“I realise now that I wanted to disappear. To get so lost that nobody ever found me. To go so far away that I’d never be able to make my way home again. But I have no idea why.” -Jessica Warman
When you think about the galaxies up there in the night sky, only visible with the most powerful telescopes in the world, it also behooves us to think about how incredibly rapidly they're moving.
As the Universe expands, the space between us and them expands as well, causing an incredibly fast apparent recession. It also means that these galaxies, given enough time, disappear from the farthest regions of space we'll ever be able to reach. In other words, as time marches on, the number of galaxies reachable by us continues to drop!
How many are left? And how quickly are things disappearing? Go read the whole thing and find out!
To understand the expanding universe is very easy. Anyone who has put one drop of dish washing detergent into an oily pan prior to washing it has observed the same effect on a far smaller scale. Just imagine a pan that goes forever and the drop is the big bang- of COURSE it's going to go on forever and gain speed because there's no friction- such as gravity to slow it down.
"[...] another one fades [...]"
Another one galaxy? That sounds like a strange number. I expected it to be a percentage, like 0.0005%.
Isn't the future dictated by what exactly is Dark Energy? If it's vacuum energy then yes, it will expand forever and we'll only be left with Virgo Cluster.
If you model vacuum energy so it can decay, then it's not the same picture any longer. In some more exotic versions, with quintesence having a negative potential, then it can recollapse. Or if the potential of DE turns out to be less than -1, then it will win over gravity in the end and not even galaxies or planets will remain.
So, as far as I know, until we know the true equation of state of DE and what exactly it is and isn't (if it's -1, a bit less, a bit more, does it change with time..), we can't predict what the Universe will do in future with any certainty.
is pretty much discredited now, too bad because I like
the idea of it. No Big Bang, just an ongoing series of little
bangs, necessary to populate the space between galaxies
as they pull away from one another. A nifty arrangement
worked out between matter, gravity, and recession. It gives
assurance that the universe will maintain a consistent look,
no break in continuity. A great concept, a guarantee that
whenever we look to the heavens we will see the same thing. Constancy is comforting. Anyway, I could never whipsaw my mind around the notion of a Big Bang, the making of something from nothing. It violates some scientific principle, I think. The thought that a universe could be packed into a levitating subatomic mote. I don’t believe we mortals were blessed with the mental apparatus to grasp such a thing. But Steady State is a different hypothesis. A universe that has existed forever is something I can deal with. It takes the big cosmic pyrotechnics out of the picture, my fevered brain relaxes, it’s receptive to clearer concepts.
Infinity allows for a Deity with a role to play, some design work; new stars, new planets, intelligent life; omnipotent creations that harmonize the celestial order. So I give Bondi, Hoyle, and Gold a nod, they developed an attractive theory, a comfortable theory. I think they were on to something.
I don’t believe we can blithely ignore a proposition that is built around scientific rigor and the circular plot of a movie.
When you meld physics and the film industry you have
to give the conclusions serious consideration.
Personally I hope the Steady State Theory makes a comeback.
I know, I know there’s still the issue of that pesky cosmic microwave background radiation … but hey! No theory is perfect.
I could never whipsaw my mind around the notion of a Big Bang, the making of something from nothing. It violates some scientific principle, I think.
It violates our human common sense notion of how the world works, because on the scale of meters and grams and such it never ever appears to happen. But one thing the 20th century taught us (or should have taught us) is that our common sense notions about how the world works can be deeply, fundamentally wrong. If the empirical data shows that something can come from nothing under certain circumstances, we're better off trying to figure out why and how - rather than rejecting the notion because it doesn't feel sensible to us.
I enjoyed your comments on my tongue-in-cheek lampoon of the Steady State Theory.
but it's not something from nothing. It's something from something. It's an inflationary field dropoing it's potential and creating matter and energy in the process. What remains is where did the inflation field and spacetime come from. Is it eternal or not... etc.. But Big Bang is definately not something from nothing.
There's a fundamental mistake in this article, isn't there?
"If something is receding from us right now at more than 299,792.458 km/s — faster than light speed ".
And on that is the idea that not even a beam of light would ever reach that something. But "something" CANNOT travel even AT light speed, much less faster than light speed. So why would it be unreachable?
Am I missing something here?
Thanks, Sinisa. You do understand, don't you, that my little parody is not to be taken seriously. It's a spoof, nothing more; not a scientific assertion or cosmological naiveté.
Can anyone answer Don's question? I thought that nothing could exceed the speed of light.
“If something is receding from us right now at more than 299,792.458 km/s — faster than light speed ”.
One number in that whole thing keeps bugging me. "populating an observable Universe some 92 billion light years across. " I've heard that the universe is supposed to be around 13.7 billion years old. If two objects were moving away from each other at the speed of light, that would make them (13.7 * 2 =) 27.4 billion light years apart. Has the acceleration of the universe really accelerated to (92 / 27.4 =) over 3x the speed of light just within the 'observable' universe? Am I missing something?
If two objects are moving in opposite directions at over half the speed of light we are separating at over the speed of light. All of our calculations and observations are directly based on reference.
@ Don & Rhonda
the galaxy in question is NOT moving faster than speed of light on itself (intrinsic speed), just like we are not moving faster than speed of light... but combined accelerated expansion of space between us and them is larger than the speed of light. Thus no signal sent now would ever be able to reach it, just like light from it will fade ever more untill it get's infinitely redshifted and dissapears from our observable horizon
I have two questions for the author:
1. Why is it incredibly frightening that galaxies are slipping out of our reach? They've always been out of our reach and likely always would have been (Particularly as individuals), so while impressive, how does it affect us?
2. What is our concern to get to these other galaxies before they disappear?
@ Don & Rhonda
I think it's easier to understand if you realize that the receding galaxies can reach the speed of light (but no faster). At that point, any photon launched from earth simply can't reach the receding galaxy because the launched photon can't exceed the speed of light to make up the difference (the same applies in the other direction). As more galaxies hit "terminal velocity", they slip out of our reach... (BTW, I'm highly doubtful that this acceleration can break the fundamental rule governing the speed of light - in my experience, these claims tend to fall away under scrutiny)
How is it that science writers don't know about Warp speed? Besides, when they outermost galaxies hit the wall - sproooiiinnng!
"expansion of space between us"
How does "space" expand? I know, there's a mathematical theory that says it does, but I've always understood the idea of "expansion" as just a model to explain the math, it didn't mean space really expands.
Like the idea that gravity "bends" space - again, I've always understood that idea as a model, a way of showing that mathematically it's "as if" space bends, but it didn't mean space really bent. It just meant that for the purposes of calculation, you can treat it as if it does. Not that it actually does bend - or expand.
Is there some actual proof (measurement, not just math) that space can "bend" or "expand"? I'd like to read about it.
It's not a mathematical theory.. it's a physical one, and is just as real as electricity of magnetism.
Something that I don't understand is this:
If nothing can travel faster than the speed of light, then how are they traveling away from us at greater than the speed of light?
I understand that it has to do with your inertial frame of reference, but from what I understand, there will never be anything travelling faster than light in your frame of reference, and yet we used our frame of reference to discuss how a galaxy is travelling away at greater than light speeds.
To add to my confusion, didn't we all start out in the same frame of reference during the big bang? It seems like the speed of light speed limit is softer than physicists would generally indicate when reading about relativity.
Are we allowed to both go our separate (opposite) directions at .6 C and have us both acknowledge that?
If anyone knows why this is, I'd certainly like to know..
Never mind.. Although the included explanations above didn't really fully answer my question(s) one of the links provided above did actually answer the question in acceptable detail. I'm surprised that no one on this thread really explained it adequately (other than providing the link).
An oversimplified version is this: Relativity only applies to to things that remain in causal relationships. By going .6 C each in opposite directions due to expansion, their causal relationship has been broken, and basically all rules are off..
Now I just wonder if a causal relationship can actually be restored once broken, by somehow one of the objects/parties/galaxies somehow turning around? And if it can be, was the causal relationship ever really broken or did it just seem to be?
@Jeff, Don, Rhonda et al. Sinisa's two links (see #18) are the right place to go to address your confusions.
Special relativity applies to objects which are in motion with respect to a nearby (causally connected) observer. With the expansion of space, widely separated galaxy may or may not be causally connected. In any event, each one of those galaxies is (nearly) at rest with respect to nearby observers. For example, seen from Andromeda or the Magellanic Clouds, the Milky way is moving at something like 100 km/s or so. Not very fast, and certainly not fast enough for SR to complain :-)
The cosmological expansion involves space itself "stretching," and the various galaxies are just going along for the ride. When we look out and see a highly redshifted galaxy, that doesn't mean the galaxy is actually _moving_; rather, the light from that galaxy has gotten stretched along with the space between us, while the light was in transit. SR doesn't set any limits on how much that stretching might be.
@Michael Kelsey #21
" that doesn’t mean the galaxy is actually _moving_; rather, the light from that galaxy has gotten stretched along with the space between us, while the light was in transit."
If, in this case, the galaxy is not moving (away or toward) us, there would be no apparent red or blue shift in the spectrum. To say the light experienced stretching would imply some sort of delay in its transit to the eye (photo detector, sensory array). That seems contradictory to what we have been led to believe about an expanding universe. Most targets are in red shift - the further away, the faster they are moving. For those in blue shift, moving closer, et al.
I gather from SR, it is used as a means to allow explanation for those phenomenae which do not fit in with GR?
There is no disrespect intended in this comment.
@PJ: Sorry, it sounds like I was too telegraphic in what I wrote. The galaxy is not moving _in the rest frame of it's local neighborhood_: that is, whatever motion the galaxy might have, relative to "local observers" is small (of order a few hundred km/s).
The redshift we observe from far distant galaxies is NOT a "Doppler shift" -- it is NOT due to some intrinsic motion of the source relative to us. Rather, it is a "cosmological redshift", which is induced in the light during transit, by the global stretching of space (specifically, by the scale factor a(t) of the cosmological metric).
I found the Wikipedia article on "Hubble's Law" to be a good, quantitative explanation of the issues. The cosmological redshift can be _interpreted_ as a relative speed, provided you're in the low-redshift limit. At high redshifts, that interpretation leads to apparent paradoxes, or contradictions with special relativity. Those paradoxes are resolved by understanding what I wrote above -- each galaxy is more or less "at rest" in its neighborhood, and so no superluminal motions are ever involved.
photon's travel through space who's metric is growing. They are not "outside" of space. photon's wavelength gets stretched as a result of metric changing. Like Michael pointed out, the effect is similar to dopler shift, but the cause is completely different. The TOTAL redshift or blueshift we observe looking from earth is a shift caused by observed galaxy's local speed and direction of movement + the shift caused by cosmological expansion of metric of spacetime.
I will try to describe one analogy about metric expansion, that should clear up "faster than speed of light etc.." because it's really simple. Speed of light is 300.000 km/s.. Imagine you and me at a distance of 300.000 km, connected by a chain consisting of 300.000 links. It takes light 1 second to reach from me to you. Both me and you are stationary.. our own velocities are nothing.. zero. There is only a distance of 300.000km between us.
Now have every link in the chain grow by 15% every 0.1s. Doesn't matter how or why.. but you can certainly imagine it. Now suddenly the distance between us is rapidly growing, but I'm still standing still and you are also. Nothing around me is moving. I just see a whole more chain appearing and you growing smaller and smaller. It only LOOKS LIKE you are moving away from me faster than "c". But you needn't be moving at all from your own standpoint. The "growing" of links in chain is what metric expansion is when you overly simplify it. But you don't need math to follow the analogy. Why does the Universe have an expanding or contracting metric in the first place is bizzare on it's own.. at least to me :) But Universe has it's reasons I'm sure. Hope it helps.
You are applying a very common-sense, but very wrong, formula for addition of velocities. It is not true that if two observers are separating from each other at 0.6c that they would be causally disconnected. The velocity of separation observed by either one would NOT be 1.2c, as one is led to believe by common sense. Rather they would measure the separation velocity as (0.6c + 0.6c) / (1 + 0.6c x 0.6c/c^2) = 0.88c, which is obviously less than the speed of light. Therefore, the observers are not causally disconnected. One could send a light signal (which travels at c in ALL reference frames) to the other and that signal would get there.
See my post to Jeff Buck above. Two observers separating at ANY velocity (subject to the c limit) are always separating at a velocity less than c. The key is that velocities are NOT additive; they are only approximately additive in the limit of velocities that are small relative to the speed of light. Assuming we measure velocities in multiples of c, then the correct formula is (u + v)/(1+uv). For u and v <= 1, this formula can never yield a number greater than 1.
The real answer has been adequately explained by others. The redshift is not caused by an actual velocity, but rather by the expansion of the space between us and the distant galaxies. No limit applies to the speed of expansion of space. The SR velocity limiit only applies to energy (which also includes mass since that is shown by SR to be a form of energy).
@ #23, #24
Thankyou, gentlemen. My understanding has been enhanced a little more.
When viewing the shift of wavelength of a target, is it the whole of that object which is measured for its shift, or does one attempt to assess individual light sources within that image? For instance,with a galaxy as seen edge on, there is a case where the approaching side would appear to be in less of a red shift compared to the receding side which would be more red shifted from our perspective.
I can visualise many issues in ascertaining the real value of data gathered from these type of observations. For instance, objects which are thousands of light years distant yield very few photons from the source. Those that do make the journey will have been disturbed by their local members, subject to gravitational bending and the like, potentially travelling through the atmosphere of a planet which may be in its path (scintilation, as we observe on earth) then dust clouds in the outer reaches of its local area.
If , as has been proven, light sources can interfere with each other under certain circumstances, then there will be paths of interference with other sources taking the same journey. If two of the source wavelengths are out of phase, their respective wavelengths will be shifted toward the red, where the amount would be dependent on the degree of phaseshift.
A little humor here.
When you ask a question you create space for an answer. Then you fill that space with some answer.
Then someone asks what is after that and more space is created.
And so it goes.
So, the universe is never going to end. Not above your head (big) or below your feet (small) or sideways (alt).
Naturally some singularity oriented individual is going to insist on asking what would happen if the universe could collapse. Just tell that one that you don't know and then don't. Your space will be just fine.
@PJ #27: Good questions! For very distant galaxies, most spectrometers necessarily average over the whole galaxy to get a spectrum. With relatively nearby galaxies where we can get decent images, it is definitely possible to get strip-wise spectra (and extract rotation curves, for example).
For your second questions, the term you want to look up on Wikipedia is "extinction (astronomy)". It is extremely well understood by astronomers, and does not alter any of the conclusions about cosmological redshifts (except as interpreted by non-professionals who don't understand it).
For your last question, different light sources do not "interfere" in the sense of waves -- different sources are _incoherent_ by construction, and you will not see interference or beat effects. You _will_ see interference (technically, _correlation_) effects from photons coming from a single, spatially distributed source (look up "Hanbury-Brown and Twiss effect"). This effect can be used, for example, to measure the physical size of stars which can't be resolved as disks. It does not affect cosmological redshifts.
just a clarification about some things. You say " objects which are thousands of light years distant yield very few photons from the source". Actually, couple of thousand light years yields enough photons to be seen by naked eyes ;)
The thing is... couple of thousand light years is peanuts for measuring. Our own galaxy is about 100.000 light years in radius. ;) In order to measure cosmological redshift, you are sampling galaxies several BILLION light years from us.
Cosmological redshift (or metric expansion) only adds some 60 km/s for every 3.2 million light years. So it's incredibly tiny... but pile billion light years and you start to notice it.
p.s. but you are correct that light emitted from a faraway source passes through all sorts of things before it reaches our detectors and all those interactions have to be accounted for. That's why the most distant sources have the largest error bars. Gravitational lensing is well accounted for, dust is what's problematic. Dust can mess up the data and is very hard to account for properly, since we don't really have high-def dust maps of early universe (a problem which is now very much talked about in case of BICEP2 measurements).
Hello everyone. After reading the article and the comments, there's still something that bothers me. I understand it's the expansion of space itself that keeps pushing galaxies apart, eventually leaving an island of a few gravitationally bounded galaxies in the local group. But, in the same way that length contraction would allow us, at least in principle, to reach any point in an stationary universe, no matter how far away it is, because that distance would be asymptotically contracted from the point of view of the traveler, doesn't this same phenomenon holds when the space between the traveler and the destination stretches? is necessary some rearrangement of the equations of SR, or they just don't apply in that scenario? Is it that even with the contraction of the distance from the point of view of the traveler, it just doesn't make up for the continuously created extra space? Perhaps GR and Quantum Mechanics have to be thrown in so things make sense?
If I understood your question correctly, you're asking if space can expand, can it shrink and can we in principle do the reverse? Yes, in principle it can be done... but you are still bound by speed of light. So i.e. you could "contract" space which your beam can reach. ... a sphere with radius increasing 300.000km every second. And that contraction can in principal be faster than the speed of light. ... but that faraway galaxy will forever be beyond your reach... because your "sphere of influence" that starts this moment is bound by speed of light. Spacetime in principal can expand or contract faster than speed of light. But any and all information transfer is bound by speed of light. That's why we see that galaxy as it was several billion years ago. Where it is or does it exist at our "now" ... we can't know.
@28 Michael Kelsey
Many thanks for the response. Much to read & learn. Your suggestions are regarded highly.
Yes, I did miss out by a factor of 1,000 or so; hard to write from work with so many other souls around requiring assistance. My apologies for the oversight. Proof reading will be back on the agenda !
Thanks for the comments.
I don't quite understand the "acceleration" part of this phenomenon. Could someone explain?
Say we measure the distance between Earth and some distant galaxy. To start we measure distance d1.
After time interval x we do the same measurement getting d2. After waiting x we do one last measurement getting distance d3.
If (d3-d2) is larger than (d2-d1) then one or both are accelerating. Is the speed of light, C, the limit of
this acceleration? If so, is that where it ends, i.e. eventually everything appears to be receding from the earth at 2C?
The "acceleration" refers to observation that the rate of expansion seems to be increasing in the last 6-7 billion years (there is always gravity present as a counter force). While the universe was denser, gravity was stronger and expansion was slower, now the tables seemed to have turned.
as for question about c, 2c... it was answered. There is no "c" restriction on spacetime itself. At least not in any theory we have. But for everything in that spacetime, there is a limit of "c".
"The “acceleration” refers to observation that the rate of expansion seems to be increasing in the last 6-7 billion years (there is always gravity present as a counter force). While the universe was denser, gravity was stronger and expansion was slower, now the tables seemed to have turned."
What is the force to which gravity is counter?
If you travel at 1 Earth gravity (1g) to the Andromeda galaxy, 2 million light years away from us, commencing braking at the midpoint (also at 1g) to arrive at Andromeda at low speed relative to it, you'll get there in about 28 years on your clock, says special relativity. Then a beacon floating at the the midpoint you passed will have receded 1 million light years away from you in the 14 years after you passed it. That can happen only when the beacon accelerates away from you to achieve an *apparently* greater than a light speed rate of travel away from you, an average apparent recession speed of 1 million light years per 14 years. Occam's razor tells us that this behavior is most likely what we're observing when galaxies seem to move away from us at greater than the speed of light; after all, the beacon is free-floating like the galaxies are, and those galaxies are receding in the Milky Way's gravity well like the beacon was receding in your gravity well.. The notion of space itself expanding has always been an unnecessary assumption, leading to three major problems in cosmology: the horizon and flatness problems (the latter the focus of the article above), and the mystery of the observation leading to the made-up idea of dark energy.
@Joe #39: Your analysis is flawed. You correctly use SR to compute the traveller's time dilation (more correctly, the transit time in their own rest frame), but you fail to properly compute their Lorentz contraction, or more correctly, the distance they _measure_ themselves travelling during their journey.
They will not see the beacon recede by a total distance of 1 Mly, but rather only about 14 light years! Why? Because of the speed the Universe is passing by them (or vice versa :-), they measure the thickness of the Universe as just 14 ly. When they come to a stop there in Andromeda, and do a parallax measurement of the beacon, only _then_ will they see that it's "really" 1 Mly distant (i.e., that far away in the common rest frame of the beacon and Andromeda.
@Michael #40: After your "Why?" is correct, but the sentence before it is incorrect. At the midpoint you pass right by the beacon, 0 distance. 14 years later on your clock it's 1 million ly away. Both are *real* distances to you (anything anyone measures is just as real, Lorentz contraction or no), so it's correct to say that the beacon receded by 1 million ly in 14 years as you measure, using those 2 measurements. It's perfectly okay to use only 2 measurements.
You are right that the distance you measure yourself travel cumulatively, factoring in Lorentz contraction, is less than 1 million ly, but that doesn't matter to my point. My point was, the beacon recedes faster than the speed of light in the same observed way that other galaxies do from us. We don't measure cumulative recession travel for each those galaxies, instead we compare two or more galaxies at different distances from us now, perfectly analogous to the 2 measurements we took of the beacon. There's no way to distinguish one "faster than c" travel over the other, which makes the the expanding space paradigm a superfluous idea. As you recede from the beacon, signals emitted from it to you will observably stretch in transit (that's Lorentz un-contraction at work) in the same way we observe light signals to stretch when observing light from other galaxies. Expanding space need be nothing more than the Lorentz un-contraction predicted by both SR and GR. Occam's razor favors that simplicity.
After passing the beacon it must measurably accelerate away from you, since its speed relative to you when you passed it was less than the speed of light, whereas its average recession speed was greater than (1 / 14 million times) the speed of light. Then dark energy is also a superfluous idea. The horizon problem vanishes, since you never lost causal contact with the beacon even as it receded from you at greater than the speed of light on average. And the flatness problem vanishes, because that problem depends on the expanding space paradigm we've discarded.
@Joe #41: You are still mixing values from two separate reference frames, and making the same mistake as in your #39 post. There are some really excellent SR simulators available; you might try running one of them to see if you can adjust your intuition.
Let's extend your example a bit, and see if we can clarify it. Instead of just one beacon at the halfway point, let's suppose that somehow we have beacons placed every light year between here and Andromeda (so 2.3 million beacons), and they are all sitting in the common rest frame of the two galaxies (for now, I neglect the small relative motion, just as you did in your thought experiment).
Further, let's take acceleration out of the picture, and just pretend we're cruising at uniform speed, such that the trip from here to Andromeda would take 14 internal years. In that case, according to our _internal_ trip distance meter, the beacons would appear to be a bit more than 6 microlightyears apart -- we would pass a beacon once every 3.2 _internal_ minutes.
To an external observer watching our progress through a telescope, we'll pass each beacon a little more than one year after the previous one, in their (rest) frame.
In order to get consistent results in SR, you must relate time and distance values in the SAME rest frame. Under those conditions, the laws of physics will look the same to observers in any single frame. But if you mix measurements from two different frames, then you will get inconsistent, and nonphysical, results.
@Michael #42: I agree with you on your paragraphs 2 through 4. They're well put. But I say that's irrelevant because those measurements aren't analogous to Hubble's.
In your extension of my example you're measuring the cumulative distance traveled, by cumulatively measuring the distance between adjacent beacons as they pass by. But Hubble didn't measure that way. He measured the distance and redshift of "beacons" far away, providing the evidence for the expanding space paradigm.
Both Hubble and you, in my original example, were in an accelerating frame. Both the galaxies Hubble measured and the beacon you measured are free-floating. Replace yourself with Hubble. When he's 3/4 of the way to Andromeda as we on Earth reckon (having braked since the midpoint), let him simultaneously measure the distances to all of the 0.5+ million of your beacons between himself and the midpoint. Now the scenarios are mostly analogous. The equations of SR (for an accelerating relativistic rocket) will show that the further the beacon the faster the rate of change of distance over time (hence higher redshift), and now cosmologists are inferring from his data that the space between those beacons is expanding.
When you say "In order to get consistent results in SR, you must relate time and distance values in the SAME rest frame", note that SR supports constant acceleration with its relativistic rocket equations. For example, an observer standing on the ground can use those equations to plot with high precision the trajectory of a ball tossed upward. Such observer is analogous to Hubble in the braking rocket, in the example above. The beacons are "tossed upward" in Hubble's accelerating frame as he passes by them.
 It isn't necessary to feel the acceleration, though. It's enough to be in a gravity well. If Hubble had been floating between the stars, presumably his results wouldn't differ.
 Not perfectly analogous, because your beacons share a rest frame, whereas the galaxies Hubbled measured presumably move apart from one another.
 And they'd be right, but it's Lorentz un-contraction, a relative expansion that depends on the observer, and not space itself expanding in an absolute way (the current thinking) that could physically stretch objects.
@ Joe Blechtel
You use SR to make your point, yet expanding spacetime is a mathematical solution to GR for a flat spacetime without matter. And no stretching of space is physically stretching objects. It's coordinates that are getting further from one another. Check de Sitter space.
@ Sinisa #44: From Wikipedia on "Metric expansion of space": "In addition to slowing the overall expansion, gravity causes local clumping of matter into stars and galaxies. Once objects are formed and bound by gravity, they "drop out" of the expansion and do not subsequently expand under the influence of the cosmological metric, there being no force compelling them to do so."
When space *itself* expands, the generally accepted viewpoint, sufficiently large objects do physically stretch because gravity (the weakest such compelling force) isn't strong enough to maintain equilibrium (keep the object the same size). If space *itself* wasn't thought to be expanding (even between the nucleus and electron cloud of the atoms of your body), you'd be right. "Coordinates that are getting further from one another" is consistent with "space itself expanding".
It's okay that I used SR to make my point. I showed that SR predicts a redshift that increases the further the receding object, like Hubble observed. Because GR resolves to SR locally, GR's Schwarzschild metric must also predict such redshift, and that metric doesn't predict that space itself expands. Then the expanding space paradigm, an interpretation of Hubble's data, is superfluous, and my point stands. I needn't predict Hubble's exact data.
No, the metric is either expanding or contracting, since metric is tied to scale factor (a(t)) which is a function of time. So as time passes, the metric gets either larger or smaller. It's not static. And then there is Lambda, which is in the solution for de Sitter space.
@ Sinisa #46: That's not inconsistent with what I said. The metric expansion of space is compatible with the idea of space itself expanding.
From http://goo.gl/HRXUhk: "But in fact, while the space between and inside everything increases, the things themselves don’t. Or at least, they snap back faster than they can be stretched." They "snap back" because one or more of the 4 fundamental forces is strong enough to prevent the object from physically stretching when the "space between and inside" it expands. According to the generally accepted theory, if not for one or more of the 4 fundamental forces holding it together, the Earth (or a galaxy) would expand over time due to the metric expansion of space.
"GR’s Schwarzschild metric must also predict such redshift, and that metric doesn’t predict that space itself expands."
your words, not mine...
And besides, now I see you mix an match terms and sentences as you see fit for your argument. You were using SR to disprove DE, when SR has no notion of any of that. It's GR that deals with spacetime curvature or expansion. Your #45 is so riddled with grammar errors, I have a hard time trying to realize what you're saying. You don't think spacetime is expanding, and DE doesn't exists, fine... enjoy your theory, just don't advertise here.
@Sinisa #48: Yes those are my words. And I backed them up with logic and evidence. Anyone can input values into the generally accepted equations to see that the result matches what I said.
"You were using SR to disprove DE, when SR has no notion of any of that. It’s GR that deals with spacetime curvature or expansion." SR does predict the expansion that Hubble observed, and by extension so must GR's Schwarzschild metric, which is not currently generally accepted. That's not advertising *my* theory. There is no *my* theory here. I'm only pointing out something unnoticed in the generally accepted theory. Again, anyone can prove it to themselves.
As far as grammar errors or "mix an match terms and sentences" go, you provide no evidence.
however hard you try, it still makes your comments false.
1. Despite you wanting to be so, SR doesn't have any metric formula. It does have relativistic doppler shift (which you think is the same as cosmological shift, but is not)
2. Total observed redshift can't be explained ONLY by relativistic doppler shift. Like you correctly wrote, anyone can input values into generally accepted equations, and see that you are wrong. You need classical + relativistic + cosmological redshift in order to match observation to formula.
3. And it's not Schwarzschild metric that applies to the universe, but FRW metric. Schwarzschild metric is used for spherical objects like stars or black holes, and it describes gravity outside of that object, Universe is not modeled with it. Friedmann-Robertson-Walker metric is used for what you want to talk about.
@Sinisa #50: On your points:
1. SR doesn't need a metric formula to predict what Hubble observed. Its relativistic rocket equations can predict what Hubble observed. Those equations also predict that light emitted from distant receding objects stretches on its way to the observer (Lorentz un-contraction of the light). If it predicts the same as the observational evidence for cosmological redshift, then it predicts cosmological redshift, period.
2. There are 2 and only 2 pieces of observational evidence for cosmological redshift: ever higher redshift the further the receding object from the observer, and stretching of light during transit from the receding object to the observer. SR's relativistic rocket equations predict both pieces of evidence, not just relativistic redshift. It's not currently generally accepted that SR predicts cosmological redshift, but that's not my problem.
3. There's no scientific requirement that the universe be modeled with the FRW metric or only that metric. Our Solar system used to be modeled by the Ptolemaic system, where the Sun revolved around the Earth. But it was a flawed approach, as we now know, and after people like me pointed out the evidence against it.
The article was pretty interesting and insightful, but it gives the impression that its a big deal that all these galaxies are slowly getting out of reach, when actually it isn't. There is way too much universe for mankind to ever hope to even start exploring, so it doesn't really matter if it's reachable or not. Just exploring our own galaxy (were it possible) would occupy humanity for an unimaginable amount of time, and i think it's sizable enough, that we wouldn't ever need to venture to other galaxies. But even if we did, Andromeda is pretty close, relatively speaking.