Celestia Forums

so if the universe is centerless, is it possible that if we could see far enough, we might see our own milkyway.

since at the speed of light time stops and space-time converge to a one-dimensional point, light experiences eveything and anything at once...so

1. We cannot see light move with in it's reference frame? like spin or something?

2. does space move? is it a taught fixed "fabric" or does it move...and to say the universe is expanding is it to say that space is expanding pulling the outer matter with it, or is the matter moving outward, "making" new space?

I'm not sure about being able to see the Milky Way if you look far enough, as this is just a theory and has not been proven.

Space does move in the essence of being warped by gravitational pull, but other than that I'm not sure.

Michael Kilderry

chrisr wrote:so if the universe is centerless, is it possible that if we could see far enough, we might see our own milkyway.

Now, cosmology isn't a strong subject of mine, but I'll give it a try... While a curved universe is a plausible idea, I suspect the distance from here to "here 2" may be longer than the 15-20 billion lightyears (ly) to the event horizon, the sphere around us from which we are now seeing the light that was emitted at the creation of the universe 15-20 billion years ago. If it is, then we can't see our galaxy simply because it hadn't been created when the picture we are now looking at was "taken".

The event horizon expands with time, and the whole universe supposedly expands too, but perhaps not as fast. If the latter expansion slows down, the event horizon may eventually catch up with the whole universe, and an observer on Earth may (theoretically) be able to watch the creation of the Milky Way played back in slow motion across most of the sky. The Doppler effect will cause a severe shift of the spectrum, perhaps well below infrared.

If the universe has a finite (albeit growing) volume, how big is it right now? One way of determining that is to count the number of galaxies at different distances. In linear space, you would expect to find eight times as many galaxies within 2 Gly as within 1 Gly (the number grows with the cube of the distance), assuming uniform distribution. In a curved space however, that ratio would be different.

To make an analogy with a curved surface, imagine Santa Claus sitting at the North Pole, trying to calculate the size of the Earth by counting the number of children within a radius of 100 miles (from the North Pole), 200 miles, 300 miles and so on. If the Earth were flat, he would find that the number of children grows in porportion to the square of the distance. In reality however, he finds that the number grows with less than that amount, and the effect is more visible the further away from the North Pole he gets (let's assume Santa has never seen the Antarctic, because no children live there). By extrapolating his numbers, Santa finds that there won't be much territory left for any children to live on more than 12,400 miles away from the North Pole, and he correctly concludes that the Earth is close to a sphere with a near 25,000-mile circumference.

I don't know whether the deep sky surveys conducted so far have obtained any useful statistics indicating a non-linear universe, or yielded a rough estimate of its size. Anybody else who could fill us out on this?

But we know for sure from C(cosmic)M(icrowave)B(ackground) precision experiments (BOOMERANG, MAXIMA, WMAP) that the universe is flat to within a few percent uncertainty only!

Bye Fridger

Yes, the universe appears to have been observed as having a flat space-time structure, but I thought the explanation by andersa of how we might tell using galaxy and children counting was excellent and simple to understand! Nice...

Spiff.

I should point out that the analogy between a curved space and a curved surface isn't my own; I learned it long ago from some popular science book or magazine. However, I think the version I read used a gasoline company counting gas stations at various distances from its headquarters, not a very intuitive image in my mind. I also wanted to use the North Pole for an origin anybody can locate on a globe, and thus the choice of Santa became obvious.

If you want to continue the analogy, you need a way to transmit information to an observer at the North Pole, but regular light won't bend easily along the surface. Instead you can used pulsed trains of flying reindeer. Generations of Santas have been sending those reindeer in all directions since the beginning of time, and if they go straight ahead they will eventually make a full circle and return home from all directions (after having passed the South Pole, where Anti Claus lives, still trying to teach the penguins to fly). When that happens, Santa can measure the distance between individual reindeer and draw conclusions about their journey. At times the Earth has grown (maybe due to falling meteorites) and made the journey longer; thus Rudolph the red-nosed reindeer can be explained as the result of Doppler shift!

Even if scientific results currently point to a flat universe, it would be really neat to be able to illustrate a curved universe in Celestia, just as you can add fictional stars, planets, and spacecraft. At least it would be better than overflow errors.

When I went to school 30 years ago, the only non-static illustration of celestial phenomena available was a mechanical Sun-Earth-Moon model to show seasons and eclipses. I found it interesting, but I was way more fascinated by the crude computer-generated graphical simulations shown on TV to illustrate the planned trajectories of the Pioneer and Voyager probes. They provided a glimpse of the future in astronomy education. Why did it take so long?

andersa wrote:I should point out that the analogy between a curved space and a curved surface isn't my own; [snip]

Interesting!

Oh yes, I expected it wasn't necessarily original, but what I was pleased by was after all this speed of light confusion recently we get a really good argument that helps explain something, and is worth adopting - thanks!

Following some of the Phys and Astron discussions here, I'm not only interested in what is 'right', but what misconceptions exist, and how people come by them. Also, any good ways of explaining things more clearly to 'correct' this are worth collecting.

The beauty of your explanation is that you convert what looked like something really bizarre (cosmological space-time curvature) into a simple counting and measuring experiment. Previously, I had only tried in vain to think how cosmologists would for example tell if parallel lines converge or diverge one billion light years away. It can't be done! Galaxy counting is so much more practical.

I think your conversion of the gas station counting to childre counting is a big improvement: it can also actually appeal to parents and children when trying to explain cosmology!

Perhaps we could add improvements: The task for Santa Claus is to inventory the children's requests for Xmas pressies. Children write letters to Santa. These are postmarked with a date. Letters travel at a constant speed, trying to get to the North Pole. What does Santa see? The nearest childrens' letters arrive soonest and may be some days old, but those from farther away turn out to be older: this is an analogy to looking 'back' in time into the Universe.

But also, when Santa's elves start to plot how many letters arrive from each distance, they find less letters from further away than expected, if the world was flat. So, is the world round?

That takes care of the finite light speed and curved universe analogies, but for the expanding universe, I think it's easier to say, what would Santa see if the world was gradually growing. If Anti-Claus sent a letter on 1st Jan to Santa Claus and it would take six month to arrive for that size of Earth, when would the letter arrive if the Earth doubles its size every year? Would it arrive in time for Xmas?

It's funny, people nowadays say people of old believed the world was flat (they didn't really), but now we know it to be round. Now, people in recent decades wondered if the Universe is curved, but obbservations suggest it is flat...

Spiff.

I personally don't believe the universe is infinite in size, I think there is an outer boundary to all the matter that exists. Just because we can't see the end of it doesn't mean it's infinite, we only know it's a large universe. I'd rather believe in curved space than to believe matter is infinite, because with curved space we're saying there is a finite amount of matter.

Polchey wrote:I think there is an outer boundary to all the matter that exists.

...and this is where Truman bumps into the horizon, steps out of his boat, opens a door in the sky and leaves his universe for another!

But I agree; a universe with finite mass makes more sense than an infinite one. It could be curved, or it could have a boundary with a shape, like a box or a sphere resting on the backs of four elephants, in turn standing on a giant turtle...

...and before you ask, it's turtles all the way down!

WARNING: Spiff-style lllloonnnggg post. Make brew for comfort (tea and biccies, or preferred home brew recommended).

I suppose we ought to actually try and answer chrisr's questions.

chrisr wrote:so if the universe is centerless, ...

Not necessarily. It may be that if the universe has a space-time curvature (geometry) that is 'closed', it has a centre but the centre is 'off' our space dimensions. A typical analogy downgrades the universe's four-dimensional space-time to a three-dimensional space, and looks at our spherical Earth. A sphere is considered 'closed' because if you start to draw a straight line on it, it'll follow a great circle, and end up back where it started. The Earth has a centre, no doubt, but if you look at a (two dimensional) map of the Earth, you can't point to the centre, because it's 'off' the map, somewhere 'underneath'.

chrisr wrote:... is it possible that if we could see far enough, we might see our own milkyway.

If the universe has a closed space-time geometry, then any light beam should also at first appear to go off into the distance in a straight line. But after a long distance, it'll start curving round, and eventually it should reach back where it started. This has lead to some people to say that in a closed universe, we should receive light from our very own Milky Way, perhaps even take a picture of it. There are some problems. First, there're the practical problems of a very small and dim image, and who would recognise the Milky Way from far outside it anyway? Second, there's the light travel time problem. If the light takes billions of years to make the round trip, then who'll recognise our Milky Way in its infancy? Third, there's a very serious light travel problem if the universe expands so fast, that parts of it can move apart at or faster than the speed of light. If that's the case, then light from our Milky Way would have to pass through that part of the Universe, and then it would be carried off away from us so fast by expanding space-time, it could never catch us up again.

Puzzled? Well think of it with the Earth analogy again. This time, we're at the North Pole, and we have a Ham radio set. Because Ham radios can transmit radio waves that bounce between the ionosphere and ground, they can transmit to other ham amateurs around the world: the radio waves follow the Earth's surface closely, but still travel at the speed of light. So, we at the North Pole would listen and send radio waves and discover that the South Pole is the furthest place away from us at 20,000km. We could also send a signal and listen to ourselves: the radio waves take 1/7 second to travel the 40,000km right round the Earth. But, what if the Earth was expanding, so that as it grew larger the North and South Poles each moved apart from the centre of the Earth at slightly less than the speed of light? Our radio waves should have taken 1/14 second (half-way!) to get to the South Pole. Problem is, the Earth is now almost 2 ?— 1/14s ?— 300,000km/s + 12,756km = 55,613km in diameter, and the South pole is 3.14159 ?— 55,613km = 173,300km away from the North Pole. Our radio signal has only travelled 20,000km, so it's still got another 153,300km to go! Clearly, our radio signal is never going to get back to us...

chrisr wrote:since at the speed of light time stops and space-time converge to a one-dimensional point,

Two-dimensional plane. The Lorentz transform 'compression' is only in the direction of travel.

chrisr wrote:1. We cannot see light move with in it's reference frame? like spin or something?

Not really. We can't even talk about spinning, and as far as I know, in the particle scheme of things, photons (light as particles) don't spin. But yes, it is better to say that light experiences the universe all in one instance, rather than time 'stops' for light (how can you imagine someone/thing noticing time has stopped for itself??? It's a paradox).

There is an interesting outcome of this that is the only 'crossover' of relativity and quantum mechanics that I know of: in quantum mechanics, it's possible to 'split' a photon into two with a polariser. Each shares the same 'quantum state' and if you change the quantum state of one, the other changes instantaneously, that is, the effect seems to go from one to the other at infinite speed. Why? An answer is because photons see everything happen at once, because they travel at the speed of light.

However, interesting as this is in explaining why the photons do what they do here, it doesn't explain to me why we see what we do. I mean, how does 'everything at once' for photons map into 'cause before effect' and 'same time together' for us lowly observers'?

chrisr wrote:2. does space move? is it a taught fixed "fabric" or does it move...and to say the universe is expanding is it to say that space is expanding pulling the outer matter with it, or is the matter moving outward, "making" new space?

Space can 'move' according to Einstein's General Theory of Relativity: a rotating black hole can drag space around it, so that any x,y,z position in space will move off. In cosmological expansion, space doesn't drag or drift from any place or centre. What's thought to be happening is that new space is being created right within old space at all parts of space. If any collection of objects sit in this expanding space, they seem to get further apart from each other, and none can say who's moving or not - hence the apparent lack of a centre of expansion (except the illusion of yourself being at that centre). What definitely isn't thought to be happening is that galaxies are moving through space away from us, while space happens to hang around stationary.

I don't know whether we can really differentiate between saying that space is 'growing' or 'stretching', but the rate of expansion is incredibly small. Hubble's constant (the factor in the rate of the expansion of the universe) is now settled to be about 75 km/s per Megaparsec. This is an observational result, which means that for every Megaparsec a galaxy is distant from us, it seems to be racing away at an extra 75km/s, we can tell from its redshift. Now because one Megaparsec is 1,000,000 parsecs or 3,260,000 light years, which is (>inhale!<) 31,198,200,000,000,000,000km, then the rate of exansion is 75km / 31,198,200,000,000,000,000km = 0.000,000,000,000,000,240 % per second, or 0.000,000,007,58 % per year (which is my annual pay rise). As it happens, this means any patch of space you care to choose within the universe will double its size after 13 billions years, which happens to be the accepted age of the universe. However, if you had a metre rule to hand, it would have to measure the expansion distance to about a 1/100th of atom's width a year later to detect this expansion - not easy.

If space is expanding, then why don't galaxies expand? Maybe they do, but we'd have to see if galaxies half way to the 'edge' of the universe are really half the size of ones today, and I don't think that's been managed yet.

However, I think it's not the case that solid objects like Eath or metre rules get larger as the Universe expands. As space expands at such a tiny rate, the molecular forces that keep ordinary things together would easily overcome a tiny expansion 'pressure'. Even if you had a rope across the entire universe, it would still only expand by 0.000,000,007,58 % per year - it would not snap, and it would be hard to detect any 'tension'.

If space is expanding, then another question is 'where's this new space coming from?'. That's a good one. Of the top of my head, I wonder if it's dark energy being converted into space and dark matter. The recent discovery that the expansion of space in our age is speeding up might suggest otherwise. Maybe one day, space will convert back to dark energy, and start contracting. Ooops.

Another question I've wondered is: if space expands, how much energy is needed to create (or destroy) 1 cubic metre of space?

Polchey wrote:I personally don't believe the universe is infinite in size, I think there is an outer boundary to all the matter that exists. Just because we can't see the end of it doesn't mean it's infinite, we only know it's a large universe. I'd rather believe in curved space than to believe matter is infinite, because with curved space we're saying there is a finite amount of matter.

Hmm, yes. Actually, there was a very good argument by an ancient greek philopsopher (Epicurus (c. 341?€“271 B.C.), I believe) about why the universe couldn't have an edge so must be unbounded, hence infinite. Since then, we have had to unify this with the universe being necessarily finite (Olbers paradox) whereupon people settle for the finite but unbounded goemetry of space-time as discussed above.

Finally, the observation that the universe is nearly 'flat'. I wonder if there is a problem if the universe is supposed to be absolutely flat, because once again, you bring in the problem of an edge. Inflation theory makes the universe nearly flat, but not quite flat, so avoids this problem by keeping the universe closed.

Spiff.

P.s., If anyone makes it down to here, I'd like to know if any of the above was informative, and a explanation-worthiness credit rating would be nice too .

Spaceman Spiff wrote:This has lead to some people to say that in a closed universe, we should receive light from our very own Milky Way, perhaps even take a picture of it. There are some problems. First, there're the practical problems of a very small and dim image, and who would recognise the Milky Way from far outside it anyway?

While the image of our galaxy (or whatever was there when the light began its journey around the universe) might be very dim, it would not be very small, but very large, actually covering the entire sky, as the light would be coming in from all directions around us. It would be somewhat like looking at yourself in a concave mirror with your eye near the "center" of its curvature (not quite the same as its focal point I think, but close to it), seeing no real image but just the colour of your eye across the whole mirror. If the universe stood perfectly still for eternity, we would be seeing the image of Polaris near our southern celestial pole, unless of course it had been obscured by interstellar dust. Eventually, we would be looking at the opposite side of the Earth, assuming it had existed for that long.

By the way, the rule that says light gets dimmer by the the square of the distance supposedly assumes a linear (non-curved) space. If all light from the same object eventually hits the same spot again, wouldn't it appear as bright as when it started? A curved universe acts like a big lens, concentrating any emitted light onto its own source.

Then we have Olbers' paradox, saying the night sky should really be as bright as the Sun if there were a star at every point in the sky, regardless how distant. I'm not sure how Olbers deals with a curved universe either. Maybe interstellar dust absorbs most of the light?

Spaceman Spiff wrote:P.s., If anyone makes it down to here, I'd like to know if any of the above was informative, and a explanation-worthiness credit rating would be nice too .

It was quite informative, though I may have skipped a portion of it. If there was anything else besides the notion of a "small" galaxy image I would disagree with, then I didn't notice it.

andersa wrote:While the image of our galaxy (or whatever was there when the light began its journey around the universe) might be very dim, it would not be very small, but very large, actually covering the entire sky, ...

That's what I like about these discussions, it makes you realise your own unrealised assumptions...

Now that I think about it., of course! The image would be spread all over the sky. Thinking more, if the speed of light was infinite, the image would actually just be the same as the Milky Way, but 'mirrored' through the observer. If you are correct that a closed space-time curvature would refocus the light back at us, then the image might still be as bright as the real, barring absorption.

Then again, with finite light speed, if the light takes 13,000,000,000 years to get back to us, then maybe our galaxy drifting with a small peculiar motion of say 50km/s would have drifted a couple of million light years away from where it was. Then the image would be offset, and appear like the Andromeda galaxy. Ohmygod, you don't suppose..! . (Nah, the Andromeda galaxy looks evolved, not 13 billion years old).

Oblers paradox: I think it doesn't deal with a closed (finite) universe, it was supposed to show that the universe could not be seen to be infinite. It's not really the finite extent of the universe that solves the paradox, rather the finite age.

Fred Hoyle and Chandra Wickramasinghe tried to defend the Steady State Theory against Olber's Paradox by invoking interstellar/intergalactic dust absorption (they even suggested the dust might actually be panspermia bacteria). However, most cosmologists won't go with this, because if the universe was infinite in size and age, all that starlight absorbed by this dust would have heated it up to the same temperature as the stars' surface - 5,000K.

The resolution of Olber's Paradox is that the universe is in thermal disequilibirum, hence 'young'.

Spiff.

Spaceman Spiff wrote:Then again, with finite light speed, if the light takes 13,000,000,000 years to get back to us, then maybe our galaxy drifting with a small peculiar motion of say 50km/s would have drifted a couple of million light years away from where it was. Then the image would be offset, and appear like the Andromeda galaxy. Ohmygod, you don't suppose..! . (Nah, the Andromeda galaxy looks evolved, not 13 billion years old).

Add an expanding universe to that, and a 50 km/s drift would be insignificant compared to the other problem you mentioned, the light never getting back to us because of the circumference of the universe expanding faster than the speed of light (or at least sufficiently fast to shift the spectrum of this light down to non-optical or "invisible" frequencies).

As for what we might actually see if we did receive any round-trip light, I suppose the entire supercluster or whatever structure we are located in may have moved "out of focus" before the light returns, so that we are instead looking at some random point in intergalactic (intercluster?) space. If I have understood those recent models of the universe correctly, aren't the clusters distributed rather unevenly in space, forming membranes between empty bubbles? If so, our round-trip view of the universe may well be focused right into such a bubble, which is why the sky is dark. If you have ever watched dishwater foam decay, you know that bubbles keep merging and moving all the time. Am I overestimating the fluidness of the universe?

Some galaxies may actually be receiving round-trip light from other galaxies, in which case an observer in such a galaxy should be seeing two sets of stars, equally bright, but the remote set extremely distant, reddish beyond imagination, and probably moving across the sky at blazing speed (much like the reflections from a disco ball). If the focus ended up in some ancient star, would the observer's planet be fried as if in a microwave oven?

Then again, all this assumes that the universe is a perfect hypersphere, or the round-trip light from the same source would arrive at different times from different directions, leading to a very blurred image (if any image at all).

Wow, what an interesting and enjoyable discussion! andersa and Spiff, your posts have been bery well explained. (Just when I thought the web had ruined my attention span, it's nice to be able to sit and read such a long thread in one go!)

I have one question though: Could someone explain the difference between a flat and a curved universe? If a closed curved universe can be compared to a sphere, would a closed flat universe be like flat monitor that wraps around? (e.g if you move your mouse off the right hand side, it reappears on the left).

stonedyak wrote:I have one question though: Could someone explain the difference between a flat and a curved universe?

I am also confused by this terminology...

If the Universe started with a big BANG, wouldn't it be expanding in ALL
directions at once? How can you get a "flat" universe from particles of matter
and energy which are travelling out into every direction?

Thanks, Curious Bob

stonedyak wrote:I have one question though: Could someone explain the difference between a flat and a curved universe? If a closed curved universe can be compared to a sphere, would a closed flat universe be like flat monitor that wraps around? (e.g if you move your mouse off the right hand side, it reappears on the left).

I don't think I have seen the term "closed flat universe" before; a "flat" universe is by default without edges and therefore infinite in all three dimensions (like a mathematical plane is in two dimensions). What you describe is more like a cylinder (disregarding the "edges" at the top and bottom of your monitor, but instead considering it vertically infinite), and while it might be interesting to study the properties of such a universe, it seems like a rather non-natural shape. Light would return to its source in a single direction only, letting light in any other direction disappear into infinity. Or, the universe could be finite in two dimensions while infinite in the third, allowing light sent anywhere along a plane to return home.

Adding edges to the two-dimensional "universe" would be like adding walls to the three-dimensional one, and the obvious follow-up question would be: What is it like behind that wall? People have tried to answer such questions for thousands of years, coming up with more or less elaborate constructs such as a flat Earth resting on the backs of four elephants and so on, but they never seem to result in any deeper understanding of what the universe is really like, they just postpone the issue while draping it in colorful images.

There are other curved shapes than the finite sphere that can be used as two-dimensional analogies for a curved universe; one is the parabolic (?) "saddle" that is infinite in all directions, but where the area within a particular distance from the point of origin grows faster than the square of the distance. I'm short on words to describe it, but I think the formula is something like x*x-y*y=z (while the formula of the sphere is x*x+y*y+z*z=1). If Santa finds there are five times as many children within a 2000-mile radius as within a 1000-mile one, the Earth being shaped like a saddle would be one possible explanation. Now imagine a curved universe with corresponding properties.

Then we have Klein's Bottle (a variant of the Moebius strip), the three-dimensional counterpart of which would let us send a batch of right-hand gloves into space in one direction, and see it arrive back after quite some time as a batch of left-hand gloves. If I recall correctly, this particular analogy is from One two three - infinity by George Gamow, published in the 1940's I suppose.

Bob Hegwood wrote:If the Universe started with a big BANG, wouldn't it be expanding in ALL
directions at once? How can you get a "flat" universe from particles of matter
and energy which are travelling out into every direction?

None of the models we have discussed assumes a specific point in space where Big Bang took place, but it's easy (and perhaps misleading) to visualize a curved universe as a globe where all the points on the surface are at equal distance from a particular point, namely the center of the globe. Since the globe is just a rough real-world analogy, this point doesn't represent a location in space, but at most a point in time, which then spanned the entire universe.

A "flat" universe (i.e. one that extends infinitely far in all three dimensions) is capable of expanding just as well as a curved universe is; it's just that it neither expands "from" any particular location within itself. Any perceived motion of an object in the universe is relative to other objects, and when you see a galaxy moving away from us, it may just as well be us who are moving away from that galaxy.

If this image is problematic, try visualizing the shrinking of a group of people to one tenth of their original size. If they are standing in a row, one meter apart from each other, and remain in their positions while shrinking, they will instead get the impression that the floor below them is growing, and that they are suddenly ten meters apart from each other, according to their own scale. Yet none of them has moved an inch! It's just their frame of reference (the floor, or the wavelength of light) that has grown. This is the case regardless of whether their "floor" is an infinitely wide, flat surface or a finite, curved sphere.

The most distant galaxies in the Hubble deep field are already expanding away from us at a rate faster than the speed of light, as they have been accelerating for 13+ billion years since they fired their photons off toward us; there is no way that we could ever see the image of our own galaxy beyond them, assuming space were curved.

If it is curved, it is closed on a scale much bigger than the observable universe; so you can't ever see the back of your own head, that is why they call it the observable universe.

Another Brain-Dead question...

If you set off an explosion here on Earth, the initial event starts with matter
and energy speeding up and out in all directions as the explosion event
unfolds.

If the universe is currently speeding up in its expansion, isn't this a lot like
what happens when an explosion on the Earth first begins? First, everything
gathers speed, then it gradually slows down because of gravity and friction
within the atmosphere, etc.

Could it be that Einstein's "Cosmological Constant" is simply a way to
describe the first few "seconds" of the event (as it happens on Earth) in
terms which are relevant to this gigantic explosion?

In other words, maybe we're still seeing just the first few seconds of the
Big Bang, and we don't know enough about what exists around
the explosion (i.e. - the environment in which it occurred) to understand
what's going on here.

Thanks, Bob

eburacum45 wrote:The most distant galaxies in the Hubble deep field are already expanding away from us at a rate faster than the speed of light, as they have been accelerating for 13+ billion years since they fired their photons off toward us; there is no way that we could ever see the image of our own galaxy beyond them, assuming space were curved.

That is assuming the Milky Way isn't older than 13 billion years, in which case it might very well be visible. It also assumes that those remote galaxies have continued moving away from us since they were last seen "13 billion years ago", even though we have no direct visual evidence of that motion. Both are very reasonable assumptions, and they may even be supported by facts, but it doesn't rule out the possibility that light may eventually travel around the entire curved universe.

eburacum45 wrote:If it is curved, it is closed on a scale much bigger than the observable universe; so you can't ever see the back of your own head, that is why they call it the observable universe.

I mentioned this in my first comment on this thread, but I also suggested that the expansion of the universe may eventually slow down enough to allow the event horizon to reach beyond the most distant objects in space, including ourselves. It may not happen in the lifetime of our solar system or our galaxy, and I will certainly not live to see the back of my own head, but maybe one day somebody else, somewhere in the universe, will at least theoretically be able to see the back of my head.

Or maybe the universe will collapse before that. When it collapses, will anybody still living in it notice? Would a collapse imply the universe shrinking back towards its earlier and smaller size, which will by then fit nicely within the still expanding event horizon?