Did the expansion rate of the universe exceed lightspeed?

I agree. Those are meaningfull statements. The statement I was talking about was the one in the OP, though. The expansion rate of the universe is measured in Km/second/Megaparsecs (or some equivalent unit).There is no way to compare that with the speed of light (in Km/s) and come out with the conclusion that it is several times greater.

Can we be certain that the speed of light has been 'constant' since the beginning of time?Could it be that the rate of expansion of the universe is the limiting speed in the universe and that the speed of light and the rate of expansion of the universe are intrinsically related or even one and the same thing?This would mean that to all intents and purposes the speed of light is contant from our limited point of view but not in cosmological terms. During the period of expansion the speed of light would have been much greater than it is now for exampleBefore anyone jumps down my throat - I am not proposing this as true or even supported. I am thinking about why a certain limiting speed should exist in the universe and am interested as to any possible correlation between that limiting speed and the properties of the universe as we know them.Is there evidence either for or against the idea above and if so what is that evidence?Edited by Straggler, : No reason given.

No. They are entirely different concepts with very little relation The only 'limit' is an *observational* limit on the speed of another object. If you were to accelerate towards another star, you would find that there is actually no limit to how quickly you can get there. If you could survive the acceleration, you could cross the Galaxy in a day. If you came back a few days later, you would have spent less than a week on a trip of over 100,000 light years. But because you cannot be *observed* to travel faster than the speed of light, by necessity, the earth and its inhabitants will have aged about 100,000 years - i.e. the time it would take to make that journey at the speed of light.

Now I am confused (and I suspect I am not alone)I thought the limit of the speed of light was related to the increase of an objects mass as it approaches the speed of light and that at the speed of light the mass would be infinite thus requiring infinite force to accelerate it furtherIn the case of physical matter at least there is a limit. Is this wrong?

No, you are not alone, Straggler. cavediver... you totally lost us there. Aren’t you talking about time-dilation now?Further..
I find this "expansion of space but not time or matter" incredible complicated. When I looked at wikipedia on this subject (for the term "space") I got just as confused. There seems to be no good explanation for a concept that is mainly "imagined". Even though it is observable, talking about the expansion of the universe, the whole concept of WHAT is actually expanding is beyond my current understanding. Lets say that the matter in the universe at some point in time creates enough gravity for a "global" gravity-hole (big crunch scenario) that makes all the matter in the universe travel towards that hole. Even when it does the expansion of "space" wouldn’t stop as I understand it? It would be a battle of some kind between the "space-expansion" and the gravity force. Wherever that leads us...

You're correct that this is why you'll never observe anything moving faster than the speed of light.But Cavediver's example of traveling light years in just days *was* very confusing. How could this be if you can never observe anything traveling faster than the speed of light? Well, the answer is that time is relative, too.Let's add more detail to Cavediver's example and say that there are two stars 10 light years apart, call them A and B, and that you are at some other star observing a friend travel from A to B. You observe him leave star A toward star B and accelerate faster and faster to .9 the speed of light, then .99 the speed of light, then .999 the speed of light. He keeps going faster and faster and getting closer to the speed of light, but never reaching it. Then, when he's halfway between the two stars he begins decelerating, finally reaching a speed of zero when he reaches star B.You observe that it has taken your friend 11 years to go 10 light years, and so deduce that he's traveled at an average speed of .9 c in your reference frame.But let's say that you have a very good telescope and are able to observe your friend's clock. What you discover is that during the journey his clock was moving much more slowly than your own, and that after 11 years on your clock only a year had gone by on your friend's clock. It would appear to you that your friend would think he has traveled 10 light years in just a year, and that therefore there must have been periods during his journey when he observed his own speed as being much greater than the speed of light.But relativity still survives intact, and that's because no one can ever observe anything traveling faster than the speed of light, including your friend during his journey. The reason for this is that objects and distances shrink in size in the direction of observed motion, so as your friend accelerates to near the speed of the light, the distance he measures between the two stars becomes smaller and smaller. So although his clock says only a year has passed, the distance he has measured himself actually traveling is not 10 light years but perhaps only .9 light years. Since he took a year to travel .9 light years, he would not think his speed ever exceeded the speed of light.Now if you were to do something invalid, such as use the clock from your friend's reference frame to measure the rate of motion across distances measured in your own reference frame, then you'll get bogus results that say he is traveling faster than the speed of light. One should never combine measurements from different reference frames without making the necessary relativistic adjustments.--PercyEdited by Percy, : Typo.

Hi Explorer,I'm no Cavediver, but let me try to tackle just this portion: I hope this isn't too far off, at least at a simplistic level, and as always Cavediver can correct me if I'm wrong, but the short answer is that the forces of gravity cancel out.An analogy would be the gravity you would experience at the center of the earth. Since there are equal amounts of matter in all directions pulling equally on you, you would experience no gravity and would have zero weight at the earth's center.Even though the very early universe was incredibly dense, certainly sufficient to produce a black hole, it was incredibly dense everywhere throughout the universe. This means the net gravity at any given point in the early universe was the same, approximately zero, since equal amounts of matter existed in all directions.--Percy

Well explained. Even to the point were I think I actually get it now. So thankyou for that.In terms of the OP - What reference frame do we use to determine the rate of expansion of the universe?
Where is the conceptual clock and what does that show as the universe expands? How does the frame of reference maintain relativity intact during periods of expansion at rates that appear to be faster than the speed of light in other frames of reference. Which frames of reference are these that do suggest expansion rates greater than the speed of light?Is the rate of expansion of the universe (esp the idea of it exceeding the speed of light) even a meaningful concept if the frame of reference is taken into account?I am well baffled by the expanding universe now.Edited by Straggler, : No reason given.

Okay, let's go back to the example of the sphere. Geodesics in the time direction are lines of longitude. Our experience of time passing means that we are all moving down lines of longitude. Hence, latitude is our measure of time, while longitude is a measure of spatial location. A person on this world sees her universe as having one spatial dimension (she thinks she lives on a line) and one time dimension.Now imaging three galaxies, one, where our protaganist is located, at longitude 0, which we will call O, galaxy A at 30 degrees longitude, and galaxy B at 60 degrees longitude.Now, as observed by our scientists at O, both A and B seem to be moving a way from her since the lines of longitude are diverging. (Unless they have already passed the equator, in which case they will seem to be coming together). What is more, as the galaxies move down the lines of longitude, the further galaxy, B, seems to be receding at a faster rate than A.In fact, it could be that the rate at which O and B are moving apart seems to be faster than the speed of light. Now, in this case, the scientist at O cannot actually see galaxy B. However, she may be familiar with General Relativity, and can hypothesize that her universe is a curved 2-manifold, and may even theorize that it is a sphere. She may not be able to physically construct this model of a 2-sphere existing in a 3-d universe in her 1-d space, but if she knows differential geometry she can do all the math.In this case, she can then put a coordinate system on the sphere, perhaps based on lines of latitude and longitude. She can then figure out how to calculate actual distances in her standard system of units on this sphere based on their coordinates, much like we can calculate the distances between any two cities on the surface of the earth if we only know their coordinates.Now she can deduce that even if she cannot see it, there exists a geodesic along the 60 degree longitude line. Furthermore, she can now calculate the distance along a line of latitude between 0 and the hypothetical galaxy B (distance along a line of latitude being an actual distance in space), and she will notice that this distance is increasing at a rate faster than the speed of light.I'll leave it to cavediver or Son Goku to critique the accuracy of this analogy.Edited by Chiroptera, : construct -> physically constructEdited by Chiroptera, : criticize -> critique

---

...Onward to Victory is the last great illusion the Republican Party has left to sell in this country, even to its own followers. They can't sell fiscal responsibility, they can't sell "values," they can't sell competence, they can't sell small government, they can't even sell the economy. -- Matt Taibbi

Another good explanationWhat does the equator on this imaginary sphere represent in terms of the lifecycle of the universe?Is rate of expansion a misleading phrase? It seems more like a rate of divergence/convergence?

One thing we all have to keep in mind about analogies is that not every detail of the representation is analogous to the event/thing being discussed.

Well, that would be the point in time when the expansion of the universe stops and begins to contract.However, remember that all analogies are flawed (if an analogy was perfect, it would probably be as difficult to understand as the original problem). In this case, a sphere is a geometrical shape with two spatial dimensions, one of which I'm pretending is a time dimension. It might be possible to put a non-positive definite metric on the sphere -- I don't have enough intuition about pseudo-Riemannian manifolds (or even a good basic knowledge) to determine whether the 2-sphere can be a pseudo-Riemannian manifold. Cavediver? Son Goku?I mention this, because I can change the model from a sphere to an elliptic paraboloid (look it up to see what it looks like) in which our closed 1-d space expands forever; however, I think I've read that if the expansion does go on forever, then the spatial dimensions cannot be compact -- space must go on for infinity. So either an elliptic paraboloid cannot be given a Lorentzian metric consistent with GR, or 4-manifolds are different than 2-manifolds.- Well, at one latitude, a cross-section perpendicular to the time direction gives a circle;' at a later "time" (a lower latitude) the circle is larger; space has expanded. This expansion occurred between two different latitudes (that is, between two different times). Amount of expansion divided by time is rate of expansion.Whether you want to see this as the fact that the circle is bigger, or whether you want to see this as the geodesics diverging from one another is a matter of choice. The latter, I believe, is more natural in terms of the mathematics of what is happening; the former is what we observe in the real world when we point our telescopes at the sky.Edited by Chiroptera, : typos; also a "parabaloid" -> "an elliptic paraboloid"

---

...Onward to Victory is the last great illusion the Republican Party has left to sell in this country, even to its own followers. They can't sell fiscal responsibility, they can't sell "values," they can't sell competence, they can't sell small government, they can't even sell the economy. -- Matt Taibbi

No, this just another observational effect. It is not why there is a 'limit'. I appreciate that this is the way it is often explained, but that doesn't make it correct!Let's try the longer version, as the short version seems to have created confusion all round As an object with rest-mass, you have a 4-dimensional velocity vector with fixed length (which we will call length c). When you are at rest, your vector points purely in the time direction. We sometimes loosely say that you are always travelling at the speed of light into the future. What you think of as velocity is actually a rotation of this vector, such that it now points a little into space (in your direction of travel) but still predominantly into the time direction. Thus you do not notice the difference in time, but you do start moving in space. As the 'velocity increases', the vector rotates further, until you start to notice that the component of the vector pointing in the time direction is substantially less than normal - say only half c. You are thus moving in space considerably, but only aging half as much as normal. As your vector tips towards horizontal, your time component approaches zero, while your space component approaches c. You are thus moving through space at almost the maximum possible given by your vector, but hardly aging at all. As far as you are concerned, you are traversing space with almost no passage of time - this is effectively infinite velocity. As an object with rest-mass, you cannot tip your vector perfectly horizontal (i.e. so that it points purely in a space-direction, with no component in the time direction), but you can approach as close as you like. A particle with zero rest-mass always has its vector pointing in a purely space direction.You can now see the limit. It is simply that your 4-velocity vector always has fixed length, and the most it can ever be rotated is such that it (almost) points totally in the space-direction. Stationary observers watching you are still moving through time as normal, so you do not appear to have the near infinite velocity you are experiencing. They will see your vector as tipped 45 degrees, equal amounts in time and space. This is what we usually call 'the speed of light'.What does 'inifinite' velocity look like? Well, as mentioned, you can never see an object move faster than the speed of light. So as you approach a star, travelling light years in days, what gives? Well, the 'observed' distance actually contracts, so that as soon as you reach your relativistic velocity, you already appear to have crossed most of the distance! Thus the star nevers appears to be approaching at more than c!

Ah. This is what I was missing. Certain things are bit clearer in my mind now. Thanks.

---

...Onward to Victory is the last great illusion the Republican Party has left to sell in this country, even to its own followers. They can't sell fiscal responsibility, they can't sell "values," they can't sell competence, they can't sell small government, they can't even sell the economy. -- Matt Taibbi

No, he's not - as explained in my last post. Yes, it is confusing, but if you are asking: then you are into something much deeper than simple time dilation. My reply was an attempt at a very short version of my above post.