the Milky Way which started out getting further away from us (that's why the past lightcone on the spacetime diagrams have a teardrop shape). The photons were pointed at us and trying to make their way across the distance to us, but space was expanding too quickly back then so that the distance between the Milky Way and the photon was initially increasing. The reason we see those photons is because expansion decelerated for the first few billion years sufficiently that some photons did cross the Hubble distance and started making progress in our direction. The deceleration of expansion fell less and less until it became negative (which is the onset of acceleration... negative deceleration is acceleration). Any photon emitted towards us now by a galaxy with a current superluminal recession speed will never reach us. They will move away from us at an ever increasing rate.

I'm afraid that didn't make sense to me. A small example, I can't make sense of that. I don't think expounding on it would help.