The farthest point in the universe

[Hand of Nergal]

Given that the universe and space time is curved if we were to leave the planet Earth in some remarkable spacecraft and head for the farthest point in the universe we would circumnavigate the universe and return to the Earth much later. (I have not noted what type of propulsion the ship uses, what its speed is, and how long the trip was, for the purposes of the argument it is not important).
Similarly, if we had a telescope powerful enough to look through the universe for the farthest point we would see the backs of our heads, because of the aforementioned curvature of space-time. Theoretically wherever you stand is the center of the observable universe, but the back of your head is also the farthest point.
Am I oversimplifying the complexities of this paradox or not making it simple enough? Is there more to this, am I leaving something out, or is the universe just really that fundamentally wacky?! :hmmm:

[Stavroforos]

Wouldn't the universe's horizon limit us from seeing the backs of our heads? Much like I can't see the back of my head right now no matter how hard I try.

[Playfishpaste]

This belongs in the atheneum. Also, no, you would not see the back of your head, the universe doesn't curve back in on itself, it is an everexpanding blotch in a void of spacetime, you'd just see nothing if you had a telescope that powerful.

[Hand of Nergal]

This belongs in the atheneum. Also, no, you would not see the back of your head, the universe doesn't curve back in on itself, it is an everexpanding blotch in a void of spacetime, you'd just see nothing if you had a telescope that powerful.

By the way Im afraid I have to wave the BS flag on this one because the universe space-time continuum IS curved, and Im not making this up, this is the accepted convention of the day, we can prove space-time curvature, but I dont have to, because Einstein already did for me when he proved the warping of light by gravity. And yeah, if an ant walks around a ballon he will keep going in circles, that is just a three dimensional illustration of fourth dimensional space-time, so dont write me back and tell me that a spaceship isnt an ant cos I already knew that...
As for not being able to see the back of your head no matter how hard you try, you should try to use the imaginary telescope I invented when I posed this paradox, smart-ass. If you cant see THAT youre no better than the people who think the world is flat and supported by the back of a giant turtle...

[Roger the Shrubber]

Mind boggling.

[Hand of Nergal]

This thread does belong in the Atheneum, that was the plan at least. I apologize for submitting it here, I messed upI hope that a moderator can move it for both our sakes.

[touchmaster]

Mind boggling.

Indeed, it's hard to imagine this kind of stuff.

[Xavier Dragnesi]

No one knows if there is even an end to the universe for the farthest point to be found.

[Ahlerich]

ever been to idaho?

[italiano]

If you cant see THAT youre no better than the people who think the world is flat and supported by the back of a giant turtle...

It's better than assuming that humanity is actually capable of understanding the dimensions of the univerise, let alone how to calculate them. Whatever we think right now is likely wrong.

[Atterdag]

This belongs in the Athenaeum

[Simetrical]

Given that the universe and space time is curved

We don't know that space-time is curved on a large scale. Most astronomers currently believe that space-time is flat (Euclidean) overall, with deviations only near large masses.

if we were to leave the planet Earth in some remarkable spacecraft and head for the farthest point in the universe we would circumnavigate the universe and return to the Earth much later.

Whether the universe is curved (non-Euclidean) is unrelated to whether it "wraps around" like that. The universe could be completely flat, but still wrap around; or curved but not wrap around. Whether the universe is "curved" is related to questions like: if you draw a really really really big triangle (whose sides are geodesics, i.e., the shortest distance between two points), will its angles add up to 180°, more, or less?

We don't know whether the universe "wraps around" either. It's an open question. If you keep on going and going, you might end up where you started (possibly in some strange way, like reflected), or you might just keep going forever. Nobody knows, yet.

Similarly, if we had a telescope powerful enough to look through the universe for the farthest point we would see the backs of our heads, because of the aforementioned curvature of space-time.

This isn't actually true, because information can't travel faster than the speed of light. Whatever mechanism you have for looking out into the universe, the image of the back of your head would never travel far enough to wrap around and get back to you before your death, even if the universe does wrap around. (I need to figure out the technical term for "wrapping around".)

Theoretically wherever you stand is the center of the observable universe, but the back of your head is also the farthest point.

If the universe wrapped around, and were small enough to see all the way around, I don't think it would be meaningful to assign it a center. What's the center of the Earth's surface? Any point is as good as any other (neglecting deviation from a perfect sphere, rotation, and similar considerations).

In any event your head is always going to be at distance zero from itself, not far away. In the same way, you aren't 40,000 km away from yourself just because you can travel straight around the world for 40,000 km and get back to where you are now.

Am I oversimplifying the complexities of this paradox or not making it simple enough? Is there more to this, am I leaving something out, or is the universe just really that fundamentally wacky?! :hmmm:

It's possible that the universe is basically as you describe, yes, although we don't know yet. Of course such a geometry would not be embeddable in R³ and so we have a lot of trouble actually visualizing it. It's best to think of it like the surface of a sphere or torus or similar thing, but where everything (including light, etc.) moves only along the surface, never being able to leave it. That's a two-dimensional analog.

Wouldn't the universe's horizon limit us from seeing the backs of our heads? Much like I can't see the back of my head right now no matter how hard I try.

The horizon, on Earth, is caused by the fact that light does not stay on the surface of the Earth, but travels in straight lines in the flat space that the Earth's surface is embedded in. To make a sphere's surface a decent analogy to a curved/wrapping-around universe, you should picture nothing as being able to leave the surface: light would have to stick to the surface too, so it would indeed wrap around and get back to your eyes.

By the way Im afraid I have to wave the BS flag on this one because the universe space-time continuum IS curved, and Im not making this up, this is the accepted convention of the day, we can prove space-time curvature, but I dont have to, because Einstein already did for me when he proved the warping of light by gravity.

It's correct that general relativity demonstrates that near large masses, space-time becomes significantly curved. However, that doesn't mean that the universe is significantly curved on average. That's an entirely separate question, which is still unresolved. It might be Euclidean, elliptic, or hyperbolic on average.

As a somewhat related issue, general relativity also permits space-time to follow relatively generic topologies. Some solutions to the field equations have behavior like "wrapping around", or regions that are not simply connected (wormholes), or other exotic things that nobody would have considered physically meaningful before general relativity. But it only permits them, it mostly doesn't mandate them. Nobody knows yet if those solutions to the field equations are physically meaningful: if things like wormholes or wrapping around are possible.

And yeah, if an ant walks around a ballon he will keep going in circles, that is just a three dimensional illustration of fourth dimensional space-time

The surface of a balloon is two-dimensional, not three-dimensional.

As for not being able to see the back of your head no matter how hard you try, you should try to use the imaginary telescope I invented when I posed this paradox

As I mentioned above, such a telescope probably violates at least one fundamental physical law, although not in the way Stavroforos was suggesting.

No one knows if there is even an end to the universe for the farthest point to be found.

Correct. This is all still unresolved. Cosmologists are hoping to be able to investigate these questions better as better instrumentation comes online.

[Playfishpaste]

Simetrical already covered most of it, except, sim, I think he is assuming for the sake of argument that the telescope got around the light loophole, though this in effect wouldn't be a telescope at all. So we should just call it a "tachyonic super-information recieving device". My issue with this is that whether or not our universe is curved, open, or closed, it is still part of a much much larger void of spacetime, and there is no border to spacetime. It is important to note that the border of the universe is not the border of spacetime. Spacetime was here before the universe. Now if you made this device that could see all the way to this supposed border, you'd still get nothingness, because outside of it, there'd still be nothingness.

[Simetrical]

My issue with this is that whether or not our universe is curved, open, or closed, it is still part of a much much larger void of spacetime, and there is no border to spacetime. It is important to note that the border of the universe is not the border of spacetime. Spacetime was here before the universe. Now if you made this device that could see all the way to this supposed border, you'd still get nothingness, because outside of it, there'd still be nothingness.

I don't think this is accurate, although my knowledge of cosmology is limited. At the very least, I'm fairly sure that it's considered possible that the universe does really "wrap around". Some cosmologists have been searching telescope data for faint repeats of constellations, similar patterns seen twice, with the dimmer copy being one that we see from all the way around the universe. So far they haven't found any, but some of them are looking.

The relationship of space-time to the universe's matter is beyond me. I don't think it's so simple as to say that there was some static space-time manifold that existed before the universe. I think space-time itself is considered to have actually originated at the Big Bang too, and spread out from a point. But I can't say I know for sure.

[Playfishpaste]

Our universe is made up of matter, energy, and "empty" space (much like an atom, however, there is again, no such thing as truly empty space, but we won't get into zero dimensional particles). The field in which all this is contained is manipulated by gravity and is spacetime. think of it as not just the rubber blanket that holds the balls, but an eternal rubber blanket that has held the balls since before they were balls. At the birth of the universe since the gravitational pull was so large at the singularity that was the whole universe space time was totally wrapped all up in it as well, distorted and contorted so much that mechanics wouldn't work anywhere near how they should assuming gaussian curvature or normal field dynamics (at the quantum level anyway, it's not even worth discussing classical mechanics there because the singularity is a point particle anyway).

That said, I think there is a grand misunderstanding here on the term "wrap around" and I agree a scientific term is needed, don't know what it is either, but I haven't read any papers or books relating to such phenomena, when physicists mention it they always mean wrap around in the layperson sense, as in torodial or basket-shaped, but not necessarily having a nature that makes light curve around all the way back to the other side. Even so, I'm pretty sure you'd still only see black, given the anisotropy survey we took recently, because if that weren't the case, the survey wouldn't have worked since the background radiation would have been going on forever.

EDIT: Sorry, I didn't mean forever, I mean it wouldn't be soley coming from the point where it was recorded, it should have been coming from various spots.

[Simetrical]

Our universe is made up of matter, energy, and "empty" space

You could so divide it, I suppose. Matter is really a form of energy, though; I don't know whether empty space should be considered something "making up" the universe; and there are other things too, like force fields (which can store energy, admittedly, as matter can) or momentum.

(much like an atom, however, there is again, no such thing as truly empty space, but we won't get into zero dimensional particles).

It depends on what you call "truly empty space". Given that all matter is composed of particles that have no volume, one could argue that all of space is entirely empty (since the amount of space that's not empty has volume zero). In practice, we say that space is "empty" as long as there are no force fields in it that are strong enough to exclude ordinary matter; or optionally, if the density of matter in the space is sufficiently low.

It's not a terribly interesting issue, anyway: the term empty is just vague, that's all.

The field in which all this is contained is manipulated by gravity and is spacetime. think of it as not just the rubber blanket that holds the balls, but an eternal rubber blanket that has held the balls since before they were balls.

And is space-time actually thought to have been eternal, or to have predated the Big Bang? Do you have a source for this? My understanding is that no physicist is willing to say anything more than sheer speculation about what might have preceded the Big Bang, or indeed what might have occurred at the instant of the Big Bang. Physicists speak only of events fractions of a second after the Big Bang, that I've seen.

That said, I think there is a grand misunderstanding here on the term "wrap around" and I agree a scientific term is needed, don't know what it is either, but I haven't read any papers or books relating to such phenomena, when physicists mention it they always mean wrap around in the layperson sense, as in torodial or basket-shaped, but not necessarily having a nature that makes light curve around all the way back to the other side.

Well, as a mathematician, my definition is thus. A space is said to wrap around itself if one can construct a sequence of finitely many points, such that the first point in the sequence is the same as the last point, and if one constructs the line segment between each point and the next (taking the shortest path between them), all the line segments so constructed are parallel (the definition of parallel is left as an exercise for the reader). So in other words, you have a line, but it's closed.

In particular, given that light travels in straight lines, the existence of such a set of points appears to me necessary and sufficient for being able to "see the back of your own head": for an unobstructed beam of light to eventually return to its origin.

Even so, I'm pretty sure you'd still only see black, given the anisotropy survey we took recently, because if that weren't the case, the survey wouldn't have worked since the background radiation would have been going on forever.

If the radius is large enough, it could be that the telltale light hasn't reached us yet, or that it's so diffuse we don't notice. There are lower bounds people have put on the radius of the universe if it does wrap around.

[Playfishpaste]

You could so divide it, I suppose. Matter is really a form of energy, though; I don't know whether empty space should be considered something "making up" the universe; and there are other things too, like force fields (which can store energy, admittedly, as matter can) or momentum.

I exclude matter and energy simply due to their properties, and to seperate dark matter and dark energy, energy wouldn't affect spacetime so we'll make it different for this case. Empty space actually takes up space, that's why I brought it up, I could have included Information, momentum, and fields like spacetime or quantum fields too but I think that would just over-complicate things.

It depends on what you call "truly empty space". Given that all matter is composed of particles that have no volume, one could argue that all of space is entirely empty (since the amount of space that's not empty has volume zero). In practice, we say that space is "empty" as long as there are no force fields in it that are strong enough to exclude ordinary matter; or optionally, if the density of matter in the space is sufficiently low.

you can argue that point particles have no volume, but they'd still have mass, I'm talking about things without mass, which can still be there, taking up space and affecting spacetime due to QED and QCD, but it's not really relevant to this.

And is space-time actually thought to have been eternal, or to have predated the Big Bang? Do you have a source for this? My understanding is that no physicist is willing to say anything more than sheer speculation about what might have preceded the Big Bang, or indeed what might have occurred at the instant of the Big Bang. Physicists speak only of events fractions of a second after the Big Bang, that I've seen.

Einstein posited in his own orginal work, Relativity, that this was in fact the case, but I'm quite sure this would only be speculation on his part, he didn't have QCD to back him up and he didn't even know the scope of our universe. Even if he had known, he still wouldn't have been able to explain the physics during the time of the singularity fully with just general and special. Either way, at present, it's also put forward in Feynman's QED and Jim Gates' work in M theory and string theory that quantum relatavstic fields were present before the big bang, just heavily effected and distorted by the singularity. Gates also, if you're familiar with him, is a supporter of the "many Crunches and Bangs" theory, so in order for his views to even work spacetime would have had to have existed. However, I don't want to emphasize gates too much because then we'll get into M theory and string theory, which messes with QRFT very significantly and certainly makes the physics of inflation and bangs and crunches very different. So I'd suggest merely QED, and maybe Khalili's stuff on CQD for a general statement of "the fields were here before hand and that's why x, y, and z can be said".

Well, as a mathematician, my definition is thus. A space is said to wrap around itself if one can construct a sequence of finitely many points, such that the first point in the sequence is the same as the last point, and if one constructs the line segment between each point and the next (taking the shortest path between them), all the line segments so constructed are parallel (the definition of parallel is left as an exercise for the reader). So in other words, you have a line, but it's closed.

an exercise? I dislike critical thinking, wah. But okay, so help me out here, do you mean parallel to each other in the sense that they'll go over each other? Indefinitely? I assume we're talking euclidean here.

In particular, given that light travels in straight lines, the existence of such a set of points appears to me necessary and sufficient for being able to "see the back of your own head": for an unobstructed beam of light to eventually return to its origin.

light doesn't necessarily travel in straight lines, unless the field it travels through is flat and doesn't have a gaussian curve, but I get what you're saying. And yes, I think that would be necessary. However, I simply have not heard of it being posited like that. That light would go around in such a fashion.

If the radius is large enough, it could be that the telltale light hasn't reached us yet, or that it's so diffuse we don't notice. There are lower bounds people have put on the radius of the universe if it does wrap around.

But that's the thing, it has reached us, we'd have to assume it's been going round and round, but if that were the case it would have passed more then once and would have been less powerful.

[Pickle_mole]

Simetrical plus rep for your well thought out and wonderfully articulated answers

[Simetrical]

Einstein posited in his own orginal work, Relativity, that this was in fact the case

What work "Relativity"? His original works on relativity were published before the Big Bang theory existed, obviously.

Either way, at present, it's also put forward in Feynman's QED and Jim Gates' work in M theory and string theory that quantum relatavstic fields were present before the big bang, just heavily effected and distorted by the singularity.

Right, but this is more like speculation, right? The underlying theories haven't been verified.

an exercise? I dislike critical thinking, wah. But okay, so help me out here, do you mean parallel to each other in the sense that they'll go over each other? Indefinitely? I assume we're talking euclidean here.

No, we're not talking Euclidean geometry, otherwise I could have simplified what I said. A line segment is the shortest distance between two points, not necessary "straight". Suppose we call two lines parallel if the angle between them is zero, where we assume that we're in an inner product space, where we can meaningfully speak of angles.

Or here, a simpler definition: a (connected) space wraps around itself if there are two points so that there is no unique curve of shortest length that connects them. So on a cylinder, pick two points on opposite sides of the round part of the cylinder, and there are two shortest paths between them. On a sphere, pick antipodes, and there are infinitely many shortest paths between them. I think this is a satisfactory way to look at it. But I don't really know any advanced geometry, so I can't say.

light doesn't necessarily travel in straight lines, unless the field it travels through is flat and doesn't have a gaussian curve, but I get what you're saying.

I should probably have said "geodesic" or something. By "straight line" I mean "the shortest distance between two points", which is not what you'd usually call straight in non-Euclidean geometry.

But that's the thing, it has reached us, we'd have to assume it's been going round and round, but if that were the case it would have passed more then once and would have been less powerful.

What do you mean? The light left us a finite period of time ago. It wouldn't necessarily have reached the edge of the universe yet.

[Playfishpaste]

What work "Relativity"? His original works on relativity were published before the Big Bang theory existed, obviously.

Relativity: the special and the general theory. It's just his papers on both published in book form, I have the translated version by Robert Lawson. And not on the big bang, he stated that space-time would have been necessary assuming the universe was created or not, because of the physics of the actual creation of matter (even at that time, without qcd, it was still known that you'd need a field in which these entities would interact). He lays this out quite nicely, stating: "Every physical description resolves itself into a number of statements, each of which refers to the space-time coincidence of two events A and B." One might say he is an error in reference to the modern interpretation of information, as he later goes on to say matter would not have an effect on dependent geometrical properties of space. However, this again goes into why he would not be able to explain the physics, as well as the theory on the origin of the universe not even being fleshed out by the time of publishing

Right, but this is more like speculation, right? The underlying theories haven't been verified.

Supersymmetry, QED, and quantum relatavistic field theory haven't been verified? I'll give you supersymmetry (even though that's a very, very rough bargain) but the latter? Am I misunderstanding you here?

No, we're not talking Euclidean geometry, otherwise I could have simplified what I said. A line segment is the shortest distance between two points, not necessary "straight". Suppose we call two lines parallel if the angle between them is zero, where we assume that we're in an inner product space, where we can meaningfully speak of angles.

got it, I was tripped up by straight lines, I assumed you were talking about several points with straight beams in between them, like airplane wavepoints, but in terms of gaussian curves I see what you're saying. However, in all the "basket" and "wrap-around" models I've seen, the actual planes don't have a curvature in which they affect light so that it loops about to the other side, it's just a complementary model to the open model, and proposes that light would simply be completely distorted or bent in the wrong direction due to the immense curvature and warping of the space at the border of the basket.

Or here, a simpler definition: a (connected) space wraps around itself if there are two points so that there is no unique curve of shortest length that connects them. So on a cylinder, pick two points on opposite sides of the round part of the cylinder, and there are two shortest paths between them. On a sphere, pick antipodes, and there are infinitely many shortest paths between them. I think this is a satisfactory way to look at it. But I don't really know any advanced geometry, so I can't say.

Again I see your reasoning in that, but I just haven't seen a model with light and the fields behaving in such a way.

I should probably have said "geodesic" or something. By "straight line" I mean "the shortest distance between two points", which is not what you'd usually call straight in non-Euclidean geometry.

yups

What do you mean? The light left us a finite period of time ago. It wouldn't necessarily have reached the edge of the universe yet.

I was talking about the background radiation, but were you bringing up the whole telescope thing again? Going back to that, if you did, in your model, yes you would see the back of the head (dismissing all the preventing factors except the geometry of spacetime). However, in the wrap arounds I've seen the light wouldn't bend back, but instead warp similarly to how it would around a black hole due to the sharp bend. Though the point I was making on background radiation was that if your model were true, the radiation shouldn't have reached us.